LLM-Based Program Synthesis

Parent selection significantly affects exploration, exploitation, and complexity control in genetic programming (GP) for symbolic regression. It is unclear whether large language models (LLMs) can synthesize effective operators in a zero-shot setting without iterative meta-evolution. Here, zero-shot means that the model receives only the task description, with no reference operators or iterative feedback. In this work, we benchmark zero-shot synthesis of parent-selection operators across eight LLMs within a standard GP framework for symbolic regression. Each model receives the same natural-language prompt to generate a parent-selection operator, which is then evaluated in a standard GP framework with only the parent-selection operator replaced, while all other components and the evolutionary-search budget are held constant. For each LLM, ten independent zero-shot operators are evaluated on twelve OpenML regression benchmarks and compared against automatic lexicase and tournament selection baselines. Claude Sonnet4.6 and Gemini3.1 Pro stand out for consistently strong performance on both training and held-out test $R^2$. The strongest operator in our benchmark---a Kimi~K2.5 zero-shot synthesis---surpasses the automatic lexicase and tournament baselines in search effectiveness. These results suggest that zero-shot LLM synthesis is a viable approach to generating competitive GP selection operators. Analysis shows that many generated operators use semantics to guide selection, suggesting that LLMs can produce non-trivial search heuristics from the task description alone. We also examine the relationship between public LLM leaderboard rankings and GP performance. Widely used benchmarks, such as Humanity's Last Exam and SWE-bench Verified, strongly correlate with training $R^2$, while their relationship to held-out test $R^2$ is weaker and less clear.

Automatic feature engineering (AutoFE) for tabular data requires discovering informative transformations from a large program space. Existing approaches suffer from three limitations: classical methods rely on fixed operator libraries with limited expressivity, LLM-based methods generate proposals from static prompts without retaining search experience, and evolutionary methods use fixed migration policies that ignore task-specific cross-family transfer utility. We introduce TOPOFE, a framework that formulates AutoFE as graph-structured multi-island evolutionary program search. The transformation space is partitioned into semantically coherent families, each explored by an island through LLM-guided mutation and crossover. Each island maintains a Prompt Adaptation Memory that accumulates accept/reject feedback to steer proposals toward productive regions without parameter updates. To coordinate global exploration, TOPOFE dynamically learns a directed topology graph whose edge weights encode transfer utility between transformation families. Cross-island transfer is triggered by adaptive saturation detection and performed through LLM-mediated hybrid synthesis, enabling discovery of compositional feature programs that cannot emerge from isolated local search. Experiments on 29 tabular datasets show that TOPOFE consistently outperforms most state-of-the-art AutoFE methods on classification and regression tasks. Beyond predictive performance, TOPOFE produces feature sets with lower redundancy and higher representational coverage, while the learned topology graph acquires meaningful task-specific transfer structure correlated with downstream gains. The discovered feature programs transfer reliably across diverse predictors and LLM backbones, demonstrating that improvements arise from TOPOFE's structured search and adaptive coordination rather than backbone-specific generation capability.

Fine-tuned code LLMs are routinely conditioned on a design-intent specification, but the correctness axis of such a signal -- a wrong intent rather than an absent one -- has not been tested, and the benefit of conditioning is usually scored with the same detector that defines the signal. We study CADCON, a five-feature design-intent header prepended to CadQuery-style programs during LoRA fine-tuning of Qwen2.5-Coder-1.5B, scoring adherence with executable geometric assertions that share no code with the header-defining extractor. On a pre-registered sample of 400 deduplicated held-out programs stratified over eleven intent profiles, at 40% prefix and three seeds, a semantically wrong header degrades adherence below the never-header-trained baseline on 3/3 seeds under both tokenizations at the program level, and on 3/3 token and 2/3 text seeds at the 298 distinct model inputs they present. Wrong-header executability is not depressed relative to that baseline. A derangement control, retrained so every program receives another program's header -- holding the header marginal fixed while destroying its correlation with the program -- saw the same programs, indices and wrong headers. Its correct-to-wrong change is -0.006/+0.016/-0.003 against 0.124/0.241/0.230 for the standard model, and the interaction is significant on 3/3 seeds (p <= 5.9e-7), so the model's sensitivity to whether the header is right or wrong requires the learned mapping. The control sits below the baseline by the same margin under a correct as under a wrong header, so we claim that sensitivity and not the below-baseline level. On features the true intent lacks, the standard model realizes a feature far more often when the wrong header names it; the control does not. Ground truth itself scores only 0.567 here, the scale on which arm levels should be read. Wrong design intent is not inert: it actively misdirects generation.

