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At least 73 records · Page 4

PANTHER: A Programmable Architecture for Neural Network Training Harnessing Energy-Efficient ReRAM

The wide adoption of deep neural networks has been accompanied by ever-increasing energy and performance demands due to the expensive nature of training them. Additionally, numerous special-purpose architectures have been proposed to accelerate training: both digital and hybrid digital-analog using resistive RAM (ReRAM) crossbars. ReRAM-based accelerators have demonstrated the effectiveness of ReRAM crossbars at performing matrix-vector multiplication operations that are prevalent in training. However, they still suffer from inefficiency due to the use of serial reads and writes for performing the weight gradient and update step. A few works have demonstrated the possibility of performing outer products in crossbars, which can be used to realize the weight gradient and update step without the use of serial reads and writes. However, these works have been limited to low precision operations which are not sufficient for typical training workloads. Moreover, they have been confined to a limited set of training algorithms for fully-connected layers only. To address these limitations, we propose a bit-slicing technique for enhancing the precision of ReRAM-based outer products, which is substantially different from bit-slicing for matrix-vector multiplication only. We incorporate this technique into a crossbar architecture with three variants catered to different training algorithms. To evaluate our design on different types of layers in neural networks (fully-connected, convolutional, etc.) and training algorithms, we develop PANTHER, an ISA-programmable training accelerator with compiler support. Our design can also be integrated into other accelerators in the literature to enhance their efficiency. Our evaluation shows that PANTHER achieves up to 8.02×, 54.21×, and 103× energy reductions as well as 7.16×, 4.02×, and 16× execution time reductions compared to digital accelerators, ReRAM-based accelerators, and GPUs, respectively.

42 ENGINEERING↗

Exchange‐Interaction‐Like Behavior in Ferroelectric Bilayers

Abstract Interlayer coupling in materials, such as exchange interactions at the interface between an antiferromagnet and a ferromagnet, can produce exotic phenomena not present in the parent materials. While such interfacial coupling in magnetic systems is widely studied, there is considerably less work on analogous electric counterparts (i.e., akin to electric “exchange‐bias‐like” or “exchange‐spring‐like” interactions between two polar materials) despite the likelihood that such effects can also engender new features associated with anisotropic electric dipole alignment. Here, electric analogs of such exchange interactions are reported, and their physical origins are explained for bilayers of in‐plane polarized Pb 1−x Sr x TiO 3 ferroelectrics. Variation of the strontium content and thickness of the layers provides for deterministic control over the switching properties of the bilayer system resulting in phenomena analogous to an exchange‐spring interaction and, leveraging added control of these interactions with an electric field, the ability to realize multistate‐memory function. Such observations not only hold technological promise for ferroelectrics and multiferroics but also extend the similarities between ferromagnetic and ferroelectric materials to include the manifestation of exchange‐interaction‐like phenomena.

Kavle, Pravin↗

Strong Axiality in a Dysprosium(III) Bis(borolide) Complex Leads to Magnetic Blocking at 65 K

Substituted dysprosocenium complexes of the type [Dy(Cp R ) 2 ] + exhibit slow magnetic relaxation at cryogenic temperatures and have emerged as top-performing single-molecule magnets. The remarkable properties of these compounds derive in part from the strong axial ligand field afforded by the cyclopentadiene anions, and the design of analogous compounds with even stronger ligand fields is one promising route toward identifying new single-molecule magnets that retain a magnetic memory at even higher temperatures. Here, we report the synthesis and characterization of a dysprosium bis(borolide) compound, [K(18-crown-6)][Dy(BC 4 Ph 5 ) 2 ] (1), featuring the dysprosocenate anion [Dy(BC 4 Ph 5 ) 2 ] - with a pseudoaxial coordination environment afforded by two dianionic pentaphenyl borolide ligands. Variable-field magnetization data reveal open magnetic hysteresis up to 66 K, establishing 1 as a top-performing single-molecule magnet among its dysprosocenium analogues. Ac magnetic susceptibility data indicate that 1 relaxes via an Orbach mechanism above ~80 K with U eff = 1500(100) cm -1 and τ 0 = 10 -12.0(9) s, whereas Raman relaxation and quantum tunneling of the magnetization dominate at lower temperatures. Compound 1 exhibits a 100 s blocking temperature of 65 K, among the highest reported for dysprosium-based single-molecule magnets. Ab initio spin dynamics calculations support the experimental U eff and τ 0 values and enable a quantitative comparison of the relaxation dynamics of 1 and two representative dysprosocenium cations, yielding additional insights into the impact of the crystal field splitting and vibronic coupling on the observed relaxation behavior. Importantly, compound 1 represents a step toward the development of alternatives to substituted dysprosocenium single-molecule magnets with increased axiality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanosecond Gated CMOS Camera (NSGCC) ICD (Rev. 2.1)

