Related papers: Compression of enumerations and gain
We numerically study the magnetization of small metallic clusters. The magnetic susceptibility is enhanced for lower electronic densities due to the stronger influence of electron-electron interactions. The magnetic susceptibility…
The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…
Interpretability is a pressing issue for machine learning. Common approaches to interpretable machine learning constrain interactions between features of the input, rendering the effects of those features on a model's output comprehensible…
Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
Deep learning-based computer vision systems adopt complex and large architectures to improve performance, yet they face challenges in deployment on resource-constrained mobile and edge devices. To address this issue, model compression…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
Alice and Bob are given two correlated n-bit strings x_1 and, respectively, x_2, which they want to losslessly compress and send to Zack. They can either collaborate by sharing their strings, or work separately. We show that there is no…
Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…
We introduce a generic presentation of 'syntactic objects built by mixed induction and coinduction' encompassing all standard kinds of infinitary terms, as well as derivation trees in non-wellfounded proof systems. We then define a notion…
Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of…
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
A theorem of A.A. Brudno says that the Kolmogorov-Sinai entropy of a subshift X over $\mathbb{N}$ with respect to an ergodic measure $\mu$ equals the asymptotic Kolmogorov complexity of almost every word $\omega$ in X. The purpose of this…
We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $\mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
Nowadays data compressors are applied to many problems of text analysis, but many such applications are developed outside of the framework of mathematical statistics. In this paper we overcome this obstacle and show how several methods of…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…