arXiv AI June 24, 2026 By Borui Cai, Yao Zhao

Topological Neural Dynamics: A Neuron-wise Framework for Sequence Modeling

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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

arXiv Machine Learning

Jun 4

Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks

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.

By Ram\'on Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely

rag agents diffusion

arXiv Machine Learning

Aug 10

When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series

arXiv:2608. 07333v1 Announce Type: new Abstract: Modeling multivariate time series by representing them as graphs, where individual series act as nodes and pairwise temporal corre- lations serve as edges, has gained significant traction.

By Chen Shao, Yue Wang, Zhenyi Zhu, Zhanbo Huang, Tobias K\"afer, Zonghan Wu, Danai Koutra

llms benchmarks

arXiv Machine Learning

Jun 3

A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity

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.

By Chengrui Li, Yunmiao Wang, Yule Wang, Weihan Li, Dieter Jaeger, Anqi Wu

safety

arXiv Machine Learning

Jun 11

Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization

arXiv:2606. 12077v1 Announce Type: new Abstract: Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency.

By Yifan Wang, Lifeng Shen, Shuyin Xia, Yi Wang

benchmarks

Hugging Face Trending Papers

Aug 3

Topological Simplification in Predictive Coding Networks

We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis. We train well-performing PCNs on a synthetic classification dataset ($\geq 99.

arXiv AI

Jun 4

Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models

arXiv:2606. 04672v1 Announce Type: cross Abstract: Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data.

By Ayushman Raghuvanshi, Thummaluru Siddartha Readdy, Sundeep Prabhakar Chepuri, Mahesh Chandran

benchmarks

Related stories

Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks

When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series

A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity

Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization

Topological Simplification in Predictive Coding Networks

Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models