19 papers
Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
Liane Galanti, Devan Shah, Shlomo Fortgang +1
Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem? We give a prova…
A Linearly Convergent Projection-Free Algorithm for Smooth Convex Sets
Elad Hazan
We consider minimizing a smooth, strongly convex function over a convex set. Projected gradient descent is known to converge linearly in this setting, but each iteration requires a…
SFO: Learning PDE Operators via Spectral Filtering
Noam Koren, Rafael Moschopoulos, Kira Radinsky +1
Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their sol…
Measuring Intelligence Beyond Human Scale
Jerry Han, Rafael Moschopoulos, Ella Colby +5
How can we measure intelligence beyond human capability? Human-authored benchmarks saturate, and above human capability, examiners may not know which tasks are both hard and verifi…
A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systems
Yuval Ran-Milo, Angelos Assos, Elad Hazan
Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction. Our goal is to…
The Power of Second Order Methods for Sequence Preconditioning
Annie Marsden, Elad Hazan
Sequence prediction methods for linear dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows linearly with the hidden dimension of…