Large reasoning models (LRMs) have demonstrated impressive capabilities in domains like mathematics and program synthesis. Despite their strong performance, LRMs often exhibit overthinking -- excessive and redundant reasoning steps that introduce inefficiencies during inference. This phenomenon raises an important question for LRM self-evaluation: How can a model autonomously assess the correctness of its own reasoning trajectory without external labels? To address this, we propose Chain-of-Reasoning Embedding (CoRE), a series of hidden states in latent space to enable label-free self-evaluation on intermediate reasoning steps of LRMs, so as to enhance metacognition abilities for improved reasoning efficiency. By analyzing the geometric properties of the CoRE trajectories, we reveal that redundant reasoning usually presents cyclical fluctuations, which correspond to repetitive and unconscious reflection/exploration. Leveraging this insight, we further introduce a training-free, label-free self-evaluation framework, CoRE-Eval, to detect such patterns and dynamically determine whether to terminate reasoning early. Extensive experiments on mathematical reasoning benchmarks (GSM8K, MATH-500, and AIME) and across model sizes from 7B to 32B demonstrate that CoRE-Eval reduces chain-of-thought length by 13.7% to 33.2% while improving answer accuracy by around 10%, achieving 70.0% accuracy on the challenging AIME benchmark with the 32B model.
The IPARC Challenge, inspired by ARC, provides controlled program synthesis tasks over synthetic images to evaluate automatic program construction, focusing on sequence, selection, and iteration. This set of 600 tasks has resisted automated solutions. This paper presents a structured inductive programming approach with LLMs that successfully solves tasks across all IPARC categories. The controlled nature of IPARC reveals insights into LLM-based code generation, including the importance of prior structuring, LLMs' ability to aid structuring (requiring human refinement), the need to freeze correct code, the efficiency of code reuse, and how LLM-generated code can spark human creativity. These findings suggest valuable mechanisms for human-LLM collaboration in tackling complex program synthesis.
The rise of Large Language Models (LLMs) has driven progress in reasoning tasks -- from program synthesis to scientific hypothesis generation -- yet their ability to handle ranked preferences and structured algorithms in combinatorial domains remains underexplored. We study matching markets, a core framework behind applications like resource allocation and ride-sharing, which require reconciling individual ranked preferences to ensure stable outcomes. We evaluate several state-of-the-art models on a hierarchy of preference-based reasoning tasks -- ranging from stable-matching generation to instability detection, instability resolution, and fine-grained preference queries -- to systematically expose their logical and algorithmic limitations in handling ranked inputs. Surprisingly, even top-performing models with advanced reasoning struggle to resolve instability in large markets, often failing to identify blocking pairs or execute algorithms iteratively. We further show that parameter-efficient fine-tuning (LoRA) significantly improves performance in small markets, but fails to bring about a similar improvement on large instances, suggesting the need for more sophisticated strategies to improve LLMs' reasoning with larger-context inputs.
