Neuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large Models

Xiongye Xiao; Heng Ping; Chenyu Zhou; Defu Cao; Yaxing Li; Yi-Zhuo Zhou; Shixuan Li; Nikos Kanakaris; Paul Bogdan

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arXiv · 2402.09099

Neuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large Models

Xiongye Xiao·Heng Ping·Chenyu Zhou·Defu Cao·Yaxing Li·Yi-Zhuo Zhou·Shixuan Li·Nikos Kanakaris·Paul Bogdan

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Abstract

In recent years, there has been increasing attention on the capabilities of large models, particularly in handling complex tasks that small-scale models are unable to perform. Notably, large language models (LLMs) have demonstrated ``intelligent'' abilities such as complex reasoning and abstract language comprehension, reflecting cognitive-like behaviors. However, current research on emergent abilities in large models predominantly focuses on the relationship between model performance and size, leaving a significant gap in the systematic quantitative analysis of the internal structures and mechanisms driving these emergent abilities. Drawing inspiration from neuroscience research on brain network structure and self-organization, we propose (i) a general network representation of large models, (ii) a new analytical framework, called Neuron-based Multifractal Analysis (NeuroMFA), for structural analysis, and (iii) a novel structure-based metric as a proxy for emergent abilities of large models. By linking structural features to the capabilities of large models, NeuroMFA provides a quantitative framework for analyzing emergent phenomena in large models. Our experiments show that the proposed method yields a comprehensive measure of network's evolving heterogeneity and organization, offering theoretical foundations and a new perspective for investigating emergent abilities in large models.

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Xiongye Xiao, Heng Ping, Chenyu Zhou, Defu Cao, Yaxing Li, Yi-Zhuo Zhou, Shixuan Li, Nikos Kanakaris, Paul Bogdan. 2024-02-14. Neuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large Models. https://arxiv.org/abs/2402.09099

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