4 papers
Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference
Benjamin Walker, Andrew D. McLeod, Tiexin Qin +3
The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) treat time…
Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations
Tiexin Qin, Benjamin Walker, Terry Lyons +2
This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynami…
Signature Methods in Machine Learning
Terry Lyons, Andrew D. McLeod
Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical…
Theoretical Foundations of Deep Selective State-Space Models
Nicola Muca Cirone, Antonio Orvieto, Benjamin Walker +2
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs…