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Unimodular gravity (UG) is classically considered identical to General Relativity (GR). However, due to restricted diffeomorphism symmetry, the Bianchi identites do not lead to the conservation of energy-momentum tensor. Thus, the conservation of energy-momentum tensor needs to be separately assumed in order to reconcile with GR. Relaxing this assumption, one finds that the conservation violation can lead to differences with GR, which can be subsequently examined in astrophysical and cosmological scenarios. To this end, we examine the predictions of UG in the context of binary systems emitting gravitational radiation. Primarily, we show how the field equations involve a diffusion function which quantifies the measure of non-conservation. Due to this violation, the dispersion relation is modified. Incorporating these changes, we provide an expression for the energy loss by the binaries, which reduces to Peters-Mathews result in the GR limit. Using binary pulsar data, we constrain the theory parameter $\zeta$ (which signifies non-conservation) by determining the rate of orbital decay. The strongest constrain on $\zeta$ comes out to be $\vert \zeta \vert \leq 5\times 10^{-4}$ which is better by an order of magnitude than an existing equivalent constraint coming from the tidal deformability of the neutron stars., Comment: 16 pages, References added

In this article, we examine entangled quantum probes in geodesic trajectories in a background with gravitational wave (GW) burst. In particular, these quantum probes are prepared initially either in the symmetric or anti-symmetric Bell's states and we study the radiative process as the GW burst passes. Our considered GW burst backgrounds have the profiles of -- Heaviside-theta, $tanh$, Gaussian, and $sech$-squared functions respectively. The first two burst profiles have an asymmetric nature and thus result in non-zero gravitational wave memory. Whereas, for the last two symmetric profiles there is no asymptotic memory. For eternal switching, our observations suggest that the collective transition rate for the entangled probes due to symmetric GW bursts remains the same as obtained in the flat space. Whereas, for asymmetric bursts with memory, there is a finite change, indicating a direct possibility to distinguish between the two above-mentioned scenarios. We also consider finite switching in terms of Gaussian functions and observe characteristic differences in the radiative process between the GW backgrounds with and without memory. Notably, if the Gaussian switching is peaked much later compared to the passing of GW, only memory profiles contribute to the radiative process. We further discuss the physical implications of our findings., Comment: 22 pages, 5 figures, comments are welcome

Deep learning has proved successful in many applications but suffers from high computational demands and requires custom accelerators for deployment. Crossbar-based analog in-memory architectures are attractive for acceleration of deep neural networks (DNN), due to their high data reuse and high efficiency enabled by combining storage and computation in memory. However, they require analog-to-digital converters (ADCs) to communicate crossbar outputs. ADCs consume a significant portion of energy and area of every crossbar processing unit, thus diminishing the potential efficiency benefits. Pruning is a well-studied technique to improve the efficiency of DNNs but requires modifications to be effective for crossbars. In this paper, we motivate crossbar-attuned pruning to target ADC-specific inefficiencies. This is achieved by identifying three key properties (dubbed D.U.B.) that induce sparsity that can be utilized to reduce ADC energy without sacrificing accuracy. The first property ensures that sparsity translates effectively to hardware efficiency by restricting sparsity levels to Discrete powers of 2. The other 2 properties encourage columns in the same crossbar to achieve both Unstructured and Balanced sparsity in order to amortize the accuracy drop. The desired D.U.B. sparsity is then achieved by regularizing the variance of $L_{0}$ norms of neighboring columns within the same crossbar. Our proposed implementation allows it to be directly used in end-to-end gradient-based training. We apply the proposed algorithm to convolutional layers of VGG11 and ResNet18 models, trained on CIFAR-10 and ImageNet datasets, and achieve up to 7.13x and 1.27x improvement, respectively, in ADC energy with less than 1% drop in accuracy., Comment: 11 pages, 5 figures

Many astrophysical and cosmological observations consistently indicate that the universe is currently accelerating. Despite many possible explanations, the exact cause of this acceleration remains unknown. Therefore, additional observational probes are necessary to pinpoint the cause. Gravitational waves (GWs) have the potential to unravel some of the unresolved mysteries in cosmology. In this work, we highlight the potential utility of gravitational wave memory as a tool to identify the cause of this acceleration. We evaluate cosmological memory as a particular case of the master equation for GW memory in Locally Rotationally Symmetric type II spacetimes. Unlike the previous works, the master equation for GW memory contains non-linear dependence of the background quantities. Hence, even though the successive GWs generated are smaller than their predecessors, we demonstrate that their cumulative effect over cosmological time leads to observable signatures, akin to the growth of density perturbations resulting in large-scale structures. Finally, we show that the GW memory exhibits distinct signatures between accelerated and decelerated universes, potentially enabling the identification of the transition redshift from a matter-dominated to a dark-energy-dominated universe., Comment: 26 pages, 5 figures

