LLM-Based Program Synthesis

Developing high-performance kernels for Neural Processing Units (NPUs) is a critical industry bottleneck, requiring developers to manually navigate implicit hardware constraints and strict memory hierarchies. While large language models offer immense automation potential, they fail catastrophically on NPUs due to a fundamental lack of hardware-specific priors. Naively transplanting code snippets from similar NPU kernels may pass the compiler, but it consistently triggers runtime crashes and performance degradation by blindly violating underlying hardware constraints. To overcome this, we introduce Hawk, a training-free framework that harnesses hardware-aware knowledge through three core modules: (1) Run-Time Knowledge Synthesis Module, which employs a Triple-Part Executable Knowledge Representation to inherently couple the error context with executable semantics; (2) Bottleneck-Aware Knowledge Retrieval Module, which implements a 2D-Retrieval paradigm to project queries into orthogonal syntactic and hardware-aligned semantic spaces; and (3) Effect-Driven Knowledge Distillation Module, which leverages LLM-driven semantic arbitration to continuously distill the knowledge by pruning errors and consolidating redundancies based on the empirical execution feedback. Extensive evaluations on real-world NPU workloads demonstrate that Hawk elevates generation accuracy from 49.4% to 80.0%, while achieving up to a 2.2x execution speedup over state-of-the-art baselines.

Learning how an environment behaves from interaction is central to building agents that adapt to unfamiliar tasks. World models learned with deep networks are flexible but data-hungry and transfer poorly beyond their training distribution. Program-synthesized world models, written as source code by LLMs and refined through counterexample-guided inductive synthesis (CEGIS), are instead data-efficient and reusable, yet they have been demonstrated mainly on structured-state worlds with a given object vocabulary, and a single program search does not scale to pixel-rendered environments whose object structure must be hypothesized flexibly. We introduce OPINE-World, an LLM agent that learns an object-centric programmatic world model online from interaction. OPINE-World couples two cooperating agents in a loop of hypothesis and test, one acting in the environment and one synthesizing the model in code with replay verification and model-based planning, and it steers exploration with a Bayesian measure of object-type adequacy we call ontology error. We evaluate OPINE-World on ARC-AGI-3, a benchmark for skill-acquisition efficiency in which the object vocabulary, the goal, and the action semantics are withheld. OPINE-World solves 20 of 25 games without per-game training and reaches an action-efficiency score of 78.4 against the human baseline.

We present RuleChef, a framework that uses large language models (LLMs) to generate executable rules for NLP tasks such as text classification, Named Entity Recognition (NER), or relation extraction. Rules are generated based on a task description and a set of labeled examples, then they are iteratively improved based both on additional examples and on human feedback overexisting rules. RuleChef can also be used to bootstrap rules using the observed input-output pairs from any existing model for a given task. LLMs are used only at learning time, synthesizing rules and iteratively patching them based on failures measured on a held-out split. The result of this process is a fast, deterministic, and inspectable rule system. Preliminary evaluation is performed on both classification and NER tasks. We release RuleChef as open-source software under an Apache 2.0

Language models increasingly write probabilistic programs (in NumPyro, Stan, or Pyro), but a program that compiles, runs, and passes every unit test can still be \emph{statistically} wrong -- a Gaussian likelihood for heavy-tailed data, a Poisson for over-dispersed counts, an invalid prior support, or a pathological parameterization. The right verifier is therefore not a test suite but the Bayesian workflow itself: posterior predictive checks, simulation-based calibration, sampler diagnostics ($\hat R$, divergences, ESS), and held-out predictive density. We study this calibration oracle along three axes. \textbf{Detection:} on a benchmark of $14$ misspecification types across $10$ model families ($200$ instances), it flags the bug with AUC $0.97$ ($88\%$ at $2\%$ FPR \emph{when handed the correct reference program, an upper bound}) -- and a fully \emph{reference-free} version that uses no correct program reaches $62$--$78\%$ (the upper figure from a small automated model search), versus $0\%$ for a unit-test oracle. \textbf{Repair:} used as feedback in an LLM repair loop across fifteen models, calibration significantly outperforms unit-test feedback -- which is itself \emph{significantly worse than no feedback at all}, a passing test inducing false confidence that suppresses repair -- and improves over no feedback on strong-but-unsaturated models (GPT-5.1 $33{\to}92\%$, Claude $75{\to}100\%$; paired McNemar, $n{=}228$). \textbf{Reality:} on programs LLMs write from scratch for neutral briefs, $15$--$47\%$ of runnable ones are statistically misspecified (unit tests catch none), and calibration-guided repair significantly beats LLM-as-judge review, a Bayesian-workflow checklist, and data-summary self-debug. Across all three, the lesson is the same: for probabilistic programs, correctness is calibration, not compilation.

