arXiv:2601. 19019v3 Announce Type: replace-cross Abstract: Neural population activity in sensory cortex is organized on low-dimensional manifolds, but why such manifolds arise and what determines their geometry remain unclear.
arXiv:2605. 12763v2 Announce Type: replace Abstract: Rich learning in recurrent neural networks often proceeds through sudden transitions in latent dynamics, but there is little theory predicting how gradient descent behaves during these events.
arXiv:2606. 14975v1 Announce Type: cross Abstract: How the wiring and functional organization of cortex shape recurrent computation remains a central question in both neuroscience and machine learning.
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.
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:2511. 13899v2 Announce Type: replace-cross Abstract: Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity.
arXiv:2607. 10430v1 Announce Type: cross Abstract: Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity.
arXiv:2512. 12225v3 Announce Type: replace Abstract: Developing artificial agents that unify representation, memory, adaptation, and prediction remains a fundamental challenge in artificial intelligence.
arXiv:2606. 02993v1 Announce Type: new Abstract: Understanding how structured internal structure emerges during neural network training is central to the study of deep learning.
arXiv:2606. 21295v2 Announce Type: replace-cross Abstract: Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently.
arXiv:2602. 03082v2 Announce Type: replace Abstract: A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs.
arXiv:2607. 11666v1 Announce Type: new Abstract: Grokking is a phenomenon in which neural networks initially memorize training data and only later exhibit strong generalization after prolonged optimization.
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.