Compute-in-memory (CiM) has emerged as a highly energy efficient solution for performing matrix multiplication during Machine Learning (ML) inference. However, integrating compute in memory poses key questions, such as 1) What type of CiM to use: Given a multitude of CiM design characteristics, determining their suitability from architecture perspective is needed. 2) When to use CiM: ML inference includes workloads with a variety of memory and compute requirements, making it difficult to identify when CiM is more beneficial. 3) Where to integrate CiM: Each memory level has different bandwidth and capacity, creating different data reuse opportunities for CiM integration. To answer such questions regarding on-chip CiM integration for accelerating ML workloads, we use an analytical architecture evaluation methodology where we tailor the dataflow mapping. The mapping algorithm aims to achieve highest weight reuse and reduced data movements for a given CiM prototype and workload. Our experiments show that CiM integrated memory improves energy efficiency by up to 3.4x and throughput by up to 15.6x compared to tensor-core-like baseline architecture, with INT-8 precision under iso-area constraints. We believe the proposed work provides insights into what type of CiM to use, and when and where to optimally integrate it in the cache hierarchy for efficient matrix multiplication., Comment: updated methodology

Neutrinos with large self-interactions, arising from exchange of light scalars or vectors with mass $M_\phi\simeq 10{\rm MeV}$, can play a useful role in cosmology for structure formation and solving the Hubble tension. It has been proposed that large self-interactions of neutrinos may change the observed properties of supernova like the neutrino luminosity or the duration of the neutrino burst. In this paper, we study the gravitational wave memory signal arising from supernova neutrinos. Our results reveal that memory signal for self-interacting neutrinos are weaker than free-streaming neutrinos in the high frequency range. Implications for detecting and differentiating between such signals for planned space-borne detectors, DECIGO and BBO, are also discussed., Comment: Revised, rewritten version with some additions and omissions, matches with the published version in PRD letters

In the present article, we study how different gravitational wave (GW) burst profiles in linearized gravity, with and without the asymptotic memory, may influence the harvesting between two static Unruh-DeWitt detectors. To this end, we investigate the following burst profiles -- Gaussian, sech-squared, Heaviside step function, and tanh. Out of these, the first two bursts contain no memory, while the latter two consist of a non-vanishing memory effect. We find that in all of these cases, entanglement harvesting is possible, and it decreases with the increasing distance between detectors and the detector transition energy. We observe that the harvesting differs qualitatively based on the presence or absence of the memory, which is prominent in a low transition energy regime. With memory, the harvesting keeps increasing with decreasing transition energy, while without memory, it tends to reach finite values. Furthermore, for the two burst profiles without memory, longer bursts correspond to greater harvesting in the low detector transition energy regime, and this characteristic is reversed for larger transition energy. Meanwhile, for the tanh-type profile with memory, harvesting is always greater for shorter bursts. We discuss various implications of our findings., Comment: Some additions and clarifications, matches with the published version in JHEP

Gravitational wave memory is studied in the context of a certain class of braneworld wormholes. Unlike other wormhole geometries, this novel class of wormholes do not require any exotic matter fields for its traversability. First, we study geodesics in this wormhole spacetime, in the presence of a gravitational wave pulse. The resulting evolution of the geodesic separation shows the presence of displacement and velocity memory effects. Motivated by the same, we study the memory effects at null infinity using the Bondi-Sachs formalism, adapted for braneworld wormhole. Our analysis provides a non-trivial change of the Bondi mass after the passage of a burst of gravitational radiation and hence manifests the memory effect at null infinity. In both of these exercises, the presence of extra dimension and the wormhole nature of the spacetime geometry gets imprinted in the memory effect. Since future gravitational wave detectors will be able to probe the memory effect, the present work provides another avenue to search for compact objects other than black holes., Comment: Some additions and clarifications, matches with the published version in Phys. Rev. D