Designing an algorithm from a natural-language problem statement requires identifying the problem structure, reading constraints, choosing a suitable paradigm, checking correctness, and refining complexity. Existing large language model (LLM) methods often rely on direct generation or generic self-refinement, leaving these steps implicit. We propose AlgoSkill, which models algorithm design as sequential decision-making over a typed library of algorithmic skills, including abstraction, constraint analysis, state design, data-structure selection, proof checking, counterexample construction, and complexity refinement. A learned scheduler proposes skills from the current design state, while a Monte Carlo Tree Search (MCTS) controller explores skill sequences using verification feedback from compilation, testing, stress testing, and complexity analysis. Experiments on competitive programming and combinatorial optimization benchmarks show that AlgoSkill improves over direct LLM generation, chain-of-thought prompting, self-refinement, and MCTS without typed skills. Ablations show that typed skills, verification-based repair, and search-based scheduling each contribute to performance. These results support treating automatic algorithm design as verification-guided skill scheduling rather than one-shot code generation.

Computer-aided design (CAD) plays a fundamental role in modern manufacturing by providing the high precision required for industrial production. Recent large language model based approaches formulate CAD generation as a sequence prediction problem and have achieved promising results. However, existing methods and evaluation protocols primarily emphasize visual similarity, while overlooking precise geometric parameters and correct metric scale. Small numerical deviations that are negligible at the shape-level may still violate industrial tolerance requirements, a problem further compounded by current autoregressive paradigms that utilize command sequence representations, aggressively quantize numerical parameters to ease LLM prediction. In this work, we present Pointer-CAD v2. Compared with v1 (arXiv:2603.04337), this version directly predicts continuous values, bypassing the need for quantized numerical parameters and thereby eliminating quantization errors. Specifically, we propose a unified framework that decouples parameter reasoning from geometric construction through a Plan-Then-Construct paradigm. Our method first produces a structured design plan with explicit metric scale parameters. These parameters are organized into a dictionary and directly referenced during sequence generation via a pointer mechanism, eliminating discretization errors and ensuring dimensionally consistent execution. In addition, we construct a new large-scale dataset with plan-level annotation and introduce three hierarchical geometry accuracy metrics to evaluate parametric fidelity at the vertex, edge, and face levels. Extensive experiments demonstrate that Pointer-CAD v2 consistently outperforms existing baselines and achieves substantial improvements in geometric accuracy, enabling reliable CAD generation for precision-critical engineering applications.

High-performance GPU kernels are critical for reducing the exponentially growing computational costs of large language models (LLMs), but their development heavily relies on manual tuning by domain experts. While recent advances in LLM-based approaches show promise for automating kernel generation, they still struggle to achieve both correctness and high performance. This limitation primarily arises from the lack of domain-specific optimization guidance, hindering effective exploration of the optimization space. We propose EGG, an Expert-Guided Agent Framework for Kernel Generation, which incorporates expert optimization principles to guide LLMs' decisions. Inspired by expert workflows, we decompose kernel generation into two hierarchical stages: 1) algorithmic structure design, which establishes a high-quality computational structure foundation; 2) hardware-specific tuning, which performs targeted adjustments through parallel mapping, tensor tiling, and memory optimization. This staged decomposition defines explicit optimization objectives, structuring the design space to achieve progressive refinement. To this end, a stage-aware multi-agent collaboration mechanism is designed for inter and intra-stage context management, ensuring stable optimization trajectories. Experiments on KernelBench and real-world workloads show that EGG achieves a 2.13x average speedup over PyTorch, outperforming existing agent-based and RL-based approaches.

