Efficient Subproblem Solves for Convergent Neural Network Training
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Javeed, Aurya↗
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Results for “Network convergence”
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Jet rotational metrics
Abstract Embedding symmetries in the architectures of deep neural networks can improve classification and network convergence in the context of jet substructure. These results hint at the existence of symmetries in jet energy depositions, such as rotational symmetry, arising from the physical features of the underlying processes. We introduce new jet observables, Jet Rotational Metrics (JRMs), which provide insights into the substructure of jets by comparing them to jets with perfect discrete rotational symmetry. We show that JRMs are formidable jet features, achieving good classification scores when used as inputs to deep neural networks. We also show that when used in combination with other jet observables, like N-subjettiness and EFPs, our features increase classification performance. The results suggest that JRMs may capture information not efficiently captured by the other observables, motivating the design of future jet observables for learning the underlying symmetries in the physical processes.
Physics↗
Exponential Backoff and Its Security Implications for Safety-Critical OT Protocols over TCP/IP Networks
The convergence of Operational Technology (OT) and Information Technology (IT) networks has become increasingly prevalent with the growth of Industrial Internet of Things (IIoT) applications. This shift, while enabling enhanced automation, remote monitoring, and data sharing, also introduces new challenges related to communication latency and cybersecurity. Oftentimes, legacy OT protocols were adapted to the TCP/IP stack without an extensive review of the ramifications to their robustness, performance, or safety objectives. To further accommodate the IT/OT convergence, protocol gateways were introduced to facilitate the migration from serial protocols to TCP/IP protocol stacks within modern IT/OT infrastructure. However, they often introduce additional vulnerabilities by exposing traditionally isolated protocols to external threats. This study investigates the security and reliability implications of migrating serial protocols to TCP/IP stacks and the impact of protocol gateways, utilizing two widely used OT protocols: Modbus TCP and DNP3. Our protocol analysis finds a significant safety-critical vulnerability resulting from this migration, and our subsequent tests clearly demonstrate its presence and impact. A multi-tiered testbed, consisting of both physical and emulated components, is used to evaluate protocol performance and the effects of device-specific implementation flaws. Through this analysis of specifications and behaviors during communication interruptions, we identify critical differences in fault handling and the impact on time-sensitive data delivery. The findings highlight how reliance on lower-level IT protocols can undermine OT system resilience, and they inform the development of mitigation strategies to enhance the robustness of industrial communication networks.
DNP3↗
Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent
Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.
Whiting, Wes (ORCID:0000000247505060)↗
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.
97 MATHEMATICS AND COMPUTING↗
Stabilization of the 81-channel coherent beam combination using machine learning
We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.
Wang, Dan↗
AEPF: Attention-Enabled Point Fusion for 3D Object Detection
Current state-of-the-art (SOTA) LiDAR-only detectors perform well for 3D object detection tasks, but point cloud data are typically sparse and lacks semantic information. Detailed semantic information obtained from camera images can be added with existing LiDAR-based detectors to create a robust 3D detection pipeline. With two different data types, a major challenge in developing multi-modal sensor fusion networks is to achieve effective data fusion while managing computational resources. With separate 2D and 3D feature extraction backbones, feature fusion can become more challenging as these modes generate different gradients, leading to gradient conflicts and suboptimal convergence during network optimization. To this end, we propose a 3D object detection method, Attention-Enabled Point Fusion (AEPF). AEPF uses images and voxelized point cloud data as inputs and estimates the 3D bounding boxes of object locations as outputs. An attention mechanism is introduced to an existing feature fusion strategy to improve 3D detection accuracy and two variants are proposed. These two variants, AEPF-Small and AEPF-Large, address different needs. AEPF-Small, with a lightweight attention module and fewer parameters, offers fast inference. AEPF-Large, with a more complex attention module and increased parameters, provides higher accuracy than baseline models. Experimental results on the KITTI validation set show that AEPF-Small maintains SOTA 3D detection accuracy while inferencing at higher speeds. AEPF-Large achieves mean average precision scores of 91.13, 79.06, and 76.15 for the car class’s easy, medium, and hard targets, respectively, in the KITTI validation set. Results from ablation experiments are also presented to support the choice of model architecture.
