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Neural network weight norm linked to Kolmogorov complexity

By PulseAugur Editorial · [1 sources] ·

Researchers have demonstrated a theoretical link between the weight norm of a neural network and the Kolmogorov complexity of the output string it generates. The study proves that in fixed-precision settings, the minimum weight norm of a looped neural network corresponds to the Kolmogorov complexity of its output, up to a logarithmic factor. This finding suggests that weight decay acts as a prior that aligns with Solomonoff's universal prior, which is optimal for computable functions. The proof relies on encoding Turing machine programs into neural weights and enumerating network parameters, with the logarithmic factor being realized by permutation encodings. AI

IMPACT Establishes a theoretical foundation for why weight decay is effective, potentially guiding future regularization techniques in neural networks.

RANK_REASON Academic paper published on arXiv detailing a theoretical finding in machine learning. [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 weight norm linked to Kolmogorov complexity

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Academic paper published on arXiv detailing a theoretical finding in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Tiberiu Musat ·

    Neural Weight Norm = Kolmogorov Complexity

    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 implies that weight decay induces a prior mat…

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