Software-compilable C programs routinely fail to complete the four-stage pipeline of a high-level synthesis (HLS) toolchain -- compilation, C simulation (CSim), synthesis, and C/RTL co-simulation (CoSim) -- because HLS accepts only a synthesizable subset of C (HLS-C). Yet most existing large language model (LLM) systems built for HLS code repair only cover the early pipeline stages and feed raw tool logs directly to the model, yielding brittle and hard-to-reproduce fixes. We formulate C-to-HLS-C conversion as a closed-loop generation-verification-diagnosis-repair problem on an HLS tool (Xilinx Vitis), contributing three components: an end-to-end workflow of cooperating agents closed by the four-stage verifier under strict evidence isolation; a Progressive Mismatch Localization Chain (PMLC) that localizes CSim/CoSim mismatches through log normalization, AST backward slicing, and dual-trace instrumentation; and a typed-query, two-stage evidence RAG backed by a self-evolving, family-routed repair-card pool. Experimental results show that the proposed workflow substantially outperforms all comparable state-of-the-art models.

For most of scientific history, researchers studying behavior could only infer hidden mechanisms from outward actions: an inverse problem that becomes more tractable when observation is augmented by targeted intervention. We pose a computational analogue: given only behavioral traces of an agent in a game environment, can a learner reconstruct the underlying decision program as executable code, and how much does this reconstruction improve with the ability to design controlled experiments? We introduce RevengeBench, a benchmark of 75 LLM generated, Elo-calibrated policies across five game environments, drawn from CodeClash tournament trajectories. The learner observes the hidden target policy play against sampled opponents and designs behavioral probes in the form of custom opponent policies that elicit informative behavior. It then submits an executable hypothesis, which is evaluated using continuous action-distance metrics. We further validate that recovered code carries informative signal in downstream player-versus-player tournaments. Across twelve frontier LLMs, recovery quality varies substantially (34 to 72% of initial distance closed), with reconstructed policies yielding measurable competitive advantage, particularly for weaker models that otherwise struggle to design effective counter-strategies. Our benchmark positions behavioral recovery of programmatic policies as a tractable inverse problem in code-space, opening a path to opponent modeling, policy interpretability, and the broader question of inferring latent mechanisms from observations.

Recent work shows that Large Language Models (LLMs) can act as semantic mutation operators for the evolutionary discovery of programs and proofs. Most current applications focus on static coding benchmarks. We extend this paradigm to algorithmic trading. This domain is uniquely challenging because it is noisy, non-stationary, and highly discontinuous. We present AlgoEvolve, an LLM-driven evolutionary framework that generates, evaluates, and iteratively improves executable trading strategies. These strategies are expressed as Python code and evaluated through a rigorous testing protocol. Across multiple experiments, the system exhibits emergent regime-adaptive strategy logic, including autonomous shifts in trading rules. We further introduce a meta-evolutionary outer loop that evolves the prompts guiding program synthesis in the inner loop. This outer loop discovers improved search heuristics. These heuristics balance exploration and exploitation while reducing zero-trade failures. They consistently outperform initial human-designed instructions. The results demonstrate that LLM-based semantic evolution provides a viable approach for continual program synthesis in complex environments.

We extend our prior work on Text2DSL automatic generation of domain-specific language (DSL) code from natural language descriptions along two complementary axes. First, we replace prompt-only synthetic generation with context-aware distillation, in which a teacher large language model (DeepSeek-V4-Flash) operates under an explicitly defined structured context comprising a BNF grammar, an API specification, and a closed identifier vocabulary; the resulting corpus is verified by a two-tier pipeline combining AST validation through esprima and runtime acceptance through the production polkitd daemon and the pkcheck client. This scales the verified PolkitBench corpus from 4,204 to 10,073 natural-language-to-Polkit-rule pairs at 100.0% AST validity and 99.7% runtime pass rate. Second, we conduct the per-component factorial ablation of structured context that was identified as future work in the precursor study: eight conditions C0-C7 are evaluated on GigaChat-10B-A1.8B with the new corpus. Three findings emerge. (i) The new harder corpus collapses the baseline mode (Syntax Valid 97.6% -> 58.5%, Combined Score 0.482 -> 0.252), whereas the context-enhanced mode degrades only marginally (Syntax 98.6% -> 97.4%, Combined 0.801 -> 0.750), confirming that structured context is not a cosmetic improvement but a load-bearing mechanism. (ii) The best absolute condition is the full context C7 across all metrics, while the strongest partial conditions (C5 = BNF + Vocabulary, C6 = API + Vocabulary) both contain the vocabulary. (iii) A Shapley-style decomposition assigns the largest semantic-quality effect to the vocabulary (Combined +0.198), the largest structural-validity effects to API (+24.7 pp) and BNF (+22.3 pp).