We report an analytical example of the gravitational wave memory effect in exact plane wave spacetimes. A square pulse profile is chosen which gives rise to a curved wave region sandwiched between two flat Minkowski spacetimes. Working in the Brinkmann coordinate system, we solve the geodesic equations exactly in all three regions. Issues related to the continuity and differentiability of the solutions at the boundaries of the pulse are addressed. The evolution of the geodesic separation reveals displacement and velocity memory effects with quantitative estimates depending on initial values and the amplitude, width of the pulse. The deformation caused by the pulse on a ring of particles is then examined in detail. Formation of caustics is found in both scenarios i.e. evolution of separation for a pair of geodesics and shape deformation of a ring of particles -- a feature consistent with previous work on geodesic congruences in this spacetime. In summary, our analysis provides a useful illustration of memory effects involving closed-form exact expressions., Comment: Some minor typos corrected, matches with the published version in EPJP

We explore memory effects for novel Kundt wave spacetimes in the recently proposed Eddington-inspired Born-Infeld (EiBI) theory of gravity. First, we construct new, exact Kundt wave geometries in this theory for two different matter sources--(i) generic matter designed to satisfy the field equations as well as energy conditions, and (ii) electromagnetic field. For both sources we find that the EiBI theory parameter $\kappa$ couples only with the nonradiative part of the physical metric solution. Thereafter, we solve the geodesic and the geodesic deviation equations, in the above spacetimes with the aim of arriving at memory effects. This analysis is carried out numerically and reveals unique memory features depending on the type of matter source present and the signature of the spacetime scalar curvature. The role of $\kappa$ in influencing the memory effect, for a given background spacetime, is also noted. Thus, apart from providing novel radiative solutions in EiBI gravity, we also show how different matter configurations are responsible for distinct memory characteristics., Comment: Motivation has been clearly outlined in the revised version. Figures improved and references added. To appear in Physical Review D

Applications based on Deep Neural Networks (DNNs) have grown exponentially in the past decade. To match their increasing computational needs, several Non-Volatile Memory (NVM) crossbar based accelerators have been proposed. Recently, researchers have shown that apart from improved energy efficiency and performance, such approximate hardware also possess intrinsic robustness for defense against adversarial attacks. Prior works quantified this intrinsic robustness for vanilla DNNs trained on unperturbed inputs. However, adversarial training of DNNs is the benchmark technique for robustness, and sole reliance on intrinsic robustness of the hardware may not be sufficient. In this work, we explore the design of robust DNNs through the amalgamation of adversarial training and intrinsic robustness of NVM crossbar-based analog hardware. First, we study the noise stability of such networks on unperturbed inputs and observe that internal activations of adversarially trained networks have lower Signal-to-Noise Ratio (SNR), and are sensitive to noise compared to vanilla networks. As a result, they suffer on average 2x performance degradation due to the approximate computations on analog hardware. Noise stability analyses show the instability of adversarially trained DNNs. On the other hand, for adversarial images generated using Square Black Box attacks, ResNet-10/20 adversarially trained on CIFAR-10/100 display a robustness gain of 20-30%. For adversarial images generated using Projected-Gradient-Descent (PGD) White-Box attacks, adversarially trained DNNs present a 5-10% gain in robust accuracy due to underlying NVM crossbar when $\epsilon_{attack}$ is greater than $\epsilon_{train}$. Our results indicate that implementing adversarially trained networks on analog hardware requires careful calibration between hardware non-idealities and $\epsilon_{train}$ for optimum robustness and performance., Comment: 13 pages, 14 figures

The ubiquitous use of IoT and machine learning applications is creating large amounts of data that require accurate and real-time processing. Although edge-based smart data processing can be enabled by deploying pretrained models, the energy and memory constraints of edge devices necessitate distributed deep learning between the edge and the cloud for complex data. In this paper, we propose a distributed AI system to exploit both the edge and the cloud for training and inference. We propose a new architecture, MEANet, with a main block, an extension block, and an adaptive block for the edge. The inference process can terminate at either the main block, the extension block, or the cloud. The MEANet is trained to categorize inputs into easy/hard/complex classes. The main block identifies instances of easy/hard classes and classifies easy classes with high confidence. Only data with high probabilities of belonging to hard classes would be sent to the extension block for prediction. Further, only if the neural network at the edge shows low confidence in the prediction, the instance is considered complex and sent to the cloud for further processing. The training technique lends to the majority of inference on edge devices while going to the cloud only for a small set of complex jobs, as determined by the edge. The performance of the proposed system is evaluated via extensive experiments using modified models of ResNets and MobileNetV2 on CIFAR-100 and ImageNet datasets. The results show that the proposed distributed model has improved accuracy and energy consumption, indicating its capacity to adapt., Comment: 41st IEEE International Conference on Distributed Computing Systems, 2021

