Daily Papers

This paper discusses pairing double/debiased machine learning (DDML) with stacking, a model averaging method for combining multiple candidate learners, to estimate structural parameters. In addition to conventional stacking, we consider two stacking variants available for DDML: short-stacking exploits the cross-fitting step of DDML to substantially reduce the computational burden and pooled stacking enforces common stacking weights over cross-fitting folds. Using calibrated simulation studies and two applications estimating gender gaps in citations and wages, we show that DDML with stacking is more robust to partially unknown functional forms than common alternative approaches based on single pre-selected learners. We provide Stata and R software implementing our proposals.

Neural networks can be significantly compressed by pruning, yielding sparse models with reduced storage and computational demands while preserving predictive performance. Model soups (Wortsman et al., 2022) enhance generalization and out-of-distribution (OOD) performance by averaging the parameters of multiple models into a single one, without increasing inference time. However, achieving both sparsity and parameter averaging is challenging as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. This work addresses these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varied hyperparameter configurations such as batch ordering or weight decay yields models suitable for averaging, sharing identical sparse connectivity by design. Averaging these models significantly enhances generalization and OOD performance over their individual counterparts. Building on this, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model from the previous phase. SMS preserves sparsity, exploits sparse network benefits, is modular and fully parallelizable, and substantially improves IMP's performance. We further demonstrate that SMS can be adapted to enhance state-of-the-art pruning-during-training approaches.

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a O(1/T) regret bound for perfectly pretrained ICL, where T is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings , we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression. The code is available at the following link, https://github.com/sidak/otfusion.

Recent studies suggest that with sufficiently wide models, most SGD solutions can, up to permutation, converge into the same basin. This phenomenon, known as the model re-basin regime, has significant implications for model averaging by ensuring the linear mode connectivity. However, current re-basin strategies are ineffective in many scenarios due to a lack of comprehensive understanding of underlying mechanisms. Addressing this gap, this paper provides novel insights into understanding and improving the standard practice. Firstly, we decompose re-normalization into rescaling and reshift, uncovering that rescaling plays a crucial role in re-normalization while re-basin performance is sensitive to shifts in model activation. The finding calls for a more nuanced handling of the activation shift. Secondly, we identify that the merged model suffers from the issue of activation collapse and magnitude collapse. Varying the learning rate, weight decay, and initialization method can mitigate the issues and improve model performance. Lastly, we propose a new perspective to unify the re-basin and pruning, under which a lightweight yet effective post-pruning technique is derived, which can significantly improve the model performance after pruning. Our implementation is available at https://github.com/XingyuQu/rethink-re-basin.

LLMs acquire a wide range of abilities during pre-training, but aligning LLMs under Reinforcement Learning with Human Feedback (RLHF) can lead to forgetting, which is also known as the alignment tax. To empirically verify this hypothesis, we conducted experiments with existing RLHF algorithms using OpenLLaMA-3B, which revealed a pronounced alignment tax in NLP tasks. On the other hand, despite various techniques to mitigate forgetting, they are often at odds with the RLHF performance, leading to a trade-off between reward maximization and forgetting mitigation. In light of the above pressing issue in aligning LLMs, in this paper we explore model averaging, which interpolates between pre and post RLHF model weights, to achieve a more efficient reward-tax Pareto front. To understand its effectiveness, We offer theoretical insights into model averaging, revealing that it enhances performance Pareto front by increasing feature diversity on the layers where tasks share overlapped feature spaces. Empirical evidence corroborates our analysis by showing the benefits of averaging low-level transformer layers. Building on the analysis and the observation that averaging different layers of the transformer leads to significantly different reward-tax trade-offs, we propose Adaptive Model Averaging (AMA) to adaptively find various combination ratios of model layers. AMA seeks to maximize the alignment reward while incurring minimal alignment tax. Moreover, we validate AMA's performance across a range of RLHF algorithms over OpenLLaMA-3B and further extend our findings to Mistral-7B.

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

Transfer learning has recently shown significant performance across various tasks involving deep neural networks. In these transfer learning scenarios, the prior distribution for downstream data becomes crucial in Bayesian model averaging (BMA). While previous works proposed the prior over the neural network parameters centered around the pre-trained solution, such strategies have limitations when dealing with distribution shifts between upstream and downstream data. This paper introduces nonparametric transfer learning (NPTL), a flexible posterior sampling method to address the distribution shift issue within the context of nonparametric learning. The nonparametric learning (NPL) method is a recent approach that employs a nonparametric prior for posterior sampling, efficiently accounting for model misspecification scenarios, which is suitable for transfer learning scenarios that may involve the distribution shift between upstream and downstream tasks. Through extensive empirical validations, we demonstrate that our approach surpasses other baselines in BMA performance.

We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and because it is a natural companion to dropout) designed to both facilitate optimization by dropout and improve the accuracy of dropout's fast approximate model averaging technique. We empirically verify that the model successfully accomplishes both of these tasks. We use maxout and dropout to demonstrate state of the art classification performance on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.

Modern mobile devices have access to a wealth of data suitable for learning models, which in turn can greatly improve the user experience on the device. For example, language models can improve speech recognition and text entry, and image models can automatically select good photos. However, this rich data is often privacy sensitive, large in quantity, or both, which may preclude logging to the data center and training there using conventional approaches. We advocate an alternative that leaves the training data distributed on the mobile devices, and learns a shared model by aggregating locally-computed updates. We term this decentralized approach Federated Learning. We present a practical method for the federated learning of deep networks based on iterative model averaging, and conduct an extensive empirical evaluation, considering five different model architectures and four datasets. These experiments demonstrate the approach is robust to the unbalanced and non-IID data distributions that are a defining characteristic of this setting. Communication costs are the principal constraint, and we show a reduction in required communication rounds by 10-100x as compared to synchronized stochastic gradient descent.

It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.

Due to the scarcity of high-quality data, large language models (LLMs) are often trained on mixtures of data with varying quality levels, even after sophisticated data curation. A natural approach to better leverage high-quality data is curriculum-based pretraining, where the model is trained on data sorted in ascending order of quality as determined by a quality metric. However, prior studies have reported limited improvements from such curriculum-based pretraining strategies. This work identifies a critical factor constraining these methods: the incompatibility between the ascending data quality order and the decaying learning rate (LR) schedule. We find that while curriculum-based training substantially outperforms random shuffling when using a constant LR, its advantage diminishes under standard LR decay schedules. Our experiments show this incompatibility can be mitigated by two simple strategies: (1) employing a more moderate LR decay schedule, where the final LR is only moderately smaller than the peak LR, and (2) replacing LR decay with model averaging, i.e., computing a weighted average of the final few checkpoints. By combining these strategies, we improve the average score on a suite of standard benchmarks by 1.64% over random shuffling, without additional data refinement. Validated on 1.5B-parameter models trained over 30B tokens with various data-quality metrics, our findings call for a re-evaluation of curriculum-based LLM pretraining and underscore the potential of co-designing data curricula with optimization methods.

Before deploying autonomous agents in the real world, we need to be confident they will perform safely in novel situations. Ideally, we would expose agents to a very wide range of situations during training, allowing them to learn about every possible danger, but this is often impractical. This paper investigates safety and generalization from a limited number of training environments in deep reinforcement learning (RL). We find RL algorithms can fail dangerously on unseen test environments even when performing perfectly on training environments. Firstly, in a gridworld setting, we show that catastrophes can be significantly reduced with simple modifications, including ensemble model averaging and the use of a blocking classifier. In the more challenging CoinRun environment we find similar methods do not significantly reduce catastrophes. However, we do find that the uncertainty information from the ensemble is useful for predicting whether a catastrophe will occur within a few steps and hence whether human intervention should be requested.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

Supervised Fine-Tuning (SFT) on domain-specific datasets is a common approach to adapt Large Language Models (LLMs) to specialized tasks but is often believed to degrade their general capabilities. In this work, we revisit this trade-off and present both empirical and theoretical insights. First, we show that SFT does not always hurt: using a smaller learning rate can substantially mitigate general performance degradation while preserving comparable target-domain performance. We then provide a theoretical analysis that explains these phenomena and further motivates a new method, Token-Adaptive Loss Reweighting (TALR). Building on this, and recognizing that smaller learning rates alone do not fully eliminate general-performance degradation in all cases, we evaluate a range of strategies for reducing general capability loss, including L2 regularization, LoRA, model averaging, FLOW, and our proposed TALR. Experimental results demonstrate that while no method completely eliminates the trade-off, TALR consistently outperforms these baselines in balancing domain-specific gains and general capabilities. Finally, we distill our findings into practical guidelines for adapting LLMs to new domains: (i) using a small learning rate to achieve a favorable trade-off, and (ii) when a stronger balance is further desired, adopt TALR as an effective strategy.

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

The conventional recipe for maximizing model accuracy is to (1) train multiple models with various hyperparameters and (2) pick the individual model which performs best on a held-out validation set, discarding the remainder. In this paper, we revisit the second step of this procedure in the context of fine-tuning large pre-trained models, where fine-tuned models often appear to lie in a single low error basin. We show that averaging the weights of multiple models fine-tuned with different hyperparameter configurations often improves accuracy and robustness. Unlike a conventional ensemble, we may average many models without incurring any additional inference or memory costs -- we call the results "model soups." When fine-tuning large pre-trained models such as CLIP, ALIGN, and a ViT-G pre-trained on JFT, our soup recipe provides significant improvements over the best model in a hyperparameter sweep on ImageNet. The resulting ViT-G model, which attains 90.94% top-1 accuracy on ImageNet, achieved a new state of the art. Furthermore, we show that the model soup approach extends to multiple image classification and natural language processing tasks, improves out-of-distribution performance, and improves zero-shot performance on new downstream tasks. Finally, we analytically relate the performance similarity of weight-averaging and logit-ensembling to flatness of the loss and confidence of the predictions, and validate this relation empirically. Code is available at https://github.com/mlfoundations/model-soups.