Concurrent stateful library APIs expose behavior through evolving resource ownership, lifecycle states, and competing interleavings. Large language models can synthesize executable Rust tests, but their outputs often violate API preconditions, remain shallow, or reduce concurrency to accidental sequential traces. Conversely, model-based and systematic testing techniques provide semantic control but commonly require substantial handwritten code to turn abstract scenarios into executable tests. This paper addresses the gap between formal scenario design and low-cost test concretization. We present a Petri-net-guided methodology for test generation over concurrent stateful Rust APIs. The method represents API resources, lifecycle conditions, and causal dependencies as colored tokens and transitions; derives legal deep-state, near-legal, and partial-order concurrent scenarios; and uses these scenarios as a constrained intermediate representation for LLM-based code synthesis. A local-faithfulness contract and structural repair loop preserve the modeled intent during concretization, while Petri-guided schedule shaping prioritizes high-conflict concurrency skeletons for systematic exploration. A layered semantic oracle then distinguishes synthesis failures from violations of the target API's expected behavior.

Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.

Neural simulation-based inference enables parameter estimation for complex models, but typically requires the user to specify a simulator encoding a fixed model structure. We present a framework for joint model selection and parameter estimation that combines large language models for program synthesis with neural simulation-based inference. Given a natural language description of the system and data under investigation, an LLM proposes candidate simulator programs which are iteratively refined via feedback-driven mutation and evaluated using neural density estimation. The approach enables simulation-based inference over a pool of models, not just parameters within a fixed model. On benchmarks spanning deterministic dynamics, stochastic epidemic models, and dark matter substructure inference from gravitational-lensing images, the method identifies plausible model families from open-ended prompts, with accuracy that reflects the information content of the data and identifiability of candidate models.

Coding agents can fix a failing example without preserving the domain rule that made it fail. We present agentic synthesis against counterexample-supplemented sketches, a repository-native method for systems whose policy is discovered during implementation. A human starts with a partial sketch, and a coding agent compiles a replaceable projection. When simulation exposes missing or mistaken policy, an operator approves the corrected behavior and the minimum general rule the case authorizes. Every Developer call names its change authority and the rules, holes, anchors, and approved behavior that must survive. Conflict or ambiguous permission leaves the files unchanged and produces a clarification question. A complete archive preserves provenance; a curated regression set gates distinct boundaries. Before another candidate is revealed, the active case and curated regressions must pass both deterministic approved-output comparison and a separate review against the current sketch. Periodic clean regeneration tests whether the sketch carries the learned policy. We demonstrate the method with CatSynth, a captured synthetic application. In one open-world run with GPT-5.4-mini, 8 of 14 frozen candidates became counterexamples. Under the corrected protocol, replay-all, evolved-sketch rebuild, and retained Sketch-CE each passed all 8 accepted cases. They passed 14, 17, and 16 of 21 withheld cases, respectively. Sketch review rejected premature empty-input and tag policies and restored dropped anchors; adjudicated reviewer errors did not become policy. One model and one reveal order cannot establish general correctness or superiority. On this suite, the second check exposed drift hidden by deterministic replay, and the reviewed sketch passed three more withheld cases than raw example replay.

Workflow generation in visual creation systems such as ComfyUI demands not only syntactic accuracy but also expert-level reasoning over modular compositions. Existing large language model (LLM) approaches often treat this as a direct text-to-JSON generation task, struggling with structural brittleness and lacking the experiential knowledge required for effective design. We argue that successful workflow generation requires modeling knowledge itself, including its structure, hierarchy, and reasoning dynamics. To this end, we propose a knowledge-centric framework that learns to invert, inject, and infer with knowledge across multiple abstraction levels. We first perform knowledge inversion to distill hierarchical representations, ranging from full pseudo-codes and skeletons to high-level strategies, from large collections of real-world workflows. We then conduct knowledge injection through supervised fine-tuning, teaching the model to reason from task descriptions to strategies and from strategies to executable structures. During inference, the model performs reversible reasoning to synthesize executable workflows, augmented by self-refinement for structural coherence. Extensive experiments demonstrate that our method produces workflows with richer node diversity, more coherent structures, and higher execution success rates than existing systems, establishing a new foundation for knowledge-driven, agentic workflow generation.

