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Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications.…
In this four-part prospectus, we first give a brief introduction to the motivation for studying entanglement entropy and some recent development. Then follows a summary of our recent work about entanglement entropy in states with…
Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…
Autoencoder-based structures have dominated recent learned image compression methods. However, the inherent information loss associated with autoencoders limits their rate-distortion performance at high bit rates and restricts their…
Inspired by the Thomson problem in physics where the distribution of multiple propelling electrons on a unit sphere can be modeled via minimizing some potential energy, hyperspherical energy minimization has demonstrated its potential in…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
We provide a general framework for the optimal design of surface energies on networks. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferromagnetic interactions by constructing optimal…
We show how parameter redundancy in Convolutional Neural Network (CNN) filters can be effectively reduced by pruning in spectral domain. Specifically, the representation extracted via Discrete Cosine Transform (DCT) is more conducive for…
We present and implement an efficient variational method to simulate two-dimensional finite size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there…
The field of neural image compression has witnessed exciting progress as recently proposed architectures already surpass the established transform coding based approaches. While, so far, research has mainly focused on architecture and model…
Numerically simulating spinful, fermionic systems is of great interest from the perspective of condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders an exact parameterization of…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
We investigate superpositions of two-mode squeezed states (TMSSs), which have potential applications to quantum information processing and quantum sensing. Firstly we study some properties of these nonclassical states such as the statistics…
We consider the conductivity tensor for composite fermions in a close to half-filled Landau band in the temperature regime where the scattering off the potential and the trapped gauge field of random impurities dominates. The Boltzmann…
Deep neural networks have achieved state-of-the-art performance across numerous applications, but their high memory and computational demands present significant challenges, particularly in resource-constrained environments. Model…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
An analytical method for the visualization and prediction of trapped-mode resonances based on the dimensions of a dispersive microwave network is described. The method as explained is intuitive, easy to implement, and has proven itself to…
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…
Feature coding for machines (FCM) is a lossy compression paradigm for split-inference. The transmitter encodes the outputs of the first part of a neural network before sending them to the receiver for completing the inference. Practical FCM…