The key to understanding intricate dynamics in QFTs is a representation in terms of the relevant degrees of freedom which are usually associated with emergent composites (e.g. observable particles, but also Cooper-pairs, resonances...) and may change with the scale. In this talk, we aim for a combination of Machine learning methods and the functional Renormalisation Group (fRG) to identify an...
I will discuss how “relevance”, as defined in the the renormalisation group (RG), is in fact equivalent to the notion of “relevant” information defined in the Information Bottleneck (IB) formalism of compression theory, and how order parameters and, more generally, scaling operators are solutions to a suitably posed compression problem. These solutions can be numerically obtained from raw...
The key to the performance of ML algorithms is an ability to segregate relevant features in input datasets from the irrelevant ones. In a setup where data features play the role of an energy scale, we develop a Wilsonian RG framework to integrate out unlearnable modes associated with the Neural Network Gaussian Process (NNGP) kernel, in the regression context. In this scenario, Gaussian...
The ideas at the heart of the renormalisation group have greatly influenced many areas of Physics, in particular field theory and statistical mechanics. In the course of the past few decades, the field of coarse-graining in soft matter has developed at an increasingly high pace, leveraging RG-like methods and tools to build simple yet realistic representations of biological and artificial...
The renormalization group is a powerful technique in studies of phase transitions but manifests one limitation: it can only be applied for a finite number of steps before the degrees of freedom vanish. I will briefly discuss the construction of inverse renormalization group transformations with the use of machine learning which enable the iterative generation of configurations for increasing...
Studying systems with tunable couplings between subsystems poses challenges in determining their phase diagrams and uncovering potential emergent phases. Using machine learning and a quasidistance metric, we investigate layered spin models where coupling between spin layers induces composite order parameters. Focusing on Ising and Ashkin–Teller models, we employ a machine learning algorithm on...
We develop a multiscale approach to estimate high-dimensional probability distributions. Our approach applies to cases in which the energy function (or Hamiltonian) is not known from the start. Using data acquired from experiments or simulations we can estimate the underlying probability distribution and the associated energy function. Our method—the wavelet-conditional renormalization group...
In this talk I'll review an old result from machine learning theory that relates infinite neural networks and generalized free field theories. With that backdrop, I'll present modern developments connecting field theory and neural networks, including the origin of interactions and relation to the central limit theorem, the appearance of symmetries, and realizing phi^4 theory.
RG improved lattice actions provide a possible way to extract continuum physics with coarser lattices, thereby allowing to circumvent problems with critical slowing down and topological freezing toward the continuum limit. So-called fixed point (FP) lattice actions for example have continuum classical properties unaffected by discretization effects, while lattice actions on the renormalized...
RG improved lattice actions provide a possible way to extract continuum physics with coarser lattices, thereby allowing to circumvent problems with critical slowing down and topological freezing toward the continuum limit. So-called fixed point (FP) lattice actions for example have continuum classical properties unaffected by discretization effects, while lattice actions on the renormalized...
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. In this talk, we show examples on how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are presented:...
As neural networks become wider their accuracy improves, and their behavior becomes easier to analyze theoretically. I will give an introduction to a growing body of work which examines the learning dynamics and distribution over functions induced by infinitely wide, randomly initialized, neural networks. Core results that I will discuss include: that the distribution over functions computed...
Large neural networks perform extremely well in practice, providing the backbone of modern machine learning. In this talk, we'll first overview how the statistics and dynamics of deep neural networks drastically simplify at large width and become analytically tractable. We'll then see how the concepts of the renormalization-group flow and critical phenomena naturally emerge in computing and...
In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a...
I will explain how Polchinski’s formulation of the renormalization group of a statistical field theory can be seen as a gradient flow equation for a relative entropy functional. Subsequently, I will explain how this idea can be used to design adaptive bridge sampling schemes for lattice field theories. or equivalently diffusion models which learn the RG flow of the theory (in a precise...
It has been observed that diffusion models have similarities with RG (on a lattice). This intuition suggests a new design space for the diffusion process, unifying the usual diffusion models with e.g. wavelet conditional diffusion, and may shed light on how diffusion models work. We explore this perspective (work in progress with Miranda Cheng & Max Welling).
“It has been widely argued that non-trivial topological features of the Yang-Mills vacuum are responsible for colour confinement. However, both analytical and numerical progress have been limited by the lack of understanding of the nature of relevant topological excitations in the full quantum description of the model. Recently, Topological Data Analysis (TDA) has emerged as a widely...
In this exploratory study we investigate the correlation between different elements of the output sequence of a GPT. The dependence of this correlation on positions of elements as well as on hyper parameters of the model is investigated. The connection with validation metrics is explored too.
We demonstrate that the update of weight matrices in learning algorithms has many features of random matrix theory, allowing for a stochastic Coulomb gas description in a modified Gaussian orthogonal ensemble. We relate the level of stochasticity to the ratio of the learning rate and the batch size. We identify the Wigner surmise and Wigner semicircle explicitly in a teacher-student model and...