arXiv subjects

Gabriel Poesia

Publications and source records attributed to Gabriel Poesia.

At least 19 recordsLinked to original sources

arXiv2026

Formal Disco: Scalable Open-Ended Generation of Formally Verified Programs

The cost of producing code is rapidly diminishing with increasingly capable AI agents, while quality assurance of generated programs has not kept pace. Formal verification provides the strongest possible guarantees, but the ability of AI models to work with verification-aware languages is hindered by the scarcity of human-written examples of programs in those languages. To tackle this prevalent data scarcity issue, we propose Formal Disco: a distributed system for coordination of LLM-based workers that can be easily applied to open-ended synthetic data generation at scale. We use Formal Disco to share tasks and programs between three classes of workers: "initiators", which read random READMEs from open-source repositories and documentation snippets to sketch a related verified program, "fixers" which take compiler and verifier feedback and attempt to resolve issues, and "extenders" that take working programs and propose patches to expand them. Formal Disco records all agent-generated traces and uses them both for initial distillation from a stronger model as well as self-improvement. We also propose a principle of maximum entropy for synthetic program generation, and use entropy maximization via iterative supervised fine-tuning to learn to generate increasingly diverse programs over time. We release large datasets of synthetic verified programs in three languages - Dafny, Verus, and Frama-C -, and fine-tune open models for verification-relevant tasks, often matching or exceeding the performance of Claude Opus 4.5. Overall, our work offers a path to create synthetic data at scale for formal reasoning domains and overcome the long-standing data barrier.

cs.AI↗

arXiv2026

Learning to Rank the Initial Branching Order of SAT Solvers

Finding good branching orders is key to solving SAT problems efficiently, but finding such branching orders is a difficult problem. Using a learning based approach to predict a good branching order before solving, therefore, has potential. In this paper, we investigate predicting branching orders using graph neural networks as a preprocessing step to conflict-driven clause learning (CDCL) SAT solvers. We show that there are significant gains to be made in existing CDCL SAT solvers by providing a good initial branching. Further, we provide three labeling methods to find such initial branching orders in a tractable way. Finally, we train a graph neural network to predict these branching orders and show through our evaluations that a GNN-initialized ordering yields significant speedups on random 3-CNF and pseudo-industrial benchmarks, with generalization capabilities to instances much larger than the training set. However, we also find that the predictions fail at speeding up more difficult and industrial instances. We attribute this to the solver's dynamic heuristics, which rapidly overwrite the provided initialization, and to the complexity of these instances, making GNN prediction hard.

cs.AI↗

arXiv2026

The Token Games: Evaluating Language Model Reasoning with Puzzle Duels

Evaluating the reasoning capabilities of Large Language Models is increasingly challenging as models improve. Human curation of hard questions is highly expensive, especially in recent benchmarks using PhD-level domain knowledge to challenge the most capable models. Even then, there is always a concern about whether these questions test genuine reasoning or if similar problems have been seen during training. Here, we take inspiration from 16th-century mathematical duels to design The Token Games (TTG): an evaluation framework where models challenge each other by creating their own puzzles. We leverage the format of Programming Puzzles - given a function that returns a boolean, find inputs that make it return True - to flexibly represent problems and enable verifying solutions. Using results from pairwise duels, we then compute Elo ratings, allowing us to compare models relative to each other. We evaluate 10 frontier models on TTG, and closely match the ranking from existing benchmarks such as Humanity's Last Exam, spending less than $200 USD and without involving any human effort in creating puzzles. We also find that creating good puzzles is still a highly challenging task for current models. Overall, our work suggests new paradigms for evaluating reasoning that avoid saturation by design, and that allow testing models for other skills like creativity and task creation alongside problem solving.

cs.AI↗

arXiv2025

A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models

The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems, particularly large language models (LLMs) that operate flexibly over natural language and formal mathematics, are increasingly used in mathematics research and education, it becomes crucial to characterize how closely their judgments align with people from different mathematical backgrounds. We study whether LLMs align with human interestingness judgments by comparing LLM ratings with those of two populations, crowdsourced participants with college math experience and International Math Olympiad competitors. Although many LLMs broadly agree with human notions of interestingness, they largely fail to match the distribution of human judgments. They also weakly align with why humans find problems interesting, with low correlation to human-selected rationales. Finally, we evaluate LLMs' ability to generate interesting problems and find that, after filtering for validity, LLMs are able to generate engaging problems. We conclude with takeaways, including the need for multi-LLM human-AI collaborative systems, that highlight both the promise and current limits of LLMs as partners in mathematical reasoning.

