The paper presents a non-equilibrium dynamical mean-field theory (DMFT) that explains how learning reshapes the dynamics of recurrent neural networks, turning initially chaotic activity into stable, task-dependent behavior. It shows that a slow, feedback-driven learning process gradually increases effective feedback strength, driving the network through a bifurcation that marks the transition from chaotic to stable dynamics. By deriving the two-time correlation function, the authors identify a critical feedback strength and a learning-rate-dependent critical time that separate these regimes, and they demonstrate that the theory accurately predicts the network’s output evolution during training, matching numerical simulations.
By Varun Vaidya
arXiv:2606. 29519v1 Announce Type: new Abstract: Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data.
By Lorenzo Livi
Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data. This fade is captured by an envelope $f(\ell)$.
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.
By Wenbo Wei, Fan Xu, Nicholas Chong Jia Le, Choy Heng Lai, Ling Feng
The paper models the dynamics of Stochastic Gradient Descent (SGD) as a percolation process, showing that architectural symmetries cause subnetworks to merge in discrete blocks rather than sequentially. These structural transitions produce variance spikes in a macroscopic order parameter, analogous to physical phase transitions. The authors also demonstrate that this trapping mechanism and its scaling cascade apply to Adam and AdamW under a heavy‑tailed noise model.
By Sai Niranjan Ramachandran, Suvrit Sra
The paper introduces ELiSe, a model that leverages cortical network scaffolds and dendritic compartments to learn complex non‑Markovian spatio‑temporal patterns using only local, always‑on, phase‑free synaptic plasticity. It demonstrates the model’s ability to acquire and replay intricate sequences, exemplified by a birdsong learning mock‑up, and shows robustness to external disturbances and flexibility in parameter settings.
By Laura Kriener, Kristin V\"olk, Ben von H\"unerbein, Federico Benitez, Walter Senn, Mihai A. Petrovici
arXiv:2604. 00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised.
By Anamika Paul Rupa
arXiv:2608. 01833v1 Announce Type: cross Abstract: Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization.
By Lai Shun Chan, Xiaotian Zhang, Yue Shang, Ge Zhang, Entao Yang
arXiv:2507.10383v5 Announce Type: replace-cross
Abstract: Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neu...
By Uri Cohen, M\'at\'e Lengyel
arXiv:2606. 10530v1 Announce Type: cross Abstract: Recent developments in brain recording are driving a demand for machine learning tools capable of decoding the latent structure of large populations of neurons.
By Shufeng Kong, Fumei Deng, Xinyi Dong, Caihua Liu, Weiwei Chen, Yingheng Wang, Daniel Cao, Azahara Oliva, Antonio Fernandez-Ruiz, Carla Gomes
arXiv:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.
By Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner
arXiv:2605. 05113v2 Announce Type: replace Abstract: We study signal propagation in linear recurrent models at finite width.
By Mariia Seleznova