Recent reports claim that large language models (LLMs) now outperform elite humans in competitive programming. Drawing on knowledge from a group of medalists in international algorithmic contests, we revisit this claim, examining how LLMs differ from human experts and where limitations still remain. We introduce LiveCodeBench Pro, a benchmark composed of problems from Codeforces, ICPC, and IOI that are continuously updated to reduce the likelihood of data contamination. A team of Olympiad medalists annotates every problem for algorithmic categories and conducts a line-by-line analysis of failed model-generated submissions. Using this new data and benchmark, we find that frontier models still have significant limitations: without external tools, the best model achieves only 53\% pass@1 on medium-difficulty problems and 0\% on hard problems, domains where expert humans still excel. We also find that LLMs succeed at implementation-heavy problems but struggle with nuanced algorithmic reasoning and complex case analysis, often generating confidently incorrect justifications. High performance appears largely driven by implementation precision and tool augmentation, not superior reasoning. LiveCodeBench Pro thus highlights the significant gap to human grandmaster levels, while offering fine-grained diagnostics to steer future improvements in code-centric LLM reasoning.

Combining diverse foundation models is promising, but weight-merging is limited by mismatched architectures and closed APIs. The coordinator, comprising a compact language model ( 0.6B parameters) and a lightweight head ( 10K parameters), is optimized with an evolutionary strategy for efficient and adaptive delegation. Theoretical and empirical analyses highlight two key factors driving this success: (1) the coordinator's hidden-state representations provide rich contextualization of inputs, and (2) under high dimensionality and strict budget constraints, the separable Covariance Matrix Adaptation Evolution Strategy algorithm provides substantial advantages over RL, imitation learning, and random search, leveraging potential block-ε-separability. A prominent line of work involving large language models (LLMs) aspires to scale in line with empirical scaling laws, targeting gains by enlarging model size, training tokens, and compute (Kaplan et al., 2020; Hoffmann et al., 2022). Y et the extent to which such scaling remains efficient and yields sustained returns is uncertain and often resource intensive. An alternative at the micro level is model merging (Akiba et al., 2025; Wortsman et al., 2022; Y ang et al., 2024; Kuroki et al., 2024), which seeks parameter-level integration. However, this approach is frequently impractical due to architectural incompatibilities and the closed-source nature of many high-performing models. In light of these limitations, we adopt a macro-level approach: test-time model composition via coordination, which fuses the complementary strengths of multiple state-of-the-art models from diverse providers without modifying their weights. Leveraging prior data and training investments, this coordination can deliver performance improvements without retraining individual models. The central challenge for such a coordinator is to acquire a rich contextual understanding of a given query to make an effective decision. We posit that this signal can be efficiently extracted from the internal representation of a compact language model, specifically, its hidden states (Allen-Zhu & Li, 2023). In a self-attention-based transformer model, hidden states encode contextual representations of the input (and, after generation, the output) sequence.

Inference-time scaling trades efficiency for increased reasoning accuracy by generating longer or more parallel sequences. However, in Transformer LLMs, generation cost is bottlenecked by the size of the key-value (KV) cache, rather than the number of generated tokens. Hence, we explore inference-time hyper-scaling: by compressing the KV cache, we can generate more tokens within the same compute budget and further improve the accuracy of scaled inference. The success of this approach, however, hinges on the ability of compression methods to preserve accuracy even at high compression ratios. To make hyper-scaling practical, we introduce Dynamic Memory Sparsification (DMS), a novel method for sparsifying KV caches that only requires 1K training steps to achieve 8$\times$ compression, while maintaining better accuracy than training-free sparse attention. Instead of prematurely discarding cached tokens, DMS delays token eviction, implicitly merging representations and preserving critical information. We demonstrate the effectiveness of inference-time hyper-scaling with DMS on multiple families of LLMs, showing that it boosts accuracy for comparable inference latency and memory load. For instance, we enhance Qwen-R1 32B by 12.0 points on AIME 24, 8.6 on GPQA, and 9.7 on LiveCodeBench on average for an equivalent number of memory reads.

Large Language Models (LLMs) have achieved remarkable success in code generation, and the race to improve their performance has become a central focus of AI research. Benchmarks and leaderboards are increasingly popular, offering quantitative rankings of LLMs. However, they provide limited insight into the tasks that LLMs consistently fail to solve - information that is crucial for understanding current limitations and guiding the development of more capable models. To address this gap, we examined code generation tasks across four popular benchmarks, identifying those that major LLMs are most likely to fail. To understand the causes of these failures, we investigated whether the static complexity of solution code contributes to them, followed by a systematic inspection of 114 tasks that LLMs consistently struggled with. Our analysis revealed four recurring patterns of weaknesses in LLMs, as well as common complications within benchmark tasks that most often lead to failure.

