Many decoding methods for large language models can be understood as shifting probability mass toward outputs that are more likely under the model, either locally at the token level or globally at the sequence level. Therefore, their success depends on a fundamental question: when does sequence probability, that is, the conditional probability of a continuation given a prompt, actually align with correctness? In this paper, we set out to quantify this relationship across decoding methods, models, and benchmarks at four levels: across decoding methods, across hyperparameters within a method, across prompt-answer pairs within a dataset, and across repeated responses to the same prompt. We find that higher sequence probability is often predictive of correctness across prompt-answer pairs within a fixed dataset. However, this relationship does not generally transfer to decoding decisions: increasing sequence probability by changing hyperparameters or methods does not reliably improve accuracy. Further, sequence probability is not a good indicator of correctness for responses to the same prompt. These findings clarify when decoding can and cannot be expected to improve correctness, and provide practical guidance for decoding, self-consistency, and verifier-free self-improvement.

Compilers, while essential, are notoriously complex systems that demand prohibitively expensive human expertise to develop and maintain. The recent advancements in Large Language Models (LLMs) offer a compelling new paradigm: Neural Compilation, which could potentially simplify compiler development for new architectures and facilitate the discovery of innovative optimization techniques. However, several critical obstacles impede its practical adoption. Firstly, a significant lack of dedicated benchmarks and robust evaluation methodologies hinders objective assessment and tracking of progress in the field. Secondly, systematically enhancing the reliability and performance of LLM-generated assembly remains a critical challenge.

Optimizing Register Transfer Level (RTL) code is crucial for improving the efficiency and performance of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts.

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

The remarkable progress of Large Language Models (LLMs) presents promising opportunities for Verilog code generation which is significantly important for automated circuit design. The lacking of meaningful functional rewards hinders the preference optimization based on Reinforcement Learning (RL) for producing functionally correct Verilog code. In this paper, we propose Signal-Aware Learning for Verilog code generation (QiMeng-SALV) by leveraging code segments of functionally correct output signal to optimize RL training. Considering Verilog code specifies the structural interconnection of hardware gates and wires so that different output signals are independent, the key insight of QiMeng-SALV is to extract verified signal-aware implementations in partially incorrect modules, so as to enhance the extraction of meaningful functional rewards. Roughly, we verify the functional correctness of signals in generated module by comparing with that of reference module in the training data. Then abstract syntax tree (AST) is employed to identify signal-aware code segments which can provide meaningful functional rewards from erroneous modules. Finally, we introduce signal-aware DPO which is optimized on the correct signal-level code segments, thereby preventing noise and interference from incorrect signals. The proposed QiMeng-SALV underscores the paradigm shift from conventional module-level to fine-grained signal-level optimization in Verilog code generation, addressing the issue of insufficient functional rewards. Experiments demonstrate that our method achieves state-of-the-art performance on VerilogEval and RTLLM, with a 7B parameter model matching the performance of the DeepSeek v3 671B model and significantly outperforming the leading open-source model CodeV trained on the same dataset.

How can we trust the correctness of a learned model on a particular input of interest? Model accuracy is typically measured on average over a distribution of inputs, giving no guarantee for any fixed input. This paper proposes a theoreticallyfounded solution to this problem: to train Self-Proving models that prove the correctness of their output to a verification algorithm V via an Interactive Proof. SelfProving models satisfy that, with high probability over an input sampled from a given distribution, the model generates a correct output and successfully proves its correctness to V. The soundness property of V guarantees that, for every input, no model can convince V of the correctness of an incorrect output. Thus, a Self-Proving model proves correctness of most of its outputs, while all incorrect outputs (of any model) are detected by V. We devise and analyze two generic methods for learning Self-Proving models: Transcript Learning (TL) which relies on access to transcripts of accepting interactions, and Reinforcement Learning from Verifier Feedback (RLVF) which trains a model by emulating interactions with the verifier.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce SelfPlay Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, SPC can guide the test-time search of diverse LLMs and significantly improve their mathematical reasoning performance on MATH500 and AIME2024, surpassing those guided by state-of-the-art process reward models.

Text-to-SQL systems translate natural language (NL) questions into SQL queries, enabling non-technical users to interact with structured data. While large language models (LLMs) have shown promising results on the text-to-SQL task, they often produce semantically incorrect yet syntactically valid queries, with limited insight into their reliability. We propose SQLENS, an end-to-end framework for fine-grained detection and correction of semantic errors in LLM-generated SQL. SQLENS integrates error signals from both the underlying database and the LLM to identify potential semantic errors within SQL clauses. It further leverages these signals to guide query correction. Empirical results on two public benchmarks show that SQLENS outperforms the best LLM-based self-evaluation method by 25.78% in F1 for error detection, and improves execution accuracy of out-of-thebox text-to-SQL systems by up to 20%.

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Programming assistants powered by large language models have improved dramatically, yet existing benchmarks still evaluate them in narrow code-generation settings. Recent efforts such as InfiBench and StackEval rely on Stack Overflow questions and remain limited to single-turn interactions, manually curated data, and isolated snippets rather than full project environments. We introduce CodeAssistBench (CAB), the first benchmark for evaluating multi-turn, project-grounded programming assistance at scale. CAB automatically constructs datasets from GitHub issues tagged as questions, using an LLM-driven pipeline that filters noise, extracts runnable contexts, builds executable containers, and verifies environment correctness. This enables continuous, automated expansion across diverse repositories without manual intervention. Using CAB, we create a testbed of 3,286 real-world issues across 214 repositories, spanning seven languages. Evaluating state-of-theart models reveals a substantial gap: while models achieve 70-83% accuracy on Stack Overflow-style questions, they solve only 7.22-16.49% of CAB issues from post-training-cutoff repositories. These results highlight a fundamental challenge: current LLMs struggle to provide assistance in realistic, project-specific contexts despite strong performance on traditional Q&A benchmarks. CAB provides a scalable, reproducible framework for advancing research in multi-turn, codebasegrounded programming agents.