We report on CoreForge, an experience in using large language models (LLMs) to build an unweighted MaxSAT solver from research papers rather than from an existing solver codebase. The project focuses on unsatisfiability-based MaxSAT algorithms and follows an iterative workflow that combines paper discussions with ChatGPT, implementation through Codex prompts, and repeated LLM-assisted code audits and revisions. Although the codebase implements several algorithms and solver components, our evaluation focuses on configurations that combine core-guided optimization, lightweight preprocessing, core minimization, integration with integer linear optimization backends, and a new core-sequence lookahead approach. Our experience suggests that LLMs can support solver implementation from papers, while requiring external validation, benchmarking, and human guidance. In our experiments, fuzzing and MaxSAT Evaluation instances did not reveal wrong answers in the tested configurations, although performance remains below the best hand-engineered MaxSAT solvers. We summarize what worked, what remained difficult, and the lessons for future LLM-assisted solver development.

Transparent educational question answering asks for answers that are not only correct but explainable, and doing so with small models rules out the reasoning power of the largest proprietary systems. The EXACT 2026 competition poses this problem concretely: open-weight language models of at most 8B parameters, self-hosted, with a natural-language explanation for every answer. It pairs two tasks: logical reasoning over university regulations, and multi-step physics problem solving. We describe the system that team \cotu{} developed to address both, a neuro-symbolic Program-of-Thought pipeline in which a 4B backbone writes a program rather than stating an answer directly: for regulation queries it emits a Z3 encoding whose entailment verdict grounds the deduction, and for physics it emits numerical Python, both wrapped in a shared self-correction loop and a unified explained-JSON output. Answer-type routing, distillation-based task fine-tuning, and a latency-aware serving stack -- SGLang with speculative decoding -- keep the system within the 60-second per-query limit. The system achieved a \textbf{perfect score} on the physics task in both automated selection rounds and obtained the \textbf{highest final-round technical score} of any team -- $13.44/15$, combining automated answer evaluation with expert-judged reasoning depth -- with the equally weighted presentation score included, \cotu{} placed 3rd overall. Grounding answers in a symbolic solver yields correct, verifiable deductions at the 4B scale, and the residual difficulty lies in premise selection rather than the deduction itself.

Financial question answering over hybrid tabular and textual data may require multi-source reasoning and precise numerical computation. While large language models (LLMs) can generate intermediate reasoning steps, natural-language rationales remain prone to arithmetic errors, making them an unreliable supervision source for distillation. Building on programmatic distillation, we develop an approach that transfers reliable numerical reasoning from a large teacher model to a compact student using execution-verified Python programs instead of free-form textual rationales. It leverages gold derivations to guide teacher-side program synthesis and retains only programs that execute correctly and produce the gold answer, ensuring high-quality supervision. We further introduce an iterative recovery stage that revisits teacher-failed examples, enabling the student to recover and incorporate newly verified programs into training. Experiments on TAT-QA show that our framework is highly effective for hybrid financial reasoning. Our best 7B student achieves 87.00 EM / 87.18 F1 on the test set, substantially outperforming the 72B teacher (78.46 EM) as well as traditional and strong LLM-based baselines, including TAGOP and TAT-LLM. These results demonstrate that execution-verified programmatic distillation provides an effective and extensible framework for training smaller models to perform reliable numerical reasoning.

