Machine-learning hidden symmetries
Ziming Liu, Max Tegmark
[ arXiv:2109.09721 ]
AbstractWe present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painleve metric that manifests hidden translational symmetry in the Schwarzschild metric of non-rotating black holes, as well as Hamiltonicity, modularity and other simplifying traits not traditionally viewed as symmetries.
Deep Set Auto Encoders for Anomaly Detection in Particle Physics
[ arXiv:2109.01695 ]
AbstractThere is an increased interest in model agnostic search strategies for physics beyond the standard model at the Large Hadron Collider. We introduce a Deep Set Variational Autoencoder and present results on the Dark Machines Anomaly Score Challenge. We find that the method attains the best anomaly detection ability when there is no decoding step for the network, and the anomaly score is based solely on the representation within the encoded latent space. This method was one of the top-performing models in the Dark Machines Challenge, both for the open data sets as well as the blinded data sets.
Hardware-accelerated Inference for Real-Time Gravitational-Wave Astronomy
Alec Gunny, Dylan Rankin, Jeffrey Krupa, Muhammed Saleem, Tri Nguyen, Michael Coughlin, Philip Harris, Erik Katsavounidis, Steven Timm, Burt Holzman
[ arXiv:2108.1243 ]
AbstractThe field of transient astronomy has seen a revolution with the first gravitational-wave detections and the arrival of multi-messenger observations they enabled. Transformed by the first detection of binary black hole and binary neutron star mergers, computational demands in gravitational-wave astronomy are expected to grow by at least a factor of two over the next five years as the global network of kilometer-scale interferometers are brought to design sensitivity. With the increase in detector sensitivity, real-time delivery of gravitational-wave alerts will become increasingly important as an enabler of multi-messenger followup. In this work, we report a novel implementation and deployment of deep learning inference for real-time gravitational-wave data denoising and astrophysical source identification. This is accomplished using a generic Inference-as-a-Service model that is capable of adapting to the future needs of gravitational-wave data analysis. Our implementation allows seamless incorporation of hardware accelerators and also enables the use of commercial or private (dedicated) as-a-service computing. Based on our results, we propose a paradigm shift in low-latency and offline computing in gravitational-wave astronomy. Such a shift can address key challenges in peak-usage, scalability and reliability, and provide a data analysis platform particularly optimized for deep learning applications. The achieved sub-millisecond scale latency will also be relevant for any machine learning-based real-time control systems that may be invoked in the operation of near-future and next generation ground-based laser interferometers, as well as the front-end collection, distribution and processing of data from such instruments.
Towards an Optimal Estimation of Cosmological Parameters with the Wavelet Scattering Transform
Georgios Valogiannis, Cora Dvorkin
[ arXiv:2108.07821 ]
AbstractOptimal extraction of the non-Gaussian information encoded in the Large-Scale Structure (LSS) of the universe lies at the forefront of modern precision cosmology. We propose achieving this task through the use of the Wavelet Scattering Transform (WST), which subjects an input field to a layer of non-linear transformations that are sensitive to non-Gaussianity in spatial density distributions through a generated set of WST coefficients. In order to assess its applicability in the context of LSS surveys, we apply the WST on the 3D overdensity field obtained by the Quijote simulations, out of which we extract the Fisher information in 6 cosmological parameters. It is subsequently found to deliver a large improvement in the marginalized errors on all parameters, ranging between 1.2−4× tighter than the corresponding ones obtained from the regular 3D cold dark matter + baryon power spectrum, as well as a 50% improvement over the neutrino mass constraint given by the marked power spectrum. Through this first application on 3D cosmological fields, we demonstrate the great promise held by this novel statistic and set the stage for its future application to actual galaxy observations.
Deep multi-task mining Calabi-Yau four-folds
Harold Erbin, Riccardo Finotello, Robin Schneider, Mohamed Tamaazousti
[ arXiv:2108.02221 ]
AbstractWe continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for h(1,1) and 97% for h(2,1) (100% for both), 81% (96%) for h(3,1), and 49% (83%) for h(2,2). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.
