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Subword tokenization introduces a computational layer in language models where many distinct token sequences decode to the same surface form and preserve meaning, yet induce different internal computations. Despite this non-uniqueness,…

Recent reasoning large language models (LLMs) have demonstrated remarkable improvements in mathematical reasoning capabilities through long Chain-of-Thought. The reasoning tokens of these models enable self-correction within reasoning…

Chain-of-thought (CoT) supervision can substantially improve transformer performance, yet the mechanisms by which models learn to follow and benefit from CoT remain poorly understood. We investigate these learning dynamics through the lens…

Large language models solve complex tasks by generating long reasoning chains, achieving higher accuracy at the cost of increased computational cost and reduced ability to isolate functionally relevant reasoning. Prior work on compact…

Large Language Models (LLMs) have shown impressive performance on complex tasks through Chain-of-Thought (CoT) reasoning. However, conventional CoT relies on explicitly verbalized intermediate steps, which constrains its broader…

A major limitation for the broader scope of problems solvable by transformers is the quadratic scaling of computational complexity with input size. In this study, we investigate the recurrent memory augmentation of pre-trained transformer…

Current approaches for scaling inference-time compute in transformers train them to emit explicit chain-of-thought tokens before producing an answer. While these methods are powerful, they are limited because they cannot be applied during…

Chain-of-Thought (CoT) prompting has significantly advanced task-solving capabilities in natural language processing with large language models. Unlike standard prompting, CoT encourages the model to generate intermediate reasoning steps,…

Modern reasoning models, such as OpenAI's o1 and DeepSeek-R1, exhibit impressive problem-solving capabilities but suffer from critical inefficiencies: high inference latency, excessive computational resource consumption, and a tendency…

We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect…

Chain-of-Thought (CoT) prompting has improved the reasoning performance of large language models (LLMs), but it remains unclear why it works and whether it is the unique mechanism for triggering reasoning in large language models. In this…

In Transformer architectures, tokens\textemdash discrete units derived from raw data\textemdash are formed by segmenting inputs into fixed-length chunks. Each token is then mapped to an embedding, enabling parallel attention computations…

Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that…

This work provides the first theoretical analysis of training transformers to solve complex problems by recursively generating intermediate states, analogous to fine-tuning for chain-of-thought (CoT) reasoning. We consider training a…

The chain-of-thought (CoT) paradigm uses the elicitation of step-by-step rationales as a proxy for reasoning, gradually refining the model's latent representation of a solution. However, it remains unclear just how early a Large Language…

Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that…

Recent thinking models trained with reinforcement learning and backward-checking CoT often suffer from overthinking: they produce excessively long outputs even on simple problems, wasting computation. Existing evaluations, based on token…

With the success of language pretraining, it is highly desirable to develop more efficient architectures of good scalability that can exploit the abundant unlabeled data at a lower cost. To improve the efficiency, we examine the…

Large language models (LLMs) have demonstrated remarkable capabilities in tasks requiring reasoning and multi-step problem-solving through the use of chain-of-thought (CoT) prompting. However, generating the full CoT process results in…

Chain-of-thought (CoT) prompting combined with few-shot in-context learning (ICL) has unlocked significant reasoning capabilities in large language models (LLMs). However, ICL with CoT examples is ineffective on novel tasks when the…