cs.AI↗

arXiv2025

Code-enabled language models can outperform reasoning models on diverse tasks

Reasoning models (RMs), language models (LMs) trained with reinforcement learning to produce long-form natural language reasoning, have been remarkably successful, but they still require large amounts of computation and data to train, and can be slow and expensive to run. In this paper, we show that standard instruct LMs can already be elicited to be strong reasoners at a level comparable to or even surpassing their corresponding RMs (e.g., DeepSeek V3 vs R1) without finetuning, across diverse domains from instruction following and creative generation to mathematical reasoning. This is achieved by CodeAdapt, our simple recipe that combines the CodeAct framework, where LMs interleave natural language reasoning with code execution in a multi-step fashion, with few-shot bootstrap in-context learning from as few as five training problems. Analyzing four matched pairs of LMs and RMs, we find that CodeAdapt enables three LMs to outperform the corresponding RMs on average over eight tasks (up to 22.9%) while being 10-81% more token efficient, and delivers superior performance on six tasks when averaged over the four models (up to 35.7%). Furthermore, the code-augmented reasoning traces display rich and varied problem-solving strategies. Our findings support that (1) CodeAdapt-style learning and reasoning may be robust and domain general and (2) code-enabled LMs are cognitively grounded and powerful systems, potentially providing a strong foundation for in-weight reinforcement learning.

cs.CL↗

arXiv2025

Programmatic Representation Learning with Language Models

Classical models for supervised machine learning, such as decision trees, are efficient and interpretable predictors, but their quality is highly dependent on the particular choice of input features. Although neural networks can learn useful representations directly from raw data (e.g., images or text), this comes at the expense of interpretability and the need for specialized hardware to run them efficiently. In this paper, we explore a hypothesis class we call Learned Programmatic Representations (LeaPR) models, which stack arbitrary features represented as code (functions from data points to scalars) and decision tree predictors. We synthesize feature functions using Large Language Models (LLMs), which have rich prior knowledge in a wide range of domains and a remarkable ability to write code using existing domain-specific libraries. We propose two algorithms to learn LeaPR models from supervised data. First, we design an adaptation of FunSearch to learn features rather than directly generate predictors. Then, we develop a novel variant of the classical ID3 algorithm for decision tree learning, where new features are generated on demand when splitting leaf nodes. In experiments from chess position evaluation to image and text classification, our methods learn high-quality, neural network-free predictors often competitive with neural networks. Our work suggests a flexible paradigm for learning interpretable representations end-to-end where features and predictions can be readily inspected and understood.

cs.LG↗

arXiv2025

ProofCompass: Enhancing Specialized Provers with LLM Guidance

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 ($54.9\% \rightarrow 55.3\%$) while using 25x fewer attempts ($3200 \rightarrow 128$). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.

cs.AI↗

arXiv2025

Automated Discovery of Tactic Libraries for Interactive Theorem Proving

Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial for proof modularity and automation. This paper presents a novel approach to tactic discovery, which leverages Tactic Dependence Graphs (TDGs) to identify reusable proof strategies across multiple proofs. TDGs capture logical dependencies between tactic applications while abstracting away irrelevant syntactic details, allowing for both the discovery of new tactics and the refactoring of existing proofs into more modular forms. We have implemented this technique in a tool called TacMiner and compare it against an anti-unification-based approach Peano to tactic discovery. Our evaluation demonstrates that TacMiner can learn 3x as many tactics as Peano and reduces the size of proofs by 26% across all benchmarks. Furthermore, our evaluation demonstrates the benefits of learning custom tactics for proof automation, allowing a state-of-the-art proof automation tool to achieve a relative increase of 172% in terms of success rate.

cs.PL↗

arXiv2024

Formal Mathematical Reasoning: A New Frontier in AI

AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large language models on carefully curated math datasets in text form. As a complementary yet less explored avenue, formal mathematical reasoning is grounded in formal systems such as proof assistants, which can verify the correctness of reasoning and provide automatic feedback. In this position paper, we advocate for formal mathematical reasoning and argue that it is indispensable for advancing AI4Math to the next level. In recent years, we have seen steady progress in using AI to perform formal reasoning, including core tasks such as theorem proving and autoformalization, as well as emerging applications such as verifiable generation of code and hardware designs. However, significant challenges remain to be solved for AI to truly master mathematics and achieve broader impact. We summarize existing progress, discuss open challenges, and envision critical milestones to measure future success. At this inflection point for formal mathematical reasoning, we call on the research community to come together to drive transformative advancements in this field.

