Daily Papers

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Current benchmarks for evaluating neural code models focus on only a small subset of programming languages, excluding many popular languages such as Go or Rust. To ameliorate this issue, we present the BabelCode framework for execution-based evaluation of any benchmark in any language. BabelCode enables new investigations into the qualitative performance of models' memory, runtime, and individual test case results. Additionally, we present a new code translation dataset called Translating Python Programming Puzzles (TP3) from the Python Programming Puzzles (Schuster et al. 2021) benchmark that involves translating expert-level python functions to any language. With both BabelCode and the TP3 benchmark, we investigate if balancing the distributions of 14 languages in a training dataset improves a large language model's performance on low-resource languages. Training a model on a balanced corpus results in, on average, 12.34% higher pass@k across all tasks and languages compared to the baseline. We find that this strategy achieves 66.48% better pass@k on low-resource languages at the cost of only a 12.94% decrease to high-resource languages. In our three translation tasks, this strategy yields, on average, 30.77% better low-resource pass@k while having 19.58% worse high-resource pass@k.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

We introduce meta-prompting, an effective scaffolding technique designed to enhance the functionality of language models (LMs). This approach transforms a single LM into a multi-faceted conductor, adept at managing and integrating multiple independent LM queries. By employing high-level instructions, meta-prompting guides the LM to break down complex tasks into smaller, more manageable subtasks. These subtasks are then handled by distinct "expert" instances of the same LM, each operating under specific, tailored instructions. Central to this process is the LM itself, in its role as the conductor, which ensures seamless communication and effective integration of the outputs from these expert models. It additionally employs its inherent critical thinking and robust verification processes to refine and authenticate the end result. This collaborative prompting approach empowers a single LM to simultaneously act as a comprehensive orchestrator and a panel of diverse experts, significantly enhancing its performance across a wide array of tasks. The zero-shot, task-agnostic nature of meta-prompting greatly simplifies user interaction by obviating the need for detailed, task-specific instructions. Furthermore, our research demonstrates the seamless integration of external tools, such as a Python interpreter, into the meta-prompting framework, thereby broadening its applicability and utility. Through rigorous experimentation with GPT-4, we establish the superiority of meta-prompting over conventional scaffolding methods: When averaged across all tasks, including the Game of 24, Checkmate-in-One, and Python Programming Puzzles, meta-prompting, augmented with a Python interpreter functionality, surpasses standard prompting by 17.1%, expert (dynamic) prompting by 17.3%, and multipersona prompting by 15.2%.

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify Transformers, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how Transformers' performance will rapidly decay with increased task complexity.

While generalization over tasks from easy to hard is crucial to profile language models (LLMs), the datasets with fine-grained difficulty annotations for each problem across a broad range of complexity are still blank. Aiming to address this limitation, we present Easy2Hard-Bench, a consistently formatted collection of 6 benchmark datasets spanning various domains, such as mathematics and programming problems, chess puzzles, and reasoning questions. Each problem within these datasets is annotated with numerical difficulty scores. To systematically estimate problem difficulties, we collect abundant performance data on attempts to each problem by humans in the real world or LLMs on the prominent leaderboard. Leveraging the rich performance data, we apply well-established difficulty ranking systems, such as Item Response Theory (IRT) and Glicko-2 models, to uniformly assign numerical difficulty scores to problems. Moreover, datasets in Easy2Hard-Bench distinguish themselves from previous collections by a higher proportion of challenging problems. Through extensive experiments with six state-of-the-art LLMs, we provide a comprehensive analysis of their performance and generalization capabilities across varying levels of difficulty, with the aim of inspiring future research in LLM generalization. The datasets are available at https://huggingface.co/datasets/furonghuang-lab/Easy2Hard-Bench.