Chemistry↗
Levenberg–Marquardt multi-classification using hinge loss function
Incorporating higher-order optimization functions, such as Levenberg-Marquardt (LM) have revealed better generalizable solutions for deep learning problems. However, these higher-order optimization functions suffer from very large processing time and training complexity especially as training datasets become large, such as in multi-view classification problems, where finding global optima is a very costly problem. To solve this issue, we develop a solution for LM-enabled classification with, to the best of knowledge first-time implementation of hinge loss, for multiview classification. Hinge loss allows the neural network to converge faster and perform better than other loss functions such as logistic or square loss rates. Here we prove our method by experimenting with various multiclass classification challenges of varying complexity and training data size. The empirical results show the training time and accuracy rates achieved, highlighting how our method outperforms in all cases, especially when training time is limited. Our paper presents important results in the relationship between optimization and loss functions and how these can impact deep learning problems.
97 MATHEMATICS AND COMPUTING↗
Aggregate attack surface management for network discovery of operational technology
Interconnectivity has become a substratum of technology as the benefits of data-driven functionality are being realized in nearly all industries. Increased connectivity of Operational Technology (OT) exacerbates cyber risks because Industrial Control Systems (ICS) are becoming exposed to the Internet. These exposures are often done inadvertently through misconfigurations as additional network devices come online. Attack surface management (ASM) platforms can be used to identify vulnerabilities by performing external network discovery over the Internet using web spiders. These web spiders enable big data analytics of Internet of Things (IoT) devices as identifiable information of Internet-exposed equipment are archived in searchable databases that are made publicly available. There are a multitude of ASM service providers on the market. Here, this study was conducted to evaluate several commonly known tools to determine the aggregate attack surface of control systems. Queries were crafted by targeting commonly known manufacturers and communication protocols found in OT networks. Identified devices were that categorized based on technology types. Each query was replicated between several tools to target identical ICS equipment. Findings in this paper suggested a significant variance in the exposures discovered by each tool, but unique contributions were identified for each tool when a merged attack surface was derived. Therefore, all tools should be used in aggregate.
97 MATHEMATICS AND COMPUTING↗
Recipes for when physics fails: recovering robust learning of physics informed neural networks
Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.
97 MATHEMATICS AND COMPUTING↗
Polynomial-Spline Networks with Exact Integrals and Convergence Rates.
Abstract not provided.
Actor, Jonas↗
Accurate Consensus-based Distributed Averaging with Variable Time Delay in Support of Distributed Secondary Control Algorithms
We report that distributed secondary control has been widely used in hierarchical control structures, where multiple distributed generators (DGs) need to coordinate to regulate system voltage and frequency. In these systems, consensus algorithms determine the average of a group of dynamic states (e.g. voltages measured by a group of DGs). To be useful, consensus algorithms must be computationally efficient, stable and accurate. In practice, numerous practical implementation challenges significantly affect the consensus equilibrium. In this paper, we quantify the accuracy deviations of the distributed average observer algorithms proposed in the literature to demonstrate the problems with the state-of-the-art distributed averaging techniques. A novel approach is proposed that achieves accurate average tracking in the presence of time-varying communication delays among agents. In our implementation, time synchronization of all distributed controllers is enabled by a novel software platform, called Resilient Information Architecture Platform for the Smart Grid (RIAPS). The proposed distributed average observer is implemented on hardware controllers and its effectiveness is validated in a controller hardware-in-the-loop testbed.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Polynomial-Spline Networks with Exact Integrals and Convergence Rates.
Abstract not provided.