Accurately classifying chemical structures is essential for cheminformatics and bioinformatics, including tasks such as identifying bioactive compounds of interest, screening molecules for toxicity to humans, finding non-organic compounds with desirable material properties, or organizing large chemical libraries for drug discovery or environmental monitoring. However, manual classification is labor-intensive and difficult to scale to large chemical databases. Existing automated approaches either rely on manually constructed classification rules, or the use of deep learning methods that lack explainability. This work presents an approach that uses generative artificial intelligence to automatically write chemical classifier programs for classes in the Chemical Entities of Biological Interest (ChEBI) database. These programs can be used for efficient deterministic run-time classification of SMILES structures, with natural language explanations. The programs themselves constitute an explainable computable ontological model of chemical class nomenclature, which we call the ChEBI Chemical Class Program Ontology (C3PO). We validated our approach against the ChEBI database, and compared our results against state of the art deep learning models. We also demonstrate the use of C3PO to classify out-of-distribution examples taken from metabolomics repositories and natural product databases. We also demonstrate the potential use of our approach to find systematic classification errors in existing chemical databases, and show how an ensemble artificial intelligence approach combining generated ontologies, automated literature search, and multimodal vision models can be used to pinpoint potential errors requiring expert validation
Abstraction and reasoning in program synthesis has seen significant progress through both inductive and transductive paradigms. Inductive approaches generate a program or latent function from input-output examples, which can then be applied to new inputs. Transductive approaches directly predict output values for given inputs, effectively serving as the function themselves. Current approaches combine inductive and transductive models via isolated ensembling, but they do not explicitly model the interaction between both paradigms. In this work, we introduce \acs{tiips}, a novel framework that unifies transductive and inductive strategies by explicitly modeling their interactions through a cooperative mechanism: an inductive model generates programs, while a transductive model constrains, guides, and refines the search to improve synthesis accuracy and generalization. We evaluate \acs{tiips} on two widely studied program synthesis domains: string and list manipulation. Our results show that \acs{tiips} solves more tasks and yields functions that more closely match optimal solutions in syntax and semantics, particularly in out-of-distribution settings, yielding state-of-the-art performance. We believe that explicitly modeling the synergy between inductive and transductive reasoning opens promising avenues for general-purpose program synthesis and broader applications.
We introduce ${\rm C{\small LEVER}}$, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, ${\rm C{\small LEVER}}$ avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use ${\rm C{\small LEVER}}$ to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).
Learning how the world works is central to building AI agents that can adapt to complex environments. Traditional world models based on deep learning demand vast amounts of training data, and do not flexibly update their knowledge from sparse observations. Recent advances in program synthesis using Large Language Models (LLMs) give an alternate approach which learns world models represented as source code, supporting strong generalization from little data. To date, application of program-structured world models remains limited to natural language and grid-world domains. We introduce a novel program synthesis method for effectively modeling complex, non-gridworld domains by representing a world model as an exponentially-weighted product of programmatic experts (PoE-World) synthesized by LLMs. We show that this approach can learn complex, stochastic world models from just a few observations. We evaluate the learned world models by embedding them in a model-based planning agent, demonstrating efficient performance and generalization to unseen levels on Atari's Pong and Montezuma's Revenge. We release our code and display the learned world models and videos of the agent's gameplay at https://topwasu.github.io/poe-world.
Large Language Models (LLMs) have demonstrated unprecedented capability in code generation. However, LLM-generated code is still plagued with a wide range of functional errors, especially for complex programming tasks that LLMs have not seen before. Recent studies have shown that developers often struggle with inspecting and fixing incorrect code generated by LLMs, diminishing their productivity and trust in LLM-based code generation. Inspired by the mutual grounding theory in communication, we propose an interactive approach that leverages code comments as a medium for developers and LLMs to establish a shared understanding. Our approach facilitates iterative grounding by interleaving code generation, inline comment generation, and contextualized user feedback through editable comments to align generated code with developer intent. We evaluated our approach on two popular benchmarks and demonstrated that our approach significantly improved multiple state-of-the-art LLMs, e.g., 17.1% pass@1 improvement for code-davinci-002 on HumanEval. Furthermore, we conducted a user study with 12 participants in comparison to two baselines: (1) interacting with GitHub Copilot, and (2) interacting with a multi-step code generation paradigm called Multi-Turn Program Synthesis. Participants completed the given programming tasks 16.7% faster and with 10.5% improvement in task success rate when using our approach. Both results show that interactively refining code comments enables the collaborative establishment of mutual grounding, leading to more accurate code generation and higher developer confidence.
