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Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we…

Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one…

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human…

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that…

The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their…

Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse…

Large language models (LLMs) have demonstrated remarkable potential across numerous applications and have shown an emergent ability to tackle complex reasoning tasks, such as mathematical computations. However, even for the simplest…

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle…

Large Language Models (LLMs) do not differentially represent numbers, which are pervasive in text. In contrast, neuroscience research has identified distinct neural representations for numbers and words. In this work, we investigate how…

Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis,…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

Brain localization, which describes the association between specific regions of the brain and their corresponding functions, is widely accepted in the field of cognitive science as an objective fact. Today's large language models (LLMs)…

Large language models (LLMs) have complicated internal dynamics, but induce representations of words and phrases whose geometry we can study. Human language processing is also opaque, but neural response measurements can provide (noisy)…

The cognitive mechanism by which Large Language Models (LLMs) solve mathematical problems remains a widely debated and unresolved issue. Currently, there is little interpretable experimental evidence that connects LLMs' problem-solving with…

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing…

The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in…

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in…

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…