Related papers: Communication Complexity of Permutation-Invariant …
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…
Transformer-based language models have demonstrated impressive capabilities across a range of complex reasoning tasks. Prior theoretical work exploring the expressive power of transformers has shown that they can efficiently perform…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
We establish novel connections between magic in quantum circuits and communication complexity. In particular, we show that functions computable with low magic have low communication cost. Our first result shows that the $\mathsf{D}\|$…
Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple…
Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with…
Let $(X, \sigma_X), (Y, \sigma_Y)$ be one-sided subshifts with the specification property and $\pi:X\rightarrow Y$ a factor map. Let $\mu$ be a unique invariant Gibbs measure for a sequence of continuous functions $\F=\{\log…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…
New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…
Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for…
Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
Let $(X, d)$ be a semimetric space. A permutation $\Phi$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(\Phi(x), \Phi(y))) $$ for all…
Communication complexity quantifies how difficult it is for two distant computers to evaluate a function f(X,Y), where the strings X and Y are distributed to the first and second computer respectively, under the constraint of exchanging as…
We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…