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Shallow Neural Networks Over Finite Fields Explored in New Research

By PulseAugur Editorial · [1 sources] ·

Researchers have explored the expressivity of shallow polynomial neural networks (PNNs) utilizing monomial activation functions over finite fields. They defined a 'neuromanifold' for a given architecture as the image of the map from network weights to product polynomial rings, quantifying expressivity by the neuromanifold's cardinality. This work connects to counting rational points over finite fields and the Weil conjectures, revealing a significant difference in neuromanifolds between characteristic zero and finite-characteristic fields, highlighting the importance of field characteristic. AI

IMPACT This research contributes to the theoretical understanding of neural network expressivity, potentially influencing future model design and analysis.

RANK_REASON Academic paper published on arXiv detailing theoretical research into neural networks. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.NE (Neural & Evolutionary) →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Shallow Neural Networks Over Finite Fields Explored in New Research

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Academic paper published on arXiv detailing theoretical research into neural networks. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Yifei Chen ·

    Expressivity of Shallow Neural Networks Over Finite Fields

    We study the expressivity of shallow polynomial neural networks (PNNs) with monomial activation functions over finite fields. For a given architecture, we define a neuromanifold as the image of the map from all possible network weights into the product of polynomial rings. We qua…

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