Related papers: On the Duality of Additivity and Tensorization
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
Recent algorithmic developments have enabled computers to automatically determine and prove the capacity regions of small hypergraph networks under network coding. A structural theory relating network coding problems of different sizes is…
A pairwise correlation function in relative momentum space is discussed as a tool to characterize the properties of an incoherent source of non-interacting Abelian anyons. This is analogous to the Hanbury--Brown Twiss effect for particles…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
A class of graphs is bridge-addable if given a graph $G$ in the class, any graph obtained by adding an edge between two connected components of $G$ is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, that says that…
This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as…
In the context of neural network models, overparametrization refers to the phenomena whereby these models appear to generalize well on the unseen data, even though the number of parameters significantly exceeds the sample sizes, and the…
Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…
The Wyner-Ahlswede-K\"orner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques,…
Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…
We prove recognition theorems for codimension one manifold factors of dimension $n \geq 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled…
The analytic rank of a tensor, first defined by Gowers and Wolf in the context of higher-order Fourier analysis, is defined to be the logarithm of the bias of the tensor. We prove that it is a subadditive measure of rank: that is, the…
Tensor network codes enable structured construction and manipulation of stabilizer codes out of small seed codes. Here, we apply reinforcement learning to tensor network code geometries and demonstrate how optimal stabilizer codes can be…
We investigate the coboundary expansion property of tensor product codes, known as product expansion, which plays an important role in recent constructions of good quantum LDPC codes and classical locally testable codes. Prior research has…
Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for…