Related papers: Petz reconstruction in random tensor networks
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…
We study the problem of finding the root vertex in large growing networks. We prove that it is possible to construct confidence sets of size independent of the number of vertices in the network that contain the root vertex with high…
Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a…
In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of…
Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal…
This paper explores the current state-of-the-art of object reconstruction from multiple orthographic drawings using deep neural networks. It proposes two algorithms to extract multiple views from a single image. The paper proposes a system…
We give a group-theoretic interpretation of relativistic holography as equivalence between representations of the anti de Sitter algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the…
This paper addresses how a recursive neural network model can automatically leave out useless information and emphasize important evidence, in other words, to perform "weight tuning" for higher-level representation acquisition. We propose…
We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator…
There exist many scenarios where pixel information is available only on a non-regular subset of pixel positions. For further processing, however, it is required to reconstruct such images on a regular grid. Besides many other algorithms,…
We explore a generalization of set reconciliation, where the goal is to reconcile sets of sets. Alice and Bob each have a parent set consisting of $s$ child sets, each containing at most $h$ elements from a universe of size $u$. They want…
In this paper, we explore a novel method for tomographic image reconstruction in the field of SPECT imaging. Deep Learning methodologies and more specifically deep convolutional neural networks (CNN) are employed in the new reconstruction…
Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble…
In this Essay we construct a concrete, non-perturbative realization of metric reconstruction using quantum-optical model of particle detectors in relativistic quantum information. The non-perturbative approach allows us to realize a version…
The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…