Speed Limit for Information Acquisition in Stochastic Learning Dynamics
Neural networks acquire internal representations through learning. In this work, we formulate stochastic gradient descent (SGD) as a Markovian stochastic process and derive a Fisher-information flow speed limit that bounds the rate at which trainable parameters can acquire information about latent variables in the data-generating process. The resulting inequality decomposes the information flow into drift and noise contributions, thereby quantifying the roles of deterministic learning forces and SGD-induced fluctuations from an information-theoretic perspective. We verify the bound in analytically tractable basis-function linear regression, where the information budget predicted by the bo...
| Authors | Shuta Kobayashi, Andreas Dechant |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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