In-Memory Computing (IMC) hardware using Memristive Crossbar Arrays (MCAs) are gaining popularity to accelerate Deep Neural Networks (DNNs) since it alleviates the "memory wall" problem associated with von-Neumann architecture. The hardware efficiency (energy, latency and area) as well as application accuracy (considering device and circuit non-idealities) of DNNs mapped to such hardware are co-dependent on network parameters, such as kernel size, depth etc. and hardware architecture parameters such as crossbar size. However, co-optimization of both network and hardware parameters presents a challenging search space comprising of different kernel sizes mapped to varying crossbar sizes. To that effect, we propose NAX -- an efficient neural architecture search engine that co-designs neural network and IMC based hardware architecture. NAX explores the aforementioned search space to determine kernel and corresponding crossbar sizes for each DNN layer to achieve optimal tradeoffs between hardware efficiency and application accuracy. Our results from NAX show that the networks have heterogeneous crossbar sizes across different network layers, and achieves optimal hardware efficiency and accuracy considering the non-idealities in crossbars. On CIFAR-10 and Tiny ImageNet, our models achieve 0.8%, 0.2% higher accuracy, and 17%, 4% lower EDAP (energy-delay-area product) compared to a baseline ResNet-20 and ResNet-18 models, respectively., Comment: 10 pages, 9 figures

Memory effects are studied in the simplest scalar-tensor theory, the Brans--Dicke (BD) theory. To this end, we introduce, in BD theory, novel Kundt spacetimes (without and with gyratonic terms), which serve as backgrounds for the ensuing analysis on memory. The BD parameter $\omega$ and the scalar field ($\phi$) profile, expectedly, distinguishes between different solutions. Choosing specific localised forms for the free metric functions $H'(u)$ (related to the wave profile) and $J(u)$ (the gyraton) we obtain displacement memory effects using both geodesics and geodesic deviation. An interesting and easy-to-understand exactly solvable case arises when $\omega=-2$ (with $J(u)$ absent) which we discuss in detail. For other $\omega$ (in the presence of $J$ or without), numerically obtained geodesics lead to results on displacement memory which appear to match qualitatively with those found from a deviation analysis. Thus, the issue of how memory effects in BD theory may arise and also differ from their GR counterparts, is now partially addressed, at least theoretically, within the context of this new class of Kundt geometries., Comment: Some minor typos corrected, matches with the published version in EPJC

The increasing computational demand of Deep Learning has propelled research in special-purpose inference accelerators based on emerging non-volatile memory (NVM) technologies. Such NVM crossbars promise fast and energy-efficient in-situ Matrix Vector Multiplication (MVM) thus alleviating the long-standing von Neuman bottleneck in today's digital hardware. However, the analog nature of computing in these crossbars is inherently approximate and results in deviations from ideal output values, which reduces the overall performance of Deep Neural Networks (DNNs) under normal circumstances. In this paper, we study the impact of these non-idealities under adversarial circumstances. We show that the non-ideal behavior of analog computing lowers the effectiveness of adversarial attacks, in both Black-Box and White-Box attack scenarios. In a non-adaptive attack, where the attacker is unaware of the analog hardware, we observe that analog computing offers a varying degree of intrinsic robustness, with a peak adversarial accuracy improvement of 35.34%, 22.69%, and 9.90% for white box PGD (epsilon=1/255, iter=30) for CIFAR-10, CIFAR-100, and ImageNet respectively. We also demonstrate "Hardware-in-Loop" adaptive attacks that circumvent this robustness by utilizing the knowledge of the NVM model., Comment: to appear in Proceedings of DAC, 2021

