Publications

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Bayesian RG flow in neural network field theories

Jessica N. Howard, Marc S. Klinger, Anindita Maiti, Alexander G. Stapleton

SciPost Phys. Core 8, 027 (2025) · published 5 March 2025 | · pdf

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 graining scheme that generalizes the principles of the exact renormalization group (ERG) to arbitrarily parameterized probability distributions, including those of NNs. In BRG, coarse graining is performed in parameter space with respect to an information-theoretic distinguishability scale set by the Fisher information metric. In this paper, we unify NNFT and BRG to form a powerful new framework for exploring the space of NNs and SFTs, which we coin BRG-NNFT. With BRG-NNFT, NN training dynamics can be interpreted as inducing a flow in the space of SFTs from the information-theoretic 'IR' $→$ 'UV'. Conversely, applying an information-shell coarse graining to the trained network's parameters induces a flow in the space of SFTs from the information-theoretic 'UV' $→$ 'IR'. When the information-theoretic cutoff scale coincides with a standard momentum scale, BRG is equivalent to ERG. We demonstrate the BRG-NNFT correspondence on two analytically tractable examples. First, we construct BRG flows for trained, infinite-width NNs, of arbitrary depth, with generic activation functions. As a special case, we then restrict to architectures with a single infinitely-wide layer, scalar outputs, and generalized cos-net activations. In this case, we show that BRG coarse-graining corresponds exactly to the momentum-shell ERG flow of a free scalar SFT. Our analytic results are corroborated by a numerical experiment in which an ensemble of asymptotically wide NNs are trained and subsequently renormalized using an information-shell BRG scheme.
Unraveling complexity: Singular value decomposition in complex experimental data analysis

Judith F. Stein, Aviad Frydman, Richard Berkovits

SciPost Phys. Core 7, 061 (2024) · published 11 September 2024 | · pdf

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses conventional approaches in understanding complex physics data. Singular values and vectors distinguish and highlight various physical mechanisms and scales, revealing previously challenging elements. SVD emerges as a powerful tool for navigating complex experimental landscapes, showing promise for diverse experimental measurements.
Interferometric microscale measurement of refractive index at VIS and IR wavelengths

Meguya Ryu, Simonas Varapnickas, Darius Gailevicius, Domas Paipulas, Eulalia Puig Vilardell, Zahra Khajehsaeidimahabadi, Saulius Juodkazis, Junko Morikawa, Mangirdas Malinauskas

SciPost Phys. Core 7, 059 (2024) · published 30 August 2024 | · pdf

Determination of refractive index of micro-disks of a calcinated ( $1100^\circ$ C in air) photo-resist SZ2080 $^\mathrm{TM}$ was carried out using transmission and reflection spectroscopy. Interference fringes at specific wavenumbers/wavelengths were selected for determination of the optical thickness, hence, the refractive index when the thickness of micro-disks was measured by scanning electron microscopy (SEM). Refractive index of disks of $\sim 6\pm 1~\mu$ m thickness were determined at visible and IR (2.5-13~ $\mu$ m) spectral ranges and where $2.2\pm 0.2$ at visible and IR wavelengths. Peculiarities of optical characterisation of micro-optical structures are discussed in view of possible uncertainties in the definition of geometric parameters, shape and mass density redistribution.
M5-brane prongs, string soliton bound states and wall-crossing

Varun Gupta, K. Narayan

SciPost Phys. Core 8, 004 (2025) · published 13 January 2025 | · pdf

We study Abelian M5-brane field configurations representing BPS bound states of self-dual string solitons whose locations correspond to the endlines of M2-branes ending on the M5-branes. The BPS equations are obtained from appropriate Bogomolny completion of the effective Abelian low energy functional with two transverse scalars, using two vectors representing the directions along which these endline strings extend. Then we impose boundary conditions on the scalars near the string soliton cores. This leads to a molecule-like equilibrium structure of two non-parallel string solitons at fixed transverse separations, with the M5-brane "prong" deformations comprising two "spikes", each shaped like a ridge. The resulting picture becomes increasingly accurate as one approaches the wall of marginal stability, on which these states decay. There are various parallels with wall-crossing phenomena for string web configurations obtained from D3-brane deformations.
Characterizing far from equilibrium states of the one-dimensional nonlinear Schrödinger equation

Abhik Kumar Saha, Romain Dubessy

SciPost Phys. Core 8, 028 (2025) · published 6 March 2025 | · pdf

We use the mathematical toolbox of the inverse scattering transform to study quantita- tively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schrödinger equation. We present a simple method to iden- tify the discrete eigenvalues in the Lax spectrum and provide a extensive benchmark of its efficiency. Our method can be applied in principle to all physical systems described by the defocusing nonlinear Schrödinger equation and allows to identify the solitons velocity distribution in numerical simulations and possibly experiments.
The quantum cartpole: A benchmark environment for non-linear reinforcement learning

