Time-Varying Data as Sheaves: an Invitation to Narratives
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
The Flow has not summarised this story yet — read it at arXiv AI.
arXiv:2609.06006v1 Announce Type: cross Abstract: Deep learning for time series has progressed through successive architectural paradigms, from recurrent networks and transformers to structured state...
arXiv:2607. 23556v1 Announce Type: cross Abstract: Temporal graphs are increasingly used to model dynamic systems in diverse domains such as social networks, financial networks, and traffic networks.
The paper investigates how information-theoretic and geometric compression unfolds over time in recurrent neural networks, specifically discretized LSTMs. It finds that compression is strongest at the final timesteps of many datasets and attributes this to three mechanisms: class separability, temporal stationarity of shared dynamics, and limited representational capacity. Through synthetic and real-world experiments, the authors demonstrate that these factors jointly determine the extent of temporal compression and its role as a regularizer when excess capacity exists, but can harm generalization when it consumes task-relevant memory.
arXiv:2607. 18620v1 Announce Type: cross Abstract: This paper develops temporal-causal unity (TCU), a framework connecting a process-philosophical thesis -- time is the ordered unfolding of causal change -- to an operational model of cognitive and social dynamics.
arXiv:2607. 09232v1 Announce Type: new Abstract: Temporal knowledge graphs (TKGs) represent evolving relational systems, whose underlying data-generating processes often change over time.
The paper introduces a formal definition of the structural role of latent factors in dynamical systems, describing where a latent factor is expressed, whether it receives influence from past observations, and whether it transmits influence to future observations. It addresses the challenge of correspondence across different structural identifications and proves that, under certain conditions, all three roles can be jointly identified using a common permutation at each time point. Building on this theory, the authors present RoleTrace, a framework that traces these structural roles in a shared latent coordinate system, and validate its effectiveness through synthetic experiments and real-world multiparty meeting data.