Massively multilingual language models have displayed strong performance in zero-shot (ZS-XLT) and few-shot (FS-XLT) cross-lingual transfer setups, where models fine-tuned on task data in a source language are transferred without any or with only a few annotated instances to the target language(s). However, current work typically overestimates model performance as fine-tuned models are frequently evaluated at model checkpoints that generalize best to validation instances in the target languages. This effectively violates the main assumptions of "true" ZS-XLT and FS-XLT. Such XLT setups require robust methods that do not depend on labeled target language data for validation and model selection. In this work, aiming to improve the robustness of "true" ZS-XLT and FS-XLT, we propose a simple and effective method that averages different checkpoints (i.e., model snapshots) during task fine-tuning. We conduct exhaustive ZS-XLT and FS-XLT experiments across higher-level semantic tasks (NLI, extractive QA) and lower-level token classification tasks (NER, POS). The results indicate that averaging model checkpoints yields systematic and consistent performance gains across diverse target languages in all tasks. Importantly, it simultaneously substantially desensitizes XLT to varying hyperparameter choices in the absence of target language validation. We also show that checkpoint averaging benefits performance when further combined with run averaging (i.e., averaging the parameters of models fine-tuned over independent runs).

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conventional training. We also show that this Stochastic Weight Averaging (SWA) procedure finds much flatter solutions than SGD, and approximates the recent Fast Geometric Ensembling (FGE) approach with a single model. Using SWA we achieve notable improvement in test accuracy over conventional SGD training on a range of state-of-the-art residual networks, PyramidNets, DenseNets, and Shake-Shake networks on CIFAR-10, CIFAR-100, and ImageNet. In short, SWA is extremely easy to implement, improves generalization, and has almost no computational overhead.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Training large language models is generally done via optimization methods on clusters containing tens of thousands of accelerators, communicating over a high-bandwidth interconnect. Scaling up these clusters is expensive and can become impractical, imposing limits on the size of models that can be trained. Several recent studies have proposed training methods that are less communication intensive, avoiding the need for a highly connected compute cluster. These state-of-the-art low communication training methods still employ a synchronization step for model parameters, which, when performed over all model replicas, can become costly on a low-bandwidth network. In this work, we propose a novel optimization method, NoLoCo, that does not explicitly synchronize all model parameters during training and, as a result, does not require any collective communication. NoLoCo implicitly synchronizes model weights via a novel variant of the Nesterov momentum optimizer by partially averaging model weights with a randomly selected other one. We provide both a theoretical convergence analysis for our proposed optimizer as well as empirical results from language model training. We benchmark NoLoCo on a wide range of accelerator counts and model sizes, between 125M to 6.8B parameters. Our method requires significantly less communication overhead than fully sharded data parallel training or even widely used low communication training method, DiLoCo. The synchronization step itself is estimated to be one magnitude faster than the all-reduce used in DiLoCo for few hundred accelerators training over the internet. We also do not have any global blocking communication that reduces accelerator idling time. Compared to DiLoCo, we also observe up to 4% faster convergence rate with wide range of model sizes and accelerator counts.

We propose MindVL, a multimodal large langauge model trained on Ascend NPUs. Similar to Qwen2.5-VL, MindVL adopts native-resolution Vision Transformers, which enables it to process images at their original variable resolutions. This design avoids the degradation caused by fixed-resolution tiling while preserving fine-grained details and global layouts, which is crucial for visually dense content such as complex charts and diagrams. To ensure the smooth training of MindVL on Ascend NPUs, we develop Mindspeed-MLLM, a distributed multimodal training framework tailored for Ascend NPUs. To maintain training accuracy, we implement equivalent replacements for certain operators. MindVL undergoes a three-phase training process, namely the warm-up phase, multitask training phase, and supervised instruction tuning phase, to gradually enhance its capabilities. This process starts with basic visual and multimodal pre-training, followed by large-scale multiask trainging and instruction tuning. We also adopt multimodal data packaging and hybrid parallelism techniques, which significantly improve end-to-end training speed. To further boost model performance, we specifically introduce test-time resolution search and model weight averaging. Notably, despite using about 1/10 of the training data required by Qwen2.5-VL, MindVL achieves performance on par with Qwen2.5-VL in evaluations of general multimodal understanding and document/table comprehension. Beyond overall scores, MindVL also delivers leading performance in OCR assessments.

Continual learning (CL) can help pre-trained vision-language models efficiently adapt to new or under-trained data distributions without re-training. Nevertheless, during the continual training of the Contrastive Language-Image Pre-training (CLIP) model, we observe that the model's zero-shot transfer ability significantly degrades due to catastrophic forgetting. Existing CL methods can mitigate forgetting by replaying previous data. However, since the CLIP dataset is private, replay methods cannot access the pre-training dataset. In addition, replaying data of previously learned downstream tasks can enhance their performance but comes at the cost of sacrificing zero-shot performance. To address this challenge, we propose a novel method ZSCL to prevent zero-shot transfer degradation in the continual learning of vision-language models in both feature and parameter space. In the feature space, a reference dataset is introduced for distillation between the current and initial models. The reference dataset should have semantic diversity but no need to be labeled, seen in pre-training, or matched image-text pairs. In parameter space, we prevent a large parameter shift by averaging weights during the training. We propose a more challenging Multi-domain Task Incremental Learning (MTIL) benchmark to evaluate different methods, where tasks are from various domains instead of class-separated in a single dataset. Our method outperforms other methods in the traditional class-incremental learning setting and the MTIL by 9.7% average score. Our code locates at https://github.com/Thunderbeee/ZSCL.

Federated learning allows edge devices to collaboratively learn a shared model while keeping the training data on device, decoupling the ability to do model training from the need to store the data in the cloud. We propose Federated matched averaging (FedMA) algorithm designed for federated learning of modern neural network architectures e.g. convolutional neural networks (CNNs) and LSTMs. FedMA constructs the shared global model in a layer-wise manner by matching and averaging hidden elements (i.e. channels for convolution layers; hidden states for LSTM; neurons for fully connected layers) with similar feature extraction signatures. Our experiments indicate that FedMA not only outperforms popular state-of-the-art federated learning algorithms on deep CNN and LSTM architectures trained on real world datasets, but also reduces the overall communication burden.

In this paper, we propose KaLM-Embedding-V2, a versatile and compact embedding model, which achieves impressive performance in general-purpose text embedding tasks by leveraging superior training techniques and data. Our key innovations include: (1) To better align the architecture with representation learning, we remove the causal attention mask and adopt a fully bidirectional transformer with simple yet effective mean-pooling to produce fixed-length embeddings; (2) We employ a multi-stage training pipeline: (i) pre-training on large-scale weakly supervised open-source corpora; (ii) fine-tuning on high-quality retrieval and non-retrieval datasets; and (iii) model-soup parameter averaging for robust generalization. Besides, we introduce a focal-style reweighting mechanism that concentrates learning on difficult samples and an online hard-negative mixing strategy to continuously enrich hard negatives without expensive offline mining; (3) We collect over 20 categories of data for pre-training and 100 categories of data for fine-tuning, to boost both the performance and generalization of the embedding model. Extensive evaluations on the Massive Text Embedding Benchmark (MTEB) Chinese and English show that our model significantly outperforms others of comparable size, and competes with 3x, 14x, 18x, and 26x larger embedding models, setting a new standard for a versatile and compact embedding model with less than 1B parameters.

We investigate the unsupervised constituency parsing task, which organizes words and phrases of a sentence into a hierarchical structure without using linguistically annotated data. We observe that existing unsupervised parsers capture differing aspects of parsing structures, which can be leveraged to enhance unsupervised parsing performance. To this end, we propose a notion of "tree averaging," based on which we further propose a novel ensemble method for unsupervised parsing. To improve inference efficiency, we further distill the ensemble knowledge into a student model; such an ensemble-then-distill process is an effective approach to mitigate the over-smoothing problem existing in common multi-teacher distilling methods. Experiments show that our method surpasses all previous approaches, consistently demonstrating its effectiveness and robustness across various runs, with different ensemble components, and under domain-shift conditions.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Fine-tuning pre-trained language models has become the prevalent paradigm for building downstream NLP models. Oftentimes fine-tuned models are readily available but their training data is not, due to data privacy or intellectual property concerns. This creates a barrier to fusing knowledge across individual models to yield a better single model. In this paper, we study the problem of merging individual models built on different training data sets to obtain a single model that performs well both across all data set domains and can generalize on out-of-domain data. We propose a dataless knowledge fusion method that merges models in their parameter space, guided by weights that minimize prediction differences between the merged model and the individual models. Over a battery of evaluation settings, we show that the proposed method significantly outperforms baselines such as Fisher-weighted averaging or model ensembling. Further, we find that our method is a promising alternative to multi-task learning that can preserve or sometimes improve over the individual models without access to the training data. Finally, model merging is more efficient than training a multi-task model, thus making it applicable to a wider set of scenarios.

In this paper, we uncover that Language Models (LMs), either encoder- or decoder-based, can obtain new capabilities by assimilating the parameters of homologous models without retraining or GPUs. Typically, new abilities of LMs can be imparted by Supervised Fine-Tuning (SFT), reflected in the disparity between fine-tuned and pre-trained parameters (i.e., delta parameters). We initially observe that by introducing a novel operation called DARE (Drop And REscale), most delta parameters can be directly set to zeros without affecting the capabilities of SFT LMs and larger models can tolerate a higher proportion of discarded parameters. Based on this observation, we further sparsify delta parameters of multiple SFT homologous models with DARE and subsequently merge them into a single model by parameter averaging. We conduct experiments on eight datasets from the GLUE benchmark with BERT and RoBERTa. We also merge WizardLM, WizardMath, and Code Alpaca based on Llama 2. Experimental results show that: (1) The delta parameter value ranges for SFT models are typically small, often within 0.005, and DARE can eliminate 99% of them effortlessly. However, once the models are continuously pre-trained, the value ranges can grow to around 0.03, making DARE impractical. We have also tried to remove fine-tuned instead of delta parameters and find that a 10% reduction can lead to drastically decreased performance (even to 0). This highlights that SFT merely stimulates the abilities via delta parameters rather than injecting new abilities into LMs; (2) DARE can merge multiple task-specific LMs into one LM with diverse abilities. For instance, the merger of WizardLM and WizardMath improves the GSM8K zero-shot accuracy of WizardLM from 2.2 to 66.3, retaining its instruction-following ability while surpassing WizardMath's original 64.2 performance. Codes are available at https://github.com/yule-BUAA/MergeLM.

