Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser ($x$-prediction) and noise-prediction ($\epsilon$-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models (LLMs) have unveiled their promising capabilities to formalize even competition-level math problems. However, we observe a considerable discrepancy between pass@1 and pass@k accuracies in LLM-generated formalizations. To address this gap, we introduce a novel framework that scores and selects the best result from k autoformalization candidates based on two complementary self-consistency methods: symbolic equivalence and semantic consistency. Elaborately, symbolic equivalence identifies the logical homogeneity among autoformalization candidates using automated theorem provers, and semantic consistency evaluates the preservation of the original meaning by informalizing the candidates and computing the similarity between the embeddings of the original and informalized texts. Our extensive experiments on the MATH and miniF2F datasets demonstrate that our approach significantly enhances autoformalization accuracy, achieving up to 0.22-1.35x

In the domain of code generation, self-debugging is crucial. It allows LLMs to refine their generated code based on execution feedback. This is particularly important because generating correct solutions in one attempt proves challenging for complex tasks. Prior works on self-debugging mostly focus on prompting methods by providing LLMs with few-shot examples, which work poorly on small open-sourced LLMs. In this work, we propose LeDex, a training framework that significantly improves the self-debugging capability of LLMs. Intuitively, we observe that a chain of explanations on the wrong code followed by code refinement helps LLMs better analyze the wrong code and do refinement. We thus propose an automated pipeline to collect a high-quality dataset for code explanation and refinement by generating a number of explanations and refinement trajectories from the LLM itself or a larger teacher model and filtering via execution verification. We perform supervised fine-tuning (SFT) and further reinforcement learning (RL) on both success and failure trajectories with a novel reward design considering code explanation and refinement quality.

Large Language Models (LLMs) with vast context windows offer new avenues for in-context learning (ICL), where providing many examples ("many-shot" prompting) is often assumed to enhance performance. We investigate this assumption for the complex task of code translation. Through a large-scale empirical study of over 90,000 translations, we systematically evaluate the impact of scaling in-context examples from zero-shot to many-shot configurations of up to 625 examples, with prompts spanning from approximately 100,000 to 800,000 tokens. Our findings reveal a "many-shot paradox": while static similarity metrics may modestly improve with more examples, functional correctness consistently peaks with few-shot prompting (5-25 examples). Providing substantially more examples often degrades this crucial functional performance. This study highlights that for code translation, the quality of a few well-chosen examples outweighs sheer quantity, challenging the universal efficacy of "more is better" for ICL and underscoring the task-dependent nature of optimal prompting strategies. Our results have significant implications for effectively leveraging LLMs in software engineering.

Large Language Model (LLM)-based agents demonstrate advanced reasoning capabilities, yet practical constraints frequently limit outputs to single responses, leaving significant performance potential unrealized. This paper introduces MARINE (Multi-Agent Recursive IN-context Enhancement), a theoretically grounded framework that reconceptualizes test-time reasoning as iterative refinement of a persistent reference trajectory, fundamentally departing from conventional one-shot or multi-sample paradigms. The MARINE refinement operator systematically converts a base model's pass@N capabilities into near-optimal pass@1 performance. Rigorous theoretical analysis establishes that minimal feasible batches maximize expected performance gains under fixed invocation budgets, while logarithmically growing batch schedules ensure continuous improvement without computational constraints. Comprehensive evaluation on the BrowserComp-ZH benchmark demonstrates state-of-the-art results, with a 685B-parameter implementation achieving 46.0% pass@1 accuracy. Meanwhile, MARINE establishes a new paradigm for parameter-efficient reasoning: an 80B-parameter model augmented with MARINE matches the performance of standalone 1000B-parameter agents, reducing parameter requirements by over an order of magnitude. Notably, within a fixed computational budget, the proposed MARINE delivers higher-quality samples to alignment and optimization processes than traditional sampling-and-ranking strategies. Consequently, it has great potential to boost post-training efficiency.

Despite recent advances in LLMs, the task of code generation is still challenging. To cope, code selection algorithms select the best program from multiple programs generated by an LLM. However, existing algorithms can fail to identify the correct program, either because they fail to distinguish nonequivalent programs or because they rely on an LLM and assume it always correctly determines the output for every input. We present ExPairT-LLM, an exact learning algorithm for code selection that selects a program by posing two new types of queries to an LLM oracle: pairwise membership and pairwise equivalence. These queries are simpler for LLMs and enable ExPairT-LLM to identify the correct program through a tournament, which is robust to some LLM mistakes. We evaluate ExPairT-LLM on four popular code datasets. Its pass@1 (success rate) outperforms the state-of-the-art code selection algorithm on average by +13.0% and up to +27.1%. It also improves the pass@1 of LLMs performing complex reasoning by +24.0%.

