# Variational Kernel Design for Internal Noise: Gaussian Chaos Noise, Representation Compatibility, and Reliable Deep Learning

Source: [Variational Kernel Design for Internal Noise: Gaussian Chaos Noise, Representation Compatibility, and Reliable Deep Learning](<https://www.sota2.com/research/paper/69bb831d0636e5bf4afc1aea>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-20T05:00:04.947Z

Authors: Ziran Liu

Published: 2026-03-18T05:12:56.000Z

## Abstract

Internal noise in deep networks is usually inherited from heuristics such as dropout, hard masking, or additive perturbation. We ask two questions: what correlation geometry should internal noise have, and is the implemented perturbation compatible with the representations it acts on? We answer these questions through Variational Kernel Design (VKD), a framework in which a noise mechanism is specified by a law family, a correlation kernel, and an injection operator, and is derived from learning desiderata. In a solved spatial subfamily, a quadratic maximum-entropy principle over latent log-fields yields a Gaussian optimizer with precision given by the Dirichlet Laplacian, so the induced geometry is the Dirichlet Green kernel. Wick normalization then gives a canonical positive mean-one gate, Gaussian Chaos Noise (GCh). For the sample-wise gate used in practice, we prove exact Gaussian control of pairwise log-ratio deformation, margin-sensitive ranking stability, and an exact expected intrinsic roughness budget; hard binary masks instead induce singular or coherence-amplified distortions on positive coherent representations. On ImageNet and ImageNet-C, GCh consistently improves calibration and under shift also improves NLL at competitive accuracy.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on ImageNet clean (val)](<https://www.sota2.com/research/sota/image-classification-on-imagenet-clean-val.md>): Image Classification; ImageNet clean (val); Top-1 Accuracy: 76.23.

- [Image Classification on ImageNet-C Overall Average (7x5 Severities)](<https://www.sota2.com/research/sota/image-classification-on-imagenet-c-overall-average-7x5-severities.md>): Image Classification; ImageNet-C overall (mean over 7 corruptions x 5 severities); Top-1 Accuracy: 38.3.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.17365>)

[PDF](<https://arxiv.org/pdf/2603.17365.pdf>)