Interpreting State Space Models from a Geometric Perspective and Its Application to Solid Earth Science

Reference No.	2026a043
Type/Category	Grant for Project Research- Short-term Visiting Researcher
Title of Research Project	Interpreting State Space Models from a Geometric Perspective and Its Application to Solid Earth Science
Principal Investigator	Toshiro Kusui（Graduate School of Information Science and Technology, The University of Tokyo・Doctoral Program, 1st year）
Research Period	June 22,2026. - June 26,2026.
Keyword(s) of Research Fields	State-Space Model, Data Assimilation, Latent Variable
Abstract for Research Report	[Objective] A primary challenge in applying deep learning to solid earth science is balancing computational efficiency with physical consistency. While recently popularized State Space Models (SSMs) such as Mamba offer excellent computational efficiency, standard SSMs inherently act as low-pass filters. This characteristic makes it difficult to represent high-frequency discontinuities critical in earth science, such as fault ruptures and shock waves. Furthermore, the internal behavior of SSMs—specifically, what they remember and how they perform inferences—remains largely unexplored from the perspectives of energetics and dynamical systems. This study aims to provide a mathematical interpretation based on a hybrid dynamical system, which combines continuous state transitions with nonlinear gating mechanisms, for a physically consistent model currently under development by the applicant. By concurrently advancing model architecture development and theoretical analysis, we aim to eliminate the black-box nature of these models and establish highly reliable simulation and data assimilation methods. [Expected Outcomes] Establishment of interpretability: By mathematically formulating the model's internal states as an attraction to memory or harmonic energy minimization, we will provide mathematical guarantees, which are safety that prevent the model from generating hallucinations in unexplored domains. Elucidation of mechanisms for representing discontinuities: We will theoretically demonstrate how high-frequency components, such as fault ruptures, emerge from a smooth internal state by interpreting the SSM's gating mechanism as a physical switch that triggers discontinuous changes. Innovation in data assimilation: We will apply this computationally efficient and physically consistent model to the Schrödinger Bridge, realizing a next-generation data assimilation framework that operates in real-time while properly accounting for uncertainties.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Toshiro Kusui（Graduate School of Information Science and Technology, The University of Tokyo・Doctoral Program, 1st year）