Large Language Models (LLMs) have achieved remarkable progress in code-related tasks. Despite their advancement, empirical evidence reveals that they still struggle with \emph{deductive code reasoning}, the ability to reason about the program execution process. While prior studies have recognized this limitation, the underlying causes remain largely underexplored. In this paper, we begin by presenting a comprehensive empirical study that reveals three key challenges undermining deductive code reasoning: (1) an intrinsic gap between generation and reasoning abilities, (2) a consistent bias towards code sources, and (3) weak zero-shot generalization on complex benchmarks. In light of these challenges, we propose \texttt{ReMind}, a multi-agent framework composed of \texttt{Mutator}, \texttt{Executor}, and \texttt{Inspector}. The \texttt{Mutator} generates code variants to mitigate bias towards code sources, the \texttt{Executor} traces variable states step-by-step to expose inconsistency, and the \texttt{Inspector} identifies problematic reasoning steps and provides control-flow refinement to bridge the intrinsic reasoning gap. Through their coordinated collaboration, \texttt{ReMind} systematically identifies and refines reasoning flaws, achieving outstanding performance and enabling robust zero-shot generalization. Extensive experiments on two benchmarks with five LLMs demonstrate the superior advantages of \texttt{ReMind} compared to baseline approaches in deductive code reasoning.

Today's pursuit of a single Large Language Model (LMM) for all software engineering tasks is resource-intensive and overlooks the potential benefits of complementarity, where different models contribute unique strengths. However, the degree to which coding LLMs complement each other and the best strategy for maximizing an ensemble's potential are unclear, leaving practitioners without a clear path to move beyond single-model systems. To address this gap, we empirically compare ten individual LLMs from five families, and three ensembles of these LLMs across three software engineering benchmarks covering code generation and program repair. We assess the complementarity between models and the performance gap between the best individual model and the ensembles. Next, we evaluate various selection heuristics to identify correct solutions from an ensemble's candidate pool. We find that the theoretical upperbound for an ensemble's performance can be 83% above the best single model. Our results show that consensus-based strategies for selecting solutions fall into a "popularity trap," amplifying common but incorrect outputs. In contrast, a diversity-based strategy realizes up to 95% of this theoretical potential, and proves effective even in small two-model ensembles, enabling a cost-efficient way to enhance performance by leveraging multiple LLMs.

The application of Reinforcement Learning with Verifiable Rewards (RLVR) to mathematical and coding domains has demonstrated significant improvements in the reasoning and problem-solving abilities of Large Language Models. Despite its success in single generation problem solving, the reinforcement learning fine-tuning process may harm the model's exploration ability, as reflected in decreased diversity of generations and a resulting degradation of performance during Best-of-N sampling for large N values. In this work, we focus on optimizing the max@k metric, a continuous generalization of pass@k. We derive an unbiased on-policy gradient estimate for direct optimization of this metric. Furthermore, we extend our derivations to the off-policy updates, a common element in modern RLVR algorithms, that allows better sample efficiency. Empirically, we show that our objective effectively optimizes max@k metric in off-policy scenarios, aligning the model with the Best-of-N inference strategy.

Reasoning models represent a significant advance in LLM capabilities, particularly for complex reasoning tasks such as mathematics and coding. Previous studies confirm that parallel test-time compute-sampling multiple solutions and selecting the best one-can further enhance the predictive performance of LLMs. However, strategies in this area often require complex scoring, thus increasing computational cost and complexity. In this work, we demonstrate that the simple and counterintuitive heuristic of selecting the shortest solution is highly effective. We posit that the observed effectiveness stems from models operating in two distinct regimes: a concise, confident conventional regime and a verbose overthinking regime characterized by uncertainty, and we show evidence of a critical point where the overthinking regime begins to be significant. By selecting the shortest answer, the heuristic preferentially samples from the conventional regime. We confirm that this approach is competitive with more complex methods such as self-consistency across two challenging benchmarks while significantly reducing computational overhead. The shortest-answer heuristic provides a Pareto improvement over self-consistency and applies even to tasks where output equality is not well defined.

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

Reliable verifiable data has become a key driver of capability gains in modern language models, enabling stable reinforcement learning with verifiable rewards and effective distillation that transfers competence across math, coding, and agentic tasks. Yet constructing generalizable synthetic verifiable data remains difficult due to hallucination-prone generation, and weak or trivial verification artifacts that fail to separate strong from weak solutions. Existing approaches often rely on task-specific heuristics or post-hoc filters that do not transfer across domains and lack a principled, universal evaluator of verifiability. In this work, we introduce an evolutionary, task-agnostic, strategy-guided, executably-checkable data synthesis framework that, from minimal seed supervision, jointly synthesizes problems, diverse candidate solutions, and verification artifacts, and iteratively discovers strategies via a consistency-based evaluator that enforces agreement between human-annotated and strategy-induced checks. This pipeline upgrades filtering into principled synthesis: it reliably assembles coherent, verifiable training instances and generalizes without domain-specific rules. Our experiments demonstrate the effectiveness of the proposed approach under both RLVR and model distillation training paradigms. The results show that training with our synthesized data yields significant improvements on both the LiveCodeBench and AgentBench-OS tasks, highlighting the robust generalization of our framework.