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse domains, but their training remains resource- and time-intensive, requiring massive compute power and careful orchestration of training procedures. Model souping-the practice of averaging weights from multiple models of the same architecture-has emerged as a promising pre- and post-training technique that can enhance performance without expensive retraining. In this paper, we introduce Soup Of Category Experts (SoCE), a principled approach for model souping that utilizes benchmark composition to identify optimal model candidates and applies non-uniform weighted averaging to maximize performance. Contrary to previous uniform-averaging approaches, our method leverages the observation that benchmark categories often exhibit low inter-correlations in model performance. SoCE identifies "expert" models for each weakly-correlated category cluster and combines them using optimized weighted averaging rather than uniform weights. We demonstrate that the proposed method improves performance and robustness across multiple domains, including multilingual capabilities, tool calling, and math and achieves state-of-the-art results on the Berkeley Function Calling Leaderboard.

This paper introduces an efficient fine-tuning method for large pre-trained models, offering strong in-distribution (ID) and out-of-distribution (OOD) performance. Breaking away from traditional practices that need a multitude of fine-tuned models for averaging, our approach employs significantly fewer models to achieve final weights yet yield superior accuracy. Drawing from key insights in the weight space of fine-tuned weights, we uncover a strong link between the performance and proximity to the center of weight space. Based on this, we introduce a method that approximates a center-close weight using only two fine-tuned models, applicable during or after training. Our innovative layer-wise weight averaging technique surpasses state-of-the-art model methods such as Model Soup, utilizing only two fine-tuned models. This strategy can be aptly coined Model Stock, highlighting its reliance on selecting a minimal number of models to draw a more optimized-averaged model. We demonstrate the efficacy of Model Stock with fine-tuned models based upon pre-trained CLIP architectures, achieving remarkable performance on both ID and OOD tasks on the standard benchmarks, all while barely bringing extra computational demands. Our code and pre-trained models are available at https://github.com/naver-ai/model-stock.

Knowledge distillation (KD) is a powerful model compression technique broadly used in practical deep learning applications. It is focused on training a small student network to mimic a larger teacher network. While it is widely known that KD can offer an improvement to student generalization in i.i.d setting, its performance under domain shift, i.e. the performance of student networks on data from domains unseen during training, has received little attention in the literature. In this paper we make a step towards bridging the research fields of knowledge distillation and domain generalization. We show that weight averaging techniques proposed in domain generalization literature, such as SWAD and SMA, also improve the performance of knowledge distillation under domain shift. In addition, we propose a simplistic weight averaging strategy that does not require evaluation on validation data during training and show that it performs on par with SWAD and SMA when applied to KD. We name our final distillation approach Weight-Averaged Knowledge Distillation (WAKD).

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters.

By merging models, AI systems can combine the distinct strengths of separate language models, achieving a balance between multiple capabilities without requiring substantial retraining. However, the integration process can be intricate due to differences in training methods and fine-tuning, typically necessitating specialized knowledge and repeated refinement. This paper explores model merging techniques across a spectrum of complexity, examining where automated methods like evolutionary strategies stand compared to hyperparameter-driven approaches such as DARE, TIES-Merging and simpler methods like Model Soups. In addition, we introduce Differentiable Adaptive Merging (DAM), an efficient, adaptive merging approach as an alternative to evolutionary merging that optimizes model integration through scaling coefficients, minimizing computational demands. Our findings reveal that even simple averaging methods, like Model Soups, perform competitively when model similarity is high, underscoring each technique's unique strengths and limitations. We open-sourced DAM, including the implementation code and experiment pipeline, on GitHub: https://github.com/arcee-ai/DAM.

In this paper, we focus on quantifying model stability as a function of random seed by investigating the effects of the induced randomness on model performance and the robustness of the model in general. We specifically perform a controlled study on the effect of random seeds on the behaviour of attention, gradient-based and surrogate model based (LIME) interpretations. Our analysis suggests that random seeds can adversely affect the consistency of models resulting in counterfactual interpretations. We propose a technique called Aggressive Stochastic Weight Averaging (ASWA)and an extension called Norm-filtered Aggressive Stochastic Weight Averaging (NASWA) which improves the stability of models over random seeds. With our ASWA and NASWA based optimization, we are able to improve the robustness of the original model, on average reducing the standard deviation of the model's performance by 72%.

Stochasticity in language model fine-tuning, often caused by the small batch sizes typically used in this regime, can destabilize training by introducing large oscillations in generation quality. A popular approach to mitigating this instability is to take an Exponential moving average (EMA) of weights throughout training. While EMA reduces stochasticity, thereby smoothing training, the introduction of bias from old iterates often creates a lag in optimization relative to vanilla training. In this work, we propose the Bias-Corrected Exponential Moving Average (BEMA), a simple and practical augmentation of EMA that retains variance-reduction benefits while eliminating bias. BEMA is motivated by a simple theoretical model wherein we demonstrate provable acceleration of BEMA over both a standard EMA and vanilla training. Through an extensive suite of experiments on Language Models, we show that BEMA leads to significantly improved convergence rates and final performance over both EMA and vanilla training in a variety of standard LM benchmarks, making BEMA a practical and theoretically motivated intervention for more stable and efficient fine-tuning.

Developing large language models is expensive and involves making decisions with small experiments, typically by evaluating on large, multi-task evaluation suites. In this work, we analyze specific properties which make a benchmark more reliable for such decisions, and interventions to design higher-quality evaluation benchmarks. We introduce two key metrics that show differences in current benchmarks: signal, a benchmark's ability to separate better models from worse models, and noise, a benchmark's sensitivity to random variability between training steps. We demonstrate that benchmarks with a better signal-to-noise ratio are more reliable when making decisions at small scale, and those with less noise have lower scaling law prediction error. These results suggest that improving signal or noise will lead to more useful benchmarks, so we introduce three interventions designed to directly affect signal or noise. For example, we propose that switching to a metric that has better signal and noise (e.g., perplexity rather than accuracy) leads to better reliability and improved scaling law error. We also find that filtering noisy subtasks, to improve an aggregate signal-to-noise ratio, leads to more reliable multi-task evaluations. We also find that averaging the output of a model's intermediate checkpoints to reduce noise leads to consistent improvements. We conclude by recommending that those creating new benchmarks, or selecting which existing benchmarks to use, aim for high signal and low noise. We use 30 benchmarks for these experiments, and 375 open-weight language models from 60M to 32B parameters, resulting in a new, publicly available dataset of 900K evaluation benchmark results, totaling 200M instances.

Despite the remarkable capabilities of Language Models (LMs) across diverse tasks, no single model consistently outperforms others, necessitating efficient methods to combine their strengths without expensive retraining. Existing model merging techniques, such as parameter averaging and task-guided fusion, often rely on data-dependent computations or fail to preserve internal knowledge, limiting their robustness and scalability. We introduce SeMe (Semantic-based Merging), a novel, data-free, and training-free approach that leverages latent semantic alignment to merge LMs at a fine-grained, layer-wise level. Unlike prior work, SeMe not only preserves model behaviors but also explicitly stabilizes internal knowledge, addressing a critical gap in LM fusion. Through extensive experiments across diverse architectures and tasks, we demonstrate that SeMe outperforms existing methods in both performance and efficiency while eliminating reliance on external data. Our work establishes a new paradigm for knowledge-aware model merging and provides insights into the semantic structure of LMs, paving the way for more scalable and interpretable model composition.

While recent text-to-image (T2I) models show impressive capabilities in synthesizing images from brief descriptions, their performance significantly degrades when confronted with long, detail-intensive prompts required in professional applications. We present DetailMaster, the first comprehensive benchmark specifically designed to evaluate T2I models' systematical abilities to handle extended textual inputs that contain complex compositional requirements. Our benchmark introduces four critical evaluation dimensions: Character Attributes, Structured Character Locations, Multi-Dimensional Scene Attributes, and Explicit Spatial/Interactive Relationships. The benchmark comprises long and detail-rich prompts averaging 284.89 tokens, with high quality validated by expert annotators. Evaluation on 7 general-purpose and 5 long-prompt-optimized T2I models reveals critical performance limitations: state-of-the-art models achieve merely ~50% accuracy in key dimensions like attribute binding and spatial reasoning, while all models showing progressive performance degradation as prompt length increases. Our analysis highlights systemic failures in structural comprehension and detail overload handling, motivating future research into architectures with enhanced compositional reasoning. We open-source the dataset, data curation code, and evaluation tools to advance detail-rich T2I generation and enable broad applications that would otherwise be infeasible due to the lack of a dedicated benchmark.

Recent advances in diffusion-based lip-syncing generative models have demonstrated their ability to produce highly synchronized talking face videos for visual dubbing. Although these models excel at lip synchronization, they often struggle to maintain fine-grained control over facial details in generated images. In this work, we identify "lip averaging" phenomenon where the model fails to preserve subtle facial details when dubbing unseen in-the-wild videos. This issue arises because the commonly used UNet backbone primarily integrates audio features into visual representations in the latent space via cross-attention mechanisms and multi-scale fusion, but it struggles to retain fine-grained lip details in the generated faces. To address this issue, we propose UnAvgLip, which extracts identity embeddings from reference videos to generate highly faithful facial sequences while maintaining accurate lip synchronization. Specifically, our method comprises two primary components: (1) an Identity Perceiver module that encodes facial embeddings to align with conditioned audio features; and (2) an ID-CrossAttn module that injects facial embeddings into the generation process, enhancing model's capability of identity retention. Extensive experiments demonstrate that, at a modest training and inference cost, UnAvgLip effectively mitigates the "averaging" phenomenon in lip inpainting, significantly preserving unique facial characteristics while maintaining precise lip synchronization. Compared with the original approach, our method demonstrates significant improvements of 5% on the identity consistency metric and 2% on the SSIM metric across two benchmark datasets (HDTF and LRW).

