The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
By Shaojie Li, Yunbei Xu
arXiv:2608. 15632v1 Announce Type: cross Abstract: Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret.
By Yehonatan Avidan, Daniel D. Lee, Haim Sompolinsky
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
By Yuchen Lin, Yong Zhang, Sihan Feng, Hong Zhao
arXiv:2609.07755v1 Announce Type: new
Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
By Yuqing Wang, Ioannis G. Kevrekidis, Mikhail Belkin
arXiv:2606. 07007v1 Announce Type: cross Abstract: We propose a unified mathematical framework for a geometric understanding of concept learning and neuron interpretation in sparse autoencoders (SAEs).
By Chenhao Zhang, Chris Lin, Su-In Lee
arXiv:2606. 04409v1 Announce Type: cross Abstract: Modern deep neural networks usually have large parameter scales and nonlinear hierarchical structures, and they have achieved strong performance in computer vision.
By Luoyidi Zhou
The paper investigates how the geometry of teacher neural networks affects the learnability of student networks in teacher‑student setups. By formalizing learnability as the success rate of reaching the global minimum, the authors identify two teacher distributions—one maximizing node dissimilarity (easy) and one minimizing it (hard)—that lead to markedly different success rates across various settings and activation functions. They analyze the loss landscape of small networks, revealing two types of suboptimal local minima (out‑of‑bounds and interior) whose attraction regions depend on teacher structure, and demonstrate that adjusting learning rates for the readout layer and inner biases can improve success rates.
whyItMatters:"The study highlights that teacher geometry, often overlooked, plays a crucial role in determining how effectively a student network can learn, offering guidance for designing more realistic teacher‑student experiments."
By Kai J. Sandbrink, Flavio Martinelli, Alexander van Meegen, Wulfram Gerstner, Johanni Brea
arXiv:2607. 11666v1 Announce Type: new Abstract: Grokking is a phenomenon in which neural networks initially memorize training data and only later exhibit strong generalization after prolonged optimization.
By Maksim A Kazanskii
arXiv:2606. 29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks.
By Ziyu Cheng, Xitong Zhang, Longxiu Huang, Rongrong Wang
arXiv:2606. 25008v1 Announce Type: new Abstract: Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute.
By Yizhou Liu, Jeff Gore
arXiv:2606. 30512v1 Announce Type: cross Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory.
By Srinivasa Rao P., Vangmayi P Reddy
arXiv:2501. 07400v2 Announce Type: replace-cross Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations.
By Thomas Chen