The paper demonstrates that tree tensor networks (TTNs) can encode arbitrary read‑once Boolean formulas, yielding polynomial‑size targets that are hard for gradient descent to learn in polynomial time, yet their loss landscapes are conditionally benign: every minimum‑norm local minimum is global. This shows that bad local minima are not the source of learning difficulty in TTNs; instead, high‑order degenerate saddle points caused by rank‑deficiency can impede learning. A case study on the parity function illustrates how TTNs can link landscape geometry to computational hardness.
arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
arXiv:2606. 00442v1 Announce Type: new Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
arXiv:2606. 28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.
arXiv:2607. 08380v1 Announce Type: new Abstract: An important quantity in the theory of gradient descent (GD) is the \emph{sharpness}, defined as the largest eigenvalue of the objective Hessian.
arXiv:2606. 00130v2 Announce Type: replace-cross Abstract: Large deep neural networks are costly to store and deploy because inference must move and evaluate many parameters.
arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
arXiv:2606. 29951v1 Announce Type: new Abstract: Interpretable Mesomorphic Neural Networks (IMNs) offer a promising framework that combines the predictive power of deep neural networks with the interpretability of linear models.