Related papers: Sparse Linear Dynamical System with Its Applicatio…

Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the recently presented Sparse Alternating Least Squares (SALS)…

Dictionary learning and sparse representation (DLSR) is a recent and successful mathematical model for data representation that achieves state-of-the-art performance in various fields such as pattern recognition, machine learning, computer…

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…

The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression…

Increasing the batch size of a deep learning model is a challenging task. Although it might help in utilizing full available system memory during training phase of a model, it results in significant loss of test accuracy most often. LARS…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…

Transformer LMs show emergent reasoning that resists mechanistic understanding. We offer a statistical physics framework for continuous-time chain-of-thought reasoning dynamics. We model sentence-level hidden state trajectories as a…

Forecasting in the real world requires integrating structured time-series data with unstructured textual information, but existing methods are architecturally limited by fixed input/output horizons and are unable to model or quantify…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical…

Traditional methods for solving linear systems have quickly become impractical due to an increase in the size of available data. Utilizing massive amounts of data is further complicated when the data is incomplete or has missing entries. In…

While sparse attention mitigates the computational bottleneck of long-context LLM training, its distributed training process exhibits extreme heterogeneity in both \textit{1)} sequence length and \textit{2)} sparsity sensitivity, leading to…

Learning-to-defer (L2D) routes each decision to a system's own predictor or to an external expert. Streaming time-series settings break the offline-L2D assumptions: the data are non-stationary, expert availability shifts over time, and the…

The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…