Actor, Jonas↗
CRCNS22 Learning Rules in the Hippocampus and their Mapping to Neuromorphic Systems (Final Technical Report)
Large scale biologically-realistic computational models are key to investigating the interplay between structure and function in nervous systems, thus paving the way to new clinical methods and neuro-inspired computing solutions. This project focuses on the hippocampus, in particular the CA3-CA1 regions, due to their role in associative learning and memory, pattern separation and completion, and spatial navigation. Investigations into the neuronal organization and learning rule(s) of this circuit can shed light into how declarative memories are formed, stored, recalled and forgotten and inform computational, experimental and clinical neuroscience work. Our project aims at developing a novel data-driven methodology supported by a broad heterogeneous base of neuroscience experimental knowledge and inspired from advances in computer science and engineering. Specifically, this work will benchmark existing and new learning rules within a full-scale spiking neural network simulation of the CA3-CA1 region. The model will be based on an open-source repository, called the Hippocampome, which contains neuronal morphologies, firing patterns, synapse probabilities, and most other required parameters for all known neuron types in the rodent hippocampal formation. The model will be first trained in a supervised fashion for associative memory tasks using backpropagation through time traditionally used in computer science, enhanced with a new technique called the surrogate gradient method. This optimization method will be used to obtain a global loss minimization, but it is not biologically inspired as it assumes the use of data not locally available to the synapses. However, we propose its use as a benchmarking tool, to compare the training performance of local biologically plausible and hardware-mappable learning rules at scale. New rules or combinations will be proposed and tested as needed, based on the obtained results. Progress in this area will also drive the development of novel hardware-mappable algorithms for continual lifelong learning and categorization of new events from few presented examples. This project goes beyond the existing state-of-the-art by looking at large scale realistic neuronal circuits as networks trainable via global optimization methods such as surrogate gradient descent. The objective function of the brain that supports learning is largely unknown, but it is likely that it operates through local learning rules. Studying network trajectories around local minima as proposed in this work represents a useful strategy for understanding whether a network is training by using a specific (set of) learning rule(s). Starting from a completely untrained network is a challenging test since it is difficult to determine how the learning rule affects the trajectory of the network. This interdisciplinary project will help understand what rule governs learning in these regions or if multiple learning rules are involved. The work will develop a robust methodology to measure if the network is converging to the target solution, oscillating around it, or diverging away.
59 BASIC BIOLOGICAL SCIENCES↗
Atomic resolution convergent beam electron diffraction analysis using convolutional neural networks
Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO 3 collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.
36 MATERIALS SCIENCE↗
Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks
Abstract We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ( κ ) from photometric measurements of galaxies along a given line of sight (LOS). The method is of particular interest in strong gravitational time-delay cosmography (TDC), where characterizing the “external convergence” ( κ ext ) from the lens environment and LOS is necessary for precise Hubble constant ( H 0 ) inference. Starting from a large-scale simulation with a κ resolution of ∼1′, we introduce fluctuations on galaxy–galaxy lensing scales of ∼1″ and extract random sight lines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1000 sight lines, the BGNN infers the individual κ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of κ precisely and without bias (within the 2 σ credible interval), resulting in a contribution to the H 0 error budget well under 1%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sight line, extracts a stronger κ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the κ ext characterization for precision TDC. The code is available as a public Python package, Node to Joy ⏬ .
79 ASTRONOMY AND ASTROPHYSICS↗
Real-Time Distributed Control of Smart Inverters for Network-level Optimization
The limitations of centralized optimization methods in managing electric power distribution systems operations have led to the distributed paradigm of computing and decision-making. Unfortunately, the existing distributed optimization algorithms are limited in their applicability to managing fast varying phenomena such as those resulting from highly variable Distributed Energy Resource (DER) generation patterns. They require a large number of communication rounds (in the order of 10 2 to 10 3 ) among the computing agents to solve one instance of the optimization problem. Related real-time distributed control methods are equally limited in their applications to power distribution systems with fast-changing DER generation; they require hundreds of rounds of communication and thus are slow in tracking the network-level optimal solutions. In this paper, we propose a novel distributed voltage controller that provides a fast-tracking of rapidly varying DER generation profiles while simultaneously converging to network-level optimal solutions within a few communication rounds. The proposed control algorithm leverages the radial topology of the system, which reduces the required communication rounds to reach the network-level optimum solution by order of magnitude. The novelty lies in carefully reducing the electrical network model from the perspective of each distributed controller and enabling appropriate data sharing among upstream and downstream nodes to achieve fast convergence. The simulation results demonstrate the effectiveness of the proposed approach in minimizing the feeder losses while maintaining the node voltage within the pre-specified limits.
voltage control, optimization, reactive power, inv↗