Nonperturbative renormalization for the neural network–QFT correspondence
Harold Erbin, Vincent Lahoche, Dine Ousmane Samary
[ arXiv:2108.01403 ]
AbstractIn a recent work~, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite N corrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for neural networks (since inputs can be arbitrary), however, the renormalization group provides natural notions of locality and scaling. Moreover, we comment on several subtleties, for example, that data components may not have a permutation symmetry: in that case, we argue that random tensor field theories could provide a natural generalization. Second, we improve the perturbative Wilsonian renormalization from~ by providing an analysis in terms of the nonperturbative renormalization group using the Wetterich-Morris equation. An important difference with usual nonperturbative RG analysis is that only the effective (IR) 2-point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate neural networks behavior beyond the large-width limit (i.e.~far from Gaussian limit) in a nonperturbative fashion. A major result of our analysis is that changing the standard deviation of the neural network weight distribution can be interpreted as a renormalization flow in the space of networks. We focus on translations invariant kernels and provide preliminary numerical results.
Flow-based sampling for multimodal distributions in lattice field theory
Daniel C. Hackett, Chung-Chun Hsieh, Michael S. Albergo, Denis Boyda, Jiunn-Wei Chen, Kai-Feng Chen, Kyle Cranmer, Gurtej Kanwar, Phiala E. Shanahan
[ arXiv:2107.00734 ]
AbstractRecent results have demonstrated that samplers constructed with flow-based generative models are a promising new approach for configuration generation in lattice field theory. In this paper, we present a set of methods to construct flow models for targets with multiple separated modes (i.e. theories with multiple vacua). We demonstrate the application of these methods to modeling two-dimensional real scalar field theory in its symmetry-broken phase. In this context we investigate the performance of different flow-based sampling algorithms, including a composite sampling algorithm where flow-based proposals are occasionally augmented by applying updates using traditional algorithms like HMC.
AbstractCurrent model-based reinforcement learning methods struggle when operating from complex visual scenes due to their inability to prioritize task-relevant features. To mitigate this problem, we propose learning Task Informed Abstractions (TIA) that explicitly separates reward-correlated visual features from distractors. For learning TIA, we introduce the formalism of Task Informed MDP (TiMDP) that is realized by training two models that learn visual features via cooperative reconstruction, but one model is adversarially dissociated from the reward signal. Empirical evaluation shows that TIA leads to significant performance gains over state-of-the-art methods on many visual control tasks where natural and unconstrained visual distractions pose a formidable challenge.
The Principles of Deep Learning Theory
Daniel A. Roberts, Sho Yaida, Boris Hanin
[ arXiv:2106.10165 ]
AbstractThis book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
Electron on solid neon – a new solid-state single-electron qubit platform
Xianjing Zhou, Gerwin Koolstra, Xufeng Zhang, Ge Yang, Xu Han, Brennan Dizdar, Divan Ralu, Wei Guo, Kater W. Murch, David I. Shuster, Dafei Jin
[ arXiv:2106.10326 ]
AbstractThe promise of quantum computing has driven a persistent quest for new qubit platforms with long coherence, fast operation, and large scalability. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via either motional or spin states depends critically on their material environment. Here we report our experimental realization of a new qubit platform based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. By integrating an electron trap in a circuit quantum electrodynamics architecture, we achieve strong coupling between the motional states of a single electron and microwave photons in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are used to measure the energy relaxation time T1 of 15 μs and phase coherence time T2 over 200 ns, indicating that the electron-on-solid-neon qubit already performs near the state of the art as a charge qubit.
Flow-based sampling for fermionic lattice field theories
Michael S. Albergo, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, Julian M. Urban, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan
[ arXiv:2106.05934 ]
AbstractAlgorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.
Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering
Vincent Sitzmann, Semon Rezchikov, William T. Freeman, Joshua B. Tenenbaum, Fredo Durand
[ arXiv:2106.02634 ]
AbstractInferring representations of 3D scenes from 2D observations is a fundamental problem of computer graphics, computer vision, and artificial intelligence. Emerging 3D-structured neural scene representations are a promising approach to 3D scene understanding. In this work, we propose a novel neural scene representation, Light Field Networks or LFNs, which represent both geometry and appearance of the underlying 3D scene in a 360-degree, four-dimensional light field parameterized via a neural implicit representation. Rendering a ray from an LFN requires only a *single* network evaluation, as opposed to hundreds of evaluations per ray for ray-marching or volumetric based renderers in 3D-structured neural scene representations. In the setting of simple scenes, we leverage meta-learning to learn a prior over LFNs that enables multi-view consistent light field reconstruction from as little as a single image observation. This results in dramatic reductions in time and memory complexity, and enables real-time rendering. The cost of storing a 360-degree light field via an LFN is two orders of magnitude lower than conventional methods such as the Lumigraph. Utilizing the analytical differentiability of neural implicit representations and a novel parameterization of light space, we further demonstrate the extraction of sparse depth maps from LFNs.
Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators
Anindita Maiti, Keegan Stoner, James Halverson
[ arXiv:2106.00694 ]
AbstractParameter-space and function-space provide two different duality frames in which to study neural networks. We demonstrate that symmetries of network densities may be determined via dual computations of network correlation functions, even when the density is unknown and the network is not equivariant. Symmetry-via-duality relies on invariance properties of the correlation functions, which stem from the choice of network parameter distributions. Input and output symmetries of neural network densities are determined, which recover known Gaussian process results in the infinite width limit. The mechanism may also be utilized to determine symmetries during training, when parameters are correlated, as well as symmetries of the Neural Tangent Kernel. We demonstrate that the amount of symmetry in the initialization density affects the accuracy of networks trained on Fashion-MNIST, and that symmetry breaking helps only when it is in the direction of ground truth.
Machine-Learning Non-Conservative Dynamics for New-Physics Detection
Ziming Li, Bohan Wang, Qi Meng, Wei Chen, Max Tegmark, Tie-Yan Liu
[ arXiv:2106.00026 ]
AbstractEnergy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our Neural New-Physics Detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and non-conservative components, which are represented by a Lagrangian Neural Network (LNN) and a universal approximator network (UAN), respectively, trained to minimize the force recovery error plus a constant λ times the magnitude of the predicted non-conservative force. We show that a phase transition occurs at λ=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846) and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms previous methods for predicting the future of a damped double pendulum.
The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider
T. Aarrestad, M. Van Beekveld, M. Bona, A. Bovenin, S. Caron, J. Davies, A. De Simone, C. Doglioni, J.M. Duarte, A. Farbin, H. Gupta, L. Hendriks, L. Heinrich, J. Howarth, P. Jawahar, A. Jueid, J. Lastow, A. Leinweber, J. Mamuzic, E. Merényi, A. Morandini, P. Moskvitina, C. Nellist, J. Ngadiuba, B. Ostdiek, M. Pierini, B. Ravina, R. Ruiz de Austri, S. Sekmen, M. Touranakou, M. Vaškevičiūte, R. Vilalta, J.-R. Vlimant, R. Verheyen, M. White, E. Wulff, E. Wallin, K.A. Wozniak, Z. Zhang
[ arXiv:2105.14027 | code ]
AbstractWe describe the outcome of a data challenge conducted as part of the Dark Machines initiative and the Les Houches 2019 workshop on Physics at TeV colliders. The challenged aims at detecting signals of new physics at the LHC using unsupervised machine learning algorithms. First, we propose how an anomaly score could be implemented to define model-independent signal regions in LHC searches. We define and describe a large benchmark dataset, consisting of > 1 Billion simulated LHC events corresponding to 10 fb−1 of proton-proton collisions at a center-of-mass energy of 13 TeV. We then review a wide range of anomaly detection and density estimation algorithms, developed in the context of the data challenge, and we measure their performance in a set of realistic analysis environments. We draw a number of useful conclusions that will aid the development of unsupervised new physics searches during the third run of the LHC, and provide our benchmark dataset for future studies at https://www.phenoMLdata.org. Code to reproduce the analysis is provided at https://github.com/bostdiek/DarkMachines-UnsupervisedChallenge.
Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution
Anders Andreassen, Patrick T. Komiske, Eric M. Metodiev, Benjamin Nachman, Adi Suresh, and Jesse Thaler
Workshop paper at ICLR 2021 SimDL Workshop [ arXiv:2105.04448 ]
AbstractA common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution approach in this setting called OmniFold. Deep learning enables this approach to be naturally unbinned and (variable-, and) high-dimensional. In contrast to model parameter estimation, the goal of deconvolution is to remove detector distortions in order to enable a variety of down-stream inference tasks. Our approach is the deep learning generalization of the common Richardson-Lucy approach that is also called Iterative Bayesian Unfolding in particle physics. We show how OmniFold can not only remove detector distortions, but it can also account for noise processes and acceptance effects.
