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Neural network width linked to real projective space immersions

By PulseAugur Editorial · [1 sources] ·

This paper delves into the minimal width required for deep neural networks to approximate continuous functions. It establishes a connection between the approximation capabilities of neural networks and the field of differential topology, specifically concerning the immersion of real projective space. The research demonstrates that the minimal width is at least n+min{n,m} under certain conditions, extending previous findings for ReLU networks when n is 2, 3, 4, 7, or 8. AI

IMPACT Explores theoretical limits of neural network capacity, potentially informing future architectural designs.

RANK_REASON Academic paper on theoretical aspects of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

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

Neural network width linked to real projective space immersions

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14 / 100
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Academic paper on theoretical aspects of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · BaoZhi Chu, Ben Weinkove ·

    The minimal width of neural networks and immersions of real projective space

    arXiv:2610.20229v1 Announce Type: cross Abstract: We investigate the minimal width of deep neural networks that can approximate all continuous functions from $\mathbb{R}^n$ to $\mathbb{R}^m$ in the topology of uniform convergence on compact subsets. We show that whenever the real…

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