In this work we present a LLM powered, evolutionary code synthesis system for structured data translation in a Medical Internet of Things settings. A key challenge in this domain is ensuring that the synthesized code is trustworthy and reliable. To this end, we integrate a formal verification step into our code synthesis pipeline to ensure that any generated code is guaranteed to satisfy predefined requirements. In particular, we present a case study of integrating a novel device (a pulse oximeter) into the existing network of devices. Our system generates a formally verified translation between the device's JSON schema and the Fast Healthcare Interoperability Resources (FHIR) format used by the wider system. This formal verification stage ensures structured data translated by the generated code will always be in the target output schema. We provide a set of experimental results which demonstrate that our system is able to consistently generate correct translation at low cost.

Federated learning over medical images is a demanding workflow application. Each round fans out across parallel client jobs and converges on an aggregation step that feeds the next round. At scale this yields 101 sub-workflows and 2,679 jobs on GPUs at four sites, which takes an expert months to build, mostly on workflow mechanics rather than science. We ask how far AI assistance can automate such workflows. An LLM agent, grounded in a released plugin of Pegasus-specific skills, first produces a reviewable specification of checkable constraints and acceptance criteria, then generates the executable workflow. A validation loop repairs runtime failures, checks code against those constraints, and regenerates the implementation from the specification alone. We evaluate three LLM agents, report end-to-end runs on the FABRIC testbed, and show how conformance checking against the specification caught three silent errors that failure-driven debugging missed, including one that trained 1,700 jobs on random tensors.

Large language models (LLMs) have achieved remarkable success in software development. However, they are susceptible to hallucinations, meaning that they can introduce subtle semantic and logical errors. Due to the high stakes in chip design and manufacturing, hardware engineers are still reluctant to rely on LLMs for register-transfer level (RTL) generation. In this paper, we propose a hardware generation framework that combines the creativity and broad knowledge of LLMs with the explainability and mathematical rigor of formal methods. Specifically, we devise a set of transformation rules that cover various design decisions and hardware features. By iteratively applying these rules, an LLM agent can convert a design specification into an RTL program with guaranteed correctness. Experimental results demonstrate the effectiveness and efficiency of the framework.

Recent advances in both Large Language Models (LLMs) and Vision Language Models (VLMs) have seen a step change in their ability to perform visual code completion, but the aerospace industry, which prioritizes safety and explainabilty over rapid LLM adoption, currently has no publicly announced LLM-based geometric design copilot systems in commercial use by aerospace Original Equipment Manufacturers (OEMs). This paper presents a LLM-based visual programming copilot application for aerospace engineering design tasks, using a visual programming variant of the ReAct methodology and GPT 5.4. In addition to the copilot, we describe Wingbuilder, a new Grasshopper plugin library with custom components for aerospace-specific geometry abstraction, and an associated Aerospace Visual Programming Dataset (AVPD) with 18 aerospace expert designed tasks at different levels of difficulty alongside ground truth solutions. We evaluate our copilot application with a user trial involving two experienced aerospace engineers from a large aircraft manufacturing company. We find our copilot visual programming ReAct methodology was successful in generating suggestions that participants found helpful, but slow ReAct inference times limit its usefulness to more complex time-consuming tasks where waiting for good copilot solution suggestion was worthwhile. Participants reported they liked the tool and would be willing to use it in the future.

Large multimodal language models (MLLMs) have emerged as powerful tools for guiding evolutionary search toward interpretable programmatic policies. In existing program-evolution systems, however, reusable knowledge is usually carried by whole programs in the population, and it is difficult to trace how a visual observation led to a particular code change and its measured outcome. We present REFLEX, a train-free evolutionary framework that links these steps in one loop. A vision-enabled Critic turns task-specific behavioral evidence into a structured diagnosis; the diagnosis retrieves executable code snippets from a persistent Skill Memory; a text-only Actor writes the child program; and the child--parent fitness change updates the utility of each retrieved snippet. Every step is recorded in a single trace. Under matched backends and 100-call budgets over 10 paired seeds, REFLEX reaches the solve threshold in a median of 13, 20, and 24 LLM calls on Acrobot, Pendulum, and Lunar Lander, roughly half the calls required by official MLES and by a compute-matched Actor-only ablation. Frozen Skill Memory banks from Pendulum or Lunar Lander raise the final Acrobot score on all 10 paired seeds. On a 36-dimensional antenna-array design task with equal evaluation budgets and shared initialization, REFLEX reaches the harder $25.25$ score threshold on 9/10 seeds, compared with at most 3/10 for CMA-ES, GA, and PSO.

World-model synthesis aims to turn interaction experience into an internal model of environment dynamics. Existing symbolic approaches often fit observed transitions or mixtures of local rules, but they do not produce a complete executable program that can run independently of the real environment. We present Mind-Studio, a framework that synthesizes executable pygame-style world models from state-action-next-state trajectories using large language models. Mind-Studio combines entropy-selected traces with a lightweight game skill file containing object, action, and static scene information extracted from screenshots. We evaluate synthesis quality with a K-step lookahead fidelity protocol that compares generated world-model rollouts against Real-ALE rollouts from the same state. On Montezuma's Revenge, Mind-Studio improves chosen-action next-state prediction from 0.3% for PoE-World to 48.7% while verifying 5 of 8 subgoals; across Alien, Assault, and Skiing, it achieves stronger branch-level fidelity than prior learned lookahead sources.

Machine learning (ML) pipelines require extensive data preparation, feature engineering, and integration across heterogeneous sources, making them tedious and error-prone to develop. While large language models (LLMs) have recently shown promise for assisting programming tasks, chat-based interfaces provide limited control over pipeline behavior and often produce code that is difficult to optimize or integrate into production systems. We demonstrate SemPipes, a novel programming model that extends ML pipelines with declarative, LLM-powered semantic data operators. SemPipes allows developers to specify high-level natural language instructions for data-centric operations, while seamlessly combining these operators with arbitrary Python code from standard data science libraries. For the semantic operators, it synthesizes specialized implementations at pipeline training time, conditioned on dataset characteristics and pipeline context, enabling the flexible yet controlled integration of LLM capabilities. We demonstrate SemPipes through SemPiper, an interactive interface that visualizes computational graphs of the pipelines, synthesized operator implementations, and optimization trajectories produced by an evolutionary search procedure. Attendees can explore three end-to-end scenarios, modify pipelines, inspect generated code, and observe how semantic operators are synthesized and iteratively optimized. The demonstration highlights how declarative semantic operators enable controllable, optimizable, and practical integration of LLMs into ML pipeline development.

Code-writing large language models (CodeLLMs) generate executable code policies for embodied agents by translating natural language goals and environmental constraints into structured control programs. However, policy generation in open-domain embodied environments suffers from two fundamental limitations: (i) delayed decoding caused by repetitive prefill computation over long prompts, and (ii) limited robustness due to fully generative decoding, which often produces API mismatches, missing safety guards, and unstable control logic. To address these limitations, we present FCGraft, a Functional Cache Grafting framework. FCGraft maintains a library of function-level validated code skeletons and their associated prompt-level Transformer key-value (KV) caches, and synthesizes new policies by retrieving relevant functions and grafting their KV caches when a new task is provided. Given retrieved function caches, FCGraft performs cache grafting via stitching, which composes cached function segments into a composite policy, and patching, which locally adapts only the necessary code regions to satisfy task-specific parameters and constraints with minimal additional decoding. By eliminating redundant prefill computation, this approach reduces generation latency, while reusing validated control structures improves robustness over prompt-level caching methods RAGCache, achieving 18.31% higher task success rate and 2.3x faster policy synthesis.