A reconfigurable neural network ASIC for detector front-end data compression at the HL-LHC
Giuseppe Di Guglielmo, Farah Fahim, Christian Herwig, Manuel Blanco Valentin, Javier Duarte, Cristian Gingu, Philip Harris, James Hirschauer, Martin Kwok, Vladimir Loncar, Yingyi Luo, Llovizna Miranda, Jennifer Ngadiuba, Daniel Noonan, Seda Ogrenci-Memik, Maurizio Pierini, Sioni Summers, Nhan Tran
[ arXiv:2105.01683 ]
AbstractDespite advances in the programmable logic capabilities of modern trigger systems, a significant bottleneck remains in the amount of data to be transported from the detector to off-detector logic where trigger decisions are made. We demonstrate that a neural network autoencoder model can be implemented in a radiation tolerant ASIC to perform lossy data compression alleviating the data transmission problem while preserving critical information of the detector energy profile. For our application, we consider the high-granularity calorimeter from the CMS experiment at the CERN Large Hadron Collider. The advantage of the machine learning approach is in the flexibility and configurability of the algorithm. By changing the neural network weights, a unique data compression algorithm can be deployed for each sensor in different detector regions, and changing detector or collider conditions. To meet area, performance, and power constraints, we perform a quantization-aware training to create an optimized neural network hardware implementation. The design is achieved through the use of high-level synthesis tools and the hls4ml framework, and was processed through synthesis and physical layout flows based on a LP CMOS 65 nm technology node. The flow anticipates 200 Mrad of ionizing radiation to select gates, and reports a total area of 3.6 mm^2 and consumes 95 mW of power. The simulated energy consumption per inference is 2.4 nJ. This is the first radiation tolerant on-detector ASIC implementation of a neural network that has been designed for particle physics applications.
Towards Designing and Exploiting Generative Networks for Neutrino Physics Experiments using Liquid Argon Time Projection Chambers
Paul Lutkus, Taritree Wongjirad, Schuchin Aeron
Conference paper at ICLR 2021 [ | code ]
AbstractIn this paper, we show that a hybrid approach to generative modeling via combin- ing the decoder from an autoencoder together with an explicit generative model for the latent space is a promising method for producing images of particle tra- jectories in a liquid argon time projection chamber (LArTPC). LArTPCs are a type of particle physics detector used by several current and future experiments focused on studies of the neutrino. We implement a Vector-Quantized Variational Autoencoder (VQ-VAE) and PixelCNN which produces images with LArTPC- like features and introduce a method to evaluate the quality of the images using a semantic segmentation that identifies important physics-based features.
Scalable and Flexible Deep Bayesian Optimization with Auxiliary Information for Scientific Problems
Samuel Kim, Peter Y. Lu, Charlotte Loh, Jamie Smith, Jasper Snoek, Marin Soljačić
[ arXiv:2104.11667 ]
AbstractBayesian optimization (BO) is a popular paradigm for global optimization of expensive black-box functions, but there are many domains where the function is not completely black-box. The data may have some known structure, e.g. symmetries, and the data generation process can yield useful intermediate or auxiliary information in addition to the value of the optimization objective. However, surrogate models traditionally employed in BO, such as Gaussian Processes (GPs), scale poorly with dataset size and struggle to incorporate known structure or auxiliary information. Instead, we propose performing BO on complex, structured problems by using Bayesian Neural Networks (BNNs), a class of scalable surrogate models that have the representation power and flexibility to handle structured data and exploit auxiliary information. We demonstrate BO on a number of realistic problems in physics and chemistry, including topology optimization of photonic crystal materials using convolutional neural networks, and chemical property optimization of molecules using graph neural networks. On these complex tasks, we show that BNNs often outperform GPs as surrogate models for BO in terms of both sampling efficiency and computational cost.
AbstractThe identification and description of point sources is one of the oldest problems in astronomy; yet, even today the correct statistical treatment for point sources remains as one of the field's hardest problems. For dim or crowded sources, likelihood based inference methods are required to estimate the uncertainty on the characteristics of the source population. In this work, a new parametric likelihood is constructed for this problem using Compound Poisson Generator (CPG) functionals which incorporate instrumental effects from first principles. We demonstrate that the CPG approach exhibits a number advantages over Non-Poissonian Template Fitting (NPTF) - an existing parametric likelihood method - in a series of test scenarios in the context of X-ray astronomy. These demonstrations show that the effect of the point-spread function, effective area, and choice of point-source spatial distribution cannot, in general, be factorised as they are in the NPTF construction, while the new CPG construction is validated in these scenarios. Separately, an examination of the diffuse-flux emission limit is used to show that most simple choices of priors on the standard parameterisation of the population model can result in unexpected biases: when a model comprising both a point-source population and diffuse component is applied to this limit, nearly all observed flux will be assigned to either the population or to the diffuse component. A new parametrisation is presented for these priors which is demonstrated to properly estimate the uncertainties in this limit. In this choice of priors, the CPG correctly identifies that the fraction of flux assigned to the population model cannot be constrained by the data.
Why is AI hard and Physics simple?
Daniel A. Roberts
[ arXiv:2104.00008 ]
AbstractWe discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that the underlying project of machine learning and the underlying project of physics are strongly coupled through the principle of sparsity, and we call upon theoretical physicists to work on AI as physicists. As a first step in that direction, we discuss an upcoming book on the principles of deep learning theory that attempts to realize this approach.
Machine Learning the 6th Dimension: Stellar Radial Velocities from 5D Phase-Space Correlations
Adriana Dropulic, Bryan Ostdiek, Laura J. Chang, Hongwan Liu, Timothy Cohen, and Mariangela Lisanti
The Astrophysical Journal Letters, 2021, 915, L14 [ arXiv:2103.14039 ]
AbstractThe Gaia satellite will observe the positions and velocities of over a billion Milky Way stars. In the early data releases, the majority of observed stars do not have complete 6D phase-space information. In this Letter, we demonstrate the ability to infer the missing line-of-sight velocities until more spectroscopic observations become available. We utilize a novel neural network architecture that, after being trained on a subset of data with complete phase-space information, takes in a star's 5D astrometry (angular coordinates, proper motions, and parallax) and outputs a predicted line-of-sight velocity with an associated uncertainty. Working with a mock Gaia catalog, we show that the network can successfully recover the distributions and correlations of each velocity component for stars that fall within ∼5 kpc of the Sun. We also demonstrate that the network can accurately reconstruct the velocity distribution of a kinematic substructure in the stellar halo that is spatially uniform, even when it comprises a small fraction of the total star count.
Modern Machine Learning and Particle Physics
Matthew D. Schwartz
Harvard Data Science Review, 2021, Issue 3.2, 13 May [ arXiv:2103.12226 ]
AbstractOver the past five years, modern machine learning has been quietly revolutionizing particle physics. Old methodology is being outdated and entirely new ways of thinking about data are becoming commonplace. This article will review some aspects of the natural synergy between modern machine learning and particle physics, focusing on applications at the Large Hadron Collider. A sampling of examples is given, from signal/background discrimination tasks using supervised learning to direct data-driven approaches. Some comments on persistent challenges and possible future directions for the field are included at the end.
Deep learning: a statistical viewpoint
Peter L. Bartlett, Andrea Montanari, and Alexander Rakhlin
[ arXiv:2103.09177 ]
AbstractThe remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
hls4ml: An Open-Source Codesign Workflow to Empower Scientific Low-Power Machine Learning Devices
Farah Fahim, Benjamin Hawks, Christian Herwig, James Hirschauer, Sergo Jindariani, Nhan Tran, Luca P. Carloni, Giuseppe Di Guglielmo, Philip Harris, Jeffrey Krupa, Dylan Rankin, Manuel Blanco Valentin, Josiah Hester, Yingyi Luo, John Mamish, Seda Orgrenci-Memik, Thea Aarrestad, Hamza Javed, Vladimir Loncar, Maurizio Pierini, Adrian Alan Pol, Sioni Summers, Javier Duarte, Scott Hauck, Shih-Chieh Hsu, Jennifer Ngadiuba, Mia Liu, Duc Hoang, Edward Kreinar, Zhenbin Wu
[ arXiv:2103.05579 ]
AbstractAccessible machine learning algorithms, software, and diagnostic tools for energy-efficient devices and systems are extremely valuable across a broad range of application domains. In scientific domains, real-time near-sensor processing can drastically improve experimental design and accelerate scientific discoveries. To support domain scientists, we have developed hls4ml, an open-source software-hardware codesign workflow to interpret and translate machine learning algorithms for implementation with both FPGA and ASIC technologies. We expand on previous hls4ml work by extending capabilities and techniques towards low-power implementations and increased usability: new Python APIs, quantization-aware pruning, end-to-end FPGA workflows, long pipeline kernels for low power, and new device backends include an ASIC workflow. Taken together, these and continued efforts in hls4ml will arm a new generation of domain scientists with accessible, efficient, and powerful tools for machine-learning-accelerated discovery.
