aiqbench analysis
This research identifies a specific inverted-U relationship where injecting stochastic noise into consolidation rules enhances task retention in continual learning up to an optimal threshold before degrading performance. The study isolates the mechanism as requiring coherent restoring forces toward consolidated weights and demonstrates that coupling anchor gain directly to noise variance recovers most of this benefit, outperforming existing adaptation methods like Ornstein-Uhlenbeck or MESU. While validated entirely in simulation on standard benchmarks, the findings offer a precise mathematical rule for stabilizing neural networks against catastrophic forgetting without relying on hardware-specific demonstrations.
A Noise Optimum in Rehearsal-Free Continual Learning: Isolation, Mechanism, and Scope
arXiv:2609.20162v1 Announce Type: new Abstract: Injecting stochastic noise into a consolidation rule can improve a network's retention of earlier tasks up to an optimal level, then degrade it -- an inverted-U in retention vs. noise. This paper isolates what produces that optimum and maps where it holds, entirely in simulation. (1) Phenomenon: the retention inverted-U appears on several related-task continual-learning benchmarks (Split-MNIST, FashionMNIST, continual Yin-Yang). (2) Isolation: a magnitude-matched ladder shows the effect requires coherent restoring toward the consolidated weights -- a random-direction force of identical magnitude produces no optimum, and a coherent force toward the wrong target actively hurts. (3) Active ingredient: most of the optimum is recovered by coupling the anchor gain to the injected-noise variance sigma^2 -- a one-line rule that neither Ornstein-Uhlenbeck Adaptation (fixed gain) nor MESU (posterior-variance gain) implements. A forced Ornstein-Uhlenbeck calculation derives the rising flank and predicts that the optimal noise rises with per-task interference g -- confirmed out-of-sample in direction against pre-existing measurements (the exponent is unresolved at our grid). The barrier-conditioning of the originating Doob h-transform is a low-sigma safety net that bounds forgetting where the coupled gain is too weak. (4) Scope: the optimum requires shared task structure -- it is absent on permuted-MNIST, and a controlled rotated-vs-permuted comparison localizes the boundary to task structure; the precise governing quantity is left open. (5) Length: at matched severity the advantage persists but attenuates with task count, and we show no rotation family can attribute the trend (a compact-group identity). A single-seed BrainScaleS-2 demonstration of the originating rule is reported separately (Howe, arXiv:2607.06924); this paper makes no hardware claim.
Abstract:Injecting stochastic noise into a consolidation rule can improve a network's retention of earlier tasks up to an optimal level, then degrade it -- an inverted-U in retention vs. noise. This paper isolates what produces that optimum and maps where it holds, entirely in simulation. (1) Phenomenon: the retention inverted-U appears on several related-task continual-learning benchmarks (Split-MNIST, FashionMNIST, continual Yin-Yang). (2) Isolation: a magnitude-matched ladder shows the effect requires coherent restoring toward the consolidated weights -- a random-direction force of identical magnitude produces no optimum, and a coherent force toward the wrong target actively hurts. (3) Active ingredient: most of the optimum is recovered by coupling the anchor gain to the injected-noise variance sigma^2 -- a one-line rule that neither Ornstein-Uhlenbeck Adaptation (fixed gain) nor MESU (posterior-variance gain) implements. A forced Ornstein-Uhlenbeck calculation derives the rising flank and predicts that the optimal noise rises with per-task interference g -- confirmed out-of-sample in direction against pre-existing measurements (the exponent is unresolved at our grid). The barrier-conditioning of the originating Doob h-transform is a low-sigma safety net that bounds forgetting where the coupled gain is too weak. (4) Scope: the optimum requires shared task structure -- it is absent on permuted-MNIST, and a controlled rotated-vs-permuted comparison localizes the boundary to task structure; the precise governing quantity is left open. (5) Length: at matched severity the advantage persists but attenuates with task count, and we show no rotation family can attribute the trend (a compact-group identity). A single-seed BrainScaleS-2 demonstration of the originating rule is reported separately (Howe, arXiv:2607.06924); this paper makes no hardware claim.
Machine Learning (cs.LG)
arXiv:2609.20162 [cs.LG]
(or arXiv:2609.20162v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.20162 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 356 words