arXiv:2608. 16664v1 Announce Type: cross Abstract: We study the Random Quadratic Form (RQF) on a sphere in the presence of random Brownian forcing.
arXiv:2603. 06187v2 Announce Type: replace-cross Abstract: We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere.
arXiv:2607. 04135v1 Announce Type: cross Abstract: The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points.
arXiv:2505. 19619v3 Announce Type: replace Abstract: Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge.
The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points. This phenomenon is all the more surprising given that generalization error diverges when the number of model parameters approaches a critical value from below.
arXiv:2608. 01582v1 Announce Type: cross Abstract: Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling.
arXiv:2605. 26814v2 Announce Type: replace-cross Abstract: We train a pair of autoregressive models to construct zero-mean control variates to mitigate the sign problem in quantum Monte Carlo simulations.
Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem. Here we establish the principle of a universal dynamical clock, a physical perspective in which oscillations of arbitrary dimensionality and geometry are equivalently represented as uniform rotation through an equant-induced nonlinear viewing coordinate, inspired by Ptolemy's equant and formalised through an areal-uniformity principle reminiscent of Kepler's second law.
arXiv:2607. 15472v1 Announce Type: cross Abstract: Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem.
Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque. We address this objective-behavior gap by viewing representation learning as multimode magnetization and deriving, from concrete invariant-learning objectives, a Landau-type effective free energy whose low-order coefficients form objective signatures and induce distinct regularization phenotypes.
arXiv:2410. 09973v2 Announce Type: replace-cross Abstract: We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity.
arXiv:2608. 13335v1 Announce Type: new Abstract: Neural networks trained by gradient descent on a smooth cost function can nevertheless learn in steps: the cost holds on long plateaus and then drops abruptly.
arXiv:2606. 29519v1 Announce Type: new Abstract: Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data.