Large language models can synthesize a game's rules as executable code - a Code World Model (CWM) - which a classical planner then searches over. Such models are typically accepted when they reach high transition accuracy on sampled trajectories. We argue this is the wrong notion of adequacy for planning. We show four things. (1) An LLM-synthesized CWM can pass a sampling gate at 100% transition accuracy and be $\geq 98\%$ state-accurate on the planner's own search distribution, yet lose systematically at play, because the $<1\%$ it gets wrong is exactly the pivotal dynamics; the play cost of the omitted rule is $0.091$ (seed-clustered 95% CI $[0.065,0.117]$, $n=4800$). We call this the verified-vs-correct gap, and confirm it end-to-end through the synthesis pipeline. (2) The harm follows a quantitative law, $\mathrm{danger}=\mathrm{play\_cost}\times(1-\mathrm{rarity})^N$, whose $(1-\mathrm{rarity})^N$ gate-miss factor is proven exact and whose play cost is empirically bounded. (3) The failure is not repaired by more data: LLM synthesis behaves as rule translation, not rule inference, and did not infer the omitted rule across models (GPT-5.x) and data regimes (including DAgger and targeted examples). (4) The same mechanism recurs on the belief-inference function of imperfect-information CWMs: we prove a coverage bound (a size-$N$ gate is identifying when $N\gtrsim b^{d_{\max}}$), explaining why shallow games such as Kuhn poker show no gap, and hand-construct Beacon, a verified-but-wrong inference function that passes the gate yet loses every game. These results suggest adequacy for planning-oriented world models should be measured on the search distribution or by play directly, not by prediction accuracy on sampled transitions.

Procedural material creation underpins applications in digital content creation, visual effects, and 3D asset design. Achieving high-quality results requires more than reproducing node graphs -- it demands understanding the process by which experts construct materials. We formulate procedural material generation as retrieval-time process reasoning over expert demonstrations, elevating process to a first-class representation beyond graph-only synthesis. Concretely, we represent expert workflows as process traces: textual records of construction steps, parameters, and design intent. To instantiate this idea, we use a pretrained LLM-based ProcessSynthesizer to synthesize a process trace aligned with a user's intent and a pretrained LLM-based Compiler to ground the process trace into an executable Blender material graph. Because procedural expertise is most naturally conveyed through demonstrations, we leverage tutorial videos as a source of process knowledge and extract textual, LLM-compatible traces using automated video analysis tools. In an expert study with five Blender artists (avg. 7.5 years of experience), materials generated by reflecting expert demonstrations were found to produce workflows requiring fewer edits, and more closely match professional design strategies than methods operating solely on static artifacts. A user study with 150 participants further shows that our approach achieves superior generation and editing performance compared to prior procedural systems. All code, models, and data will be available at https://materialapprentice.github.io

Formal contracts are essential for software testing and verification, yet writing them remains labor-intensive and error-prone. LLMs offer a promising path toward autoformalization: synthesizing executable assertions from natural-language specifications and thereby bridging the gap between informal developer intent and formal executable specifications. We present Monty: an autoformalization framework for assertions that tackles the challenges of expectations of validity of assertions and ambiguity in natural-language. Our techniques are based on filtering formalizations using a novel conformance score metric and validity scores obtained from testing the code against formalized assertions. We evaluate our approach on 541 assertion-generation tasks derived from 22 collection-like Java classes, and show that our technique produces the ground truth more reliably (improving upto 20 points in precision on average) than when using LLMs naively to translate assertions.

Synthesizing deployable robot behavior trees (BTs) from natural language (NL) requires grounding to ensure every generated BT references only skills a robot can actually execute. Existing LLM-based BT synthesis approaches often place this grounding responsibility on the prompt author. This makes deployment brittle when the author does not know which skills the robot can execute, how those skills are parameterized, or how the robot runtime software constrains valid BT structure. This paper proposes a contract-grounded BT synthesis architecture in which a coding agent queries a robot-side Model Context Protocol (MCP) server to retrieve an explicit contract consisting of a skill library, permitted BT operators, and optional BT composition templates, before synthesizing a BT for validation and execution. In our framework, non-expert operators issue NL commands without knowledge of robot implementation details, while a robot runtime validation gate enforces correctness before execution. We evaluate two LLMs, a closed model (Sonnet 4.6) and a smaller open-source model (Gemma4:31b), across 110 simulated tasks in PyRoboSim and 14 tasks on a physical Husarion Panther robot. Results show that contract grounding enables near-perfect BT validation and high task success, that BT composition templates substantially recover success on reactive control-flow tasks for the smaller model, and that the architecture transfers to physical hardware running a Nav2 stack opaque to both operator and agent.

