[2602.00130] On the Relationship Between Representation Geometry and Generalization in Deep Neural Networks

Computer Science > Machine Learning arXiv:2602.00130 (cs) [Submitted on 28 Jan 2026 (v1), last revised 3 Mar 2026 (this version, v2)] Title:On the Relationship Between Representation Geometry and Generalization in Deep Neural Networks Authors:Sumit Yadav View a PDF of the paper titled On the Relationship Between Representation Geometry and Generalization in Deep Neural Networks, by Sumit Yadav View PDF Abstract:We investigate the relationship between representation geometry and neural network performance. Analyzing 52 pretrained ImageNet models across 13 architecture families, we show that effective dimension -- an unsupervised geometric metric -- strongly predicts accuracy. Output effective dimension achieves partial r=0.75 ($p < 10^(-10)$) after controlling for model capacity, while total compression achieves partial r=-0.72. These findings replicate across ImageNet and CIFAR-10, and generalize to NLP: effective dimension predicts performance for 8 encoder models on SST-2/MNLI and 15 decoder-only LLMs on AG News (r=0.69, p=0.004), while model size does not (r=0.07). We establish bidirectional causality: degrading geometry via noise causes accuracy loss (r=-0.94, $p < 10^(-9)$), while improving geometry via PCA maintains accuracy across architectures (-0.03pp at 95% variance). This relationship is noise-type agnostic -- Gaussian, Uniform, Dropout, and Salt-and-pepper noise all show $|r| > 0.90$. These results establish that effective dimension provides domain-agnostic pre...