The pervasiveness of "Internet-of-Things" in our daily life has led to a recent surge in fog computing, encompassing a collaboration of cloud computing and edge intelligence. To that effect, deep learning has been a major driving force towards enabling such intelligent systems. However, growing model sizes in deep learning pose a significant challenge towards deployment in resource-constrained edge devices. Moreover, in a distributed intelligence environment, efficient workload distribution is necessary between edge and cloud systems. To address these challenges, we propose a conditionally deep hybrid neural network for enabling AI-based fog computing. The proposed network can be deployed in a distributed manner, consisting of quantized layers and early exits at the edge and full-precision layers on the cloud. During inference, if an early exit has high confidence in the classification results, it would allow samples to exit at the edge, and the deeper layers on the cloud are activated conditionally, which can lead to improved energy efficiency and inference latency. We perform an extensive design space exploration with the goal of minimizing energy consumption at the edge while achieving state-of-the-art classification accuracies on image classification tasks. We show that with binarized layers at the edge, the proposed conditional hybrid network can process 65% of inferences at the edge, leading to 5.5x computational energy reduction with minimal accuracy degradation on CIFAR-10 dataset. For the more complex dataset CIFAR-100, we observe that the proposed network with 4-bit quantization at the edge achieves 52% early classification at the edge with 4.8x energy reduction. The analysis gives us insights on designing efficient hybrid networks which achieve significantly higher energy efficiency than full-precision networks for edge-cloud based distributed intelligence systems., Comment: 6 pages, 5 figures, 4 tables

Memory effects in the exact Kundt wave spacetimes are shown to arise in the behaviour of geodesics in such spacetimes. The types of Kundt spacetimes we consider here are direct products of the form $H^2\times M(1,1)$ and $S^2\times M(1,1)$. Both geometries have constant scalar curvature. We consider a scenario in which initial velocities of the transverse geodesic coordinates are set to zero (before the arrival of the pulse) in a spacetime with non-vanishing background curvature. We look for changes in the separation between pairs of geodesics caused by the pulse. Any relative change observed in the position and velocity profiles of geodesics, after the burst, can be solely attributed to the wave (hence, a memory effect). For constant negative curvature, we find there is permanent change in the separation of geodesics after the pulse has departed. Thus, there is displacement memory, though no velocity memory is found. In the case of constant positive scalar curvature (Pleba\'nski-Hacyan spacetimes), we find both displacement and velocity memory along one direction. In the other direction, a new kind of memory (which we term as frequency memory effect) is observed where the separation between the geodesics shows periodic oscillations once the pulse has left. We also carry out similar analyses for spacetimes with a non-constant scalar curvature, which may be positive or negative. The results here seem to qualitatively agree with those for constant scalar curvature, thereby suggesting a link between the nature of memory and curvature., Comment: To appear in Physics Letters B

`In-memory computing' is being widely explored as a novel computing paradigm to mitigate the well known memory bottleneck. This emerging paradigm aims at embedding some aspects of computations inside the memory array, thereby avoiding frequent and expensive movement of data between the compute unit and the storage memory. In-memory computing with respect to Silicon memories has been widely explored on various memory bit-cells. Embedding computation inside the 6 transistor (6T) SRAM array is of special interest since it is the most widely used on-chip memory. In this paper, we present a novel in-memory multiplication followed by accumulation operation capable of performing parallel dot products within 6T SRAM without any changes to the standard bitcell. We, further, study the effect of circuit non-idealities and process variations on the accuracy of the LeNet-5 and VGG neural network architectures against the MNIST and CIFAR-10 datasets, respectively. The proposed in-memory dot-product mechanism achieves 88.8% and 99% accuracy for the CIFAR-10 and MNIST, respectively. Compared to the standard von Neumann system, the proposed system is 6.24x better in energy consumption and 9.42x better in delay., Comment: (In-proceedings)2020 Accepted in IEEE Transactions on Circuits and Systems-I Journal