Self-refinement often fails to strengthen few-shot inductive reasoning in large language models. Prompting a model to explicitly state its inferred rule does little on its own. What actually matters is a structurally enforced isolation between reasoning stages, so that information can only pass between them as a compressed symbolic state. We introduce \textbf{Hourglass reasoning}, which enforces strict context isolation between reasoning stages. The frozen LLM acts as a meta-constructor, building for each task a symbolic encoder--decoder: an Induction module compresses the support examples into a schema $φ$ (encoder) and a transient scaffold $z$; a Deduction module derives rule $T$ (decoder) from these and discards $z$; an Implementer compiles $(φ, T)$ into artifacts; an error-driven Refiner revises $(φ, T)$ and regenerates artifacts from scratch. Only $(φ, T)$ crosses stage boundaries, so all refinement stays anchored to the rule. We evaluate Hourglass across three benchmarks spanning visual abstraction, hardware synthesis, and textual rule induction, using GPT-5.5 and Gemini 3.1 Pro. On ARC-AGI-2, it raises best-of-5 accuracy by up to 14 points over an iterative-refinement baseline. On ChipBench, it nearly doubles Verilog synthesis accuracy with GPT-5.5, from 31% to 58%. BBEH-Linguini draws on puzzles from the International Linguistics Olympiad, a setting where prior work has shown that explicit verbalization can hurt performance. Hourglass mitigates this tendency, and on Gemini 3.1 Pro, it reverses the effect entirely. Ablations confirm that these gains come from the isolation between stages and the quality of the initial induction, not from prompt wording or the particular symbolic form used. It is how information flows through the reasoning process, rather than the language used to express it, that drives inductive reasoning in frozen LLMs.

Introduce a MinHash-based similarity scheduling framework that constructs a progressive curriculum over neural architecture code for LLM-based neural architecture search (NAS). Using 128-permutation MinHash signatures over normalised 7-gram source code shingles, we partition the reference pool into similarity bands and present them in increasing architectural heterogeneity, with the best LoRA adapter from each stage merged cumulatively into the backbone. We evaluate the framework on OlympicCoder-7B within the LEMUR benchmark on CIFAR-10 image classification, generating N =15 candidate architectures per epoch across six progressive fine-tuning steps. The curriculum achieves 60% peak success rate at the high-similarity level without post-processing repair. A 2*2 ablation at the most diverse level curriculum versus base model, with versus without partial interface repair reveals that without repair the base model (47% peak SR) substantially outperforms the curriculum model (7% SR), while adding partial repair brings both to 53% SR. This pattern is consistent with merge-level weight drift progressively erasing evaluator-interface priors, and suggests that interface repair and curriculum scheduling target distinct failure modes. We further report a cross-dataset transfer observation on SVHN, where direct base-model generation without curriculum warmup yields 27% peak SR at substantially lower accuracy (60.5%) than the CIFAR-10 equivalent, consistent with the increased synthesis difficulty of the unq-family anchor architecture.

Recent advances in LLMs and existing work on programming by demonstration have made it possible for end users to create automations by explicitly demonstrating their behavior to LLMs. However, these approaches rely on the assumption that users know what to automate and what is capable of being automated. Additionally, automation via LLM agents is often expensive compared with programs. We introduce Motif, a system that passively observes everyday browser activity to discover recurring interaction patterns that are programmable, makes recommendations to users whenever a pattern is discovered and generate a program to install after user confirmation. Users can review, and refine the program using natural language. We evaluated Motif in a multi-day study, comparing its ambient discoveries against automations users attempted to build via ``vibe coding.'' With eight participants, Motif discovered more automatable patterns than users recognized. Most of them matched participants' routines and were useful. Follow-up surveys showed most would continue using Motif-generated programs.