The Luminous and Double-Peaked Type Ic Supernova 2019stc: Evidence for Multiple Energy Sources
Sebastian Gomez, Edo Berger, Griffin Hosseinzadeh, Peter K. Blanchard, Matt Nicholl, V. Ashley Villar
The Astrophysical Journal, 2021, Vol. 913, Article 143 [ arXiv:2103.02611 ]
On the Minimal Error of Empirical Risk Minimization
Gil Kur, Alexander Rakhlin
[ arXiv:2102.12066 ]
AbstractRWe study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting to simplicity of the model generating the data. In the fixed design setting, we show that the error is governed by the global complexity of the entire class. In contrast, in random design, ERM may only adapt to simpler models if the local neighborhoods around the regression function are nearly as complex as the class itself, a somewhat counter-intuitive conclusion. We provide sharp lower bounds for performance of ERM for both Donsker and non-Donsker classes. We also discuss our results through the lens of recent studies on interpolation in overparameterized models.
Topological obstructions to autoencoding
Joshua Batson, C. Grace Haaf, Yonatan Kahn, Daniel A. Roberts
Journal of High Energy Physics, 2021, Issue 4, Article 280 [ arXiv:2102.08380 ]
AbstractAutoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of n-particle phase space.
On the convergence of group-sparse autoencoders
Emmanouil Theodosis, Bahareh Tolooshams, Pranay Tankala, Abiy Tasissa, Demba Ba
[ arXiv:2102.07003 ]
AbstractRecent approaches in the theoretical analysis of model-based deep learning architectures have studied the convergence of gradient descent in shallow ReLU networks that arise from generative models whose hidden layers are sparse. Motivated by the success of architectures that impose structured forms of sparsity, we introduce and study a group-sparse autoencoder that accounts for a variety of generative models, and utilizes a group-sparse ReLU activation function to force the non-zero units at a given layer to occur in blocks. For clustering models, inputs that result in the same group of active units belong to the same cluster. We proceed to analyze the gradient dynamics of a shallow instance of the proposed autoencoder, trained with data adhering to a group-sparse generative model. In this setting, we theoretically prove the convergence of the network parameters to a neighborhood of the generating matrix. We validate our model through numerical analysis and highlight the superior performance of networks with a group-sparse ReLU compared to networks that utilize traditional ReLUs, both in sparse coding and in parameter recovery tasks. We also provide real data experiments to corroborate the simulated results, and emphasize the clustering capabilities of structured sparsity models.
Path integral contour deformations for observables in SU(N) gauge theory
William Detmold, Gurtej Kanwar, Henry Lamm, Michael L. Wagman, Neill C. Warrington
Physical Review D, 2021, Vol. 103, Issue 9, Article 094517 [ arXiv:2101.12668 ]
AbstractPath integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to SU(N) lattice gauge theory that can reduce sign and signal-to-noise problems associated with complex actions and complex observables. For observables, these contours can be used to define deformed observables with identical expectation value but different variance. As a proof-of-principle, we apply machine learning techniques to optimize the deformed observables associated with Wilson loops in two dimensional SU(2) and SU(3) gauge theory. We study loops consisting of up to 64 plaquettes and achieve variance reduction of up to 4 orders of magnitude.
The LHC Olympics 2020: A Community Challenge for Anomaly Detection in High Energy Physics
Gregor Kasieczka (ed), Benjamin Nachman (ed), David Shih (ed), Oz Amram, Anders Andreassen, Kees Benkendorfer, Blaz Bortolato, Gustaaf Brooijmans, Florencia Canelli, Jack H. Collins, Biwei Dai, Felipe F. De Freitas, Barry M. Dillon, Ioan-Mihail Dinu, Zhongtian Dong, Julien Donini, Javier Duarte, D. A. Faroughy, Julia Gonski, Philip Harris, Alan Kahn, Jernej F. Kamenik, Charanjit K. Khosa, Patrick Komiske, Luc Le Pottier, Pablo Martín-Ramiro, Andrej Matevc, Eric Metodiev, Vinicius Mikuni, Inês Ochoa, Sang Eon Park, Maurizio Pierini, Dylan Rankin, Veronica Sanz, Nilai Sarda, Urous Seljak, Aleks Smolkovic, George Stein, Cristina Mantilla Suarez, Manuel Szewc, Jesse Thaler, Steven Tsan, Silviu-Marian Udrescu, Louis Vaslin, Jean-Roch Vlimant, Daniel Williams, Mikaeel Yunus
[ arXiv:2101.08320 ]
AbstractA new paradigm for data-driven, model-agnostic new physics searches at colliders is emerging, and aims to leverage recent breakthroughs in anomaly detection and machine learning. In order to develop and benchmark new anomaly detection methods within this framework, it is essential to have standard datasets. To this end, we have created the LHC Olympics 2020, a community challenge accompanied by a set of simulated collider events. Participants in these Olympics have developed their methods using an R&D dataset and then tested them on black boxes: datasets with an unknown anomaly (or not). This paper will review the LHC Olympics 2020 challenge, including an overview of the competition, a description of methods deployed in the competition, lessons learned from the experience, and implications for data analyses with future datasets as well as future colliders.
