arXiv:2505. 20030v2 Announce Type: replace-cross Abstract: We observe a novel `multiple-descent' phenomenon during the learning process of a recurrent neural network called long-short-term memory (LSTM) networks during its training on real-world task, in which the performance goes through long cycles of up and down trends multiple times after the model is overtrained.
arXiv:2606. 10384v1 Announce Type: cross Abstract: Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear.
arXiv:2607. 21716v1 Announce Type: new Abstract: Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics.
arXiv:2606. 30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory.
arXiv:2607. 27731v1 Announce Type: new Abstract: Modern deep learning typically keeps the batch size static throughout training, thus overlooking the joint effect of learning rate and batch size on the training dynamics.
arXiv:2605. 06384v3 Announce Type: replace-cross Abstract: We introduce MinMax Recurrent Neural Cascades (MinMax RNCs), a class of recurrent neural networks built from a novel form of recurrence over the MinMax algebra.
arXiv:2606. 15551v1 Announce Type: new Abstract: The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poorly understood in realistic settings.
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
arXiv:2508. 03105v3 Announce Type: replace Abstract: We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function.
arXiv:2607. 21005v1 Announce Type: new Abstract: Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable.
arXiv:2506. 05233v2 Announce Type: replace-cross Abstract: Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention.
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. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.