The Ultra-Fast X-ray Imager (UXI) program is an ongoing effort at Sandia National Laboratories to create high speed, multi-frame, time-gated Read Out Integrated Circuits (ROICs), and a corresponding suite of photodetectors to image a wide variety of High Energy Density (HED) physics experiments on both Sandia’s Z-Machine and LLNL’s National Ignition Facility (NIF). Several cameras have been designed over the length of the program; one of the most recent is the Icarus, which is an improvement on past imagers (Furi and Hippogriff). A second sensor that can be connected is the Daedalus sensor. The Icarus is a 1024 × 512-pixel array with either 25 μm or 8 µm spatial resolution containing four frames of storage per pixel and has improved timing generation and distribution components while achieved 2 ns time gating. The Daedalus sensor is also a 1024 x 512-pixel array with 25 µm special resolution containing three frames of storage per pixel and has an increased set of features for a wider variety of applications from interlacing of rows in each frame to configurability of all shutters. See Section 14 for details regarding the Icarus implementation of the firmware and Section 15 for details regarding the Daedalus implementation. Due to the unique test environments UXI sensors are targeted for, full custom hardware was required to physically mount an Icarus or Daedalus sensor, manage its various functions, and read out pixel data for transfer to a host computer. Beyond experimental functionality, the hardware also needed to accommodate sensor characterization requirements. Lawrence Livermore National Laboratory’s ‘Version 4.0 Board’ was the result of these efforts. It mounts all the components required to fully utilize the Icarus and Daedalus sensors including analog to digital converters to convert pixel data and various system voltages to digital form for readout and analysis, DAC channels for remote configuration of critical bias voltages, static random-access memories to buffer pixel data, RS422 and Gigabit Ethernet communications for remote access, and an FPGA to tie these components together. This document describes the FPGA electrical interfaces in detail to allow the reader a greater understanding of the device, and to facilitate implementation of custom software to control and manage it. The Version 4.0 Board is a continuation of the Nano-second Gated CMOS hardware design that retains much of the functionality of the Version 1.0 Board while adding features including a DAC instead of digital potentiometers, as well as sensors for pressure and radiation. The Version 4.0 board is intended for applications requiring tight form-factor enclosures. It is composed of two stacking boards; one holds the FPGA and regulators to power the various components of the board while the other contains the mating connector to the sensor, image-readoff ADCs, the DAC, and other components.

42 ENGINEERING↗

XploreNAS : Explore Adversarially Robust and Hardware-efficient Neural Architectures for Non-ideal Xbars

Compute In-Memory platforms such as memristive crossbars are gaining focus as they facilitate acceleration of Deep Neural Networks (DNNs) with high area and compute efficiencies. However, the intrinsic non-idealities associated with the analog nature of computing in crossbars limits the performance of the deployed DNNs. Furthermore, DNNs are shown to be vulnerable to adversarial attacks leading to severe security threats in their large-scale deployment. Thus, finding adversarially robust DNN architectures for non-ideal crossbars is critical to the safe and secure deployment of DNNs on the edge. This work proposes a two-phase algorithm-hardware co-optimization approach called XploreNAS that searches for hardware efficient and adversarially robust neural architectures for non-ideal crossbar platforms. We use the one-shot Neural Architecture Search approach to train a large Supernet with crossbar-awareness and sample adversarially robust Subnets therefrom, maintaining competitive hardware efficiency. Our experiments on crossbars with benchmark datasets (SVHN, CIFAR10, CIFAR100) show up to ~8–16% improvement in the adversarial robustness of the searched Subnets against a baseline ResNet-18 model subjected to crossbar-aware adversarial training. We benchmark our robust Subnets for Energy-Delay-Area-Products (EDAPs) using the Neurosim tool and find that with additional hardware efficiency–driven optimizations, the Subnets attain ~1.5–1.6× lower EDAPs than ResNet-18 baseline.