cs.AI↗

arXiv2024

Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning

The datasets and benchmarks commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several shortcomings and misdirections. These range from a restricted scope of mathematical complexity to limited fidelity in capturing aspects beyond the final, written proof (e.g. motivating the proof, or representing the thought processes leading to a proof). These issues are compounded by a dynamic reminiscent of Goodhart's law: as benchmark performance becomes the primary target for model development, the benchmarks themselves become less reliable indicators of genuine mathematical capability. We systematically explore these limitations and contend that enhancing the capabilities of large language models, or any forthcoming advancements in AI-based mathematical assistants (copilots or ``thought partners''), necessitates a course correction both in the design of mathematical datasets and the evaluation criteria of the models' mathematical ability. In particular, it is necessary for benchmarks to move beyond the existing result-based datasets that map theorem statements directly to proofs, and instead focus on datasets that translate the richer facets of mathematical research practice into data that LLMs can learn from. This includes benchmarks that supervise the proving process and the proof discovery process itself, and we advocate for mathematical dataset developers to consider the concept of "motivated proof", introduced by G. P\'olya in 1949, which can serve as a blueprint for datasets that offer a better proof learning signal, alleviating some of the mentioned limitations.

cs.LG↗

arXiv2024

dafny-annotator: AI-Assisted Verification of Dafny Programs

Formal verification has the potential to drastically reduce software bugs, but its high additional cost has hindered large-scale adoption. While Dafny presents a promise to significantly reduce the effort to write verified programs, users are often required to provide logical annotations to aid the verifier. Here, we explore using a combination of Large Language Models and search to build dafny-annotator: a tool that adds logical annotations to a Dafny method until the verifier can prove it correct. On a test set from the DafnyBench collection of programs, greedy search guided by LLaMa 3.1 8B successfully annotates only 15.7% of the methods. Since this data-driven approach is hindered by the lack of large-scale training data, we propose a method for open-ended synthesis of new Dafny programs in a flexible pipeline where LLMs formulate high-level ideas, implement them, and incrementally propose changes to existing programs, which Dafny validates. This gives us a synthetic dataset, DafnySynth, which we use to augment DafnyBench for training. Fine-tuning on both datasets boosts LLaMa 8B's success rate to 50.6% -- significantly better than the base model, or training on either dataset alone. Our results suggest a path towards capable AI assistants for languages that don't yet have large-scale human-generated examples. In turn, such assistants might reduce friction for users and ultimately drive adoption.

cs.SE↗

arXiv2024

h4rm3l: A language for Composable Jailbreak Attack Synthesis

Despite their demonstrated valuable capabilities, state-of-the-art (SOTA) widely deployed large language models (LLMs) still have the potential to cause harm to society due to the ineffectiveness of their safety filters, which can be bypassed by prompt transformations called jailbreak attacks. Current approaches to LLM safety assessment, which employ datasets of templated prompts and benchmarking pipelines, fail to cover sufficiently large and diverse sets of jailbreak attacks, leading to the widespread deployment of unsafe LLMs. Recent research showed that novel jailbreak attacks could be derived by composition; however, a formal composable representation for jailbreak attacks, which, among other benefits, could enable the exploration of a large compositional space of jailbreak attacks through program synthesis methods, has not been previously proposed. We introduce h4rm3l, a novel approach that addresses this gap with a human-readable domain-specific language (DSL). Our framework comprises: (1) The h4rm3l DSL, which formally expresses jailbreak attacks as compositions of parameterized string transformation primitives. (2) A synthesizer with bandit algorithms that efficiently generates jailbreak attacks optimized for a target black box LLM. (3) The h4rm3l red-teaming software toolkit that employs the previous two components and an automated harmful LLM behavior classifier that is strongly aligned with human judgment. We demonstrate h4rm3l's efficacy by synthesizing a dataset of 2656 successful novel jailbreak attacks targeting 6 SOTA open-source and proprietary LLMs, and by benchmarking those models against a subset of these synthesized attacks. Our results show that h4rm3l's synthesized attacks are diverse and more successful than existing jailbreak attacks in literature, with success rates exceeding 90% on SOTA LLMs.

cs.CR↗

arXiv2024

From Next-Token to Mathematics: The Learning Dynamics of Mathematical Reasoning in Language Models

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

cs.AI↗

arXiv2024

Learning Formal Mathematics From Intrinsic Motivation

How did humanity coax mathematics from the aether? We explore the Platonic view that mathematics can be discovered from its axioms - a game of conjecture and proof. We describe Minimo (Mathematics from Intrinsic Motivation): an agent that jointly learns to pose challenging problems for itself (conjecturing) and solve them (theorem proving). Given a mathematical domain axiomatized in dependent type theory, we first combine methods for constrained decoding and type-directed synthesis to sample valid conjectures from a language model. Our method guarantees well-formed conjectures by construction, even as we start with a randomly initialized model. We use the same model to represent a policy and value function for guiding proof search. Our agent targets generating hard but provable conjectures - a moving target, since its own theorem proving ability also improves as it trains. We propose novel methods for hindsight relabeling on proof search trees to significantly improve the agent's sample efficiency in both tasks. Experiments on 3 axiomatic domains (propositional logic, arithmetic and group theory) demonstrate that our agent can bootstrap from only the axioms, self-improving in generating true and challenging conjectures and in finding proofs.

