arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
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:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
The paper demonstrates that a resistor‑diode network’s port behavior solves a ReLU monotone operator equilibrium network, effectively realizing a neural network in analog hardware. It introduces hardware linearization to compute gradients directly in the circuit, enabling in‑hardware training demonstrated via device‑level simulation. The study also extends to cascaded networks for feedforward architectures and shows how different nonlinear elements yield distinct activation functions, including a novel diode ReLU from a non‑ideal diode model.
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:2402. 00152v5 Announce Type: replace Abstract: Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question.
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
arXiv:2605. 01288v3 Announce Type: replace Abstract: In deep networks with small initialization, training exhibits long plateaus separated by sharp feature-acquisition transitions.
arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.
arXiv:2504.16450v4 Announce Type: replace Abstract: We derive a differential equation that governs the evolution of the generalization gap when a model is trained by gradient descent-based methods. T...
arXiv:2605. 06938v2 Announce Type: replace-cross Abstract: Recently Brown et al.
The paper introduces Linearized Subspace Refinement (LSR), a post‑training framework that uses the local linearized model of a trained neural network to compute a low‑dimensional correction via a reduced least‑squares problem. LSR is architecture‑agnostic and improves accuracy across tasks such as function approximation, operator learning, physics‑informed fine‑tuning, and noisy inverse problems, often achieving order‑of‑magnitude error reductions. The method reveals that standard training can leave significant accuracy plateaus due to numerical ill‑conditioning, and it offers a subspace rank that balances correction strength, stability, and noise sensitivity.