The analog nature of computing in Memristive crossbars poses significant issues due to various non-idealities such as: parasitic resistances, non-linear I-V characteristics of the device etc. The non-idealities can have a detrimental impact on the functionality i.e. computational accuracy of crossbars. Past works have explored modeling the non-idealities using analytical techniques. However, several non-idealities have data dependent behavior. This can not be captured using analytical (non data-dependent) models thereby, limiting their suitability in predicting application accuracy. To address this, we propose a Generalized Approach to Emulating Non-Ideality in Memristive Crossbars using Neural Networks (GENIEx), which accurately captures the data-dependent nature of non-idealities. We perform extensive HSPICE simulations of crossbars with different voltage and conductance combinations. Following that, we train a neural network to learn the transfer characteristics of the non-ideal crossbar. Next, we build a functional simulator which includes key architectural facets such as \textit{tiling}, and \textit{bit-slicing} to analyze the impact of non-idealities on the classification accuracy of large-scale neural networks. We show that GENIEx achieves \textit{low} root mean square errors (RMSE) of $0.25$ and $0.7$ for low and high voltages, respectively, compared to HSPICE. Additionally, the GENIEx errors are $7\times$ and $12.8\times$ better than an analytical model which can only capture the linear non-idealities. Further, using the functional simulator and GENIEx, we demonstrate that an analytical model can overestimate the degradation in classification accuracy by $\ge 10\%$ on CIFAR-100 and $3.7\%$ on ImageNet datasets compared to GENIEx., Comment: 7 pages, 9 figures, Accepted in Design Automation Conference (DAC) 2020

The `Internet of Things' has brought increased demand for AI-based edge computing in applications ranging from healthcare monitoring systems to autonomous vehicles. Quantization is a powerful tool to address the growing computational cost of such applications, and yields significant compression over full-precision networks. However, quantization can result in substantial loss of performance for complex image classification tasks. To address this, we propose a Principal Component Analysis (PCA) driven methodology to identify the important layers of a binary network, and design mixed-precision networks. The proposed Hybrid-Net achieves a more than 10% improvement in classification accuracy over binary networks such as XNOR-Net for ResNet and VGG architectures on CIFAR-100 and ImageNet datasets while still achieving up to 94% of the energy-efficiency of XNOR-Nets. This work furthers the feasibility of using highly compressed neural networks for energy-efficient neural computing in edge devices., Comment: 14 pages, 4 figures, 8 tables

Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network reduces the 'space' in which adversarial examples exist. Guided by this intuition, we demonstrate that discretization greatly improves the robustness of DLNs against adversarial attacks. Specifically, discretizing the input space (or allowed pixel levels from 256 values or 8-bit to 4 values or 2-bit) extensively improves the adversarial robustness of DLNs for a substantial range of perturbations for minimal loss in test accuracy. Furthermore, we find that Binary Neural Networks (BNNs) and related variants are intrinsically more robust than their full precision counterparts in adversarial scenarios. Combining input discretization with BNNs furthers the robustness even waiving the need for adversarial training for certain magnitude of perturbation values. We evaluate the effect of discretization on MNIST, CIFAR10, CIFAR100 and Imagenet datasets. Across all datasets, we observe maximal adversarial resistance with 2-bit input discretization that incurs an adversarial accuracy loss of just ~1-2% as compared to clean test accuracy., Comment: 8 pages, 8 Figures, 6 Tables

The recent advent of `Internet of Things' (IOT) has increased the demand for enabling AI-based edge computing. This has necessitated the search for efficient implementations of neural networks in terms of both computations and storage. Although extreme quantization has proven to be a powerful tool to achieve significant compression over full-precision networks, it can result in significant degradation in performance. In this work, we propose extremely quantized hybrid network architectures with both binary and full-precision sections to emulate the classification performance of full-precision networks while ensuring significant energy efficiency and memory compression. We explore several hybrid network architectures and analyze the performance of the networks in terms of accuracy, energy efficiency and memory compression. We perform our analysis on ResNet and VGG network architectures. Among the proposed network architectures, we show that the hybrid networks with full-precision residual connections emerge as the optimum by attaining accuracies close to full-precision networks while achieving excellent memory compression, up to 21.8x in case of VGG-19. This work demonstrates an effective way of hybridizing networks which achieve performance close to full-precision networks while attaining significant compression, furthering the feasibility of using such networks for energy-efficient neural computing in IOT-based edge devices., Comment: 6 pages, 4 figures

Displacement and velocity memory effects in the exact, vacuum, plane gravitational wave line element have been studied recently by looking at the behaviour of pairs of geodesics or via geodesic deviation. Instead, one may investigate the evolution of geodesic congruences. In our work here, we obtain the evolution of the kinematic variables which characterise timelike geodesic congruences, using chosen pulse profiles (square and sech-squared) in the exact, plane gravitational wave line element. We also analyse the behaviour of geodesic congruences in possible physical scenarios describable using derivatives (first, second and third) of one of the chosen pulses. Beginning with a discussion on the generic behaviour of such congruences and consequences thereof, we find exact analytical expressions for shear and expansion with the two chosen pulse profiles. Qualitatively similar numerical results are noted when various derivatives of the sech-squared pulse are used. We conclude that for geodesic congruences, a growth (or decay) of shear causes focusing of an initially parallel congruence, after the departure of the pulse. A correlation between the `focusing time (or $u$ value, $u$ being the affine parameter)' and the amplitude of the pulse (or its derivatives) is found. Such features distinctly suggest a memory effect, named in recent literature as ${\cal B}$ memory., Comment: 27 pages, 13 figures, major changes (including title and abstract), rewritten with a different focus, new results added

Spiking Neural Networks (SNNs) offer an event-driven and more biologically realistic alternative to standard Artificial Neural Networks based on analog information processing. This can potentially enable energy-efficient hardware implementations of neuromorphic systems which emulate the functional units of the brain, namely, neurons and synapses. Recent demonstrations of ultra-fast photonic computing devices based on phase-change materials (PCMs) show promise of addressing limitations of electrically driven neuromorphic systems. However, scaling these standalone computing devices to a parallel in-memory computing primitive is a challenge. In this work, we utilize the optical properties of the PCM, Ge\textsubscript{2}Sb\textsubscript{2}Te\textsubscript{5} (GST), to propose a Photonic Spiking Neural Network computing primitive, comprising of a non-volatile synaptic array integrated seamlessly with previously explored `integrate-and-fire' neurons. The proposed design realizes an `in-memory' computing platform that leverages the inherent parallelism of wavelength-division-multiplexing (WDM). We show that the proposed computing platform can be used to emulate a SNN inferencing engine for image classification tasks. The proposed design not only bridges the gap between isolated computing devices and parallel large-scale implementation, but also paves the way for ultra-fast computing and localized on-chip learning., Comment: 14 pages, 11 figures, submitted to Physical Review Applied

The rapid growth of brain-inspired computing coupled with the inefficiencies in the CMOS implementations of neuromrphic systems has led to intense exploration of efficient hardware implementations of the functional units of the brain, namely, neurons and synapses. However, efforts have largely been invested in implementations in the electrical domain with potential limitations of switching speed, packing density of large integrated systems and interconnect losses. As an alternative, neuromorphic engineering in the photonic domain has recently gained attention. In this work, we demonstrate a purely photonic operation of an Integrate-and-Fire Spiking neuron, based on the phase change dynamics of Ge$_2$Sb$_2$Te$_5$ (GST) embedded on top of a microring resonator, which alleviates the energy constraints of PCMs in electrical domain. We also show that such a neuron can be potentially integrated with on-chip synapses into an all-Photonic Spiking Neural network inferencing framework which promises to be ultrafast and can potentially offer a large operating bandwidth., Comment: 10 pages, 5 figures, accepted in Nature Scientific Reports

The inherent stochasticity in many nano-scale devices makes them prospective candidates for low-power computations. Such devices have been demonstrated to exhibit probabilistic switching between two stable states to achieve stochastic behavior. Recently, superparamagnetic nanomagnets (having low energy barrier EB $\sim$ 1kT) have shown promise of achieving stochastic switching at GHz rates, with very low currents. On the other hand, voltage-controlled switching of nanomagnets through the Magneto-electric (ME) effect has shown further improvements in energy efficiency. In this simulation paper, we first analyze the stochastic switching characteristics of such super-paramagnetic nanomagnets in a voltage-controlled spintronic device. We study the influence of external bias on the switching behavior. Subsequently, we show that our proposed device leverages the voltage controlled stochasticity in performing low-voltage 8-bit analog to digital conversions. This eliminates the need for comparators, unlike the Complementary Metal-Oxide Semiconductor (CMOS)-based flash Analog-to-Digital converters (ADC). This device allows for a simple and compact design which can potentially be applied in implementing sensors which desire low voltage conversions., Comment: 11 pages, 6 figures

