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Life sciences · Preprint
arXiv · September 8, 2026
Raises a question worth testing. It does not answer one.
This preprint derives a Fisher-information speed limit that bounds the rate at which stochastic gradient descent can acquire information about latent variables. The bound decomposes information flow into drift and noise terms and is verified analytically in basis-function linear regression, where it predicts the ordering and time scales of latent variable encoding. The work is exploratory theory and does not establish clinical, applied, or general-purpose empirical validity.
Theoretical derivation with analytical verification.
Fisher-information flow speed limit derived for SGD as a Markovian stochastic process Bound decomposes information acquisition into deterministic drift and SGD-induced noise contributions Verification in analytically tractable basis-function linear regression reproduces ordering and characteristic time scales of latent variable encoding
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The source did not state who this applies to in practice.
This is a theoretical framework deriving information-theoretic bounds on neural network learning; it raises mechanistic questions about how SGD acquires information rather than testing a clinical or applied empirical claim.
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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 bound reproduces the ordering and characteristic time scales with which different latent variables are encoded in the learned parameters. These results establish Fisher-information speed limits as a quantitative framework for diagnosing when and how different aspects of the data-generating mechanism are acquired during stochastic learning.
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