Related papers: Criticality & Deep Learning II: Momentum Renormali…
We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We…
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the…
We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of…
Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate…
We introduce Noise Injection Node Regularization (NINR), a method of injecting structured noise into Deep Neural Networks (DNN) during the training stage, resulting in an emergent regularizing effect. We present theoretical and empirical…
In this paper we examine how the predictions of conformal invariance can be widely exploited to overcome the difficulties of the density-matrix renormalization group near quantum critical points. The main idea is to match the set of…
An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to $\phi^4$ $n$-vector models representing universality classes…
Despite the significant progress of deep reinforcement learning (RL) in solving sequential decision making problems, RL agents often overfit to training environments and struggle to adapt to new, unseen environments. This prevents robust…
The field theoretic renormalization group (RG) is applied to the model of a near-equilibrium fluid coupled to a scalar field (like temperature or density of an impurity) which is active, that is, influencing the dynamics of the fluid…
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for…
Robust and performant controllers are essential for industrial applications. However, deriving controller parameters for complex and nonlinear systems is challenging and time-consuming. To facilitate automatic controller parametrization,…
Real time calculation of inverse kinematics (IK) with dynamically stable configuration is of high necessity in humanoid robots as they are highly susceptible to lose balance. This paper proposes a methodology to generate joint-space…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and…
We propose a novel way to integrate control techniques with reinforcement learning (RL) for stability, robustness, and generalization: leveraging contraction theory to realize modularity in neural control, which ensures that combining…
We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a "renormalization-group" (RG)…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost)…
Gradient regularization (GR) has been shown to improve the generalizability of trained models. While Natural Gradient Descent has been shown to accelerate optimization in the initial phase of training, little attention has been paid to how…
Reinforcement learning (RL) is attracting attention as an effective way to solve sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Many such problems involve constraints…