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Register a new userHow neural networks find generalizable solutions: Self-tuned annealing in deep learning
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Despite the tremendous success of Stochastic Gradient Descent (SGD) algorithm in deep learning, little is known about how SGD finds generalizable solutions in the high-dimensional weight space. By analyzing the learning dynamics and loss function landscape, we discover a robust inverse relation between the weight variance and the landscape flatness (inverse of curvature) for all SGD-based learning algorithms. To explain the inverse variance-flatness relation, we develop a random landscape theory, which shows that the SGD noise strength (effective temperature) depends inversely on the landscape flatness. Our study indicates that SGD attains a self-tuned landscape-dependent annealing strategy to find generalizable solutions at the flat minima of the landscape. Finally, we demonstrate how these new theoretical insights lead to more efficient algorithms, e.g., for avoiding catastrophic forgetting.
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X-ray diffraction (XRD) data acquisition and analysis is among the most time-consuming steps in the development cycle of novel thin-film materials. We propose a machine-learning-enabled approach to predict crystallographic dimensionality and space group from a limited number of thin-film XRD patterns. We overcome the scarce-data problem intrinsic to novel materials development by coupling a supervised machine learning approach with a model agnostic, physics-informed data augmentation strategy using simulated data from the Inorganic Crystal Structure Database (ICSD) and experimental data. As a test case, 115 thin-film metal halides spanning 3 dimensionalities and 7 space-groups are synthesized and classified. After testing various algorithms, we develop and implement an all convolutional neural network, with cross validated accuracies for dimensionality and space-group classification of 93% and 89%, respectively. We propose average class activation maps, computed from a global average pooling layer, to allow high model interpretability by human experimentalists, elucidating the root causes of misclassification. Finally, we systematically evaluate the maximum XRD pattern step size (data acquisition rate) before loss of predictive accuracy occurs, and determine it to be 0.16{deg}, which enables an XRD pattern to be obtained and classified in 5.5 minutes or less.
In liquid argon time projection chambers exposed to neutrino beams and running on or near surface levels, cosmic muons and other cosmic particles are incident on the detectors while a single neutrino-induced event is being recorded. In practice, this means that data from surface liquid argon time projection chambers will be dominated by cosmic particles, both as a source of event triggers and as the majority of the particle count in true neutrino-triggered events. In this work, we demonstrate a novel application of deep learning techniques to remove these background particles by applying semantic segmentation on full detector images from the SBND detector, the near detector in the Fermilab Short-Baseline Neutrino Program. We use this technique to identify, at single image-pixel level, whether recorded activity originated from cosmic particles or neutrino interactions.
We present a simulation-based study using deep convolutional neural networks (DCNNs) to identify neutrino interaction vertices in the MINERvA passive targets region, and illustrate the application of domain adversarial neural networks (DANNs) in this context. DANNs are designed to be trained in one domain (simulated data) but tested in a second domain (physics data) and utilize unlabeled data from the second domain so that during training only features which are unable to discriminate between the domains are promoted. MINERvA is a neutrino-nucleus scattering experiment using the NuMI beamline at Fermilab. $A$-dependent cross sections are an important part of the physics program, and these measurements require vertex finding in complicated events. To illustrate the impact of the DANN we used a modified set of simulation in place of physics data during the training of the DANN and then used the label of the modified simulation during the evaluation of the DANN. We find that deep learning based methods offer significant advantages over our prior track-based reconstruction for the task of vertex finding, and that DANNs are able to improve the performance of deep networks by leveraging available unlabeled data and by mitigating network performance degradation rooted in biases in the physics models used for training.
We investigate the topics of sensitivity and robustness in feedforward and convolutional neural networks. Combining energy landscape techniques developed in computational chemistry with tools drawn from formal methods, we produce empirical evidence indicating that networks corresponding to lower-lying minima in the optimization landscape of the learning objective tend to be more robust. The robustness estimate used is the inverse of a proposed sensitivity measure, which we define as the volume of an over-approximation of the reachable set of network outputs under all additive $l_{infty}$-bounded perturbations on the input data. We present a novel loss function which includes a sensitivity term in addition to the traditional task-oriented and regularization terms. In our experiments on standard machine learning and computer vision datasets, we show that the proposed loss function leads to networks which reliably optimize the robustness measure as well as other related metrics of adversarial robustness without significant degradation in the classification error. Experimental results indicate that the proposed method outperforms state-of-the-art sensitivity-based learning approaches with regards to robustness to adversarial attacks. We also show that although the introduced framework does not explicitly enforce an adversarial loss, it achieves competitive overall performance relative to methods that do.
We investigate a stationary processs crypticity---a measure of the difference between its hidden state information and its observed information---using the causal states of computational mechanics. Here, we motivate crypticity and cryptic order as physically meaningful quantities that monitor how hidden a hidden process is. This is done by recasting previous results on the convergence of block entropy and block-state entropy in a geometric setting, one that is more intuitive and that leads to a number of new results. For example, we connect crypticity to how an observer synchronizes to a process. We show that the block-causal-state entropy is a convex function of block length. We give a complete analysis of spin chains. We present a classification scheme that surveys stationary processes in terms of their possible cryptic and Markov orders. We illustrate related entropy convergence behaviors using a new form of foliated information diagram. Finally, along the way, we provide a variety of interpretations of crypticity and cryptic order to establish their naturalness and pervasiveness. Hopefully, these will inspire new applications in spatially extended and network dynamical systems.
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