Related papers: Spectral Filtering for Complex Linear Dynamical Sy…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…

We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while…

We propose a novel multilinear dynamical system (MLDS) in a transform domain, named $\mathcal{L}$-MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal…

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…

We introduce a novel framework for Continual Learning in 3D object classification. Our approach, CL3D, is based on the selection of prototypes from each class using spectral clustering. For non-Euclidean data such as point clouds, spectral…

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…

In this work, we consider the setting of learning problems under a wide class of spectral risk (or "L-risk") functions, where a Lipschitz-continuous spectral density is used to flexibly assign weight to extreme loss values. We obtain excess…

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…

Conventional feature selection algorithms applied to Pseudo Time-Series (PTS) data, which consists of observations arranged in sequential order without adhering to a conventional temporal dimension, often exhibit impractical computational…

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven…

We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting -- the Asymmetric-Regret -- which measures regret against a benchmark predictor with longer context length than…

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that…

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…

Why depth yields a genuine computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional Gaussian setting, focusing on compositional target…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

Spectrum prediction is considered to be a promising technology that enhances spectrum efficiency by assisting dynamic spectrum access (DSA) in cognitive radio networks (CRN). Nonetheless, the highly nonlinear nature of spectrum data across…

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…

Broad learning system (BLS) has been proposed for a few years. It demonstrates an effective learning capability for many classification and regression problems. However, BLS and its improved versions are mainly used to deal with…