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Large Language Models exhibit impressive reasoning capabilities across diverse tasks, motivating efforts to distill these capabilities into smaller models through generated reasoning data. However, direct training on such synthesized…

Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on…

Reasoning Large Language Models (RLLMs) have demonstrated impressive performance on complex tasks, largely due to the adoption of Long Chain-of-Thought (Long CoT) reasoning. However, they often exhibit overthinking -- performing unnecessary…

Large Language Models (LLMs) have shown impressive performance in reasoning tasks. However, LLMs tend to generate excessively long reasoning content, leading to significant computational overhead. Our observations indicate that even on…

Large language models (LLMs) like GPT-4, DeepSeek-R1, and ReasonFlux have shown significant improvements in various reasoning tasks. However, smaller LLMs still struggle with complex mathematical reasoning because they fail to effectively…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning…

We analyze reasoning in language models during task-specific fine-tuning and draws parallel between reasoning tokens--intermediate steps generated while solving problem and the human working memory. Drawing from cognitive science, we align…

The long chain-of-thought (LongCoT) capability is central to the recent breakthroughs achieved by large language models in complex reasoning tasks. However, the accompanying issue of ''underthinking'', where models exhibit shallow reasoning…

As reasoning LLMs increasingly trade tokens for accuracy through deliberation, search, and self-correction, a single accuracy score can no longer tell whether those tokens buy useful reasoning, recovery from hard instances, or unnecessary…

Large reasoning models (LRMs) have demonstrated remarkable proficiency in tackling complex tasks through step-by-step thinking. However, this lengthy reasoning process incurs substantial computational and latency overheads, hindering the…

Large reasoning models (LRMs) often consume excessive tokens, inflating computational cost and latency. More broadly, in goal reaching sequential decision problems we often want to reach the goal quickly, and LRM reasoning can be viewed…

Reasoning-enhanced large language models (LLMs) explicitly generate intermediate reasoning steps prior to generating final answers, helping the model excel in complex problem-solving. In this paper, we demonstrate that this emerging…

Mathematical reasoning tasks pose significant challenges for large language models (LLMs) because they require precise logical deduction and sequence analysis. In this work, we introduce the concept of critical tokens -- elements within…

In high-dimensional classification settings, we wish to seek a balance between high power and ensuring control over a desired loss function. In many settings, the points most likely to be misclassified are those who lie near the decision…

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing…

Recent advances in large language models (LLMs) have shown that test-time scaling can substantially improve model performance on complex tasks, particularly in the coding domain. Under this paradigm, models use a larger token budget during…

Large language models (LLMs) such as GPT-5 and Gemini 3 have pushed the frontier of automated reasoning and code generation. Yet current benchmarks emphasize accuracy and output quality, neglecting a critical dimension: efficiency of token…

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response,…

Large Reasoning Models (LRMs) have demonstrated impressive capabilities but suffer from cognitive inefficiencies like "overthinking" simple problems and "underthinking" complex ones. While existing methods that use supervised fine-tuning…