LLMs and LLM agents should improve when given feedback, but identifying when they are able to do so is difficult: feedback is heterogeneous, domain-specific, and difficult to control. We approach this challenge by asking LLMs to perform regular-expression induction, a classical symbolic learning problem where precise mechanisms for feedback exist in the form of counterexamples. In counterexample-guided learning, a learner (LLM) proposes candidate regular expressions from positive/negative-labeled strings, and the teacher (verifier) returns counterexamples showcasing the difference between the candidate and target languages. We identify novel counterexample-guided refinement strategies that enable effective regex learning, such as regularization and symbolic counterexample clusters. We also explore agentic strategies such as reflection and repair loops. Empirically, we find that verifier feedback substantially improves sample efficiency on challenging regex-induction tasks, reducing the number of labeled examples required and enabling learning of complex target expressions where standard prompting fails. For example, on the hardest task groups, our counterexample-guided framework improves success from 3.2% to 38.1% and from 38.9% to 74.1% on two different regex domains. These results suggest that LLMs can benefit from rich feedback beyond treating it as additional data, opening the door for robust verifier-guided methods for LLM-based program synthesis and formal reasoning.

Multimodal large language models can write code to produce complex programs as well as use programs to do 3D modeling, which opens up a new avenue for 3D generation powered by their priors, world knowledge and reasoning. Yet existing benchmarks rarely evaluate 3D modeling through code. Such modeling demands more than runnable code: from a text or visual specification, a model must generate a parametric 3D program that is geometrically precise, semantically aligned and assembly-consistent. We introduce P3D-Bench, a benchmark for parametric 3D generation. Unlike a 3D mesh, a parametric 3D program exposes explicit dimensions, construction operations and part relations, revealing whether a model recovers a design's structure, not just its appearance. Under a unified protocol, P3D-Bench covers three task families (Text-to-3D, Image-to-3D and Assembly-3D) and scores each output for executability, geometric fidelity, topology, text-grounded constraints, multiview semantic alignment and part-level structure. We evaluate frontier MLLMs and text-only LLMs on 400 text cases, 400 image cases and 203 annotated assemblies, with domain-specific models as reference points. Our extensive evaluation yields three findings. First, assemblies are the hardest setting, where models still fail to compose multiple parts into a coherent structure. Second, models can often recover the global shape and semantic identity of the target object, yet fail to reproduce the precise parametric geometry specified by the input. Third, part-level modeling remains weak on assemblies, where models recover neither the geometry of each part nor the right number of parts. These results position P3D-Bench as a benchmark for evaluating precise parametric geometry and part-level structure in parametric 3D generation.

Text-driven indoor scene generation and editing require an intermediate representation that language models can both produce and revise. Existing LLM-based systems often rely on scene graphs or global constraint lists, which are compact but underspecify local geometry and make instruction-based edits difficult to localize. We frame this problem as structured program generation and local program repair, and propose Hierarchical Descriptive Scene Language (HDSL), an XML/CSS-style domain-specific language for structured 3D indoor scenes. HDSL represents rooms, regions, objects, and support surfaces as a tree with local coordinates, making complex scenes easier to plan recursively and easier to retrieve for editing. Our pipeline uses LLM agents to generate HDSL subtrees with bounded verification, grounds non-virtual nodes through multimodal asset retrieval, and applies force-directed layout optimization to repair boundary and collision errors. For editing, Hierarchical Retrieval-Augmented Generation retrieves the relevant subtree, asks the LLM to rewrite only that local context, and merges the result back through a deterministic three-way merge. In our reproduced benchmark, HDSL improves average object coverage, text-scene alignment, and generation time over full text-to-scene baselines while remaining competitive with recent layout-only reproductions on geometry metrics; for editing, HRAG reduces token use by $5.22\times$ and runtime by $6.19\times$, produces valid DSL for all eight paired edits, and better preserves unrelated scene objects.

