Related papers: Criticality & Deep Learning II: Momentum Renormali…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be…
Deep neural networks are a promising approach towards multi-task learning because of their capability to leverage knowledge across domains and learn general purpose representations. Nevertheless, they can fail to live up to these promises…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
While deep learning models excel at predictive tasks, they often overfit due to their complex structure and large number of parameters, causing them to memorize training data, including noise, rather than learn patterns that generalize to…
Reinforcement learning is an emerging approach to control dynamical systems for which classical approaches are difficult to apply. However, trained agents may not generalize against the variations of system parameters. This paper presents…
We report our results of the Monte Carlo Renormalization Group analysis in two dimensional coupling space. The qualitative features of the RG flow are described with a phenomenological RG equation. The dependence on the lattice spacing for…
We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…
We consider renormalization group (RG) transformations for classical Ising-type lattice spin systems in the infinite volume limit. Formally, the RG maps a Hamiltonian H into a renormalized Hamiltonian H': exp(-H'(\sigma'))=\sum_\sigma…
When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
Deep Reinforcement Learning (DRL) has become a popular method for solving control problems in power systems. Conventional DRL encourages the agent to explore various policies encoded in a neural network (NN) with the goal of maximizing the…
The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analysed in the setting of harmonic lattice systems in D=1 and D=2 spatial dimensions. A…
The Density Matrix Renormalization Group (DMRG) method has become a prominent tool for simulating strongly correlated electronic systems characterized by dominant static correlation effects. However, capturing the full scope of electronic…
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…
A fundamental property of deep learning normalization techniques, such as batch normalization, is making the pre-normalization parameters scale invariant. The intrinsic domain of such parameters is the unit sphere, and therefore their…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This…
In this study, we employ the recently developed recurrence microstate probabilities as features to improve accuracy of several well-established machine learning (ML) algorithms. These algorithms are applied to classify discrete and…
The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The…