The advent of strong generative AI has a considerable impact on various software engineering tasks such as code repair, test generation, or language translation. While tools like GitHub Copilot are already in widespread use in interactive settings, automated approaches require a higher level of reliability before being usable in industrial practice. In this paper, we focus on three aspects that directly influence the quality of the results: a) the effect of automated feedback loops, b) the choice of Large Language Model (LLM), and c) the influence of behavior-preserving code changes. We study the effect of these three variables on an automated C-to-Rust translation system. Code translation from C to Rust is an attractive use case in industry due to Rust's safety guarantees. The translation system is based on a generate-and-check pattern, in which Rust code generated by the LLM is automatically checked for compilability and behavioral equivalence with the original C code. For negative checking results, the LLM is re-prompted in a feedback loop to repair its output. These checks also allow us to evaluate and compare the respective success rates of the translation system when varying the three variables. Our results show that without feedback loops LLM selection has a large effect on translation success. However, when the translation system uses feedback loops the differences across models diminish. We observe this for the average performance of the system as well as its robustness under code perturbations. Finally, we also identify that diversity provided by code perturbations can even result in improved system performance.

While visual data augmentation remains a cornerstone for training robust vision models, it has received limited attention in visual language models (VLMs), which predominantly rely on large-scale real data acquisition or synthetic diversity. Consequently, they may struggle with basic perception tasks that conventional models handle reliably. Given the substantial cost of pre-training and fine-tuning VLMs, continue training on augmented data yields limited and diminishing returns. In this paper, we present Visual Augmentation Chain-of-Thought (V ACoT), a framework that dynamically invokes image augmentations during model inference. By incorporating post-hoc transformations such as denoising, VACoT substantially improves robustness on challenging and out-of-distribution inputs, especially in OCR-related adversarial scenarios. Distinct from prior approaches limited to local cropping, VACoT integrates a structured collection of general visual augmentations, broadening the query image views while reducing training complexity and computational overhead with efficient agentic reinforcement learning. W e propose a conditional reward scheme that encourages necessary augmentation while penalizing verbose responses, ensuring concise and effective reasoning in perception tasks. W e demonstrate the superiority of VACoT with extensive experiments on 13 perception benchmarks and further introduce AdvOCR to highlight the generalization benefits of post-hoc visual augmentations in adversarial scenarios.

Parallel sampling promises substantial gains in test-time scaling, but its effectiveness is sharply limited by diversity collapse, where models concentrate on a few modes and repeated samples produce the same mistakes. We propose the mode-conditioning (ModC) framework, which explicitly allocates test-time compute across reasoning modes using either specialist models or mode-specific prefixes. ModC consistently improves scaling across controlled graph-search tasks and large-scale reasoning benchmarks, spanning model families and sizes from 0.5B to 7B. On OpenThoughts, fine-tuning Qwen2.5-7B with ModC achieves a 4x efficiency gain over standard training while also improving the maximum attainable Pass@k. We further show that gradient clustering enables ModC without explicit mode labels, yielding up to 10% gains on datasets such as NuminaMath. Finally, we show that ModC improves reinforcement learning (RL) and can further boost diversity-inducing RL methods. These results demonstrate that standard training underutilizes the diversity in data, and that ModC provides a simple, effective remedy for unlocking the full benefits of diversity in test-time scaling.

Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this challenge, we propose \textbf{CA}usal \textbf{MA}thematician (\textbf{CAMA}), a two-stage causal framework that equips LLMs with explicit, reusable mathematical structure. In the learning stage, CAMA first constructs the \textbf{M}athematical \textbf{C}ausal \textbf{G}raph (\textbf{MCG}), a high-level representation of solution strategies, by combining LLM priors with causal discovery algorithms applied to a corpus of question-solution pairs. The resulting MCG encodes essential knowledge points and their causal dependencies. To better align the graph with downstream reasoning tasks, CAMA further refines the MCG through iterative feedback derived from a selected subset of the question-solution pairs. In the reasoning stage, given a new question, CAMA dynamically extracts a task-relevant subgraph from the MCG, conditioned on both the question content and the LLM's intermediate reasoning trace. This subgraph, which encodes the most pertinent knowledge points and their causal dependencies, is then injected back into the LLM to guide its reasoning process. Empirical results on real-world datasets show that CAMA significantly improves LLM performance on challenging mathematical problems. Furthermore, our experiments demonstrate that structured guidance consistently outperforms unstructured alternatives, and that incorporating asymmetric causal relationships yields greater improvements than using symmetric associations alone.