Large language models (LLMs) write Unity C# for game scenes. Yet nearly all demonstrations rest on an iterative repair loop that regenerates code until it compiles, conflating what the model writes with what the loop fixes. We remove the loop and evaluate a single pass, where the first draft is final. This isolates the model's parametric knowledge, the most stringent test of unaided generation. Models instantiate Goal Playable Concepts, playable counterparts of goal patterns, across 10,400 generations (four open-weight models, 7B--30B; two generation modes; four intermediate-representation (IR) conditioning levels; 26 goal patterns; 20 seeds). None compiled into a runnable scene, leaving no survivorship bias. To understand how the generated C# scripts fail, we categorize the 99 error codes behind 90{,}673 compiler-error occurrences as Grounding (invented or misused Unity types and APIs) or Hygiene (structural defects needing no Unity knowledge). The split differs sharply by goal pattern (e.g., Stealth fails mostly on invented engine references; Capture on plain C# structure). Larger models, stricter IRs, and different generation modes move the errors but never yield a compiling scene. The bottleneck is missing engine-specific knowledge. The census orders goal patterns by that demand, showing designers where single-pass generation breaks.

Program verification is crucial for software correctness, but producing fully verified programs remains difficult in practice. This paper studies whether implementation structure affects automated verifiability when multiple generated programs are intended to satisfy the same task-level semantics. We present Diversify2Verify, a staged LLM-based pipeline for Why3 that infers representation-specific contracts, generates and tests diverse recursive and imperative array/list implementations, and attempts verification with bounded verifier-guided annotation repair. We also construct a verification-oriented benchmark of 73 tasks over integers, arrays, and lists, yielding 292 implementation variants. Diversify2Verify verifies 96 artifacts initially and 154 after two repair passes, improving artifact-level verification from 32.9% to 52.7%. At the task level, at least one variant verifies for 49 of 73 tasks, a 67.1% success rate. These results show that task-equivalent implementations can differ substantially in verifiability and that implementation diversity helps find verification-friendly artifacts.

Recent progress on ARC-AGI-1 from disclosed architectures has come broadly from two regimes: heavy test-time compute over frontier models (evolutionary search, exhaustive sampling, extended chain-of-thought), or benchmark-specific training in which small models are fine-tuned on ARC data, often with task-specialized architectures. We study a third regime: an open-weight model in non-thinking mode (DeepSeek V3.2) under a strict budget, with no ARC-specific fine-tuning. We study what is recoverable through architecture alone, building agentic harnesses that decompose pattern-discovery and program-synthesis stages explicitly. First, we introduce an Explorer-Definer Pipeline that separates pattern discovery from executable transformation synthesis, implemented as a two-stage agent pipeline. Next, we present the Reflective Orchestrator, which augments the pipeline with autonomous exploration of new transformations when previous hypotheses fail on training pairs. On the ARC-AGI-1 public 400-task evaluation set, the pipeline reaches 57.50% pass@2 at $0.25 per task, and the orchestrator reaches 67.25% pass@2 at $0.62 per task. Together these architectures lift a 15.50% one-shot baseline by ~52 points without benchmark-specific training or heavy test-time compute. Furthermore, the orchestrator-driven lift tests a falsifiable diagnostic the pipeline produces; unbiased pass@k analysis suggests the pipeline is generation-bound, not selection-bound (selection via training-pair accuracy captures ~95% of the candidate ceiling) and predicts that significant improvement requires broader generation, not better ranking. The orchestrator implements this prediction via adaptive re-exploration and confirms it (unbiased pass@1 lift +9.81 pp, matching selection-mediated pass@2 lift). An additional pipeline ablation identifies its think tool as a significant component, with removal reducing pass@2 by 5.75 pp.

Loop invariant inference is a fundamental yet challenging problem in program verification. Recent LLM-aided guess-and-check techniques have shown strong performance on single-loop programs, but they often struggle with programs containing multiple interacting loops. This paper presents InvWeaver, a neuro-symbolic framework for synthesizing invariants for such programs. The key idea is to expose inter-loop dependencies and propagate proof obligations through a combination of loop-level abstraction, obligation-guided inference, and weakest-precondition-based refinement. We evaluate InvWeaver on a comprehensive benchmark suite, including a newly curated dataset derived from classic algorithms. Experimental results show that InvWeaver substantially outperforms existing invariant inference methods, solving 72 out of 82 multi-loop benchmark problems and maintaining strong performance on single-loop tasks.

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.

