Related papers: Bootstraps to Strings: Solving Random Matrix Model…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Recent studies have demonstrated that natural-language prompts can help to leverage the knowledge learned by pre-trained language models for the binary sentence-level sentiment classification task. Specifically, these methods utilize…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
We compute exact solutions of two--matrix models, i.e. detailed genus by genus expressions for the correlation functions of these theories, calculated without any approximation. We distinguish between two types of models, the unconstrained…
Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…
A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Consistently scaling pre-trained language models (PLMs) imposes substantial burdens on model adaptation, necessitating more efficient alternatives to conventional fine-tuning. Given the advantage of prompting in the zero-shot setting and…
Neural ranking models (NRMs) have become one of the most important techniques in information retrieval (IR). Due to the limitation of relevance labels, the training of NRMs heavily relies on negative sampling over unlabeled data. In general…
Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…
We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…