97 MATHEMATICS AND COMPUTING↗

Hardware-Based Randomized Encoding for Sensor Authentication in Power Grid SCADA Systems

Supervisory Control and Data Acquisition (SCADA) systems are utilized extensively in critical power grid infrastructures. Modern SCADA systems have been proven to be susceptible to cyber-security attacks and require improved security primitives in order to prevent unwanted influence from an adversarial party. One section of weakness in the SCADA system is the integrity of field level sensors providing essential data for control decisions at a master station. In this paper we propose a lightweight hardware scheme providing inferred authentication for SCADA sensors by combining an analog to digital converter and a permutation generator as a single integrated circuit. Through this method we encode critical sensor data at the time of sensing, so that unencoded data is never stored in memory, increasing the difficulty of software attacks. We show through experimentation how our design stops both software and hardware false data injection attacks occurring at the field level of SCADA systems.

42 ENGINEERING↗

Operator evolution from the similarity renormalization group and the Magnus expansion

The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. In this work, we show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Introduction: Neuromorphic Materials

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

Circuits↗

Ionizing radiation effects in SONOS-based neuromorphic inference accelerators

Here, we evaluate the sensitivity of neuromorphic inference accelerators based on Silicon-Oxide-Nitride-Oxide-Silicon (SONOS) charge trap memory arrays to total ionizing dose (TID) effects. Data retention statistics were collected for 16 Mbit of 40 nm SONOS digital memory exposed to ionizing radiation from a Co-60 source, showing good retention of the bits up to the maximum dose of 500 krad(Si). Using this data, we formulate a rate-equation-based model for the TID response of trapped charge carriers in the ONO stack, and predict the effect of TID on intermediate device states between ‘program’ and ‘erase’. This model is then used to simulate arrays of low-power, analog SONOS devices that store 8-bit neural network weights and support in situ matrix-vector multiplication. We evaluate the accuracy of the irradiated SONOS-based inference accelerator on two image recognition tasks – CIFAR-10 and the challenging ImageNet dataset – using state-of-the-art convolutional neural networks, such as ResNet-50. We find that across the datasets and neural networks evaluated, the accelerator tolerates a maximum TID between 10 krad(Si) and 100 krad(Si), with deeper networks being more susceptible to accuracy losses due to TID.

43 PARTICLE ACCELERATORS↗

Superconducting Hyperdimensional Associative Memory Circuit for Scalable Machine Learning

Here we propose a generalized architecture for the first rapid-single-flux-quantum (RSFQ) associative memory circuit. The circuit employs hyperdimensional computing (HDC), a machine learning (ML) paradigm utilizing vectors with dimensionality in the thousands to represent information. HDC designs have small memory footprints, simple computations, and simple training algorithms compared to superconducting neural network accelerators (SNNAs), making them a better option for scalable SFQ machine learning (ML) solutions. The proposed superconducting HDC (SHDC) circuit uses entirely on-chip RSFQ memory which is tightly integrated with logic, operates at 33.3 GHz, is applicable to general ML tasks, and is manufacturable at practically useful scales given current SFQ fabrication limits. Tailored to a language recognition task, SHDC consists of ~ 2-20 M Josephson junctions (JJs) and consumes up to three times less power than an analogous CMOS HDC circuit while achieving 78-84% higher throughput. SHDC is capable of outperforming the state of the art RSFQ SNNA, SuperNPU, by 48-99% for all benchmark NN architectures tested while occupying up to 90% less area and consuming up to nine times less power. To the best of the authors' knowledge, SHDC is currently the only superconducting ML approach feasible at practically useful scales for real-world ML tasks and capable of online learning.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with q body ( q > 2 ) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for N ≤ 64 fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching N = 64 is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature. Published by the American Physical Society 2024