Automated detection of interictal epileptiform discharges in scalp electroencephalography (EEG) is clinically important, but recent high-performing deep-learning models often trade interpretability for accuracy. We introduce EEG-SpikeAgent, a closed-loop program-synthesis framework that uses a large language model (LLM) agentic system to generate signal-processing features for spike detection in scalp EEG. The system iteratively proposes one deterministic EEG feature module at a time, executes the resulting code on EEG to generate tabular features, evaluates performance via a tabular classifier, summarizes run-level metrics, and feeds structured diagnostics back to the model for refinement. Across iterations, EEG-SpikeAgent proposes and refines candidate signal features and decision rules informed by model performance. We evaluated EEG-SpikeAgent on VEPISET, a public 29-channel dataset of 4-second epochs containing 2,516 discharge-containing and 22,933 non-discharge epochs. Across five-fold cross-validation with a gradient-boosted tree classifier, agent-generated features achieved an area under the receiver operating characteristic curve of 0.935, balanced accuracy of 0.699, F1 score of 0.557, sensitivity of 0.401, and specificity of 0.996 at the default operating point. At an operating point with sensitivity 0.80, mean precision was 0.470 and mean specificity was 0.900. Artifact-aware feature generation improved balanced accuracy and F1 score over spike-only feature search. These results indicate that LLM-based program synthesis can automate EEG feature engineering in auditable and inspectable code-driven manner for clinical and methodological review.

Every LLM agent run re-derives its behavior token by token on a frontier model: brilliant, expensive, slow, and unbounded. We present Auto, a compiler that records live agent behavior, measures which parts are secretly deterministic, extracts them into verified programs or distilled specialists, and emits cognition binaries: WebAssembly artifacts whose manifests carry measured guarantees and whose declared capabilities are physically enforced by the sandbox. A tiered runtime executes compiled behavior behind conformally calibrated guards; guard trips deopt to the reference agent, and the captured trace recompiles back down, so nothing is figured out twice. We use "AGI compiler" in one narrow, testable sense: a system that autonomously converts novel experience into permanent, verified, near-free skill while measuring what it does not know. On AUTO-BENCH, a benchmark we introduce and pre-register, 87.1% of 560 recorded frontier-agent spans are witnessed-deterministic (three of the four censused task families measure 100.0%). On a 300-item stream with three scheduled distribution shifts, the closed loop compiles three artifact generations and drives marginal cost from 59 to 2 micro-dollars per item (6.4x end-to-end) at 96.9% parity on witnessed inputs with zero errors. The same stream also quantifies the failure modes: a loose guard silently mislabels 48.9% of compiled answers, and an unfaithful deopt reference causes the verification gate to refuse recompilation. Calibration and reference fidelity, not model capability, decide whether cheap stays correct. Code: https://github.com/RightNow-AI/auto

Large Language Models are increasingly used to turn natural-language requirements into code. In access control, that shortcut is dangerous: a generated policy can compile and read correctly while granting access that no one approved. The difficulty is not only writing policy code. It is fixing what the requirements mean before code is written, and then checking that the final policy actually satisfies that intent. We present AutoCedar, a verifier-guided system that first turns natural-language access-control requirements into a reviewed, checkable target, and then synthesizes Cedar policies against that target. AutoCedar decomposes schema and policy authoring into small intent atoms: reviewable claims about vocabulary and behavior. Once those atoms pass mechanical validation and human intent review, the model proposes a candidate policy, the verifier checks it against the approved target, and each failure is turned into a repair signal that tells the model whether to broaden, narrow, or restructure the policy without changing the target. Because the model's work is split into small problems, each grounded in reviewed intent and backed by verifier feedback, end-to-end policy authoring becomes tractable. AutoCedar converges on all 221 tasks of CedarBench, our benchmark of authorization tasks paired with executable semantic boundaries. Across three requirements-corpus case studies covering healthcare, education, and conference management, AutoCedar converts noisy prose and extracted access-control fragments into reviewed schemas, formal checks, and a globally verified Cedar policy store for each scenario.