Model merging aims to combine multiple expert models into a more capable single model, offering benefits such as reduced storage and serving costs, improved generalization, and support for decentralized model development. Despite its promise, previous studies have primarily focused on merging a few small models. This leaves many unanswered questions about the effect of scaling model size and how it interplays with other key factors -- like the base model quality and number of expert models -- , to affect the merged model's performance. This work systematically evaluates the utility of model merging at scale, examining the impact of these different factors. We experiment with merging fully fine-tuned models using 4 popular merging methods -- Averaging, Task~Arithmetic, Dare, and TIES -- across model sizes ranging from 1B-64B parameters and merging up to 8 different expert models. We evaluate the merged models on both held-in tasks, i.e., the expert's training tasks, and zero-shot generalization to unseen held-out tasks. Our experiments provide several new insights about model merging at scale and the interplay between different factors. First, we find that merging is more effective when experts are created from strong base models, i.e., models with good zero-shot performance. Second, larger models facilitate easier merging. Third merging consistently improves generalization capabilities. Notably, when merging 8 large expert models, the merged models often generalize better compared to the multitask trained models. Fourth, we can better merge more expert models when working with larger models. Fifth, different merging methods behave very similarly at larger scales. Overall, our findings shed light on some interesting properties of model merging while also highlighting some limitations. We hope that this study will serve as a reference point on large-scale merging for upcoming research.

Traditional model merging methods for multi-task learning (MTL) address task conflicts with straightforward strategies such as weight averaging, sign consensus, or minimal test-time adjustments. This presumably counts on the assumption that a merged encoder still retains abundant task knowledge from individual encoders, implying that its shared representation is sufficiently general across tasks. However, our insight is that adding just a single trainable task-specific layer further can bring striking performance gains, as demonstrated by our pilot study. Motivated by this finding, we propose Model Tinting, a new test-time approach that introduces a single task-specific layer for each task as trainable adjustments. Our method jointly trains merging coefficients and task-specific layers, which effectively reduces task conflicts with minimal additional costs. Additionally, we propose a sampling method that utilizes the difference in confidence levels of both merged and individual encoders. Extensive experiments demonstrate our method's effectiveness, which achieves state-of-the-art performance across both computer vision and natural language processing tasks and significantly surpasses prior works. Our code is available at https://github.com/AIM-SKKU/ModelTinting.

Structural re-parameterization is a general training scheme for Convolutional Neural Networks (CNNs), which achieves performance improvement without increasing inference cost. As Vision Transformers (ViTs) are gradually surpassing CNNs in various visual tasks, one may question: if a training scheme specifically for ViTs exists that can also achieve performance improvement without increasing inference cost? Recently, Mixture-of-Experts (MoE) has attracted increasing attention, as it can efficiently scale up the capacity of Transformers at a fixed cost through sparsely activated experts. Considering that MoE can also be viewed as a multi-branch structure, can we utilize MoE to implement a ViT training scheme similar to structural re-parameterization? In this paper, we affirmatively answer these questions, with a new general training strategy for ViTs. Specifically, we decouple the training and inference phases of ViTs. During training, we replace some Feed-Forward Networks (FFNs) of the ViT with specially designed, more efficient MoEs that assign tokens to experts by random uniform partition, and perform Experts Weights Averaging (EWA) on these MoEs at the end of each iteration. After training, we convert each MoE into an FFN by averaging the experts, transforming the model back into original ViT for inference. We further provide a theoretical analysis to show why and how it works. Comprehensive experiments across various 2D and 3D visual tasks, ViT architectures, and datasets validate the effectiveness and generalizability of the proposed training scheme. Besides, our training scheme can also be applied to improve performance when fine-tuning ViTs. Lastly, but equally important, the proposed EWA technique can significantly improve the effectiveness of naive MoE in various 2D visual small datasets and 3D visual tasks.

Zero Redundancy Optimizer (ZeRO) has been used to train a wide range of large language models on massive GPUs clusters due to its ease of use, efficiency, and good scalability. However, when training on low-bandwidth clusters, or at scale which forces batch size per GPU to be small, ZeRO's effective throughput is limited because of high communication volume from gathering weights in forward pass, backward pass, and averaging gradients. This paper introduces three communication volume reduction techniques, which we collectively refer to as ZeRO++, targeting each of the communication collectives in ZeRO. First is block-quantization based all-gather. Second is data remapping that trades-off communication for more memory. Third is a novel all-to-all based quantized gradient averaging paradigm as replacement of reduce-scatter collective, which preserves accuracy despite communicating low precision data. Collectively, ZeRO++ reduces communication volume of ZeRO by 4x, enabling up to 2.16x better throughput at 384 GPU scale.

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

Checkpoint merging is a technique for combining multiple model snapshots into a single superior model, potentially reducing training time for large language models. This paper explores checkpoint merging in the context of parameter-efficient fine-tuning (PEFT), where only small adapter modules (e.g. LoRA) are trained. We propose Metrics-Weighted Averaging (MWA), a simple yet effective method to merge model checkpoints by weighting their parameters according to performance metrics. In particular, we investigate weighting by training loss and by training steps, under the intuition that lower-loss or later-step checkpoints are more valuable. We introduce a formula with a penalty factor to adjust weight distribution, requiring only one hyperparameter regardless of the number of checkpoints. Experiments on three fine-tuning tasks (mathematical reasoning, preference alignment, and general instruction tuning) show that MWA consistently produces merged models that outperform the naive uniform average of checkpoints. Notably, loss-weighted merging often yields the best results, delivering up to 5% higher task accuracy than the baseline uniform merge and even surpassing the final individual checkpoint's performance. These findings validate checkpoint merging for PEFT and demonstrate that a metric-driven weighting heuristic can efficiently boost model performance with minimal computational overhead.

The recent success of specialized Large Language Models (LLMs) in domains such as mathematical reasoning and coding has led to growing interest in methods for merging these expert LLMs into a unified Mixture-of-Experts (MoE) model, with the goal of enhancing performance in each domain while retaining effectiveness on general tasks. However, the effective merging of expert models remains an open challenge, especially for models with highly divergent weight parameters or different architectures. State-of-the-art MoE merging methods only work with homogeneous model architectures and rely on simple unweighted averaging to merge expert layers, which does not address parameter interference and requires extensive fine-tuning of the merged MoE to restore performance. To address these limitations, this paper introduces new MoE merging techniques, including strategies to mitigate parameter interference, routing heuristics to reduce the need for MoE fine-tuning, and a novel method for merging experts with different architectures. Extensive experiments across multiple domains demonstrate the effectiveness of our proposed methods, reducing fine-tuning costs, improving performance over state-of-the-art methods, and expanding the applicability of MoE merging.

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.

Deepfake detection has become increasingly important due to the rise of synthetic media, which poses significant risks to digital identity and cyber presence for security and trust. While multiple approaches have improved detection accuracy, challenges remain in achieving consistent performance across diverse datasets and manipulation types. In response, we propose a novel two-tier ensemble framework for deepfake detection based on deep learning that hierarchically combines multiple instances of three state-of-the-art architectures: Xception, Res2Net101, and EfficientNet-B7. Our framework employs a unique approach where each architecture is instantiated three times with different initializations to enhance model diversity, followed by a learnable weighting mechanism that dynamically combines their predictions. Unlike traditional fixed-weight ensembles, our first-tier averages predictions within each architecture family to reduce model variance, while the second tier learns optimal contribution weights through backpropagation, automatically adjusting each architecture's influence based on their detection reliability. Our experiments achieved state-of-the-art intra-dataset performance with AUC scores of 99.22% (FF++) and 100.00% (CelebDF-v2), and F1 scores of 98.06% (FF++) and 99.94% (CelebDF-v2) without augmentation. With augmentation, we achieve AUC scores of 99.47% (FF++) and 100.00% (CelebDF-v2), and F1 scores of 98.43% (FF++) and 99.95% (CelebDF-v2). The framework demonstrates robust cross-dataset generalization, achieving AUC scores of 88.20% and 72.52%, and F1 scores of 93.16% and 80.62% in cross-dataset evaluations.

Training Large Language Models (LLMs) incurs significant cost; hence, any strategy that accelerates model convergence is helpful. In this paper, we investigate the ability of a simple idea checkpoint averaging along the trajectory of a training run to improve both convergence and generalization quite early on during training. Here we show that models trained with high learning rates observe higher gains due to checkpoint averaging. Furthermore, these gains are amplified when checkpoints are sampled with considerable spacing in training steps. Our training recipe outperforms conventional training and popular checkpoint averaging baselines such as exponential moving average (EMA) and stochastic moving average (SWA). We evaluate our training recipe by pre-training LLMs, where high learning rates are inherently preferred due to extremely large batch sizes. Specifically, we pre-trained nanoGPT-2 models of varying sizes, small (125M), medium (335M), and large (770M)on the OpenWebText dataset, comprised of 9B tokens. Additionally, we present results for publicly available Pythia LLMs, ranging from 1B to 12B, which were trained on the PILE-deduped dataset containing 207B tokens.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar geometries.We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging. Such uncertainties are obtained for free by considering the Jacobians of two-view refinements. Moreover, we explore integrating a variant of the MAGSAC loss into the rotation averaging problem, instead of using classical robust losses employed in current frameworks. The proposed method leads to results superior to baselines, in terms of accuracy, on large-scale public benchmarks. The code is public. https://github.com/zhangganlin/GlobalSfMpy

Many model watermarking methods have been developed to prevent valuable deployed commercial models from being stealthily stolen by model distillations. However, watermarks produced by most existing model watermarking methods can be easily evaded by ensemble distillation, because averaging the outputs of multiple ensembled models can significantly reduce or even erase the watermarks. In this paper, we focus on tackling the challenging task of defending against ensemble distillation. We propose a novel watermarking technique named CosWM to achieve outstanding model watermarking performance against ensemble distillation. CosWM is not only elegant in design, but also comes with desirable theoretical guarantees. Our extensive experiments on public data sets demonstrate the excellent performance of CosWM and its advantages over the state-of-the-art baselines.

