Verification of model outputs is rapidly emerging as a key primitive for both training and real-world deployment of large language models (LLMs). In practice, this often involves using imperfect LLM judges and reward models since ground truth acquisition can be time-consuming and expensive. We introduce Fully Unsupervised Score Ensembling (FUSE), a method for improving verification quality by ensembling verifiers without access to ground truth correctness labels. The key idea behind FUSE is to control conditional dependencies between verifiers in a manner that improves the unsupervised performance of a class of spectral algorithms from the ensembling literature. Despite requiring zero ground truth labels, FUSE typically matches or improves upon semi-supervised alternatives in test-time scaling experiments with diverse sets of generator models, verifiers, and benchmarks. In particular, we validate our method on both conventional academic benchmarks such as GPQA Diamond and on frontier, unsaturated benchmarks such as Humanity's Last Exam and IMO Shortlist questions.

Modern LLMs scale at test-time, e.g. via repeated sampling, where inference cost grows with model size and the number of samples. This creates a trade-off that pretraining scaling laws, such as Chinchilla, do not address. We present Train-to-Test ($T^2$) scaling laws that jointly optimize model size, training tokens, and number of inference samples under fixed end-to-end budgets. $T^2$ modernizes pretraining scaling laws with pass@$k$ modeling used for test-time scaling, then jointly optimizes pretraining and test-time decisions. Forecasts from $T^2$ are robust over distinct modeling approaches: measuring joint scaling effect on the task loss and modeling impact on task accuracy. Across eight downstream tasks, we find that when accounting for inference cost, optimal pretraining decisions shift radically into the overtraining regime, well-outside of the range of standard pretraining scaling suites. We validate our results by pretraining heavily overtrained models in the optimal region that $T^2$ scaling forecasts, confirming their substantially stronger performance compared to pretraining scaling alone. Finally, as frontier LLMs are post-trained, we show that our findings survive the post-training stage, making $T^2$ scaling meaningful in modern deployments.

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

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.

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.

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.

Recent large language models achieve strong reasoning performance by generating detailed chain-of-thought traces, but this often leads to excessive token use and high inference latency. Existing efficiency approaches typically focus on model-centric interventions, such as reinforcement learning or supervised fine-tuning, to reduce verbosity. In contrast, we propose a training-free, input-centric approach. Inspired by cognitive psychology, we introduce Focused Chain-of-Thought (F-CoT), which separates information extraction from the reasoning process. F-CoT first organizes the essential information from a query into a concise, structured context and then guides the model to reason exclusively over this context. By preventing attention to irrelevant details, F-CoT naturally produces shorter reasoning paths. On arithmetic word problems, F-CoT reduces generated tokens by 2-3x while maintaining accuracy comparable to standard zero-shot CoT. These results highlight structured input as a simple yet effective lever for more efficient LLM reasoning.