arXiv:2606. 17816v1 Announce Type: cross Abstract: Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow.
arXiv:2606. 10913v1 Announce Type: new Abstract: We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks.
arXiv:2606. 11341v1 Announce Type: new Abstract: Modular neural network pipelines suffer from error compounding: noise at any module boundary propagates and potentially amplifies through subsequent modules.
arXiv:2606. 09744v1 Announce Type: new Abstract: We study feed-forward ReLU networks with fixed readout and quadratic loss.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
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.
arXiv:2502. 15952v3 Announce Type: replace Abstract: Recent works exploring the training dynamics of homogeneous neural network weights under gradient flow with small initialization have established that in the early stages of training, the weights remain small and near the origin, but converge in direction.
The paper investigates the training dynamics of attention mechanisms in high-dimensional settings, focusing on attention-indexed models that encompass multi-layer and multi-head architectures. It shows that while the loss landscape can be described by a finite set of trace order parameters, the online stochastic gradient descent dynamics involve an infinite hierarchy of matrix moments that can be accurately approximated by a finite truncated system. The study further reveals that the choice of attention parameterization acts as an implicit bias: untied attention can get trapped in uninformative states, whereas tied attention induces symmetry breaking and enables weak recovery with θ(d² log d) samples, and untied attention exhibits a fast-slow dynamic leading to weak recovery when symmetry is broken.
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
arXiv:2605. 05488v2 Announce Type: replace Abstract: We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection.
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv:2510. 22450v3 Announce Type: replace-cross Abstract: The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons.