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The increasing complexity of deep neural networks (DNNs) poses significant challenges for edge inference deployment due to resource and power constraints of edge devices. Recent works on unary-based matrix multiplication hardware aim to leverage data sparsity and low-precision values to enhance hardware efficiency. However, the adoption and integration of such unary hardware into commercial deep learning accelerators (DLA) remain limited due to processing element (PE) array dataflow differences. This work presents Tempus Core, a convolution core with highly scalable unary-based PE array comprising of tub (temporal-unary-binary) multipliers that seamlessly integrates with the NVDLA (NVIDIA's open-source DLA for accelerating CNNs) while maintaining dataflow compliance and boosting hardware efficiency. Analysis across various datapath granularities shows that for INT8 precision in 45nm CMOS, Tempus Core's PE cell unit (PCU) yields 59.3% and 15.3% reductions in area and power consumption, respectively, over NVDLA's CMAC unit. Considering a 16x16 PE array in Tempus Core, area and power improves by 75% and 62%, respectively, while delivering 5x and 4x iso-area throughput improvements for INT8 and INT4 precisions. Post-place and route analysis of Tempus Core's PCU shows that the 16x4 PE array for INT4 precision in 45nm CMOS requires only 0.017 mm^2 die area and consumes only 6.2mW of total power. We demonstrate that area-power efficient unary-based hardware can be seamlessly integrated into conventional DLAs, paving the path for efficient unary hardware for edge AI inference., Comment: Accepted in DATE 2025

Temporal Neural Networks (TNNs), a special class of spiking neural networks, draw inspiration from the neocortex in utilizing spike-timings for information processing. Recent works proposed a microarchitecture framework and custom macro suite for designing highly energy-efficient application-specific TNNs. These recent works rely on manual hardware design, a labor-intensive and time-consuming process. Further, there is no open-source functional simulation framework for TNNs. This paper introduces TNNGen, a pioneering effort towards the automated design of TNNs from PyTorch software models to post-layout netlists. TNNGen comprises a novel PyTorch functional simulator (for TNN modeling and application exploration) coupled with a Python-based hardware generator (for PyTorch-to-RTL and RTL-to-Layout conversions). Seven representative TNN designs for time-series signal clustering across diverse sensory modalities are simulated and their post-layout hardware complexity and design runtimes are assessed to demonstrate the effectiveness of TNNGen. We also highlight TNNGen's ability to accurately forecast silicon metrics without running hardware process flow., Comment: Published in IEEE Transactions on Circuits and Systems II: Express Briefs, May 2024

General matrix multiplication (GEMM) is a ubiquitous computing kernel/algorithm for data processing in diverse applications, including artificial intelligence (AI) and deep learning (DL). Recent shift towards edge computing has inspired GEMM architectures based on unary computing, which are predominantly stochastic and rate-coded systems. This paper proposes a novel GEMM architecture based on temporal-coding, called tuGEMM, that performs exact computation. We introduce two variants of tuGEMM, serial and parallel, with distinct area/power-latency trade-offs. Post-synthesis Power-Performance-Area (PPA) in 45 nm CMOS are reported for 2-bit, 4-bit, and 8-bit computations. The designs illustrate significant advantages in area-power efficiency over state-of-the-art stochastic unary systems especially at low precisions, e.g. incurring just 0.03 mm^2 and 9 mW for 4 bits, and 0.01 mm^2 and 4 mW for 2 bits. This makes tuGEMM ideal for power constrained mobile and edge devices performing always-on real-time sensory processing., Comment: Published in 2023 IEEE International Symposium on Circuits and Systems (ISCAS), Monterey, CA, USA, 2023

General Matrix Multiplication (GEMM) is a ubiquitous compute kernel in deep learning (DL). To support energy-efficient edge-native processing, new GEMM hardware units have been proposed that operate on unary encoded bitstreams using much simpler hardware. Most unary approaches thus far focus on rate-based unary encoding of values and perform stochastic approximate computation. This work presents tubGEMM, a novel matrix-multiply unit design that employs hybrid temporal-unary and binary (tub) encoding and performs exact (not approximate) GEMM. It intrinsically exploits dynamic value sparsity to improve energy efficiency. Compared to the current best unary design uGEMM, tubGEMM significantly reduces area, power, and energy by 89\%, 87\%, and 50\%, respectively. A tubGEMM design performing 128x128 matrix multiply on 8-bit integers, in commercial TSMC N5 (5nm) process node, consumes just 0.22 mm^2 die area, 417.72 mW power, and 8.86 uJ energy, assuming no sparsity. Typical sparsity in DL workloads (MobileNetv2, ResNet-50) reduces energy by more than 3x, and lowering precision to 4 and 2 bits further reduces it by 24x and 104x respectively., Comment: Published in 2023 IEEE Computer Society Annual Symposium on VLSI (ISVLSI)

This paper deals with bilateral-gamma (BG) approximation to functionals of an isonormal Gaussian process. We use Malliavin-Stein method to obtain the error bounds for the smooth Wasserstein distance. As by-products, the error bounds for variance-gamma (V G), Laplace, gamma and normal approximations are presented. Our approach is new in the sense that the Stein equation is based on integral operators rather than diferential operators commonly used in the literature. Some of our bounds are sharper than the existing ones. For the approximation of a random element from the second Wiener chaos to a BG distribution, the bounds are obtained in terms of their cumulants. Using this result, we show that a sequence of random variables (rvs) in the second Wiener chaos converges in distribution to a BG rv if their cumulants of order two to six converge. As an application of our results, we consider an approximation of homogeneous sums of independent rvs to a BG distribution, and mention some related limit theorems also. Finally, an approximation of a U-statistic to the BG distribution is discussed., Comment: 35 pages

In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method. For the smooth Wasserstein distance, an error bound between two tempered stable distributions is also derived. As examples, we discuss the approximation of a tempered stable to normal and variance gamma distributions. As corollaries, the corresponding limit theorem follows, Comment: 19 pages

In this article, we establish a general covariance identity for infinitely divisible distributions (IDD). Using this result, we derive Cacoullos type variance bounds for the IDD. Applications to some important distributions are discussed, in addition to the computation of variance bounds for certain posterior distributions. As another application, we derive the Stein-type identity for the IDD, which involves the L'evy measure. This result in turn is used to derive the Stein-type identity for the CGMY distributions and the variance-gamma distributions (VGD). This approach, especially for the VGD is new and simpler, compared to the ones available in the literature. Finally, as another nontrivial application, we apply the covariance identity in deriving known and some new formulas for the weighted premium calculation principles (WPCP) and Gini coefficient for the IDD., Comment: 26 pages

We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit representation for its distribution is obtained in terms of Bell polynomials. We then extend it to a compound Poisson process and time fractional compound Poisson process (TFCPP). It is shown that the one-dimensional distributions of the TFCPP exhibit over-dispersion property, are not infinitely divisible and possess the long-range dependence property. Also, their moments and factorial moments are derived. Finally, the fractional differential equation associated with the TFCPP is also obtained., Comment: 26 pages

Each person has a unique gait, i.e., walking style, that can be used as a biometric for personal identification. Recent works have demonstrated effective gait recognition using deep neural networks, however most of these works predominantly focus on classification accuracy rather than model efficiency. In order to perform gait recognition using wearable devices on the edge, it is imperative to develop highly efficient low-power models that can be deployed on to small form-factor devices such as microcontrollers. In this paper, we propose a small CNN model with 4 layers that is very amenable for edge AI deployment and realtime gait recognition. This model was trained on a public gait dataset with 20 classes augmented with data collected by the authors, aggregating to 24 classes in total. Our model achieves 96.7% accuracy and consumes only 5KB RAM with an inferencing time of 70 ms and 125mW power, while running continuous inference on Arduino Nano 33 BLE Sense. We successfully demonstrated realtime identification of the authors with the model running on Arduino, thus underscoring the efficacy and providing a proof of feasiblity for deployment in practical systems in near future.

General Matrix Multiply (GEMM) units, consisting of multiply-accumulate (MAC) arrays, perform bulk of the computation in deep learning (DL). Recent work has proposed a novel MAC design, Bit-Pragmatic (PRA), capable of dynamically exploiting bit sparsity. This work presents OzMAC (Omit-zero-MAC), a modified re-implementation of PRA, but extends beyond earlier works by performing rigorous post-synthesis evaluation against binary MAC design across multiple bitwidths and clock frequencies using TSMC N5 process node to assess commercial implementation potential. We demonstrate the existence of high bit sparsity in eight pretrained INT8 DL workloads and show that 8-bit OzMAC improves all three metrics of area, power, and energy significantly by 21%, 70%, and 28%, respectively. Similar improvements are achieved when scaling data precisions (4, 8, 16 bits) and clock frequencies (0.5 GHz, 1 GHz, 1.5 GHz). For the 8-bit OzMAC, scaling its frequency to normalize the throughput, it still achieves 30% improvement on both power and energy., Comment: Pre-print version of the publication in VLSI-SoC 2024

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented.

We introduce a non-homogeneous version of the generalized counting process (GCP), namely, the non-homogeneous generalized counting process (NGCP). We time-change the NGCP by an independent inverse stable subordinator to obtain its fractional version, and call it as the non-homogeneous generalized fractional counting process (NGFCP). A generalization of the NGFCP is obtained by time-changing the NGCP with an independent inverse subordinator. We derive the system of governing differential-integral equations for the marginal distributions of the increments of NGCP, NGFCP and its generalization. Then, we consider the GCP time-changed by a multistable subordinator and obtain its L\'evy measure, associated Bern\v{s}tein function and distribution of the first passage times. The GCP and its fractional version, that is, the generalized fractional counting process when time-changed by a L\'evy subordinator are known as the time-changed generalized counting process-I (TCGCP-I) and the time-changed generalized fractional counting process-I (TCGFCP-I), respectively. We obtain the distribution of first passage times and related governing equations for the TCGCP-I. An application of the TCGCP-I to ruin theory is discussed. We obtain the conditional distribution of the $k$th order statistic from a sample whose size is modelled by a particular case of TCGFCP-I, namely, the time fractional negative binomial process. Later, we consider a fractional version of the TCGCP-I and obtain the system of differential equations that governs its state probabilities. Its mean, variance, covariance, {\it etc.} are obtained and using which its long-range dependence property is established. Some results for its two particular cases are obtained.

Cognitive radio is a potential solution to meet the upcoming spectrum crunch issue. In a cognitive radio, spectrum holes can be identified using spectrum sensing techniques. A high resolution spectrum hole detection can ensure even the smallest inactive portion in the spectrum is efficiently utilized. In this paper, a spectrum hole detection technique is proposed in which coarse sensing is done initially so as to detect occupied channels simultaneously. Spectrum holes in the occupied band can be efficiently detected using a fine sensing method. A two stage Frequency Response Masking (FRM) filter sandwiched between two Pascal structure based sampling rate converters results in arbitrary variation of bandwidth. This arbitrary variation of bandwidth can be utilized for fine sensing the spectrum such that the spectrum holes can be detected with high resolution. In the proposed method, high resolution in spectrum hole detection can be achieved without increasing the hardware complexity of the design. The hardware complexity of the proposed method is compared with the state of the art and is found to be significantly less

Temporal Neural Networks (TNNs) are spiking neural networks that exhibit brain-like sensory processing with high energy efficiency. This work presents the ongoing research towards developing a custom design framework for designing efficient application-specific TNN-based Neuromorphic Sensory Processing Units (NSPUs). This paper examines previous works on NSPU designs for UCR time-series clustering and MNIST image classification applications. Current ideas for a custom design framework and tools that enable efficient software-to-hardware design flow for rapid design space exploration of application-specific NSPUs while leveraging EDA tools to obtain post-layout netlist and power-performance-area (PPA) metrics are described. Future research directions are also outlined.

Temporal Neural Networks (TNNs), inspired from the mammalian neocortex, exhibit energy-efficient online sensory processing capabilities. Recent works have proposed a microarchitecture framework for implementing TNNs and demonstrated competitive performance on vision and time-series applications. Building on these previous works, this work proposes TNN7, a suite of nine highly optimized custom macros developed using a predictive 7nm Process Design Kit (PDK), to enhance the efficiency, modularity and flexibility of the TNN design framework. TNN prototypes for two applications are used for evaluation of TNN7. An unsupervised time-series clustering TNN delivering competitive performance can be implemented within 40 uW power and 0.05 mm^2 area, while a 4-layer TNN that achieves an MNIST error rate of 1% consumes only 18 mW and 24.63 mm^2. On average, the proposed macros reduce power, delay, area, and energy-delay product by 14%, 16%, 28%, and 45%, respectively. Furthermore, employing TNN7 significantly reduces the synthesis runtime of TNN designs (by more than 3x), allowing for highly-scaled TNN implementations to be realized., Comment: To be published in ISVLSI 2022

Human limb motion tracking and recognition plays an important role in medical rehabilitation training, lower limb assistance, prosthetics design for amputees, feedback control for assistive robots, etc. Lightweight wearable sensors, including inertial sensors, surface electromyography sensors, and flexible strain/pressure, are promising to become the next-generation human motion capture devices. Herein, we present a wireless wearable device consisting of a sixteen-channel flexible sponge-based pressure sensor array to recognize various human lower limb motions by detecting contours on the human skin caused by calf gastrocnemius muscle actions. Each sensing element is a round porous structure of thin carbon nanotube/polydimethylsiloxane nanocomposites with a diameter of 4 mm and thickness of about 400 {\mu}m. Ten human subjects were recruited to perform ten different lower limb motions while wearing the developed device. The motion classification result with the support vector machine method shows a macro-recall of about 97.3% for all ten motions tested. This work demonstrates a portable wearable muscle activity detection device with a lower limb motion recognition application, which can be potentially used in assistive robot control, healthcare, sports monitoring, etc., Comment: 17 pages, 6 figures

In this paper, we develop Stein's method for binomial approximation using the stop-loss metric that allows one to obtain a bound on the error term between the expectation of call functions. We obtain the results for a locally dependent collateralized debt obligation (CDO), under certain conditions on moments. The results are also exemplified for an independent CDO. Finally, it is shown that our bounds are sharper than the existing bounds., Comment: 19 pages

Underneath the ear skin there are richly branching vascular and neural networks that ultimately connecting to our heart and brain. Hence, the three-dimensional (3D) mapping of auricular electrophysiological signals could provide a new perspective for biomedical studies such as diagnosis of cardiovascular diseases and neurological disorders. However, it is still extremely challenging for current sensing techniques to cover the entire ultra-curved auricle. Here, we report a graphene-based ear-conformable sensing device with embedded and distributed 3D electrodes which enable full-auricle physiological monitoring. The sensing device, which incorporates programable 3D electrode thread array and personalized auricular mold, has 3D-conformable sensing interfaces with curved auricular skin, and was developed using one-step multi-material 3D-printing process. As a proof-of-concept, spatiotemporal auricular electrical skin resistance (AESR) mapping was demonstrated. For the first time, 3D AESR contours were generated and human subject-specific AESR distributions among a population were observed. From the data of 17 volunteers, the auricular region-specific AESR changes after cycling exercise were observed in 98% of the tests and were validated via machine learning techniques. Correlations of AESR with heart rate and blood pressure were also studied using statistical analysis. This 3D electronic platform and AESR-based new biometrical findings show promising biomedical applications., Comment: 23 pages, 6 figures

A set of highly-optimized custom macro extensions is developed for a 7nm CMOS cell library for implementing Temporal Neural Networks (TNNs) that can mimic brain-like sensory processing with extreme energy efficiency. A TNN prototype (13,750 neurons and 315,000 synapses) for MNIST requires only 1.56mm2 die area and consumes only 1.69mW., Comment: This work is dated and will be superseded by a forthcoming work

In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several Poisson limit theorems follow as corollaries from our bounds. As applications, we compare the Poisson approximation results with the negative binomial approximation results, for the sums of Bernoulli, geometric, and logarithmic series random variables., Comment: 15 pages

In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus in the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple., Comment: 13 Pages

In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein operator, uniform and non-uniform bounds on the solution of Stein equation, and etc. Using Stein's method, we obtain the error bounds for the approximation problem considered. As special cases, we discuss two applications, namely, $2$-runs and $(k_1,k_2)$-runs and compare the bound with the existing bounds.

The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is approximated by a multivariate compound Poisson distribution and by signed compound Poisson measure. The local and $\ell_\alpha$-norms are used to obtain the error bounds. The Heinrich method is used for the proofs.

The ratio $P(S_n=x)/P(Z_n=x)$ is investigated for three cases: (a) when $S_n$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and $Z_n$ is Poisson rv; (b) when $S_n$ is a statistic of 2-runs and $Z_n$ is negative binomial rv; and (c) when $S_n$ is statistic of $N(1,1)$-events and $Z_n$ is a binomial r.v. We also consider the approximation of $P(S_n\geqslant x)$ by Poisson distribution with parameter depending on $x$., Comment: To appear in "Stochastics"

Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories intersecting at distinct times(EIDT) and self intersections of a trajectory. We prove a generalization of separation theorem for the case of linear fractional systems. This result proves existence of EIST. Based on the presence of EIST, systems are further classified in two types; Type I and Type II systems, which are analyzed further for EIDT. Besides constant solutions and limit-cycle behavior, a fractional trajectory can have nodal or cuspoidal intersections with itself. We give a necessary and sufficient condition for a trajectory to have such types of intersections., Comment: 16 pages, 4 figures

The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\dots,N$. Two cases are considered: the general case of independent random variables when their closeness is ensured by the matching of factorial moments and the case when the $S_i$ has the Markov Binomial distribution. The Kolmogorov metric is used to estimate the accuracy of approximation., Comment: Published at https://doi.org/10.15559/18-VMSTA103 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some characteristic properties of marginal log-linear parameters. Then we define collapsibility and strict collapsibility of these parameters in a general sense. Several necessary and sufficient conditions for collapsibility and strict collapsibility are derived based on simple functions of only the cell probabilities, which are easily verifiable. These include results for an arbitrary set of marginal log-linear parameters having some common effects. The connections of strict collapsibility to various forms of independence of the variables are explored. We analyze some real-life datasets to illustrate the above results on collapsibility and strict collapsibility. Finally, we obtain a result relating parameters with the same effect but different margins for an arbitrary table, and demonstrate smoothness of marginal log-linear models under collapsibility conditions.

Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions., Comment: 13 pages

We obtain the explicit expressions for the state probabilities of various state dependent fractional point processes recently introduced and studied by Garra et al. (2015). The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference differential equations governing the state probabilities of these state dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results.