Observability conditions for neural state-space models with eigenvalues and their roots of unity

arXiv:2504.15758 · cs.LG, cs.SY, eess.SY, math.DS, math.OC · Submitted 2025-04-22 · Read on arXiv

cs.LG, cs.SY, eess.SY, math.DS, math.OC

Submitted: 2025-04-22

Updated: 2026-09-05

Comments: To be presented in 62nd Allerton Conference on Communication, Control, and Computing

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Loss Function — 15× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Annual Conference on Decision and Control — 1× in this paper
• Degeneracy — 1× in this paper · explained in 3 episodes
• Foundation Model — 1× in this paper · explained in 3 episodes
• Foundation Models — 1× in this paper · explained in 7 episodes
• Mixture of Experts — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• State Space Models as Foundation Models: A Control Theoretic Overview
• BlackMamba: Mixture of Experts for State-Space Models
• Lower Bounds for Non-Convex Stochastic Optimization
• Convex Optimization: Algorithms and Complexity
• Lower Bounds for Finding Stationary Points II: First-Order Methods
• Lower Bounds for Finding Stationary Points I
• Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming
• Mamba: Linear-Time Sequence Modeling with Selective State Spaces
• Efficiently Modeling Long Sequences with Structured State Spaces
• Sparse Mamba: Introducing Controllability, Observability, And Stability To Structural State Space Models
• State-space models are accurate and efficient neural operators for dynamical systems
• Observability of complex systems via conserved quantities
• Simplified State Space Layers for Sequence Modeling
• AdaGrad stepsizes: Sharp convergence over nonconvex landscapes

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