Physics↗

Probabilistic Nanomagnetic Memories for Uncertain and Robust Machine Learning

This project evaluated the use of emerging spintronic memory devices for robust and efficient variational inference schemes. Variational inference (VI) schemes, which constrain the distribution for each weight to be a Gaussian distribution with a mean and standard deviation, are a tractable method for calculating posterior distributions of weights in a Bayesian neural network such that this neural network can also be trained using the powerful backpropagation algorithm. Our project focuses on domain-wall magnetic tunnel junctions (DW-MTJs), a powerful multi-functional spintronic synapse design that can achieve low power switching while also opening the pathway towards repeatable, analog operation using fabricated notches. Our initial efforts to employ DW-MTJs as an all-in-one stochastic synapse with both a mean and standard deviation didn’t end up meeting the quality metrics for hardware-friendly VI. In the future, new device stacks and methods for expressive anisotropy modification may make this idea still possible. However, as a fall back that immediately satisfies our requirements, we invented and detailed how the combination of a DW-MTJ synapse encoding the mean and a probabilistic Bayes-MTJ device, programmed via a ferroelectric or ionically modifiable layer, can robustly and expressively implement VI. This design includes a physics-informed small circuit model, that was scaled up to perform and demonstrate rigorous uncertainty quantification applications, up to and including small convolutional networks on a grayscale image classification task, and larger (Residual) networks implementing multi-channel image classification. Lastly, as these results and ideas all depend upon the idea of an inference application where weights (spintronic memory states) remain non-volatile, the retention of these synapses for the notched case was further interrogated. These investigations revealed and emphasized the importance of both notch geometry and anisotropy modification in order to further enhance the endurance of written spintronic states. In the near future, these results will be mapped to effective predictions for room temperature and elevated operation DW-MTJ memory retention, and experimentally verified when devices become available.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Quantum Gravity and Laser Interferometry: Towards Observable Predictions

Understanding quantum gravity remains one of the deepest challenges in modern physics, as direct experimental access to Planck-scale effects is beyond current technological reach. However, recent theoretical advances indicate that quantum fluctuations of spacetime may produce measurable effects in precision experiments, particularly near causal horizons. This opens new avenues for testing quantum gravity phenomena through high-precision measurement techniques. This dissertation develops multiple theoretical models to characterize these effects and examines their potential observational signatures in future gravitational wave interferometers. We begin by investigating the role of quantum fluctuations in near-horizon geometries through the lens of the AdS/CFT correspondence, which provides a powerful framework for understanding the interplay between quantum field theory and general relativity via holographic principles. By modeling stochastic energy-momentum sources in Rindler-AdS spacetime, we demonstrate that vacuum fluctuations transform the Einstein equations into a Langevin-type stochastic differential equation, leading to potentially observable fluctuations in photon traversal times. Extending this approach to Minkowski spacetime, we establish a correspondence between gravitational shockwaves and fluid dynamics, showing that near-horizon perturbations satisfy an equation analogous to that governing incompressible fluids, thereby reinforcing the membrane paradigm and hydrodynamic analogies in the context of the fluid/gravity duality. Furthermore, we construct the covariant phase space of a spherically symmetric causal diamond in Minkowski spacetime, identifying two fundamental charges that govern its evolution. These results provide a foundation for quantizing causal horizons and understanding their microscopic degrees of freedom. Building upon these theoretical developments, we further examine a related stochastic phenomenon: the gravitational wave memory background arising from the cumulative memory steps produced by supermassive black hole mergers. After reviewing the standard stochastic gravitational wave background, gravitational memory effects, and BMS symmetries, we model the stochastic memory background using a Brownian motion framework. We show that while the cumulative memory background initially appears above the sensitivity curve of space-based interferometers like LISA, the realistic subtraction of individually resolvable merger events substantially suppresses the residual signal, making its detection more challenging. This highlights the critical importance of source subtraction when evaluating the detectability of gravitational memory effects. By bridging fundamental theory with experimental prospects, this dissertation contributes to the ongoing effort to uncover the quantum nature of spacetime through precision measurement techniques. Whether through detecting quantum spacetime fluctuations, gravitational memory backgrounds, or probing the symmetries of causal horizons, the pursuit of observable quantum gravity phenomena continues to expand the frontiers of both theory and experiment.

