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Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…

An essential element of human mathematical reasoning is our number sense -- an abstract understanding of numbers and their relationships -- which allows us to solve problems involving vast number spaces using limited computational…

Understanding the limitations of Large Language Models, or LLMs, in mathematical reasoning has been the focus of several recent studies. However, the majority of these studies use the same datasets for benchmarking, which limits the…

Despite the remarkable advancements and widespread applications of deep neural networks, their ability to perform reasoning tasks remains limited, particularly in domains requiring structured, abstract thought. In this paper, we investigate…

It remains an open question whether LLMs can acquire or generalize genuinely new reasoning strategies, beyond the sharpened skills encoded in their parameters during pre-training or post-training. To attempt to answer this debate, we…

Large Language Models (LLMs) have unveiled remarkable capabilities in understanding and generating both natural language and code, but LLM reasoning is prone to hallucination and struggle with complex, novel scenarios, often getting stuck…

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality…

Large language models (LLMs) are often constrained by rigid reasoning processes, limiting their ability to generate creative and diverse responses. To address this, a novel framework called LADDER is proposed, combining Chain-of-Thought…

Recent reasoning large language models (LLMs), such as OpenAI o1 and DeepSeek-R1, exhibit strong performance on complex tasks through test-time inference scaling. However, prior studies have shown that these models often incur significant…

Large Language Models (LLMs) possess substantial reasoning capabilities and are increasingly applied to optimization tasks, particularly in synergy with evolutionary computation. However, while recent surveys have explored specific aspects…

Recent breakthroughs in generative reasoning have fundamentally reshaped how large language models (LLMs) address complex tasks, enabling them to dynamically retrieve, refine, and organize information into coherent multi-step reasoning…

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…

Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core…

While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains…

Large language models (LLMs) have shown significant progress in reasoning tasks. However, recent studies show that transformers and LLMs fail catastrophically once reasoning problems exceed modest complexity. We revisit these findings…

Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…

The rapid advancement of large language models has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate the strategic reasoning capabilities of LLMs, game theory, with its concise…

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…

Integrating reasoning in large language models and large vision-language models has recently led to significant improvement of their capabilities. However, the generalization of reasoning models is still vaguely defined and poorly…