Kai Meinerz, Simon Trebst, Mark Rudner, Evert van Nieuwenburg

SciPost Phys. Core 7, 026 (2024) · published 7 May 2024 | · pdf

Feedback-based control is the de-facto standard when it comes to controlling classical stochastic systems and processes. However, standard feedback-based control methods are challenged by quantum systems due to measurement induced backaction and partial observability. Here we remedy this by using weak quantum measurements and model-free reinforcement learning agents to perform quantum control. By comparing control algorithms with and without state estimators to stabilize a quantum particle in an unstable state near a local potential energy maximum, we show how a trade-off between state estimation and controllability arises. For the scenario where the classical analogue is highly nonlinear, the reinforcement learned controller has an advantage over the standard controller. Additionally, we demonstrate the feasibility of using transfer learning to develop a quantum control agent trained via reinforcement learning on a classical surrogate of the quantum control problem. Finally, we present results showing how the reinforcement learning control strategy differs from the classical controller in the non-linear scenarios.
Top-down and bottom-up: Studying the SMEFT beyond leading order in $1/\Lambda^2$

Tyler Corbett

SciPost Phys. Core 7, 053 (2024) · published 14 August 2024 | · pdf

In order to assess the relevance of higher order terms in the Standard Model effective field theory (SMEFT) expansion we consider four new physics models and their impact on the Drell Yan cross section. Of these four, one scalar model has no effect on Drell Yan, a model of fermions while appearing to generate a momentum expansion actually belongs to the vacuum expectation value expansion and so has a nominal effect on the process. The remaining two, a leptoquark and a $Z'$ model exhibit a momentum expansion. After matching these models to dimension-ten we study the how the inclusion of dimension-eight and dimension-ten operators in hypothetical effective field theory fits to the full ultraviolet models impacts fits. We do this both in the top-down approach, and in a very limited approximation to the bottom up approach of the SMEFT to infer the impact of a fully general fit to the SMEFT. We find that for the more weakly coupled models a strictly dimension-six fit is sufficient. In contrast when stronger interactions or lighter masses are considered the inclusion of dimension-eight operators becomes necessary. However, their Wilson coefficients perform the role of nuisance parameters with best fit values which can differ statistically from the theory prediction. In the most strongly coupled theories considered (which are already ruled out by data) the inclusion of dimension-ten operators allows for the measurement of dimension-eight operator coefficients consistent with theory predictions and the dimension-ten operator coefficients then behave as nuisance parameters. We also study the impact of the inclusion of partial next order results, such as dimension-six squared contributions, and find that in some cases they improve the convergence of the series while in others they hinder it.
Critical analysis of multiple reentrant localization in an antiferromagnetic helix with transverse electric field: Hopping dimerization-free scenario

Sudin Ganguly, Sourav Chattopadhyay, Kallol Mondal, Santanu K. Maiti

SciPost Phys. Core 8, 012 (2025) · published 30 January 2025 | · pdf

Reentrant localization (RL), a recently prominent phenomenon, traditionally links to the interplay of staggered correlated disorder and hopping dimerization, as indicated by prior research. Contrary to this paradigm, our present study demonstrates that hopping dimerization is not a pivotal factor in realizing RL. Considering a helical magnetic system with antiferromagnetic ordering, we uncover spin-dependent RL at multiple energy regions, in the absence of hopping dimerization. This phenomenon persists even in the thermodynamic limit. The correlated disorder in the form of Aubry-André-Harper model is introduced by applying a transverse electric field to the helical system, circumventing the use of traditional substitutional disorder. We conduct a finite-size scaling analysis on the observed reentrant phases to identify critical points, determine associated critical exponents, and examine the scaling behavior linked to localization transitions. Additionally, we explore the parameter space to identify the conditions under which the reentrant phases occur. Described within a tight-binding framework, present work provides a novel outlook on RL, highlighting the crucial role of electric field, antiferromagnetic ordering, and the helicity of the geometry. Potential applications and experimental realizations of RL phenomena are also explored.
Identifying quantum phase transitions with minimal prior knowledge by unsupervised learning

Mohamad Ali Marashli, Ho Lai Henry Lam, Hamam Mokayed, Fredrik Sandin, Marcus Liwicki, Ho-Kin Tang, Wing Chi Yu

SciPost Phys. Core 8, 029 (2025) · published 6 March 2025 | · pdf

In this work, we proposed a novel approach for identifying quantum phase transitions in one-dimensional quantum many-body systems using AutoEncoder (AE), an unsupervised machine learning technique, with minimal prior knowledge. The training of the AEs is done with reduced density matrix (RDM) data obtained by Exact Diagonalization (ED) across the entire range of the driving parameter and thus no prior knowledge of the phase diagram is required. With this method, we successfully detect the phase transitions in a wide range of models with multiple phase transitions of different types, including the topological and the Berezinskii-Kosterlitz-Thouless transitions by tracking the changes in the reconstruction loss of the AE. The learned representation of the AE is used to characterize the physical phenomena underlying different quantum phases. Our methodology demonstrates a new approach to studying quantum phase transitions with minimal knowledge, small amount of needed data, and produces compressed representations of the quantum states.
Necklace Ansatz for strongly repulsive spin mixtures on a ring

Gianni Aupetit-Diallo, Giovanni Pecci, Artem Volosniev, Mathias Albert, Anna Minguzzi, Patrizia Vignolo

SciPost Phys. Core 8, 022 (2025) · published 14 February 2025 | · pdf

We propose an alternative to the Bethe Ansatz method for repulsive strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems.

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