相关论文: The Geometry of Linear Program Compression: An Exa…

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…

We define and study the problem of predicting the solution to a linear program (LP) given only partial information about its objective and constraints. This generalizes the problem of learning to predict the purchasing behavior of a…

Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…

Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…

Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…

Understanding the relationship between data compression and the capabilities of Large Language Models (LLMs) is crucial, especially in specialized domains like code intelligence. Prior work posited a linear relationship between compression…

When training large-scale models, the performance typically scales with the number of parameters and the dataset size according to a slow power law. A fundamental theoretical and practical question is whether comparable performance can be…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…

We study the problem of Reinforcement Learning (RL) with linear function approximation, i.e. assuming the optimal action-value function is linear in a known $d$-dimensional feature mapping. Unfortunately, however, based on only this…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…

The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…

Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…