4,155 research outputs found
Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics
In this thesis, we present state-of-the-art techniques for the computation of scattering amplitudes in Quantum Field Theories. Following an introduction to the topic, we describe a robust framework that enables the calculation of multi-scale two-loop amplitudes directly relevant to modern particle physics phenomenology at the Large Hadron Collider and beyond. We discuss in detail the use of finite fields to bypass the algebraic complexity of such computations, as well as the method of integration-by-parts relations and differential equations. We apply our framework to calculate the two-loop amplitudes contributing to three process: Higgs boson production in association with a bottom-quark pair, W boson production with a photon and a jet, as well as lepton-pair scattering with an off-shell and an on-shell photon. Finally, we draw our conclusions and discuss directions for future progress of amplitude computations
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Backpropagation Beyond the Gradient
Automatic differentiation is a key enabler of deep learning: previously, practitioners were limited to models
for which they could manually compute derivatives. Now, they can create sophisticated models with almost
no restrictions and train them using first-order, i. e. gradient, information. Popular libraries like PyTorch
and TensorFlow compute this gradient efficiently, automatically, and conveniently with a single line of
code. Under the hood, reverse-mode automatic differentiation, or gradient backpropagation, powers the
gradient computation in these libraries. Their entire design centers around gradient backpropagation.
These frameworks are specialized around one specific task—computing the average gradient in a mini-batch.
This specialization often complicates the extraction of other information like higher-order statistical moments
of the gradient, or higher-order derivatives like the Hessian. It limits practitioners and researchers to methods
that rely on the gradient. Arguably, this hampers the field from exploring the potential of higher-order
information and there is evidence that focusing solely on the gradient has not lead to significant recent
advances in deep learning optimization.
To advance algorithmic research and inspire novel ideas, information beyond the batch-averaged gradient
must be made available at the same level of computational efficiency, automation, and convenience.
This thesis presents approaches to simplify experimentation with rich information beyond the gradient
by making it more readily accessible. We present an implementation of these ideas as an extension to the
backpropagation procedure in PyTorch. Using this newly accessible information, we demonstrate possible use
cases by (i) showing how it can inform our understanding of neural network training by building a diagnostic
tool, and (ii) enabling novel methods to efficiently compute and approximate curvature information.
First, we extend gradient backpropagation for sequential feedforward models to Hessian backpropagation
which enables computing approximate per-layer curvature. This perspective unifies recently proposed block-
diagonal curvature approximations. Like gradient backpropagation, the computation of these second-order
derivatives is modular, and therefore simple to automate and extend to new operations.
Based on the insight that rich information beyond the gradient can be computed efficiently and at the
same time, we extend the backpropagation in PyTorch with the BackPACK library. It provides efficient and
convenient access to statistical moments of the gradient and approximate curvature information, often at a
small overhead compared to computing just the gradient.
Next, we showcase the utility of such information to better understand neural network training. We build
the Cockpit library that visualizes what is happening inside the model during training through various
instruments that rely on BackPACK’s statistics. We show how Cockpit provides a meaningful statistical
summary report to the deep learning engineer to identify bugs in their machine learning pipeline, guide
hyperparameter tuning, and study deep learning phenomena.
Finally, we use BackPACK’s extended automatic differentiation functionality to develop ViViT, an approach
to efficiently compute curvature information, in particular curvature noise. It uses the low-rank structure
of the generalized Gauss-Newton approximation to the Hessian and addresses shortcomings in existing
curvature approximations. Through monitoring curvature noise, we demonstrate how ViViT’s information
helps in understanding challenges to make second-order optimization methods work in practice.
This work develops new tools to experiment more easily with higher-order information in complex deep
learning models. These tools have impacted works on Bayesian applications with Laplace approximations,
out-of-distribution generalization, differential privacy, and the design of automatic differentia-
tion systems. They constitute one important step towards developing and establishing more efficient deep
learning algorithms
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
UMSL Bulletin 2022-2023
The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
Semantic Security with Infinite Dimensional Quantum Eavesdropping Channel
We propose a new proof method for direct coding theorems for wiretap channels
where the eavesdropper has access to a quantum version of the transmitted
signal on an infinite-dimensional Hilbert space and the legitimate parties
communicate through a classical channel or a classical input, quantum output
(cq) channel. The transmitter input can be subject to an additive cost
constraint, which specializes to the case of an average energy constraint. This
method yields errors that decay exponentially with increasing block lengths.
Moreover, it provides a guarantee of a quantum version of semantic security,
which is an established concept in classical cryptography and physical layer
security. Therefore, it complements existing works which either do not prove
the exponential error decay or use weaker notions of security. The main part of
this proof method is a direct coding result on channel resolvability which
states that there is only a doubly exponentially small probability that a
standard random codebook does not solve the channel resolvability problem for
the cq channel. Semantic security has strong operational implications meaning
essentially that the eavesdropper cannot use its quantum observation to gather
any meaningful information about the transmitted signal. We also discuss the
connections between semantic security and various other established notions of
secrecy
Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators
We propose a novel machine learning framework for solving optimization
problems governed by large-scale partial differential equations (PDEs) with
high-dimensional random parameters. Such optimization under uncertainty (OUU)
problems may be computational prohibitive using classical methods, particularly
when a large number of samples is needed to evaluate risk measures at every
iteration of an optimization algorithm, where each sample requires the solution
of an expensive-to-solve PDE. To address this challenge, we propose a new
neural operator approximation of the PDE solution operator that has the
combined merits of (1) accurate approximation of not only the map from the
joint inputs of random parameters and optimization variables to the PDE state,
but also its derivative with respect to the optimization variables, (2)
efficient construction of the neural network using reduced basis architectures
that are scalable to high-dimensional OUU problems, and (3) requiring only a
limited number of training data to achieve high accuracy for both the PDE
solution and the OUU solution. We refer to such neural operators as multi-input
reduced basis derivative informed neural operators (MR-DINOs). We demonstrate
the accuracy and efficiency our approach through several numerical experiments,
i.e. the risk-averse control of a semilinear elliptic PDE and the steady state
Navier--Stokes equations in two and three spatial dimensions, each involving
random field inputs. Across the examples, MR-DINOs offer -- reductions in execution time, and are able to produce OUU solutions of
comparable accuracies to those from standard PDE based solutions while being
over more cost-efficient after factoring in the cost of
construction
2023-2024 Catalog
The 2023-2024 Governors State University Undergraduate and Graduate Catalog is a comprehensive listing of current information regarding:Degree RequirementsCourse OfferingsUndergraduate and Graduate Rules and Regulation
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