cs.AI↗

arXiv2024

When Do Skills Help Reinforcement Learning? A Theoretical Analysis of Temporal Abstractions

Skills are temporal abstractions that are intended to improve reinforcement learning (RL) performance through hierarchical RL. Despite our intuition about the properties of an environment that make skills useful, a precise characterization has been absent. We provide the first such characterization, focusing on the utility of deterministic skills in deterministic sparse-reward environments with finite action spaces. We show theoretically and empirically that RL performance gain from skills is worse in environments where solutions to states are less compressible. Additional theoretical results suggest that skills benefit exploration more than they benefit learning from existing experience, and that using unexpressive skills such as macroactions may worsen RL performance. We hope our findings can guide research on automatic skill discovery and help RL practitioners better decide when and how to use skills.

cs.LG↗

arXiv2024

Hypothesis Search: Inductive Reasoning with Language Models

Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which robustly generalize to novel scenarios. Recent work evaluates large language models (LLMs) on inductive reasoning tasks by directly prompting them yielding "in context learning." This works well for straightforward inductive tasks but performs poorly on complex tasks such as the Abstraction and Reasoning Corpus (ARC). In this work, we propose to improve the inductive reasoning ability of LLMs by generating explicit hypotheses at multiple levels of abstraction: we prompt the LLM to propose multiple abstract hypotheses about the problem, in natural language, then implement the natural language hypotheses as concrete Python programs. These programs can be verified by running on observed examples and generalized to novel inputs. To reduce the hypothesis search space, we explore steps to filter the set of hypotheses to implement: we either ask the LLM to summarize them into a smaller set of hypotheses or ask human annotators to select a subset. We verify our pipeline's effectiveness on the ARC visual inductive reasoning benchmark, its variant 1D-ARC, string transformation dataset SyGuS, and list transformation dataset List Functions. On a random 100-problem subset of ARC, our automated pipeline using LLM summaries achieves 30% accuracy, outperforming the direct prompting baseline (accuracy of 17%). With the minimal human input of selecting from LLM-generated candidates, performance is boosted to 33%. Our ablations show that both abstract hypothesis generation and concrete program representations benefit LLMs on inductive reasoning tasks.

cs.LG↗

arXiv2023

Certified Deductive Reasoning with Language Models

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, even when arriving at a correct final answer, their rationales are often logically unsound or inconsistent. This is a major issue when reliable reasoning traces are needed, such when fine-tuning on model-generated reasoning for self-improvement. To tackle these issues, we introduce a class of tools for language models called \emph{guides}, that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call \textsc{LogicGuide}. Given a reasoning problem in natural language, a model can formalize its assumptions for \textsc{LogicGuide} and guarantee that its step-by-step reasoning is sound. In experiments on PrOntoQA, ProofWriter and Syllogism Validity datasets, \textsc{LogicGuide} significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35\%), while drastically reducing \emph{content effects} -- the interference between unwanted prior assumptions and reasoning, which humans and language models suffer from. We then explore bootstrapping GPT-3.5 Turbo and LLaMA using their own reasoning traces. We find that LogicGuide is critical: by training only on certified self-generated reasoning, models can self-improve, avoiding learning from their own hallucinations. Moreover, bootstrapped models enjoy significant boosts on ReClor, a challenging real-world reasoning dataset, even when not relying on formalization at inference time.

cs.AI↗

arXiv2023

Parsel: Algorithmic Reasoning with Language Models by Composing Decompositions

Despite recent success in large language model (LLM) reasoning, LLMs struggle with hierarchical multi-step reasoning tasks like generating complex programs. For these tasks, humans often start with a high-level algorithmic design and implement each part gradually. We introduce Parsel, a framework enabling automatic implementation and validation of complex algorithms with code LLMs. With Parsel, we automatically decompose algorithmic tasks into hierarchical natural language function descriptions and then search over combinations of possible function implementations using tests. We show that Parsel can be used across domains requiring hierarchical reasoning, including program synthesis and robotic planning. We find that, using Parsel, LLMs solve more competition-level problems in the APPS dataset, resulting in pass rates over 75\% higher than prior results from directly sampling AlphaCode and Codex, while often using a smaller sample budget. Moreover, with automatically generated tests, we find that Parsel can improve the state-of-the-art pass@1 performance on HumanEval from 67\% to 85\%. We also find that LLM-generated robotic plans using Parsel are more than twice as likely to be considered accurate than directly generated plans. Lastly, we explore how Parsel addresses LLM limitations and discuss how Parsel may be useful for human programmers. We release our code at https://github.com/ezelikman/parsel

cs.CL↗