Related papers: Refuting approaches to the log-rank conjecture for…

We consider the space of matrices, with given number of rows and of columns, equipped with the classic trace scalar product. With any matrix (source) norm, we associate a coupling, called Capra, between the space of matrices and itself.…

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…

Approaches for appraising feature importance approximations, alternatively referred to as attribution methods, have been established across an extensive array of contexts. The development of resilient techniques for performance benchmarking…

A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…

Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…

Additive two-tower models are popular learning-to-rank methods for handling biased user feedback in industry settings. Recent studies, however, report a concerning phenomenon: training two-tower models on clicks collected by well-performing…

We study the two-party communication complexity of functions with large outputs, and show that the communication complexity can greatly vary depending on what output model is considered. We study a variety of output models, ranging from the…

Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…

We prove two new results about the randomized query complexity of composed functions. First, we show that the randomized composition conjecture is false: there are families of partial Boolean functions $f$ and $g$ such that $R(f\circ g)\ll…

Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a}…

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…

In 2009, Etzion and Siberstein proposed a conjecture on the largest dimension of a linear space of matrices over a finite field in which all nonzero matrices are supported on a Ferrers diagram and have rank bounded below by a given integer.…

Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients.…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…

In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality…

We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Every Boolean function can be uniquely represented as a multilinear polynomial. The entropy and the total influence are two ways to measure the concentration of its Fourier coefficients, namely the monomial coefficients in this…

We prove two conjectures on correlation inequalities for functions that are linear combinations of unimodal Boolean monotone nondecreasing functions