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.
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: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.
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: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.
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.
arXiv:2606. 08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
arXiv:2604. 21395v3 Announce Type: replace-cross Abstract: Ordinary supervised training minimises the task loss and then stops.
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.