Introduction to Normalizing Flows for Lattice Field Theory
Michael S. Albergo, Denis Boyda, Daniel C. Hackett, Gurtej Kanwar, Kyle Cranmer, Sébastien Racanière, Danilo Jimenez Rezende, and Phiala E. Shanahan
[ arXiv:2101.08176 ]
AbstractThis notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428, and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.
E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once
Benjamin Nachman and Jesse Thaler
Physical Review D, 2021, Vol. 103, Issue 11, Article 116013 [ arXiv:2101.07263 | code ]
AbstractThere have been a number of recent proposals to enhance the performance of machine learning strategies for collider physics by combining many distinct events into a single ensemble feature. To evaluate the efficacy of these proposals, we study the connection between single-event classifiers and multi-event classifiers under the assumption that collider events are independent and identically distributed (IID). We show how one can build optimal multi-event classifiers from single-event classifiers, and we also show how to construct multi-event classifiers such that they produce optimal single-event classifiers. This is illustrated for a Gaussian example as well as for classification tasks relevant for searches and measurements at the Large Hadron Collider. We extend our discussion to regression tasks by showing how they can be phrased in terms of parametrized classifiers. Empirically, we find that training a single-event (per-instance) classifier is more effective than training a multi-event (per-ensemble) classifier, as least for the cases we studied, and we relate this fact to properties of the loss function gradient in the two cases. While we did not identify a clear benefit from using multi-event classifiers in the collider context, we speculate on the potential value of these methods in cases involving only approximate independence, as relevant for jet substructure studies.
Fast convolutional neural networks on FPGAs with hls4ml
Thea Aarrestad, Vladimir Loncar, Nicolò Ghielmetti, Maurizio Pierini, Sioni Summers, Jennifer Ngadiuba, Christoffer Petersson, Hampus Linander, Yutaro Iiyama, Giuseppe Di Guglielmo, Javier Duarte, Philip Harris, Dylan Rankin, Sergo Jindariani, Kevin Pedro, Nhan Tran, Mia Liu, Edward Kreinar, Zhenbin Wu, Duc Hoang
Machine Learning Science and Technology, 2021, Volume 2, Issue 4, Article 045015 [ arXiv:2101.05108 ]
AbstractWe introduce an automated tool for deploying ultra low-latency, low-power deep neural networks with convolutional layers on FPGAs. By extending the hls4ml library, we demonstrate an inference latency of 5μs using convolutional architectures, targeting microsecond latency applications like those at the CERN Large Hadron Collider. Considering benchmark models trained on the Street View House Numbers Dataset, we demonstrate various methods for model compression in order to fit the computational constraints of a typical FPGA device used in trigger and data acquisition systems of particle detectors. In particular, we discuss pruning and quantization-aware training, and demonstrate how resource utilization can be significantly reduced with little to no loss in model accuracy. We show that the FPGA critical resource consumption can be reduced by 97% with zero loss in model accuracy, and by 99% when tolerating a 6% accuracy degradation.