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, $\exp(-\mathrm{MSE})$), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by $2.3\times$, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-check. We present TLA-Prover, a 20-billion-parameter model for TLA+ specification synthesis. Training combines supervised fine-tuning (SFT) on verified examples with repair-based group-relative policy optimization (GRPO). In the GRPO stage, the model learns to fix its own rejected specifications. We also train a direct preference optimization (DPO) variant from the same SFT checkpoint as an ablation. TLC provides the reward signal directly, with no learned reward model. Four tiers grade each output: Bronze (parses), Silver (no warnings), Gold (passes TLC), and Diamond. To reach Diamond, the model's correctness property is automatically altered in a small way; TLC must then detect a violation. If TLC still passes, the property was always-true and contributes nothing; the output fails Diamond. TLA-Prover reaches 9/30 (i.e. pass@1 = 30%) at both Gold and Diamond on a held-out 30-problem benchmark. This is roughly 3.5x the 8.6% untuned baseline. The DPO variant reaches 20% at Diamond. Gold and Diamond coincide at every checkpoint; this prevents the trivial-property failure mode.

Recent advances in large language models (LLMs) have enabled the automatic synthesis (generation) of register-transfer level (RTL) code from natural language instructions, offering a promising pathway to accelerate chip design. Unlike typical natural language (and software coding) tasks, LLM-based RTL code generation demands strict cycle accuracy with concurrency, where minor logical errors can render a circuit unusable or insecure. While prior work has explored hallucination mitigation via external verification, self-evaluation prompts, retrieval-augmented prompting, domain specific fine-tuning, agentic solutions, and reasoning, these approaches largely overlook the attention-oriented internal mechanisms of LLMs that may inherently correlate with RTL correctness. This work proposes CASS-RTL, a first-of-its-kind framework for discovering and leveraging LLMs' correctness-aware components to guide RTL generation toward functionally accurate outputs. We (i) identify attention heads whose activation patterns consistently differentiate correct from incorrect RTL; (ii) construct a low-dimensional subspace capturing correctness-relevant signals; and (iii) design a lightweight, geometry-aware intervention that steers the model at inference time. CASS-RTL is fully model-agnostic, requires no additional supervision or retraining, and readily integrates into existing models. Empirically, we evaluate CASS-RTL on multiple models and observe 10%-20% improvement in pass@1/5/10 accuracy on VerilogEval and 5% improvement on CVDP, demonstrating the effectiveness of our method in enhancing reliability without sacrificing model efficiency or requiring a large labeled dataset for fine-tuning.

We present a pipeline for building and aggregating task-specific, LLM-generated weak (imperfect) verifiers into a strong verifier for spatial layout domains. Given a task description, our pipeline asks an LLM to synthesize a collection of verifier programs using a layout verification DSL. Each individual LLM-generated verifier usually provides an imperfect check for a match between the layout and the corresponding task description. We show that by aggregating the responses of many such verifiers we can produce a stronger verifier. Moreover, by applying techniques from weak learning, our pipeline can learn how to aggregate the weak verifiers from a very sparse set of human labeled example layouts (about 10). We find that the strong verifiers produced by our pipeline outperform the status-quo approach of using a set of LLM judges to directly check whether a layout matches a task description, raising F1-scores by up to 7X across a variety of 3D room layout and 2D poster design tasks. We also demonstrate that verifier-guided layout generation using natural language feedback from our strong verifiers improves layout quality of a base layout generator by up to 66.2% according to a human evaluator.

Automatic generation of RTL code for digital hardware designs remains challenging due to long-horizon reasoning, multi-step dependencies, and strict correctness constraints in Verilog and VHDL. We present StepPRM-RTL, a novel framework that combines stepwise trajectory modeling, process-reward modeling (PRM), and retrieval-augmented fine-tuning (RAFT) to enhance both the functional correctness and reasoning fidelity of LLM-based RTL code generation. StepPRM-RTL constructs stepwise reasoning trajectories from canonical solutions, where each step contains a rationale and incremental code modification. A Process Reward Model (PRM) evaluates intermediate steps, providing dense feedback that guides reinforcement-style updates during RAFT fine-tuning. Monte Carlo Tree Search (MCTS) explores alternative reasoning paths, enriching the training dataset with high-quality trajectories. This integration of stepwise and outcome-aware rewards allows the model to learn both how and why to construct correct RTL, improving long-horizon reasoning beyond standard supervised or outcome-based training. Experimental evaluation on benchmark Verilog and VHDL datasets demonstrates that StepPRM-RTL outperforms the best prior methods by over 10% in functional correctness and reasoning fidelity metrics. Ablation studies confirm that the combination of PRM-guided rewards and stepwise trajectory exploration is key to its performance. StepPRM-RTL generalizes across RTL languages and provides a scalable framework for high-fidelity, interpretable code generation, establishing a new standard for LLM-assisted hardware design automation.