Zhang, Yiwen [Caltech] (ORCID:0000000323559416)↗

A structural blueprint for interleukin-21 signal modulation

Interleukin-21 (IL-21) plays a critical role in generating immunological memory by promoting the germinal center reaction, yet clinical use of IL-21 remains challenging because of its pleiotropy and association with autoimmune disease. To better understand the structural basis of IL-21 signaling, we determine the structure of the IL-21-IL-21R-γc ternary signaling complex by X-ray crystallography and a structure of a dimer of trimeric complexes using cryo-electron microscopy. Guided by the structure, we design analogs of IL-21 by introducing substitutions to the IL-21-γc interface. These IL-21 analogs act as partial agonists that modulate downstream activation of pS6, pSTAT3, and pSTAT1. These analogs exhibit differential activity on T and B cell subsets and modulate antibody production in human tonsil organoids. These results clarify the structural basis of IL-21 signaling and offer a potential strategy for tunable manipulation of humoral immunity.

59 BASIC BIOLOGICAL SCIENCES↗

Gravitational memory and Ward identities in the local detector frame

Gravitational memory, which describes the permanent shift in the strain after the passage of gravitational waves, is directly related to Weinberg’s soft graviton theorems and the Bondi-Metzner-Sachs (BMS) symmetry group of asymptotically flat space-times. In this work, we provide an equivalent description of the phenomenon in local coordinates around gravitational wave detectors, such as transverse-traceless (TT) gauge. We show that gravitational memory is encoded in large residual diffeomorphisms in this gauge, which include time-dependent anisotropic spatial rescalings, and prove their equivalence to BMS transformations when translated to TT gauge. We then derive the associated Ward identities and associated soft theorems, for both scattering amplitudes and equal-time (in-in) correlation functions, and explicitly check their validity for planar gravitational waves. Furthermore, the in-in identities are recognized as the flat-space analog of the well-known inflationary consistency relations.

General relativity↗

Atomic layer deposition and its derivatives for extreme ultraviolet (EUV) photoresist applications

Solution-processed photoresists have been forerunners in semiconductor patterning for decades. Even with the drastic reduction in photolithography wavelength, traditional spin-on resists still support the fabrication of the most advanced, sub-5 nm node logic and memory devices using EUV lithography (EUVL) (λ = 13.5 nm). However, trade-off between resolution, sensitivity, and roughness in the conventional resists pose a critical challenge in the race towards device downscaling to 1 nm node. While great efforts are being made to improve spin-on EUV photoresist performance, there has been emergence of new approaches focused on developing novel resists via vapor-phase processing routes, such as atomic layer deposition (ALD) and its analogs. This review summarizes recent advances in EUVL photoresist development based on ALD and its derivative techniques, which include ALD-based inorganic–organic dry resists and hybrid resists synthesized by infiltrating conventional spin-on resists. Despite being in the early stage, initial studies have shown the great potential of ALD applications in EUVL photoresist development.

36 MATERIALS SCIENCE↗

ECRAM Materials, Devices, Circuits and Architectures: A Perspective

Abstract Non‐von‐Neumann computing using neuromorphic systems based on two‐terminal resistive nonvolatile memory elements has emerged as a promising approach, but its full potential has not been realized due to the lack of materials and devices with the appropriate attributes. Unlike memristors, which require large write currents to drive phase transformations or filament growth, electrochemical random access memory (ECRAM) decouples the “write” and “read” operations using a “gate” electrode to tune the conductance state through charge‐transfer reactions, and every electron transferred through the external circuit in ECRAM corresponds to the migration of ≈1 ion used to store analogue information. Like static dopants in traditional semiconductors, electrochemically inserted ions modulate the conductivity by locally perturbing a host's electronic structure; however, ECRAM does so in a dynamic and reversible manner. The resulting change in conductance can span orders of magnitude, from gradual increments needed for analog elements, to large, abrupt changes for dynamically reconfigurable adaptive architectures. In this in‐depth perspective, the history of ECRAM, the recent progress in devices spanning organic, inorganic, and 2D materials, circuits, architectures, the rich portfolio of challenging, fundamental questions, and how ECRAM can be harnessed to realize a new paradigm for low‐power neuromorphic computing are discussed.

Talin, A. Alec↗

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