This paper introduces a continual learning approach named MagMax, which utilizes model merging to enable large pre-trained models to continuously learn from new data without forgetting previously acquired knowledge. Distinct from traditional continual learning methods that aim to reduce forgetting during task training, MagMax combines sequential fine-tuning with a maximum magnitude weight selection for effective knowledge integration across tasks. Our initial contribution is an extensive examination of model merging techniques, revealing that simple approaches like weight averaging and random weight selection surprisingly hold up well in various continual learning contexts. More importantly, we present MagMax, a novel model-merging strategy that enables continual learning of large pre-trained models for successive tasks. Our thorough evaluation demonstrates the superiority of MagMax in various scenarios, including class- and domain-incremental learning settings.

Training vision or language models on large datasets can take days, if not weeks. We show that averaging the weights of the k latest checkpoints, each collected at the end of an epoch, can speed up the training progression in terms of loss and accuracy by dozens of epochs, corresponding to time savings up to ~68 and ~30 GPU hours when training a ResNet50 on ImageNet and RoBERTa-Base model on WikiText-103, respectively. We also provide the code and model checkpoint trajectory to reproduce the results and facilitate research on reusing historical weights for faster convergence.

We present Diffusion Soup, a compartmentalization method for Text-to-Image Generation that averages the weights of diffusion models trained on sharded data. By construction, our approach enables training-free continual learning and unlearning with no additional memory or inference costs, since models corresponding to data shards can be added or removed by re-averaging. We show that Diffusion Soup samples from a point in weight space that approximates the geometric mean of the distributions of constituent datasets, which offers anti-memorization guarantees and enables zero-shot style mixing. Empirically, Diffusion Soup outperforms a paragon model trained on the union of all data shards and achieves a 30% improvement in Image Reward (.34 to .44) on domain sharded data, and a 59% improvement in IR (.37 to .59) on aesthetic data. In both cases, souping also prevails in TIFA score (respectively, 85.5 to 86.5 and 85.6 to 86.8). We demonstrate robust unlearning -- removing any individual domain shard only lowers performance by 1% in IR (.45 to .44) -- and validate our theoretical insights on anti-memorization using real data. Finally, we showcase Diffusion Soup's ability to blend the distinct styles of models finetuned on different shards, resulting in the zero-shot generation of hybrid styles.

End-to-end autonomous driving (E2E-AD) demands effective processing of multi-view sensory data and robust handling of diverse and complex driving scenarios, particularly rare maneuvers such as aggressive turns. Recent success of Mixture-of-Experts (MoE) architecture in Large Language Models (LLMs) demonstrates that specialization of parameters enables strong scalability. In this work, we propose DriveMoE, a novel MoE-based E2E-AD framework, with a Scene-Specialized Vision MoE and a Skill-Specialized Action MoE. DriveMoE is built upon our pi_0 Vision-Language-Action (VLA) baseline (originally from the embodied AI field), called Drive-pi_0. Specifically, we add Vision MoE to Drive-pi_0 by training a router to select relevant cameras according to the driving context dynamically. This design mirrors human driving cognition, where drivers selectively attend to crucial visual cues rather than exhaustively processing all visual information. In addition, we add Action MoE by training another router to activate specialized expert modules for different driving behaviors. Through explicit behavioral specialization, DriveMoE is able to handle diverse scenarios without suffering from modes averaging like existing models. In Bench2Drive closed-loop evaluation experiments, DriveMoE achieves state-of-the-art (SOTA) performance, demonstrating the effectiveness of combining vision and action MoE in autonomous driving tasks. We will release our code and models of DriveMoE and Drive-pi_0.

The transformer architecture by Vaswani et al. (2017) is now ubiquitous across application domains, from natural language processing to speech processing and image understanding. We propose DenseFormer, a simple modification to the standard architecture that improves the perplexity of the model without increasing its size -- adding a few thousand parameters for large-scale models in the 100B parameters range. Our approach relies on an additional averaging step after each transformer block, which computes a weighted average of current and past representations -- we refer to this operation as Depth-Weighted-Average (DWA). The learned DWA weights exhibit coherent patterns of information flow, revealing the strong and structured reuse of activations from distant layers. Experiments demonstrate that DenseFormer is more data efficient, reaching the same perplexity of much deeper transformer models, and that for the same perplexity, these new models outperform transformer baselines in terms of memory efficiency and inference time.

We introduce EarthPT -- an Earth Observation (EO) pretrained transformer. EarthPT is a 700 million parameter decoding transformer foundation model trained in an autoregressive self-supervised manner and developed specifically with EO use-cases in mind. We demonstrate that EarthPT is an effective forecaster that can accurately predict future pixel-level surface reflectances across the 400-2300 nm range well into the future. For example, forecasts of the evolution of the Normalised Difference Vegetation Index (NDVI) have a typical error of approximately 0.05 (over a natural range of -1 -> 1) at the pixel level over a five month test set horizon, out-performing simple phase-folded models based on historical averaging. We also demonstrate that embeddings learnt by EarthPT hold semantically meaningful information and could be exploited for downstream tasks such as highly granular, dynamic land use classification. Excitingly, we note that the abundance of EO data provides us with -- in theory -- quadrillions of training tokens. Therefore, if we assume that EarthPT follows neural scaling laws akin to those derived for Large Language Models (LLMs), there is currently no data-imposed limit to scaling EarthPT and other similar `Large Observation Models.'

Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good performing model if the loss surface of interest is very particular, i.e., the loss in the midpoint between the two models needs to be sufficiently low. This is impossible to guarantee for the non-convex losses of state-of-the-art networks. For averaging models trained on vastly different datasets, it was proposed to average only the parameters of particular layers or combinations of layers, resulting in better performing models. To get a better understanding of the effect of layer-wise averaging, we analyse the performance of the models that result from averaging single layers, or groups of layers. Based on our empirical and theoretical investigation, we introduce a novel notion of the layer-wise linear connectivity, and show that deep networks do not have layer-wise barriers between them.

Large language model (LLM) evaluations typically rely on aggregated metrics like accuracy or human preference, averaging across users and prompts. This averaging obscures user- and prompt-specific variations in model performance. To address this, we propose Prompt-to-Leaderboard (P2L), a method that produces leaderboards specific to a prompt. The core idea is to train an LLM taking natural language prompts as input to output a vector of Bradley-Terry coefficients which are then used to predict the human preference vote. The resulting prompt-dependent leaderboards allow for unsupervised task-specific evaluation, optimal routing of queries to models, personalization, and automated evaluation of model strengths and weaknesses. Data from Chatbot Arena suggest that P2L better captures the nuanced landscape of language model performance than the averaged leaderboard. Furthermore, our findings suggest that P2L's ability to produce prompt-specific evaluations follows a power law scaling similar to that observed in LLMs themselves. In January 2025, the router we trained based on this methodology achieved the \#1 spot in the Chatbot Arena leaderboard. Our code is available at this GitHub link: https://github.com/lmarena/p2l.

We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an iterated exponential of height logarithmic in the number of birds. We also prove the highly surprising result that this bound is optimal. The model directs the birds to adjust their velocities repeatedly by averaging them with their neighbors within a fixed radius. The model is deterministic, but we show that it can tolerate a reasonable amount of stochastic or even adversarial noise. Our methods are highly general and we speculate that the results extend to a wider class of models based on undirected flocking networks, whether defined metrically or topologically. This work introduces new techniques of broader interest, including the "flight net," the "iterated spectral shift," and a certain "residue-clearing" argument in circuit complexity.

Pretrained models are the standard starting point for training. This approach consistently outperforms the use of a random initialization. However, pretraining is a costly endeavour that few can undertake. In this paper, we create better base models at hardly any cost, by fusing multiple existing fine tuned models into one. Specifically, we fuse by averaging the weights of these models. We show that the fused model results surpass the pretrained model ones. We also show that fusing is often better than intertraining. We find that fusing is less dependent on the target task. Furthermore, weight decay nullifies intertraining effects but not those of fusing.

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is often neglected: preferences vary across individuals and should be represented with more granularity. To address this, we propose SmPO-Diffusion, a novel method for modeling preference distributions to improve the DPO objective, along with a numerical upper bound estimation for the diffusion optimization objective. First, we introduce a smoothed preference distribution to replace the original binary distribution. We employ a reward model to simulate human preferences and apply preference likelihood averaging to improve the DPO loss, such that the loss function approaches zero when preferences are similar. Furthermore, we utilize an inversion technique to simulate the trajectory preference distribution of the diffusion model, enabling more accurate alignment with the optimization objective. Our approach effectively mitigates issues of excessive optimization and objective misalignment present in existing methods through straightforward modifications. Our SmPO-Diffusion achieves state-of-the-art performance in preference evaluation, outperforming baselines across metrics with lower training costs. The project page is https://jaydenlyh.github.io/SmPO-project-page/.

Collecting high-quality preference datasets for reinforcement learning from human feedback (RLHF) is resource-intensive and challenging. As a result, researchers often train reward models on extensive offline datasets which aggregate diverse generation sources and scoring/alignment policies. We hypothesize that this aggregation has an averaging effect on reward model scores, which limits signal and impairs the alignment process. Inspired by the field of inverse RL, we define the 'inverse alignment problem' in language model training, where our objective is to optimize the critic's reward for a fixed actor and a fixed offline preference dataset. We hypothesize that solving the inverse alignment problem will improve reward model quality by providing clearer feedback on the policy's current behavior. To that end, we investigate whether repeatedly fine-tuning a reward model on subsets of the offline preference dataset aligned with a periodically frozen policy during RLHF improves upon vanilla RLHF. Our empirical results demonstrate that this approach facilitates superior alignment and faster convergence compared to using an unaligned or out-of-distribution reward model relative to the LLM policy.

Multimodal reasoning requires iterative coordination between language and vision, yet it remains unclear what constitutes a meaningful interleaved chain of thought. We posit that text and image thoughts should function as complementary, rather than isomorphic, modalities that mutually advance reasoning. Guided by this principle, we build ThinkMorph, a unified model fine-tuned on 24K high-quality interleaved reasoning traces spanning tasks with varying visual engagement. ThinkMorph learns to generate progressive text-image reasoning steps that concretely manipulate visual content while maintaining coherent verbal logic. It delivers large gains on vision-centric benchmarks (averaging 34.7% over the base model) and generalizes to out-of-domain tasks, matching or surpassing larger and proprietary VLMs. Beyond performance, ThinkMorph exhibits emergent multimodal intelligence, including unseen visual manipulation skills, adaptive switching between reasoning modes, and better test-time scaling through diversified multimodal thoughts.These findings suggest promising directions for characterizing the emergent capabilities of unified models for multimodal reasoning.