We propose capacitively driven low-swing global interconnect circuit using a receiver that utilizes magnetoelectric (ME) effect induced magnetization switching to reduce the energy consumption. Capacitively driven wire has recently been shown to be effective in improving the performance of global interconnects. Such techniques can reduce the signal swing in the interconnect by using a capacitive divider network and does not require an additional voltage supply. However, the large reduction in signal swing makes it necessary to use differential signaling and amplification for successful regeneration at the receiver, which add area and static power. ME effect induced magnetization reversal has recently been proposed which shows the possibility of using a low voltage to switch a nanomagnet adjacent to a multi-ferroic oxide. Here, we propose an ME effect based receiver that uses the low voltage at the receiving end of the global wire to switch a nanomagnet. The nanomagnet is also used as the free layer of a magnetic tunnel junction (MTJ), the resistance of which is tuned through the ME effect. This change in MTJ resistance is converted to full swing binary signals by using simple digital components. This process allows capacitive low swing interconnection without differential signaling or amplification, which leads to significant energy efficiency. Our simulation results indicate that for 5-10 mm long global wires in IBM 45 nm technology, capacitive ME design consumes 3x lower energy compared to full-swing CMOS design and 2x lower energy compared to differential amplifier based low-swing capacitive CMOS design.

Large scale digital computing almost exclusively relies on the von-Neumann architecture which comprises of separate units for storage and computations. The energy expensive transfer of data from the memory units to the computing cores results in the well-known von-Neumann bottleneck. Various approaches aimed towards bypassing the von-Neumann bottleneck are being extensively explored in the literature. Emerging non-volatile memristive technologies have been shown to be very efficient in computing analog dot products in an in-situ fashion. The memristive analog computation of the dot product results in much faster operation as opposed to digital vector in-memory bit-wise Boolean computations. However, challenges with respect to large scale manufacturing coupled with the limited endurance of memristors have hindered rapid commercialization of memristive based computing solutions. In this work, we show that the standard 8 transistor (8T) digital SRAM array can be configured as an analog-like in-memory multi-bit dot product engine. By applying appropriate analog voltages to the read-ports of the 8T SRAM array, and sensing the output current, an approximate analog-digital dot-product engine can be implemented. We present two different configurations for enabling multi-bit dot product computations in the 8T SRAM cell array, without modifying the standard bit-cell structure. Since our proposal preserves the standard 8T-SRAM array structure, it can be used as a storage element with standard read-write instructions, and also as an on-demand analog-like dot product accelerator.

The advances in the field of machine learning using neuromorphic systems have paved the pathway for extensive research on possibilities of hardware implementations of neural networks. Various memristive technologies such as oxide-based devices, spintronics and phase change materials have been explored to implement the core functional units of neuromorphic systems, namely the synaptic network, and the neuronal functionality, in a fast and energy efficient manner. However, various non-idealities in the crossbar implementations of the synaptic arrays can significantly degrade performance of neural networks and hence, impose restrictions on feasible crossbar sizes. In this work, we build mathematical models of various non-idealities that occur in crossbar implementations such as source resistance, neuron resistance and chip-to-chip device variations and analyze their impact on the classification accuracy of a fully connected network (FCN) and convolutional neural network (CNN) trained with standard training algorithm. We show that a network trained under ideal conditions can suffer accuracy degradation as large as 59.84% for FCNs and 62.4% for CNNs when implemented on non-ideal crossbars for relevant non-ideality ranges. This severely constrains the sizes for crossbars. As a solution, we propose a technology aware training algorithm which incorporates the mathematical models of the non-idealities in the standard training algorithm. We demonstrate that our proposed methodology achieves significant recovery of testing accuracy within 1.9% of the ideal accuracy for FCNs and 1.5% for CNNs. We further show that our proposed training algorithm can potentially allow the use of significantly larger crossbar arrays of sizes 784$\times$500 for FCNs and 4096$\times$512 for CNNs with a minor or no trade-off in accuracy, Comment: 10 pages, 7 figures, submitted to IEEE Transactions on Emerging Topics in Computational Intelligence

Voltage driven magneto-electric (ME) switching of ferro-magnets has shown potential for future low-energy spintronic memories. In this paper, we first analyze two different ME devices viz. ME-MTJ and ME-XNOR device with respect to writability, readability and switching speed. Our analysis is based on a coupled magnetization dynamics and electron transport model. Subsequently, we show that the decoupled read/write path of ME-MTJs can be utilized to construct an energy-efficient dual port memory. Further, we also propose a novel content addressable memory (CAM) exploiting the compact XNOR operation enabled by ME-XNOR device.