Related papers: Renormalization-Group Geometry of Homeostatically …
The Neural Network Field Theory correspondence (NNFT) is a mapping from neural network (NN) architectures into the space of statistical field theories (SFTs). The Bayesian renormalization group (BRG) is an information-theoretic coarse…
To describe the non-equilibrium dynamics of random systems, we have recently introduced (C. Monthus and T. Garel, arxiv:0802.2502) a 'strong disorder renormalization' (RG) procedure in configuration space that can be defined for any master…
The practical success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad, Landau, Vazirani, and Vidick. The convergence…
The inference of gene regulatory networks (GRNs) is a foundational stride towards deciphering the fundamentals of complex biological systems. Inferring a possible regulatory link between two genes can be formulated as a link prediction…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling. Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling. These…
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time…
Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…
The problem of learning long-term dependencies in sequences using Recurrent Neural Networks (RNNs) is still a major challenge. Recent methods have been suggested to solve this problem by constraining the transition matrix to be unitary…
We show that renormalization group(RG) flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of…
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…
We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution…
Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Stability of graph neural networks (GNNs) characterizes how GNNs react to graph perturbations and provides guarantees for architecture performance in noisy scenarios. This paper develops a self-regularized graph neural network (SR-GNN)…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
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…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…