We introduce OSVBench, a new benchmark for evaluating Large Language Models (LLMs) in generating complete specification code pertaining to operating system kernel verification tasks. The benchmark first defines the specification generation problem into a program synthesis problem within a confined scope of syntax and semantics by providing LLMs with the programming model. The LLMs are required to understand the provided verification assumption and the potential syntax and semantics space to search for, then generate the complete specification for the potentially buggy operating system code implementation under the guidance of the high-level functional description of the operating system. This benchmark is built upon a real-world operating system kernel, Hyperkernel, and consists of 245 complex specification generation tasks in total, each is a long context task of about 20k-30k tokens. Our comprehensive evaluation of 12 LLMs exhibits the limited performance of the current LLMs on the specification generation tasks for operating system verification. Significant disparities in their performance on the benchmark highlight differences in their ability to handle long-context code generation tasks. The evaluation toolkit and benchmark are available at https://github.com/lishangyu-hkust/OSVBench.
Heterogeneous deep learning systems (DLS) such as GPUs and ASICs have been widely deployed in industrial data centers, which requires to develop multiple low-level tensor programs for different platforms. An attractive solution to relieve the programming burden is to transcompile the legacy code of one platform to others. However, current transcompilation techniques struggle with either tremendous manual efforts or functional incorrectness, rendering "Write Once, Run Anywhere" of tensor programs an open question. We propose a novel transcompiler, i.e., QiMeng-Xpiler, for automatically translating tensor programs across DLS via both large language models (LLMs) and symbolic program synthesis, i.e., neural-symbolic synthesis. The key insight is leveraging the powerful code generation ability of LLM to make costly search-based symbolic synthesis computationally tractable. Concretely, we propose multiple LLM-assisted compilation passes via pre-defined meta-prompts for program transformation. During each program transformation, efficient symbolic program synthesis is employed to repair incorrect code snippets with a limited scale. To attain high performance, we propose a hierarchical auto-tuning approach to systematically explore both the parameters and sequences of transformation passes. Experiments on 4 DLS with distinct programming interfaces, i.e., Intel DL Boost with VNNI, NVIDIA GPU with CUDA, AMD MI with HIP, and Cambricon MLU with BANG, demonstrate that QiMeng-Xpiler correctly translates different tensor programs at the accuracy of 95% on average, and the performance of translated programs achieves up to 2.0x over vendor-provided manually-optimized libraries. As a result, the programming productivity of DLS is improved by up to 96.0x via transcompiling legacy tensor programs.
Program synthesis is an umbrella term for generating programs and logical formulae from specifications. With the remarkable performance improvements that GPUs enable for deep learning, a natural question arose: can we also implement a search-based program synthesiser on GPUs to achieve similar performance improvements? In this article we discuss our insights on this question, based on recent works~. The goal is to build a synthesiser running on GPUs which takes as input positive and negative example traces and returns a logical formula accepting the positive and rejecting the negative traces. With GPU-friendly programming techniques -- using the semantics of formulae to minimise data movement and reduce data-dependent branching -- our synthesiser scales to significantly larger synthesis problems, and operates much faster than the previous CPU-based state-of-the-art. We believe the insights that make our approach GPU-friendly have wide potential for enhancing the performance of other formal methods (FM) workloads.
The performance of large language models (LLMs) in program synthesis and mathematical reasoning is fundamentally limited by the quality of their pre-training corpora. We introduce two openly licensed datasets, released under the Llama 3.3 Community License, that significantly enhance LLM performance by systematically rewriting public data. SwallowCode (approximately 16.1 billion tokens) refines Python snippets from The-Stack-v2 through a novel four-stage pipeline: syntax validation, pylint-based style filtering, and a two-stage LLM rewriting process that enforces style conformity and transforms snippets into self-contained, algorithmically efficient examples. Unlike prior methods that rely on exclusionary filtering or limited transformations, our transform-and-retain approach upgrades low-quality code, maximizing data utility. SwallowMath (approximately 2.3 billion tokens) enhances Finemath-4+ by removing boilerplate, restoring context, and reformatting solutions into concise, step-by-step explanations. Within a fixed 50 billion token training budget, continual pre-training of Llama-3.1-8B with SwallowCode boosts pass@1 by +17.0 on HumanEval and +17.7 on HumanEval+ compared to Stack-Edu, surpassing the baseline model's code generation capabilities. Similarly, substituting SwallowMath yields +12.4 accuracy on GSM8K and +7.6 on MATH. Ablation studies confirm that each pipeline stage contributes incrementally, with rewriting delivering the largest gains. All datasets, prompts, and checkpoints are publicly available, enabling reproducible research and advancing LLM pre-training for specialized domains.