Detection and Parameter Estimation of Gravitational Waves from Binary Neutron-Star Mergers in Real LIGO Data using Deep Learning
Plamen G. Krastev, Kiranjyot Gill, V. Ashley Villar, Edo Berger
Physics Letters B, 2021, Vol. 815, Article 136161 [ arXiv:2012.13101 ]
AbstractOne of the key challenges of real-time detection and parameter estimation of gravitational waves from compact binary mergers is the computational cost of conventional matched-filtering and Bayesian inference approaches. In particular, the application of these methods to the full signal parameter space available to the gravitational-wave detectors, and/or real-time parameter estimation is computationally prohibitive. On the other hand, rapid detection and inference are critical for prompt follow-up of the electromagnetic and astro-particle counterparts accompanying important transients, such as binary neutron-star and black-hole neutron-star mergers. Training deep neural networks to identify specific signals and learn a computationally efficient representation of the mapping between gravitational-wave signals and their parameters allows both detection and inference to be done quickly and reliably, with high sensitivity and accuracy. In this work we apply a deep-learning approach to rapidly identify and characterize transient gravitational-wave signals from binary neutron-star mergers in real LIGO data. We show for the first time that artificial neural networks can promptly detect and characterize binary neutron star gravitational-wave signals in real LIGO data, and distinguish them from noise and signals from coalescing black-hole binaries. We illustrate this key result by demonstrating that our deep-learning framework classifies correctly all gravitational-wave events from the Gravitational-Wave Transient Catalog, GWTC-1 [Phys. Rev. X 9 (2019), 031040]. These results emphasize the importance of using realistic gravitational-wave detector data in machine learning approaches, and represent a step towards achieving real-time detection and inference of gravitational waves.
Field of Junctions: Extracting Boundary Structure at Low SNR
Dor Verbin, Todd Zickler
[ arXiv:2011.13866 ]
AbstractWe introduce a bottom-up model for simultaneously finding many boundary elements in an image, including contours, corners and junctions. The model explains boundary shape in each small patch using a 'generalized M-junction' comprising M angles and a freely-moving vertex. Images are analyzed using non-convex optimization to cooperatively find M+2 junction values at every location, with spatial consistency being enforced by a novel regularizer that reduces curvature while preserving corners and junctions. The resulting 'field of junctions' is simultaneously a contour detector, corner/junction detector, and boundary-aware smoothing of regional appearance. Notably, its unified analysis of contours, corners, junctions and uniform regions allows it to succeed at high noise levels, where other methods for segmentation and boundary detection fail.
AI Poincaré: Machine Learning Conservation Laws from Trajectories
Ziming Liu and Max Tegmark
Physical Review Letters, 2021, Volume 126, Issue 18, Article 180604 [ arXiv:2011.04698 ]
AbstractWe present AI Poincaré, a machine learning algorithm for auto-discovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational 3-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions and breakdown timescales for approximate conservation laws.
Parameter Inference from Event Ensembles and the Top-Quark Mass
Forrest Flesher, Katherine Fraser, Charles Hutchison, Bryan Ostdiek, Matthew D. Schwartz
[ arXiv:2011.04666 ]
AbstractOne of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be marginalized over when fitting the top-quark mass parameter. We compare three different methodologies for top-quark mass measurement: a classical histogram fitting procedure, similar to one commonly used in experiment optionally augmented with soft-drop jet grooming; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.
Quasi Anomalous Knowledge: Searching for new physics with embedded knowledge
Sang Eon Park, Dylan Rankin, Silviu-Marian Udrescu, Mikaeel Yunus, Philip Harris
Journal of High Energy Physics, 2021, Article 30 [ arXiv:2011.03550 | code ]
AbstractDiscoveries of new phenomena often involve a dedicated search for a hypothetical physics signature. Recently, novel deep learning techniques have emerged for anomaly detection in the absence of a signal prior. However, by ignoring signal priors, the sensitivity of these approaches is significantly reduced. We present a new strategy dubbed Quasi Anomalous Knowledge (QUAK), whereby we introduce alternative signal priors that capture some of the salient features of new physics signatures, allowing for the recovery of sensitivity even when the alternative signal is incorrect. This approach can be applied to a broad range of physics models and neural network architectures. In this paper, we apply QUAK to anomaly detection of new physics events at the CERN Large Hadron Collider utilizing variational autoencoders with normalizing flow.
Learning to Unknot
Sergei Gukov, James Halverson, Fabian Ruehle, and Piotr Sułkowski
Machine Learning - Science and Technology, 2021, Volume 2, Number 2, Article 025035 [ arXiv:2010.16263 ]
AbstractWe introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate $N$-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform well. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well for a wide range of crossing numbers and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves.
Enhancing searches for resonances with machine learning and moment decomposition
Ouail Kitouni, Benjamin Nachman, Constantin Weisser, and Mike Williams
Journal of High Energy Physics, 2021, Article 70 [ arXiv:2010.09745 | code ]