Related papers: Petz reconstruction in random tensor networks
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…
Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce…
Most of the literature in the \emph{bulk reconstruction program} in holography focuses on recovering local bulk operators propagating on a quasilocal bulk geometry and the knowledge of the bulk geometry is always assumed or guessed. The…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to…
Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, we build a…
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some…
Terahertz (THz) tomography is a rather novel technique for nondestructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from…
These lecture notes are based on a series of lectures given at the XIII Modave summer school in mathematical physics. We review the construction due to Hamilton, Kabat, Lifschytz and Lowe for reconstructing local bulk operators from CFT…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of $\mathrm{AdS}_3/\mathrm{CFT}_2$. We find that, given…
Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…
Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…
Using recent advances in generative artificial intelligence (AI) brought by diffusion models, this paper introduces a new synergistic method for spectral computed tomography (CT) reconstruction. Diffusion models define a neural network to…
Large Transformer-based models were shown to be reducible to a smaller number of self-attention heads and layers. We consider this phenomenon from the perspective of the lottery ticket hypothesis, using both structured and magnitude…