相关论文: Linear-Readout Floors and Threshold Recovery in Co…
Transistor-based memories are rapidly approaching their maximum density per unit area. Resistive crossbar arrays enable denser memory due to the small size of switching devices. However, due to the resistive nature of these memories, they…
Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
This paper provides a theoretical justification of the superior classification performance of deep rectifier networks over shallow rectifier networks from the geometrical perspective of piecewise linear (PWL) classifier boundaries. We show…
Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination…
The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map $\Xi$ from finite samples of an evaluation interface $\Lambda\subseteq\mathbb C^\Omega$ by finite-height towers of pointwise…
The massive computational costs of scaling modern deep learning architectures have driven the widespread use of parameter-efficient low-rank structures, such as LoRA and low-rank factorization. However, theoretical guarantees for their…
In this paper, we consider the setting of exact repair linear regenerating codes. Under this setting, we derive a new outer bound on the storage-repair-bandwidth trade-off for the case when $d = k = n -1$, where $(n, k, d)$ are parameters…
Double-machine-learning pipelines for the Average Dose-Response Function rely on kernel-weighted local-linear smoothers, which inherit unbounded functional influence: a single outlier within a kernel window biases the curve across the…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for…
In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…
It was recently shown that charged AdS boson stars can reproduce the universal structure of the lowest scaling dimension in the subsector of a CFT with fixed large global $U(1)$ charge $Q$. Using the model consisting of Einstein-Maxwell…
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
Since Shannon's foundational work, rate-distortion theory has defined the fundamental limits of lossy compression. Classical results, derived for memoryless and stationary ergodic sources in the asymptotic regime, have shaped both transform…
We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…