Over the years, genetic programming (GP) has evolved, with many proposed variations, especially in how they represent a solution. Being essentially a program synthesis algorithm, it is capable of tackling multiple problem domains. Current benchmarking initiatives are fragmented, as the different representations are not compared with each other and their performance is not measured across the different domains. In this work, we propose a unified framework, dubbed TinyverseGP (inspired by tinyGP), which provides support to multiple representations and problem domains, including symbolic regression, logic synthesis and policy search.
Demonstrating quantum advantage using conventional quantum algorithms remains challenging on current noisy gate-based quantum computers. Automated quantum circuit synthesis via quantum machine learning has emerged as a promising solution, employing trainable parametric quantum circuits to alleviate this. The circuit ansatz in these solutions is often designed through reinforcement learning-based quantum architecture search when the domain knowledge of the problem and hardware are not effective. However, the interpretability of these synthesized circuits remains a significant bottleneck, limiting their scalability and applicability across diverse problem domains. This work addresses the challenge of explainability in quantum architecture search (QAS) by introducing a novel genetic programming-based decompiler framework for reverse-engineering high-level quantum algorithms from low-level circuit representations. The proposed approach, implemented in the open-source tool DeQompile, employs program synthesis techniques, including symbolic regression and abstract syntax tree manipulation, to distill interpretable Qiskit algorithms from quantum assembly language. Validation of benchmark algorithms demonstrates the efficacy of our tool. By integrating the decompiler with online learning frameworks, this research potentiates explainable QAS by fostering the development of generalizable and provable quantum algorithms.
Inductive program synthesis, or programming by example, requires synthesizing functions from input-output examples that generalize to unseen inputs. While large language model agents have shown promise in programming tasks guided by natural language, their ability to perform inductive program synthesis is underexplored. Existing evaluation protocols rely on static sets of examples and held-out tests, offering no feedback when synthesized functions are incorrect and failing to reflect real-world scenarios such as reverse engineering. We propose CodeARC, the Code Abstraction and Reasoning Challenge, a new evaluation framework where agents interact with a hidden target function by querying it with new inputs, synthesizing candidate functions, and iteratively refining their solutions using a differential testing oracle. This interactive setting encourages agents to perform function calls and self-correction based on feedback. We construct the first large-scale benchmark for general-purpose inductive program synthesis, featuring 1114 functions. Among 18 models evaluated, o3-mini performs best with a success rate of 52.7%, highlighting the difficulty of this task. Fine-tuning LLaMA-3.1-8B-Instruct on curated synthesis traces yields up to a 31% relative performance gain. CodeARC provides a more realistic and challenging testbed for evaluating LLM-based program synthesis and inductive reasoning.
Modern reinforcement learning (RL) systems have demonstrated remarkable capabilities in complex environments, such as video games. However, they still fall short of achieving human-like sample efficiency and adaptability when learning new domains. Theory-based reinforcement learning (TBRL) is an algorithmic framework specifically designed to address this gap. Modeled on cognitive theories, TBRL leverages structured, causal world models - "theories" - as forward simulators for use in planning, generalization and exploration. Although current TBRL systems provide compelling explanations of how humans learn to play video games, they face several technical limitations: their theory languages are restrictive, and their planning algorithms are not scalable. To address these challenges, we introduce TheoryCoder, an instantiation of TBRL that exploits hierarchical representations of theories and efficient program synthesis methods for more powerful learning and planning. TheoryCoder equips agents with general-purpose abstractions (e.g., "move to"), which are then grounded in a particular environment by learning a low-level transition model (a Python program synthesized from observations by a large language model). A bilevel planning algorithm can exploit this hierarchical structure to solve large domains. We demonstrate that this approach can be successfully applied to diverse and challenging grid-world games, where approaches based on directly synthesizing a policy perform poorly. Ablation studies demonstrate the benefits of using hierarchical abstractions.
