arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
arXiv:2606. 21593v2 Announce Type: replace Abstract: Deep neural networks transform input data into latent representations that support a wide range of downstream tasks.
The paper proposes a structured version of the Information Bottleneck (IB) that separates label-relevant structure from within-condition variation using a dual-bottleneck formulation. It introduces a conditional KL term that targets within-condition information, allowing explicit control over nuisance-like variation in learned representations. Experiments demonstrate improved performance in low-data classification and consistent gains on dense prediction tasks.
arXiv:2603. 27631v2 Announce Type: replace Abstract: Self-supervised pre-training, where large corpora of unlabeled data are used to learn representations for downstream fine-tuning, has become a cornerstone of modern machine learning.
arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.
arXiv:2610.00751v1 Announce Type: cross Abstract: Recent theoretical work identified fundamental properties of representation geometry that shape inference ability of deep neural networks. These incl...
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.
arXiv:2606. 02765v1 Announce Type: cross Abstract: Model dimension ($d_{model}$) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored.
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason...
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
arXiv:2609.27988v1 Announce Type: cross Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
arXiv:2603. 01568v2 Announce Type: replace Abstract: Efficient coding theory predicts that biological perceptual systems compress sensory input optimally under resource constraints, with the systematic structure of errors reflecting the geometry of that compression.