Related papers: A Hierarchy for Constant Communication Complexity
Construction C (also known as Forney's multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from $L$ binary code components. If the component codes are linear, then the minimum distance is…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
This paper investigates contextual word representation models from the lens of similarity analysis. Given a collection of trained models, we measure the similarity of their internal representations and attention. Critically, these models…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-time spectrum come with such characterizations. Recent work…
The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis…
Hierarchical clustering is a stronger extension of one of today's most influential unsupervised learning methods: clustering. The goal of this method is to create a hierarchy of clusters, thus constructing cluster evolutionary history and…
We assess the descriptive complexity of *bisimilarity* or "equality of behavior" on a family of Markov decision processes over uncountable standard Borel spaces, namely *nondeterministic labelled Markov processes* (NLMP). We show that…
This work investigates into cost behaviors of binary classification measures in a background of class-imbalanced problems. Twelve performance measures are studied, such as F measure, G-means in terms of accuracy rates, and of recall and…
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic,…
We study the model checking problem, for fixed structures A, over positive equality-free first-order logic -- a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(A). We prove a complete complexity…
Human activity recognition is challenging because sensor signals shift with context, motion, and environment; effective models must therefore remain stable as the world around them changes. We introduce a categorical symmetry-aware learning…
We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely,…
We describe a four-level hierarchy mapping both all discrete estimation problems and all estimators on these problems, such that the hierarchy describes each estimator's consistency guarantees on each problem class. We show that no…
Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the \emph{Revenue} objective to handle similarity…
Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In…
Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
In this paper, we propose a comprehensive study of second-order consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four…