Multiscale nonlinear integration drives accurate encoding of input information

Giorgio Nicoletti; Daniel M. Busiello

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arXiv · 2411.11710

Multiscale nonlinear integration drives accurate encoding of input information

Giorgio Nicoletti·Daniel M. Busiello

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Abstract

Biological and artificial systems encode information through several complex nonlinear operations, making their exact study a formidable challenge. These internal mechanisms often take place across multiple timescales and process external signals to enable functional output responses. In this work, we focus on two widely implemented paradigms: nonlinear summation, where signals are first processed independently and then combined; and nonlinear integration, where they are combined first and then processed. We study a general model where the input signal is propagated to an output unit through a processing layer via nonlinear activation functions. Further, we distinguish between the two cases of fast and slow processing timescales. We demonstrate that integration and fast-processing capabilities systematically enhance input-output mutual information over a wide range of parameters and system sizes, while simultaneously enabling tunable input discrimination. Moreover, we reveal that high-dimensional embeddings and low-dimensional projections emerge naturally as optimal competing strategies. Our results uncover the foundational features of nonlinear information processing with profound implications for both biological and artificial systems.

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Giorgio Nicoletti, Daniel M. Busiello. 2024-11-18. Multiscale nonlinear integration drives accurate encoding of input information. https://arxiv.org/abs/2411.11710

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