arXiv subjects

Pan Kessel

Publications and source records attributed to Pan Kessel.

28 records · Page 2Linked to original sources

arXiv2020

Asymptotically unbiased estimation of physical observables with neural samplers

We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the 2d Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.

cond-mat.stat-mech↗

arXiv2019

Explanations can be manipulated and geometry is to blame

Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be manipulated arbitrarily by applying visually hardly perceptible perturbations to the input that keep the network's output approximately constant. We establish theoretically that this phenomenon can be related to certain geometrical properties of neural networks. This allows us to derive an upper bound on the susceptibility of explanations to manipulations. Based on this result, we propose effective mechanisms to enhance the robustness of explanations.

stat.ML↗

arXiv2019

Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Sampling

In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be corrected by using neural network-based MCMC or importance sampling which leads to asymptotically unbiased estimators for physical quantities. This modification is possible due to a singular property of VANs, namely that they provide the exact sample probability. With these modifications, we believe that their method could have a substantially greater impact on various important fields of physics, including strongly-interacting field theories and statistical physics.

cond-mat.stat-mech↗

arXiv2018

Analysis of Atomistic Representations Using Weighted Skip-Connections

In this work, we extend the SchNet architecture by using weighted skip connections to assemble the final representation. This enables us to study the relative importance of each interaction block for property prediction. We demonstrate on both the QM9 and MD17 dataset that their relative weighting depends strongly on the chemical composition and configurational degrees of freedom of the molecules which opens the path towards a more detailed understanding of machine learning models for molecules.

physics.comp-ph↗

arXiv2018

Simple Unfolded Equations for Massive Higher Spins in AdS$_3$

We propose a simple unfolded description of free massive higher spin particles in anti-de-Sitter spacetime. While our unfolded equation of motion has the standard form of a covariant constancy condition, our formulation differs from the standard one in that our field takes values in a different internal space, which for us is simply a unitary irreducible representation of the symmetry group. Our main result is the explicit construction, for the case of AdS$_3$, of a map from our formulation to the standard wave equations for massive higher spin particles, as well as to the unfolded description prevalent in the literature. It is hoped that our formulation may be used to clarify the group-theoretic content of interactions in higher spin theories.

hep-th↗

arXiv2018

Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices

This work completes the classification of the cubic vertices for arbitrary spin massless bosons in three dimensions started in a previous companion paper by constructing parity-odd vertices. Similarly to the parity-even case, there is a unique parity-odd vertex for any given triple $s_1\geq s_2\geq s_3\geq 2$ of massless bosons if the triangle inequalities are satisfied ($s_1<s_2+s_3$) and none otherwise. These vertices involve two (three) derivatives for odd (even) values of the sum $s_1+s_2+s_3$. A non-trivial relation between parity-even and parity-odd vertices is found. Similarly to the parity-even case, the scalar and Maxwell matter can couple to higher spins through current couplings with higher derivatives. We comment on possible lessons for 2d CFT. We also derive both parity-even and parity-odd vertices with Chern-Simons fields and comment on the analogous classification in two dimensions.

hep-th↗

arXiv2017

The Very Basics of Higher-Spin Theory

These notes are based on two lectures given at the Twelfth Modave Summer School in Mathematical Physics 2016. The Fronsdal equation and action for both Minkowski and (A)dS backgrounds are discussed in detail.

hep-th↗

arXiv2015

Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal

We consider four-dimensional Higher-Spin Theory at the first nontrivial order corresponding to the cubic action. All Higher-Spin interaction vertices are explicitly obtained from Vasiliev's equations. In particular, we obtain the vertices that are not determined solely by the Higher-Spin algebra structure constants. The dictionary between the Fronsdal fields and Higher-Spin connections is found and the corrections to the Fronsdal equations are derived. These corrections turn out to involve derivatives of arbitrary order. We observe that the vertices not determined by the Higher-Spin algebra produce naked infinities, when decomposed into the minimal derivative vertices and improvements. Therefore, standard methods can only be used to check a rather limited number of correlation functions within the HS AdS/CFT duality. A possible resolution of the puzzle is discussed.

hep-th↗

arXiv2015

Higher Spins and Matter Interacting in Dimension Three

The spectrum of Prokushkin--Vasiliev Theory is puzzling in light of the Gaberdiel--Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS$_3$. The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. We comment on a different higher-spin theory without such additional fields at $λ=1$.

hep-th↗

arXiv2014

Metric- and frame-like higher-spin gauge theories in three dimensions

We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like formulation. The metric-like theory is obtained by eliminating the generalised spin connection by its equation of motion, and by expressing everything in terms of the metric and a spin-3 Fronsdal field. We give an exact map between fields and gauge parameters in both formulations. To work out the gauge transformations explicitly in terms of metric-like variables, we have to make a perturbative expansion in the spin-3 field. We describe an algorithm how to do this systematically, and we work out the gauge transformations to cubic order in the spin-3 field. We use these results to determine the gauge algebra to this order, and explain why the commutator of two spin-3 transformations only closes on-shell.

hep-th↗