Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging.
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arXiv:2606. 30384v1 Announce Type: new Abstract: Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
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:2606. 05326v1 Announce Type: cross Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the loss and the sharpness.
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.