2,773 research outputs found

    Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics

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    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

    Classical and quantum algorithms for scaling problems

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    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

    Towards Neuromorphic Gradient Descent: Exact Gradients and Low-Variance Online Estimates for Spiking Neural Networks

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    Spiking Neural Networks (SNNs) are biologically-plausible models that can run on low-powered non-Von Neumann neuromorphic hardware, positioning them as promising alternatives to conventional Deep Neural Networks (DNNs) for energy-efficient edge computing and robotics. Over the past few years, the Gradient Descent (GD) and Error Backpropagation (BP) algorithms used in DNNs have inspired various training methods for SNNs. However, the non-local and the reverse nature of BP, combined with the inherent non-differentiability of spikes, represent fundamental obstacles to computing gradients with SNNs directly on neuromorphic hardware. Therefore, novel approaches are required to overcome the limitations of GD and BP and enable online gradient computation on neuromorphic hardware. In this thesis, I address the limitations of GD and BP with SNNs by proposing three algorithms. First, I extend a recent method that computes exact gradients with temporally-coded SNNs by relaxing the firing constraint of temporal coding and allowing multiple spikes per neuron. My proposed method generalizes the computation of exact gradients with SNNs and enhances the tradeoffs between performance and various other aspects of spiking neurons. Next, I introduce a novel alternative to BP that computes low-variance gradient estimates in a local and online manner. Compared to other alternatives to BP, the proposed method demonstrates an improved convergence rate and increased performance with DNNs. Finally, I combine these two methods and propose an algorithm that estimates gradients with SNNs in a manner that is compatible with the constraints of neuromorphic hardware. My empirical results demonstrate the effectiveness of the resulting algorithm in training SNNs without performing BP

    Backpropagation Beyond the Gradient

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    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

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Machine learning applications in search algorithms for gravitational waves from compact binary mergers

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    Gravitational waves from compact binary mergers are now routinely observed by Earth-bound detectors. These observations enable exciting new science, as they have opened a new window to the Universe. However, extracting gravitational-wave signals from the noisy detector data is a challenging problem. The most sensitive search algorithms for compact binary mergers use matched filtering, an algorithm that compares the data with a set of expected template signals. As detectors are upgraded and more sophisticated signal models become available, the number of required templates will increase, which can make some sources computationally prohibitive to search for. The computational cost is of particular concern when low-latency alerts should be issued to maximize the time for electromagnetic follow-up observations. One potential solution to reduce computational requirements that has started to be explored in the last decade is machine learning. However, different proposed deep learning searches target varying parameter spaces and use metrics that are not always comparable to existing literature. Consequently, a clear picture of the capabilities of machine learning searches has been sorely missing. In this thesis, we closely examine the sensitivity of various deep learning gravitational-wave search algorithms and introduce new methods to detect signals from binary black hole and binary neutron star mergers at previously untested statistical confidence levels. By using the sensitive distance as our core metric, we allow for a direct comparison of our algorithms to state-of-the-art search pipelines. As part of this thesis, we organized a global mock data challenge to create a benchmark for machine learning search algorithms targeting compact binaries. This way, the tools developed in this thesis are made available to the greater community by publishing them as open source software. Our studies show that, depending on the parameter space, deep learning gravitational-wave search algorithms are already competitive with current production search pipelines. We also find that strategies developed for traditional searches can be effectively adapted to their machine learning counterparts. In regions where matched filtering becomes computationally expensive, available deep learning algorithms are also limited in their capability. We find reduced sensitivity to long duration signals compared to the excellent results for short-duration binary black hole signals

    AI-based design methodologies for hot form quench (HFQ®)

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    This thesis aims to develop advanced design methodologies that fully exploit the capabilities of the Hot Form Quench (HFQ®) stamping process in stamping complex geometric features in high-strength aluminium alloy structural components. While previous research has focused on material models for FE simulations, these simulations are not suitable for early-phase design due to their high computational cost and expertise requirements. This project has two main objectives: first, to develop design guidelines for the early-stage design phase; and second, to create a machine learning-based platform that can optimise 3D geometries under hot stamping constraints, for both early and late-stage design. With these methodologies, the aim is to facilitate the incorporation of HFQ capabilities into component geometry design, enabling the full realisation of its benefits. To achieve the objectives of this project, two main efforts were undertaken. Firstly, the analysis of aluminium alloys for stamping deep corners was simplified by identifying the effects of corner geometry and material characteristics on post-form thinning distribution. New equation sets were proposed to model trends and design maps were created to guide component design at early stages. Secondly, a platform was developed to optimise 3D geometries for stamping, using deep learning technologies to incorporate manufacturing capabilities. This platform combined two neural networks: a geometry generator based on Signed Distance Functions (SDFs), and an image-based manufacturability surrogate model. The platform used gradient-based techniques to update the inputs to the geometry generator based on the surrogate model's manufacturability information. The effectiveness of the platform was demonstrated on two geometry classes, Corners and Bulkheads, with five case studies conducted to optimise under post-stamped thinning constraints. Results showed that the platform allowed for free morphing of complex geometries, leading to significant improvements in component quality. The research outcomes represent a significant contribution to the field of technologically advanced manufacturing methods and offer promising avenues for future research. The developed methodologies provide practical solutions for designers to identify optimal component geometries, ensuring manufacturing feasibility and reducing design development time and costs. The potential applications of these methodologies extend to real-world industrial settings and can significantly contribute to the continued advancement of the manufacturing sector.Open Acces

    UPSCALE: Unconstrained Channel Pruning

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    As neural networks grow in size and complexity, inference speeds decline. To combat this, one of the most effective compression techniques -- channel pruning -- removes channels from weights. However, for multi-branch segments of a model, channel removal can introduce inference-time memory copies. In turn, these copies increase inference latency -- so much so that the pruned model can be slower than the unpruned model. As a workaround, pruners conventionally constrain certain channels to be pruned together. This fully eliminates memory copies but, as we show, significantly impairs accuracy. We now have a dilemma: Remove constraints but increase latency, or add constraints and impair accuracy. In response, our insight is to reorder channels at export time, (1) reducing latency by reducing memory copies and (2) improving accuracy by removing constraints. Using this insight, we design a generic algorithm UPSCALE to prune models with any pruning pattern. By removing constraints from existing pruners, we improve ImageNet accuracy for post-training pruned models by 2.1 points on average -- benefiting DenseNet (+16.9), EfficientNetV2 (+7.9), and ResNet (+6.2). Furthermore, by reordering channels, UPSCALE improves inference speeds by up to 2x over a baseline export.Comment: 29 pages, 26 figures, accepted to ICML 202

    Asymptotics of stochastic learning in structured networks

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