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We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…

The human-like reasoning capabilities exhibited by Large Language Models (LLMs) challenge the traditional neural network theory's understanding of the flexibility of fixed-parameter systems. This paper proposes the "Cognitive Activation"…

To what degree should we ascribe cognitive capacities to Large Language Models (LLMs), such as the ability to reason about intentions and beliefs known as Theory of Mind (ToM)? Here we add to this emerging debate by (i) testing 11 base- and…

Reasoning based on Large Language Models (LLMs) has garnered increasing attention due to outstanding performance of these models in mathematical and complex logical tasks. Beginning with the Chain-of-Thought (CoT) prompting technique,…

We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on $2^\omega$, the so-called proper sequences. Our main results are as follows: (1) We…

The capabilities of large language models (LLMs) have been enhanced by training on data that reflects human thought processes, such as the Chain-of-Thought format. However, evidence suggests that the conventional scheme of next-word…

Why does weight decay work? We prove that, in any fixed-precision regime, the smallest weight norm of a looped neural network outputting a binary string equals the Kolmogorov complexity of that string, up to a logarithmic factor. This…

We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable…

Large language models (LLMs) are increasingly used in the social sciences to simulate human behavior, based on the assumption that they can generate realistic, human-like text. Yet this assumption remains largely untested. Existing…

Large Language Models (LLMs) have demonstrated potential in predicting mental health outcomes from online text, yet traditional classification methods often lack interpretability and robustness. This study evaluates structured reasoning…

Large language models (LLMs) demonstrate significant reasoning capabilities, particularly through long chain-of-thought (CoT) processes, which can be elicited by reinforcement learning (RL). However, prolonged CoT reasoning presents…

Theory of Mind (ToM) is the ability to understand and reflect on the mental states of others. Although this capability is crucial for human interaction, testing on Large Language Models (LLMs) reveals that they possess only a rudimentary…

Mathematical Word Problems (MWPs) are among the most challenging tasks in natural language processing because they require both linguistic understanding and multi-step numerical reasoning. While Chain-of-Thought (CoT) prompting has shown…

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT,…

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of…

Large Language Models (LLMs) have recently achieved impressive results in complex reasoning tasks through Chain of Thought (CoT) prompting. However, most existing CoT methods rely on using the same prompts, whether manually designed or…

The majority of research in computational psycholinguistics has concentrated on the processing of words. This study introduces innovative methods for computing sentence-level metrics using multilingual large language models. The metrics…

Reasoning about time and temporal relations is an integral aspect of human cognition, essential for perceiving the world and navigating our experiences. Though large language models (LLMs) have demonstrated impressive performance in many…

Like humans, Large Language Models (LLMs) struggle to generate high-quality long-form text that adheres to strict requirements in a single pass. This challenge is unsurprising, as successful human writing, according to the Cognitive Writing…

Large language models (LLMs) have rapidly progressed into general-purpose agents capable of solving a broad spectrum of tasks. However, current models remain inefficient at reasoning: they apply fixed inference-time compute regardless of…