With the rise of generative AI, synthesizing figures from text captions becomes a compelling application. However, achieving high geometric precision and editability requires representing figures as graphics programs in languages like TikZ, and aligned training data (i.e., graphics programs with captions) remains scarce. Meanwhile, large amounts of unaligned graphics programs and captioned raster images are more readily available. We reconcile these disparate data sources by presenting TikZero, which decouples graphics program generation from text understanding by using image representations as an intermediary bridge. It enables independent training on graphics programs and captioned images and allows for zero-shot text-guided graphics program synthesis during inference. We show that our method substantially outperforms baselines that can only operate with caption-aligned graphics programs. Furthermore, when leveraging caption-aligned graphics programs as a complementary training signal, TikZero matches or exceeds the performance of much larger models, including commercial systems like GPT-4o. Our code, datasets, and select models are publicly available.
We propose the problem of multi-agent path planning for a generalization of the classic Cops and Robbers game via reactive synthesis. Specifically, through the application of LTLt and Coordination Synthesis, we aim to check whether various Cops and Robbers games are realizable (a strategy exists for the cops which guarantees they catch the robbers). Additionally, we construct this strategy as an executable program for the multiple system players in our games. In this paper we formalize the problem space, and propose potential directions for solutions. We also show how our formalization of this generalized cops and robbers game can be mapped to a broad range of other problems in the reactive program synthesis space.
Large Language Models (LLMs) are rapidly saturating existing benchmarks, necessitating new open-ended evaluations. We introduce the Factorio Learning Environment (FLE), based on the game of Factorio, that tests agents in long-term planning, program synthesis, and resource optimization. FLE provides exponentially scaling challenges -- from basic automation to complex factories processing millions of resource units per second. We provide two settings: (1) lab-play consisting of eight structured tasks with fixed resources, and (2) open-play with the unbounded task of building the largest factory on an procedurally generated map. We demonstrate across both settings that models still lack strong spatial reasoning. In lab-play, we find that LLMs exhibit promising short-horizon skills, yet are unable to operate effectively in constrained environments, reflecting limitations in error analysis. In open-play, while LLMs discover automation strategies that improve growth (e.g electric-powered drilling), they fail to achieve complex automation (e.g electronic-circuit manufacturing).
Program synthesis with Large Language Models (LLMs) suffers from a "near-miss syndrome": the generated code closely resembles a correct solution but fails unit tests due to minor errors. We address this with a multi-agent framework called Synthesize, Execute, Instruct, Debug, and Repair (SEIDR). Effectively applying SEIDR to instruction-tuned LLMs requires determining (a) optimal prompts for LLMs, (b) what ranking algorithm selects the best programs in debugging rounds, and (c) balancing the repair of unsuccessful programs with the generation of new ones. We empirically explore these trade-offs by comparing replace-focused, repair-focused, and hybrid debug strategies. We also evaluate lexicase and tournament selection to rank candidates in each generation. On Program Synthesis Benchmark 2 (PSB2), our framework outperforms both conventional use of OpenAI Codex without a repair phase and traditional genetic programming approaches. SEIDR outperforms the use of an LLM alone, solving 18 problems in C++ and 20 in Python on PSB2 at least once across experiments. To assess generalizability, we employ GPT-3.5 and Llama 3 on the PSB2 and HumanEval-X benchmarks. Although SEIDR with these models does not surpass current state-of-the-art methods on the Python benchmarks, the results on HumanEval-C++ are promising. SEIDR with Llama 3-8B achieves an average pass@100 of 84.2%. Across all SEIDR runs, 163 of 164 problems are solved at least once with GPT-3.5 in HumanEval-C++, and 162 of 164 with the smaller Llama 3-8B. We conclude that SEIDR effectively overcomes the near-miss syndrome in program synthesis with LLMs.