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The paper proposes a second‑order recurrent neural network that replaces traditional neuron‑to‑neuron communication with a spatially evolving field governed by discretized partial differential equations. This design creates a structured infinite‑order RNN where each state depends on its entire history, providing an unbounded receptive field while keeping the number of parameters fixed. The authors derive conditions for marginal stability that prevent vanishing or exploding gradients, and demonstrate that the architecture outperforms other recurrent models on long‑horizon benchmarks with fewer parameters.
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:2610.01786v1 Announce Type: cross Abstract: Neural activity often exhibits multiple timescales that can vary with behavioral states and task conditions. Identifying these timescales from neural...
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.
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.
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.