Before fixing an issue, it is useful to first reproduce it by generating a bug reproduction test (BRT). However, generating a BRT is itself a challenging task, because issue descriptions tend to be informal, making it difficult to determine whether a candidate BRT indeed fails for the reason in the issue. Prior work has attempted to tackle this problem via inference scaling, using large language models to generate many BRTs and patches, then using execution feedback to select and improve them. Unfortunately, this is expensive and the feedback is unreliable. This paper explores evolutionary programming for BRT generation to sharpen the feedback, while enhancing evolutionary programming to keep costs in check. Our new approach, EvoOtter, controls test execution costs via successive halving. Furthermore, it controls LLM costs via batched crossover for an entire generation in a single LLM call, as well as via rule-based code mutations, with a new fitness score tailored for BRTs. As a result, EvoOtter generates state-of-the-art quality BRTs at the fraction of the cost of prior inference-scaling approaches to this problem. More broadly, this paper points at how to efficiently and effectively combine evolutionary programming with large language models for software engineering.

Many everyday programming tasks resist clean rule-based implementation, such as alerting on important log lines, repairing malformed JSON, or ranking search results by intent, and are increasingly outsourced to large language model APIs at the cost of locality, reproducibility, and price. We propose fuzzy-function programming: compiling such a function from a natural-language specification into a compact, locally-executable neural artifact. We instantiate this paradigm with Program-as-Weights (PAW), in which a 4B compiler trained on FuzzyBench, a 10M-example dataset we release, emits parameter-efficient adapters for a frozen, lightweight interpreter. A 0.6B Qwen3 interpreter executing PAW programs matches the performance of direct prompting of Qwen3-32B, while using roughly one fiftieth of the inference memory and running at 30 tokens/s on a MacBook M3. PAW reframes the foundation model from a per-input problem solver into a tool builder: invoked once per function definition, it produces a small reusable artifact whose subsequent calls per function application are cheap and offline.

Musical performance involves executing a set of high-level musical instructions, yet recovering those instructions from the performance is a challenging inverse problem. We present Decomposer, a post-training framework for symbolic music decompilation: the task of recovering executable, editable music programs from symbolic music. We instantiate the task as MIDI-to-Strudel decompilation, where the model takes symbolic MIDI as input and produces a program in Strudel, a music programming language, that reconstructs the input when executed. The task poses two challenges: Strudel is a low-resource language with little naturally paired MIDI-code data, and optimizing faithful reconstruction of MIDI alone can collapse to unreadable note-by-note transliteration. We address these challenges in two stages. First, we construct Strudel-Synth, a synthetic corpus of paired Strudel programs and rendered MIDI, and use it for supervised fine-tuning. Second, we refine the model with reinforcement learning on unpaired MIDI, optimizing rewards for both MIDI reconstruction faithfulness and code readability. Our evaluation across synthetic and real-world MIDI benchmarks shows that Decomposer achieves substantially higher MIDI reconstruction faithfulness than closed-source LLMs while producing more readable and diverse code than the heuristic converter.

As the scale and complexity of cloud-based AI systems continue to escalate, ensuring service reliability through rapid fault detection and adaptive recovery has become a critical challenge. While existing approaches integrate Large Language Models (LLMs) for semantic understanding and Deep Reinforcement Learning (DRL) for policy optimization, they often rely on sequential, loosely coupled architectures that underutilize the generative and reasoning capabilities of LLMs. In this paper, we propose a paradigm shift with PASE, a Planning-Aware Semantic self-healing engine, a novel fault self-healing framework that reconceptualizes recovery as a neuro-symbolic program synthesis task. PASE employs an LLM as a core Plan Synthesis Engine to generate structured recovery plans from a library of semantic primitives. A Neural-Symbolic World Model verifies plan feasibility through simulation, while a Meta-Prompt Optimizer, trained via DRL, learns to generate optimal prompts that guide the LLM's planning process. This tight reason-plan-verify-adapt loop enables dynamic, context-aware recovery strategy generation beyond predefined action spaces. Experiments on a real-world cloud fault injection dataset demonstrate that PASE significantly outperforms state-of-the-art methods, reducing average system recovery time by over 40% and improving fault detection accuracy in unknown fault scenarios. Our framework advances autonomous system management by unifying LLM-based reasoning with model-assisted verification and meta-learned guidance.