Knowledge Graphs (KGs) are widely used to mitigate the limitations of Large Language Models (LLMs), such as outdated knowledge and hallucinations. Existing LLM-KG integration frameworks typically rely on predefined operators to retrieve factual knowledge from KGs and inject it into prompts for answer generation. This paradigm faces two critical bottlenecks: 1) Inflexibility: The predefined operators are limited in scope and thus lack sufficient compositional expressiveness to fully capture the complex semantics required by KG questions. 2) Unscalability: Direct injection of factual knowledge into prompts limits scalability in handling large-scale factual knowledge. To address these two bottlenecks, we propose Code-on-Graph (CoG), a programmatic reasoning framework for LLM-KG integration. Specifically, given the factual knowledge retrieved at each reasoning step, CoG first identifies the corresponding KG schemas and represents these schemas as Python classes, which serve as abstract interfaces to the retrieved facts. It then generates executable code grounded in these classes, with the retrieved facts instantiated as objects of the corresponding classes during execution. This design enables flexible code-based reasoning while avoiding the direct injection of large-scale factual knowledge into prompts. Experiments on WebQSP, CWQ, and GrailQA demonstrate that CoG outperforms prior state-of-the-art models by up to 10.5%.

Vision-language models (VLMs) have been explored for visual programming, where they generate code to solve visual tasks. However, most prior work focuses on visual programming for productivity; it remains unclear how well current VLMs perform on education-oriented visual programming and what factors limit their performance. To bridge this gap, we introduce TurtleAI, a benchmark containing 823 tasks curated based on real-world visual programming tasks in the Turtle Graphics domain. Solving these tasks requires models to perceive geometric patterns, reason about spatial relationships, and synthesize Python code that faithfully reproduces geometric patterns. We evaluate 20+ VLMs, including GPT-5, GPT-4o, and Qwen2-VL-72B, and find that they struggle significantly, with most achieving success rates below 30%. To address these limitations, we propose a data generation technique that requires only a small set of seed samples. Fine-tuning Qwen2-VL-72B on the resulting synthetic data yields an improvement of about 20% on real-world tasks. Our failure analysis reveals that GPT-4o struggles with spatial reasoning and precise visual replication, whereas fine-tuning primarily improves the alignment between visual reasoning and code implementation.

Production inference increasingly targets a heterogeneous mix of accelerators. Agentic pipelines interleave reasoning, tool calls, and multi-agent coordination, each with distinct compute and memory profiles. For optimal efficiency, each stage should run on the accelerator best suited to it. This creates a systems challenge: each pipeline now requires high-performance kernels across a growing set of hardware backends and programming models. Writing these kernels by hand is time-consuming, demands deep low-level expertise, and does not scale as kernel complexity grows. Recently, Large Language Models (LLMs) have been leveraged for automatic kernel generation, but challenges in low-level code generation and cross-backend generalization persist. We present KForge, a cross-platform framework built around an iterative refinement loop driven by two collaborating LLM-based agents: a generation agent that produces and progressively refines kernels using compilation and correctness feedback, and a performance-analysis agent that interprets profiling data, from programmatic APIs to GUI-based tools, and emits recommendations that steer the next round of synthesis. The loop alternates between functional passes, which drive a candidate to correctness, and optimization passes, which close the performance gap to hand-tuned baselines. We evaluate KForge on two backends with very different baseline reference availability. On NVIDIA B200, KForge achieves a 2.12$\%$ improvement in end-to-end throughput compared to TensorRT-LLM on the gpt-oss-20b inference speed benchmark. On Intel Arc B580, KForge generates Triton kernels achieving a 5.13$\times$ geometric mean speedup over the faster of PyTorch eager and torch.compile on 37 GEMM + tail-ops workloads from KernelBench Level 2, primarily via operator fusion and mixed-precision execution.