Text embeddings are useful features in many applications such as semantic search and computing text similarity. Previous work typically trains models customized for different use cases, varying in dataset choice, training objective and model architecture. In this work, we show that contrastive pre-training on unsupervised data at scale leads to high quality vector representations of text and code. The same unsupervised text embeddings that achieve new state-of-the-art results in linear-probe classification also display impressive semantic search capabilities and sometimes even perform competitively with fine-tuned models. On linear-probe classification accuracy averaging over 7 tasks, our best unsupervised model achieves a relative improvement of 4% and 1.8% over previous best unsupervised and supervised text embedding models respectively. The same text embeddings when evaluated on large-scale semantic search attains a relative improvement of 23.4%, 14.7%, and 10.6% over previous best unsupervised methods on MSMARCO, Natural Questions and TriviaQA benchmarks, respectively. Similarly to text embeddings, we train code embedding models on (text, code) pairs, obtaining a 20.8% relative improvement over prior best work on code search.

Current preference learning methods achieve high accuracy on standard benchmarks but exhibit significant performance degradation when objective quality signals are removed. We introduce WritingPreferenceBench, a dataset of 1,800 human-annotated preference pairs (1,200 English, 600 Chinese) across 8 creative writing genres, where responses are matched for objective correctness, factual accuracy, and length. On this benchmark, sequence-based reward models--the standard architecture for RLHF--achieve only 52.7% mean accuracy, while zero-shot language model judges perform at 53.9%. In contrast, generative reward models that produce explicit reasoning chains achieve 81.8% accuracy. We observe high within-model variance across genres: individual models range from 18.2% to 81.8% accuracy across different writing categories, with standard deviations averaging 10.1%. This variance persists regardless of model scale, with 27B parameter models showing no consistent improvement over 8B variants. Our results suggest that current RLHF methods primarily learn to detect objective errors rather than capture subjective quality preferences (e.g., creativity, stylistic flair, and emotional resonance), and that successful preference modeling may require intermediate reasoning representations rather than direct classification.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

Diffusion Models (DM) and Consistency Models (CM) are two types of popular generative models with good generation quality on various tasks. When training DM and CM, intermediate weight checkpoints are not fully utilized and only the last converged checkpoint is used. In this work, we find that high-quality model weights often lie in a basin which cannot be reached by SGD but can be obtained by proper checkpoint averaging. Based on these observations, we propose LCSC, a simple but effective and efficient method to enhance the performance of DM and CM, by combining checkpoints along the training trajectory with coefficients deduced from evolutionary search. We demonstrate the value of LCSC through two use cases: (a) Reducing training cost. With LCSC, we only need to train DM/CM with fewer number of iterations and/or lower batch sizes to obtain comparable sample quality with the fully trained model. For example, LCSC achieves considerable training speedups for CM (23times on CIFAR-10 and 15times on ImageNet-64). (b) Enhancing pre-trained models. Assuming full training is already done, LCSC can further improve the generation quality or speed of the final converged models. For example, LCSC achieves better performance using 1 number of function evaluation (NFE) than the base model with 2 NFE on consistency distillation, and decreases the NFE of DM from 15 to 9 while maintaining the generation quality on CIFAR-10. Our code is available at https://github.com/imagination-research/LCSC.

We describe federated reconnaissance, a class of learning problems in which distributed clients learn new concepts independently and communicate that knowledge efficiently. In particular, we propose an evaluation framework and methodological baseline for a system in which each client is expected to learn a growing set of classes and communicate knowledge of those classes efficiently with other clients, such that, after knowledge merging, the clients should be able to accurately discriminate between classes in the superset of classes observed by the set of clients. We compare a range of learning algorithms for this problem and find that prototypical networks are a strong approach in that they are robust to catastrophic forgetting while incorporating new information efficiently. Furthermore, we show that the online averaging of prototype vectors is effective for client model merging and requires only a small amount of communication overhead, memory, and update time per class with no gradient-based learning or hyperparameter tuning. Additionally, to put our results in context, we find that a simple, prototypical network with four convolutional layers significantly outperforms complex, state of the art continual learning algorithms, increasing the accuracy by over 22% after learning 600 Omniglot classes and over 33% after learning 20 mini-ImageNet classes incrementally. These results have important implications for federated reconnaissance and continual learning more generally by demonstrating that communicating feature vectors is an efficient, robust, and effective means for distributed, continual learning.

Despite the success of deep learning models on instance segmentation, current methods still suffer from catastrophic forgetting in continual learning scenarios. In this paper, our contributions for continual instance segmentation are threefold. First, we propose the Y-knowledge distillation (Y-KD), a technique that shares a common feature extractor between the teacher and student networks. As the teacher is also updated with new data in Y-KD, the increased plasticity results in new modules that are specialized on new classes. Second, our Y-KD approach is supported by a dynamic architecture method that trains task-specific modules with a unique instance segmentation head, thereby significantly reducing forgetting. Third, we complete our approach by leveraging checkpoint averaging as a simple method to manually balance the trade-off between performance on the various sets of classes, thus increasing control over the model's behavior without any additional cost. These contributions are united in our model that we name the Dynamic Y-KD network. We perform extensive experiments on several single-step and multi-steps incremental learning scenarios, and we show that our approach outperforms previous methods both on past and new classes. For instance, compared to recent work, our method obtains +2.1% mAP on old classes in 15-1, +7.6% mAP on new classes in 19-1 and reaches 91.5% of the mAP obtained by joint-training on all classes in 15-5.

Existing 3D vision-language (3D-VL) benchmarks fall short in evaluating 3D-VL models, creating a "mist" that obscures rigorous insights into model capabilities and 3D-VL tasks. This mist persists due to three key limitations. First, flawed test data, like ambiguous referential text in the grounding task, can yield incorrect and unreliable test results. Second, oversimplified metrics such as simply averaging accuracy per question answering (QA) pair, cannot reveal true model capability due to their vulnerability to language variations. Third, existing benchmarks isolate the grounding and QA tasks, disregarding the underlying coherence that QA should be based on solid grounding capabilities. To unveil the "mist", we propose Beacon3D, a benchmark for 3D-VL grounding and QA tasks, delivering a perspective shift in the evaluation of 3D-VL understanding. Beacon3D features (i) high-quality test data with precise and natural language, (ii) object-centric evaluation with multiple tests per object to ensure robustness, and (iii) a novel chain-of-analysis paradigm to address language robustness and model performance coherence across grounding and QA. Our evaluation of state-of-the-art 3D-VL models on Beacon3D reveals that (i) object-centric evaluation elicits true model performance and particularly weak generalization in QA; (ii) grounding-QA coherence remains fragile in current 3D-VL models, and (iii) incorporating large language models (LLMs) to 3D-VL models, though as a prevalent practice, hinders grounding capabilities and has yet to elevate QA capabilities. We hope Beacon3D and our comprehensive analysis could benefit the 3D-VL community towards faithful developments.

Recent developments in Large Language Model (LLM)-based agents have shown impressive capabilities spanning multiple domains, exemplified by deep research systems that demonstrate superior performance on complex information-seeking and synthesis tasks. While general-purpose deep research agents have shown impressive capabilities, they struggle significantly with medical domain challenges, as evidenced by leading proprietary systems achieving limited accuracy on complex medical benchmarks. The key limitations are: (1) the model lacks sufficient dense medical knowledge for clinical reasoning, and (2) the framework is constrained by the absence of specialized retrieval tools tailored for medical contexts.We present a medical deep research agent that addresses these challenges through two core innovations. First, we develop a novel data synthesis framework using medical knowledge graphs, extracting the longest chains from subgraphs around rare medical entities to generate complex multi-hop question-answer pairs. Second, we integrate a custom-built private medical retrieval engine alongside general-purpose tools, enabling accurate medical information synthesis. Our approach generates 2100+ diverse trajectories across 12 medical specialties, each averaging 4.2 tool interactions.Through a two-stage training paradigm combining supervised fine-tuning and online reinforcement learning with composite rewards, our MedResearcher-R1-32B model demonstrates exceptional performance, establishing new state-of-the-art results on medical benchmarks while maintaining competitive performance on general deep research tasks. Our work demonstrates that strategic domain-specific innovations in architecture, tool design, and training data construction can enable smaller open-source models to outperform much larger proprietary systems in specialized domains.

Large Language Models (LLMs) have demonstrated impressive capabilities, but their high computational costs pose challenges for customization. Model merging offers a cost-effective alternative, yet existing methods suffer from interference among parameters, leading to performance degradation. In this work, we propose Optimal Brain Iterative Merging (OBIM), a novel method designed to mitigate both intra-model and inter-model interference. OBIM consists of two key components: (1) A saliency measurement mechanism that evaluates parameter importance based on loss changes induced by individual weight alterations, reducing intra-model interference by preserving only high-saliency parameters. (2) A mutually exclusive iterative merging framework, which incrementally integrates models using a binary mask to avoid direct parameter averaging, thereby mitigating inter-model interference. We validate OBIM through experiments on both Supervised Fine-Tuned (SFT) models and post-pretrained checkpoints. The results show that OBIM significantly outperforms existing merging techniques. Overall, OBIM provides an effective and practical solution for enhancing LLM merging.

Explanation methods facilitate the development of models that learn meaningful concepts and avoid exploiting spurious correlations. We illustrate a previously unrecognized limitation of the popular neural network explanation method Grad-CAM: as a side effect of the gradient averaging step, Grad-CAM sometimes highlights locations the model did not actually use. To solve this problem, we propose HiResCAM, a novel class-specific explanation method that is guaranteed to highlight only the locations the model used to make each prediction. We prove that HiResCAM is a generalization of CAM and explore the relationships between HiResCAM and other gradient-based explanation methods. Experiments on PASCAL VOC 2012, including crowd-sourced evaluations, illustrate that while HiResCAM's explanations faithfully reflect the model, Grad-CAM often expands the attention to create bigger and smoother visualizations. Overall, this work advances convolutional neural network explanation approaches and may aid in the development of trustworthy models for sensitive applications.

