arXiv:2605. 03940v4 Announce Type: cross Abstract: We describe a dynamical system in which a symbolic field is coupled to a geometric field via a bipartite Hilbert-Schmidt kernel.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.
arXiv:2606. 16730v1 Announce Type: cross Abstract: Causal self-attention is a coupling mechanism: each token's hidden state is updated by a learned mixture of preceding tokens at the same timescale.
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:2607. 09714v1 Announce Type: new Abstract: The Feedback-Coupled Memory Systems (FCMS) architecture formalizes closed-loop coordination through four abstract operators, two of which - the agent update operator $f_i$ and the environmental update operator $\Psi$ - are left axiomatically undefined in the original framework.
arXiv:2608. 07433v1 Announce Type: cross Abstract: Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space.
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:2606. 24157v1 Announce Type: new Abstract: The space $\mathcal{P}_2(\mathbb{R}^d$) of probability measures with finite second moment carries a natural geometry: the quadratic Wasserstein distance W_2 makes it a complete metric space and, following Otto, a (formal) Riemannian manifold whose geodesics are the optimal-transport interpolations.