Algorithmic Information Dynamics of Learning: A Certified, Differentiable Complexity Controller for Grokking

arXiv:2609.13197v1 Announce Type: new Abstract: Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the Block Decomposition Method, is piecewise constant, restricting the calculus to finite differences. We use $K^{\mathrm{CDM}}_{\mathrm{s}F}$, a certified, differentiable estimator, to bring the calculus into learning dynamics: grokking, where a complexity order parameter is known but has not been made to act. A\empts a transient loss kick, the estimator becomes a controller that accelerates grokking in Levin's description-length--versus-time sense, within a data-dependent Occam boundary whose finite-size trend, $f_c\sim\ln p/p$, is consistent with a coupon-collector interpretation. Ablations show that a complexity gate matches a train-loss gate in rescuing failing seeds with $27\%$ less intervention; among the tested signals, only map complexity marks the transition's completion; the certified prior and the per-parameter $\nabla K$ attribution are both fungible (a uniform-prior sensor makes bit-identical gate decisions, and random supports match $\nabla K$-selected ones above a sparsity threshold); and direct field perturbation shows a nucleation-like response to the Occam field (no linear regime is resolved over the probed amplitudes, so these measurements do not justify a fluctuation--dissipation surrogate), with a finite-field response growing by orders of magnitude toward the transition. These measurements account for the empirically tuned staircase: bang--bang pulses, stall-

Technical result, unclear societal impact

The research develops a new method for controlling learning dynamics, potentially accelerating grokking (a phase transition in learning), which could improve AI training efficiency. However, the paper is highly technical with limited direct societal claims, so the broader impact is uncertain and likely minimal in the near term.

This is a narrow theoretical contribution to understanding neural network training dynamics (grokking), with no direct claims about societal impact, capability jumps, or deployment. It has no bearing on human flourishing beyond incremental ML research value.

SOURCE     arXiv cs.LG (Machine Learning) (tier 1)
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DOCUMENT   aac1f344-2b19-4e6e-a9f2-852d3de6dce2
           https://arxiv.org/abs/2609.13197
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EVIDENCE   1 extracted excerpt
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MODEL RUN  3 runs, methodology 1.0.1
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SCORE      +4  (Mixed or uncertain)
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CONFIDENCE 70%