Today's generative models are capable of synthesizing high-fidelity images, but each model specializes on a specific target domain. This raises the need for model merging: combining two or more pretrained generative models into a single unified one. In this work we tackle the problem of model merging, given two constraints that often come up in the real world: (1) no access to the original training data, and (2) without increasing the size of the neural network. To the best of our knowledge, model merging under these constraints has not been studied thus far. We propose a novel, two-stage solution. In the first stage, we transform the weights of all the models to the same parameter space by a technique we term model rooting. In the second stage, we merge the rooted models by averaging their weights and fine-tuning them for each specific domain, using only data generated by the original trained models. We demonstrate that our approach is superior to baseline methods and to existing transfer learning techniques, and investigate several applications.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

In Large Language Model (LLM) development, Reinforcement Learning from Human Feedback (RLHF) is crucial for aligning models with human values and preferences. RLHF traditionally relies on the Kullback-Leibler (KL) divergence between the current policy and a frozen initial policy as a reference, which is added as a penalty in policy optimization algorithms like Proximal Policy Optimization (PPO). While this constraint prevents models from deviating too far from the initial checkpoint, it limits exploration of the reward landscape, reducing the model's ability to discover higher-quality solutions. As a result, policy optimization is often trapped in a narrow region of the parameter space, leading to suboptimal alignment and performance. This paper presents SALSA (Soup-based Alignment Learning for Stronger Adaptation), a novel approach designed to overcome these limitations by creating a more flexible and better located reference model through weight-space averaging of two independent supervised fine-tuned (SFT) models. This model soup allows for larger deviation in KL divergence and exploring a promising region of the solution space without sacrificing stability. By leveraging this more robust reference model, SALSA fosters better exploration, achieving higher rewards and improving model robustness, out-of-distribution generalization, and performance. We validate the effectiveness of SALSA through extensive experiments on popular open models (Llama2-7B, Mistral-7B, and Gemma-2B) across various benchmarks (MT-Bench, Arena-Hard, UltraFeedback), where it consistently surpasses PPO by fostering deeper exploration and achieving superior alignment in LLMs.

Age-related macular degeneration (AMD) and choroidal neovascularization (CNV)-related conditions are leading causes of vision loss worldwide, with optical coherence tomography (OCT) serving as a cornerstone for early detection and management. However, deploying state-of-the-art deep learning models like ConvNeXtV2-Large in clinical settings is hindered by their computational demands. Therefore, it is desirable to develop efficient models that maintain high diagnostic performance while enabling real-time deployment. In this study, a novel knowledge distillation framework, termed KD-OCT, is proposed to compress a high-performance ConvNeXtV2-Large teacher model, enhanced with advanced augmentations, stochastic weight averaging, and focal loss, into a lightweight EfficientNet-B2 student for classifying normal, drusen, and CNV cases. KD-OCT employs real-time distillation with a combined loss balancing soft teacher knowledge transfer and hard ground-truth supervision. The effectiveness of the proposed method is evaluated on the Noor Eye Hospital (NEH) dataset using patient-level cross-validation. Experimental results demonstrate that KD-OCT outperforms comparable multi-scale or feature-fusion OCT classifiers in efficiency- accuracy balance, achieving near-teacher performance with substantial reductions in model size and inference time. Despite the compression, the student model exceeds most existing frameworks, facilitating edge deployment for AMD screening. Code is available at https://github.com/erfan-nourbakhsh/KD- OCT.

This paper introduces the concept of {mutual consensus} as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the {OWA-MCC} model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.

Pretrained transformers readily adapt to new sequence modeling tasks via zero-shot prompting, but relational domains still lack architectures that transfer across datasets and tasks. The core challenge is the diversity of relational data, with varying heterogeneous schemas, graph structures and functional dependencies. In this paper, we present the Relational Transformer (RT) architecture, which can be pretrained on diverse relational databases and directly applied to unseen datasets and tasks without task- or dataset-specific fine-tuning, or retrieval of in-context examples. RT (i) tokenizes cells with table/column metadata, (ii) is pretrained via masked token prediction, and (iii) utilizes a novel Relational Attention mechanism over columns, rows, and primary-foreign key links. Pretrained on RelBench datasets spanning tasks such as churn and sales forecasting, RT attains strong zero-shot performance, averaging 94% of fully supervised AUROC on binary classification tasks with a single forward pass of a 22M parameter model, as opposed to 84% for a 27B LLM. Fine-tuning yields state-of-the-art results with high sample efficiency. Our experiments show that RT's zero-shot transfer harnesses task-table context, relational attention patterns and schema semantics. Overall, RT provides a practical path toward foundation models for relational data.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

Imitation learning uses data for training policies to solve complex tasks. However, when the training data is collected from human demonstrators, it often leads to multimodal distributions because of the variability in human actions. Most imitation learning methods rely on a maximum likelihood (ML) objective to learn a parameterized policy, but this can result in suboptimal or unsafe behavior due to the mode-averaging property of the ML objective. In this work, we propose Information Maximizing Curriculum, a curriculum-based approach that assigns a weight to each data point and encourages the model to specialize in the data it can represent, effectively mitigating the mode-averaging problem by allowing the model to ignore data from modes it cannot represent. To cover all modes and thus, enable diverse behavior, we extend our approach to a mixture of experts (MoE) policy, where each mixture component selects its own subset of the training data for learning. A novel, maximum entropy-based objective is proposed to achieve full coverage of the dataset, thereby enabling the policy to encompass all modes within the data distribution. We demonstrate the effectiveness of our approach on complex simulated control tasks using diverse human demonstrations, achieving superior performance compared to state-of-the-art methods.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

Causal language models have demonstrated remarkable capabilities, but their size poses significant challenges for deployment in resource-constrained environments. Knowledge distillation, a widely-used technique for transferring knowledge from a large teacher model to a small student model, presents a promising approach for model compression. A significant remaining issue lies in the major differences between teacher and student models, namely the substantial capacity gap, mode averaging, and mode collapse, which pose barriers during distillation. To address these issues, we introduce Temporally Adaptive Interpolated Distillation (TAID), a novel knowledge distillation approach that dynamically interpolates student and teacher distributions through an adaptive intermediate distribution, gradually shifting from the student's initial distribution towards the teacher's distribution. We provide a theoretical analysis demonstrating TAID's ability to prevent mode collapse and empirically show its effectiveness in addressing the capacity gap while balancing mode averaging and mode collapse. Our comprehensive experiments demonstrate TAID's superior performance across various model sizes and architectures in both instruction tuning and pre-training scenarios. Furthermore, we showcase TAID's practical impact by developing two state-of-the-art compact foundation models: TAID-LLM-1.5B for language tasks and TAID-VLM-2B for vision-language tasks. These results demonstrate TAID's effectiveness in creating high-performing and efficient models, advancing the development of more accessible AI technologies.

Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA) strategies were shown to perform best on the competitive DomainBed benchmark; they directly average the weights of multiple networks despite their nonlinearities. In this paper, we propose Diverse Weight Averaging (DiWA), a new WA strategy whose main motivation is to increase the functional diversity across averaged models. To this end, DiWA averages weights obtained from several independent training runs: indeed, models obtained from different runs are more diverse than those collected along a single run thanks to differences in hyperparameters and training procedures. We motivate the need for diversity by a new bias-variance-covariance-locality decomposition of the expected error, exploiting similarities between WA and standard functional ensembling. Moreover, this decomposition highlights that WA succeeds when the variance term dominates, which we show occurs when the marginal distribution changes at test time. Experimentally, DiWA consistently improves the state of the art on DomainBed without inference overhead.

Progress in machine learning is measured by careful evaluation on problems of outstanding common interest. However, the proliferation of benchmark suites and environments, adversarial attacks, and other complications has diluted the basic evaluation model by overwhelming researchers with choices. Deliberate or accidental cherry picking is increasingly likely, and designing well-balanced evaluation suites requires increasing effort. In this paper we take a step back and propose Nash averaging. The approach builds on a detailed analysis of the algebraic structure of evaluation in two basic scenarios: agent-vs-agent and agent-vs-task. The key strength of Nash averaging is that it automatically adapts to redundancies in evaluation data, so that results are not biased by the incorporation of easy tasks or weak agents. Nash averaging thus encourages maximally inclusive evaluation -- since there is no harm (computational cost aside) from including all available tasks and agents.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

As large language models increase in capability, researchers have started to conduct surveys of all kinds on these models with varying scientific motivations. In this work, we examine what we can learn from a model's survey responses on the basis of the well-established American Community Survey (ACS) by the U.S. Census Bureau. Evaluating more than a dozen different models, varying in size from a few hundred million to ten billion parameters, hundreds of thousands of times each on questions from the ACS, we systematically establish two dominant patterns. First, smaller models have a significant position and labeling bias, for example, towards survey responses labeled with the letter "A". This A-bias diminishes, albeit slowly, as model size increases. Second, when adjusting for this labeling bias through randomized answer ordering, models still do not trend toward US population statistics or those of any cognizable population. Rather, models across the board trend toward uniformly random aggregate statistics over survey responses. This pattern is robust to various different ways of prompting the model, including what is the de-facto standard. Our findings demonstrate that aggregate statistics of a language model's survey responses lack the signals found in human populations. This absence of statistical signal cautions about the use of survey responses from large language models at present time.

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare pretraining decisions involving optimizers, datasets, and model architectures. Despite the widespread use of scaling laws to model the dynamics of language model training, there has been little work on understanding how to best estimate and interpret them. We collect (and release) a large-scale dataset containing losses and downstream evaluations for 485 previously published pretrained models. We use these to estimate more than 1000 scaling laws, then derive a set of best practices for estimating scaling laws in new model families. We find that fitting scaling laws to intermediate checkpoints of training runs (and not just their final losses) substantially improves accuracy, and that -- all else equal -- estimates of performance are generally most accurate when derived from other models of similar sizes. However, because there is a significant degree of variability across model seeds, training multiple small models is sometimes more useful than training a single large one. Moreover, while different model families differ scaling behavior, they are often similar enough that a target model's behavior can be predicted from a single model with the same architecture, along with scaling parameter estimates derived from other model families.

Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness of EMA. In this paper, to better understand EMA, we establish the risk bound of online SGD with EMA for high-dimensional linear regression, one of the simplest overparameterized learning tasks that shares similarities with neural networks. Our results indicate that (i) the variance error of SGD with EMA is always smaller than that of SGD without averaging, and (ii) unlike SGD with iterate averaging from the beginning, the bias error of SGD with EMA decays exponentially in every eigen-subspace of the data covariance matrix. Additionally, we develop proof techniques applicable to the analysis of a broad class of averaging schemes.

Aligning large language models (LLMs) with human preferences through reinforcement learning (RLHF) can lead to reward hacking, where LLMs exploit failures in the reward model (RM) to achieve seemingly high rewards without meeting the underlying objectives. We identify two primary challenges when designing RMs to mitigate reward hacking: distribution shifts during the RL process and inconsistencies in human preferences. As a solution, we propose Weight Averaged Reward Models (WARM), first fine-tuning multiple RMs, then averaging them in the weight space. This strategy follows the observation that fine-tuned weights remain linearly mode connected when sharing the same pre-training. By averaging weights, WARM improves efficiency compared to the traditional ensembling of predictions, while improving reliability under distribution shifts and robustness to preference inconsistencies. Our experiments on summarization tasks, using best-of-N and RL methods, shows that WARM improves the overall quality and alignment of LLM predictions; for example, a policy RL fine-tuned with WARM has a 79.4% win rate against a policy RL fine-tuned with a single RM.

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

Model merging has emerged as an effective approach to combine multiple single-task models into a multitask model. This process typically involves computing a weighted average of the model parameters without any additional training. Existing model-merging methods focus on enhancing average task accuracy. However, interference and conflicts between the objectives of different tasks can lead to trade-offs during the merging process. In real-world applications, a set of solutions with various trade-offs can be more informative, helping practitioners make decisions based on diverse preferences. In this paper, we introduce a novel and low-compute algorithm, Model Merging with Amortized Pareto Front (MAP). MAP efficiently identifies a Pareto set of scaling coefficients for merging multiple models, reflecting the trade-offs involved. It amortizes the substantial computational cost of evaluations needed to estimate the Pareto front by using quadratic approximation surrogate models derived from a pre-selected set of scaling coefficients. Experimental results on vision and natural language processing tasks demonstrate that MAP can accurately identify the Pareto front, providing practitioners with flexible solutions to balance competing task objectives. We also introduce Bayesian MAP for scenarios with a relatively low number of tasks and Nested MAP for situations with a high number of tasks, further reducing the computational cost of evaluation.

Automating machine learning has achieved remarkable technological developments in recent years, and building an automated machine learning pipeline is now an essential task. The model ensemble is the technique of combining multiple models to get a better and more robust model. However, existing automated machine learning tends to be simplistic in handling the model ensemble, where the ensemble strategy is fixed, such as stacked generalization. There have been many techniques on different ensemble methods, especially ensemble selection, and the fixed ensemble strategy limits the upper limit of the model's performance. In this article, we present a novel framework for automated machine learning. Our framework incorporates advances in dynamic ensemble selection, and to our best knowledge, our approach is the first in the field of AutoML to search and optimize ensemble strategies. In the comparison experiments, our method outperforms the state-of-the-art automated machine learning frameworks with the same CPU time in 42 classification datasets from the OpenML platform. Ablation experiments on our framework validate the effectiveness of our proposed method.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

Regression Mean (RegMean), an approach that formulates model merging as a linear regression problem, aims to find the optimal weights for each linear layer in the merge model by minimizing the discrepancy in predictions between the merge and candidate models. RegMean provides a precise closed-form solution for the merging problem; therefore, it offers explainability and computational efficiency. However, RegMean merges each linear layer independently, overlooking how the features and information in the earlier layers propagate through the layers and influence the final prediction in the merge model. In this paper, we introduce RegMean++, a simple yet effective alternative to RegMean, that explicitly incorporates both intra- and cross-layer dependencies between merge models' layers into RegMean's objective. By accounting for these dependencies, RegMean++ better captures the behaviors of the merge model. Extensive experiments demonstrate that RegMean++ consistently outperforms RegMean across diverse settings, including in-domain (ID) and out-of-domain (OOD) generalization, sequential merging, large-scale tasks, and robustness under several types of distribution shifts. Furthermore, RegMean++ achieves competitive or state-of-the-art performance compared to various recent advanced model merging methods. Our code is available at https://github.com/nthehai01/RegMean-plusplus.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops proposed that such loops would lead to a phenomenon termed model collapse, under which performance progressively degrades with each model-data feedback iteration until fitted models become useless. However, those studies largely assumed that new data replace old data over time, where an arguably more realistic assumption is that data accumulate over time. In this paper, we ask: what effect does accumulating data have on model collapse? We empirically study this question by pretraining sequences of language models on text corpora. We confirm that replacing the original real data by each generation's synthetic data does indeed tend towards model collapse, then demonstrate that accumulating the successive generations of synthetic data alongside the original real data avoids model collapse; these results hold across a range of model sizes, architectures, and hyperparameters. We obtain similar results for deep generative models on other types of real data: diffusion models for molecule conformation generation and variational autoencoders for image generation. To understand why accumulating data can avoid model collapse, we use an analytically tractable framework introduced by prior work in which a sequence of linear models are fit to the previous models' outputs. Previous work used this framework to show that if data are replaced, the test error increases with the number of model-fitting iterations; we extend this argument to prove that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations, meaning model collapse no longer occurs.

Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM diffusion model architecture, without altering its high-level structure. Observing uncontrolled magnitude changes and imbalances in both the network activations and weights over the course of training, we redesign the network layers to preserve activation, weight, and update magnitudes on expectation. We find that systematic application of this philosophy eliminates the observed drifts and imbalances, resulting in considerably better networks at equal computational complexity. Our modifications improve the previous record FID of 2.41 in ImageNet-512 synthesis to 1.81, achieved using fast deterministic sampling. As an independent contribution, we present a method for setting the exponential moving average (EMA) parameters post-hoc, i.e., after completing the training run. This allows precise tuning of EMA length without the cost of performing several training runs, and reveals its surprising interactions with network architecture, training time, and guidance.

Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.

Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a "double penalty" effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model's effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.

Neural networks are very effective when trained on large datasets for a large number of iterations. However, when they are trained on non-stationary streams of data and in an online fashion, their performance is reduced (1) by the online setup, which limits the availability of data, (2) due to catastrophic forgetting because of the non-stationary nature of the data. Furthermore, several recent works (Caccia et al., 2022; Lange et al., 2023) arXiv:2205.13452 showed that replay methods used in continual learning suffer from the stability gap, encountered when evaluating the model continually (rather than only on task boundaries). In this article, we study the effect of model ensembling as a way to improve performance and stability in online continual learning. We notice that naively ensembling models coming from a variety of training tasks increases the performance in online continual learning considerably. Starting from this observation, and drawing inspirations from semi-supervised learning ensembling methods, we use a lightweight temporal ensemble that computes the exponential moving average of the weights (EMA) at test time, and show that it can drastically increase the performance and stability when used in combination with several methods from the literature.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Neural networks are known to produce poor uncertainty estimations, and a variety of approaches have been proposed to remedy this issue. This includes deep ensemble, a simple and effective method that achieves state-of-the-art results for uncertainty-aware learning tasks. In this work, we explore a combinatorial generalization of deep ensemble called deep combinatorial aggregation (DCA). DCA creates multiple instances of network components and aggregates their combinations to produce diversified model proposals and predictions. DCA components can be defined at different levels of granularity. And we discovered that coarse-grain DCAs can outperform deep ensemble for uncertainty-aware learning both in terms of predictive performance and uncertainty estimation. For fine-grain DCAs, we discover that an average parameterization approach named deep combinatorial weight averaging (DCWA) can improve the baseline training. It is on par with stochastic weight averaging (SWA) but does not require any custom training schedule or adaptation of BatchNorm layers. Furthermore, we propose a consistency enforcing loss that helps the training of DCWA and modelwise DCA. We experiment on in-domain, distributional shift, and out-of-distribution image classification tasks, and empirically confirm the effectiveness of DCWA and DCA approaches.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Deep learning optimizers are often motivated through a mix of convex and approximate second-order theory. We select three such methods -- Adam, Shampoo and Prodigy -- and argue that each method can instead be understood as a squarely first-order method without convexity assumptions. In fact, after switching off exponential moving averages, each method is equivalent to steepest descent under a particular norm. By generalizing this observation, we chart a new design space for training algorithms. Different operator norms should be assigned to different tensors based on the role that the tensor plays within the network. For example, while linear and embedding layers may have the same weight space of R^{mtimes n}, these layers play different roles and should be assigned different norms. We hope that this idea of carefully metrizing the neural architecture might lead to more stable, scalable and indeed faster training.

We develop task scaling laws and model ladders to predict the individual task performance of pretrained language models (LMs) in the overtrained setting. Standard power laws for language modeling loss cannot accurately model task performance. Therefore, we leverage a two-step prediction approach: first use model and data size to predict a task-specific loss, and then use this task loss to predict task performance. We train a set of small-scale "ladder" models, collect data points to fit the parameterized functions of the two prediction steps, and make predictions for two target models: a 7B model trained to 4T tokens and a 13B model trained to 5T tokens. Training the ladder models only costs 1% of the compute used for the target models. On four multiple-choice tasks written in ranked classification format, we can predict the accuracy of both target models within 2 points of absolute error. We have higher prediction error on four other tasks (average absolute error 6.9) and find that these are often tasks with higher variance in task metrics. We also find that using less compute to train fewer ladder models tends to deteriorate predictions. Finally, we empirically show that our design choices and the two-step approach lead to superior performance in establishing scaling laws.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.