MC<sup>2</sup>RAM: Markov Chain Monte Carlo Sampling in SRAM for Fast Bayesian Inference

We propose a novel compute-in-memory (CIM)-based ultralow-power framework for probabilistic localization of insect-scale drones. Localization is a critical subroutine for path planning and rotor control in drones, where a drone is required to continuously estimate its pose (position and orientation) in flying space. The conventional probabilistic localization approaches rely on the 3-D Gaussian mixture model (GMM)-based representation of a 3-D map. A GMM model with hundreds of mixture functions is typically needed to adequately learn and represent the intricacies of the map. Meanwhile, localization using complex GMM map models is computationally intensive. Since insect-scale drones operate under extremely limited area/power budget, continuous localization using GMM models entails much higher operating energy, thereby limiting flying duration and/or size of the drone due to a larger battery.Addressing the computational challenges of localization in an insect-scale drone using a CIM approach, we propose a novel framework of 3-D map representation using a harmonic mean of the "Gaussian-like" mixture (HMGM) model. We show that short-circuit current of a multiinput floating-gate CMOS-based inverter follows the harmonic mean of a Gaussian-like function. Therefore, the likelihood function useful for drone localization can be efficiently implemented by connecting many multiinput inverters in parallel, each programmed with the parameters of the 3-D map model represented as HMGM. When the depth measurements are projected to the input of the implementation, the summed current of the inverters emulates the likelihood of the measurement. We have characterized our approach on an RGB-D scenes dataset. The proposed localization framework is ∼25× energy-efficient than the traditional, 8-bit digital GMM-based processor paving the way for tiny autonomous drones.

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Section: Ultralow-power Probabilistic Localizationmentioning

confidence: 99%

Ultralow-Power Localization of Insect-Scale Drones: Interplay of Probabilistic Filtering and Compute-in-Memory

Shukla

Muralidhar

Iliev

et al. 2022

IEEE Trans. VLSI Syst.

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“…However, evaluation of likelihood models based on GMM is computationally intensive. A dimension of each mixture function in GMM requires subtractions, multiplications, additions (to compute the exponent of a Gaussian function) as well as look-ups (to add exponents using a log-ADD table [28]- [30]). Since these operations are repeated on all dimensions, mixture functions as well as the hypotheses, likelihood evaluation of a typical depth map may require tens of thousands of arithmetic operations and hundreds of memory look ups to evaluate the likelihood of a single measurement.…”

Section: Ultra-low-power Probabilistic Localizationmentioning

confidence: 99%

Probabilistic Localization of Insect-Scale Drones on Floating-Gate Inverter Arrays

Shukla,

Muralidhar,

Iliev

et al. 2021

Preprint

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We propose a novel compute-in-memory (CIM)based ultra-low-power framework for probabilistic localization of insect-scale drones. Localization is a critical subroutine for pathplanning and rotor control in drones, where a drone is required to continuously estimate its pose (position and orientation) in flying space. The conventional probabilistic localization approaches rely on the three-dimensional (3D) Gaussian Mixture Model (GMM)based representation of a 3D map. The GMM map model is synthesized by scanning the 3D space and by modeling the density of matter. A GMM model with hundreds of mixture functions is typically needed to adequately learn and represent the intricacies of the map. Meanwhile, localization using complex GMM map models is computationally intensive. Since insect-scale drones operate under extremely limited area/power budget, continuous localization using GMM models entails much higher operating energy -thereby, limiting flying duration and/or size of the drone due to a larger battery. Addressing the computational challenges of localization in an insect-scale drone using a CIM approach, we propose a novel framework of 3D map representation using a harmonic mean of "Gaussian-like" mixture (HMGM) model. We show that short-circuit current of a multi-input floating-gate CMOS-based inverter follows the harmonic mean of a Gaussianlike function. Therefore, the likelihood function useful for drone localization can be efficiently implemented by connecting many multi-input inverters in parallel, each programmed with the parameters of the 3D map model represented as HMGM. When the depth measurements are projected to the input of the implementation, the summed current of the inverters emulates the likelihood of the measurement. We have characterized our approach on an RGB-D indoor localization dataset. The average localization error in our approach is ∼0.1125 m which is only slightly degraded than software-based evaluation where the average localization error is ∼0.08 m. Meanwhile, our localization framework is ultra-low-power, consuming as little as ∼17 µW power while processing a depth frame in 1.33 ms over hundred pose hypotheses in the particle-filtering (PF) algorithm used to localize the drone. Comparatively, a custom-designed 8-bit digital processor requires ∼7.6 mW power for the same workload. Therefore, the proposed approach consumes ∼450× less energy than the traditional, paving the way for tiny autonomous drones.

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“…The new inference operators can further benefit from customdesigned computing modes. For example, multiplication-free and binary weight operators are quite suited for compute-inmemory [8], [13], [14]. A deep-shift operator can be more efficiently implemented using digital shifters [10].…”

Section: Introductionmentioning

confidence: 99%

ENOS: Energy-Aware Network Operator Search in Deep Neural Networks

et al. 2022

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This work proposes a novel Energy-aware Network Operator Search (ENOS) approach to address the energy-accuracy trade-offs of a deep neural network (DNN) accelerator. In recent years, novel hardwarefriendly inference operators such as binary-weight, multiplication-free, and deep-shift have been proposed to improve the computational efficiency of a DNN accelerator. However, simplifying DNN operators invariably comes at lower accuracy, especially on complex processing tasks. While prior works generally implement the same inference operator throughout the neural architecture, the proposed ENOS framework allows an optimal layer-wise integration of inference operators with optimal precision to maintain high prediction accuracy and high energy efficiency. The search in ENOS is formulated as a continuous optimization problem, solvable using gradient descent methods, thereby minimally increasing the training cost when learning both layer-wise inference operators and weights. Utilizing ENOS, we discuss multiply-accumulate (MAC) cores for digital spatial architectures that can be reconfigured to different operators and varying computing precision. ENOS training methods with single and bi-level optimization objectives are discussed and compared. We also discuss a sequential operator assignment strategy in ENOS that only learns the assignment for one layer in one training step. Furthermore, a stochastic mode of ENOS is also presented. ENOS is characterized on ShuffleNet and SqueezeNet using CIFAR10 and CIFAR100. Compared to the conventional uni-operator approaches, under the same energy budget, ENOS improves accuracy by 10-20%. ENOS also outperforms the accuracy of comparable mixed-precision uni-operator implementations by 3-5% for the same energy budget.INDEX TERMS Low power, deep neural network, mixed-precision learning.

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MC²RAM: Markov Chain Monte Carlo Sampling in SRAM for Fast Bayesian Inference

Cited by 23 publications

References 11 publications

Ultralow-Power Localization of Insect-Scale Drones: Interplay of Probabilistic Filtering and Compute-in-Memory

Ultralow-Power Localization of Insect-Scale Drones: Interplay of Probabilistic Filtering and Compute-in-Memory

Probabilistic Localization of Insect-Scale Drones on Floating-Gate Inverter Arrays

ENOS: Energy-Aware Network Operator Search in Deep Neural Networks

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MC2RAM: Markov Chain Monte Carlo Sampling in SRAM for Fast Bayesian Inference

Cited by 23 publications

References 11 publications

Ultralow-Power Localization of Insect-Scale Drones: Interplay of Probabilistic Filtering and Compute-in-Memory

Ultralow-Power Localization of Insect-Scale Drones: Interplay of Probabilistic Filtering and Compute-in-Memory

Probabilistic Localization of Insect-Scale Drones on Floating-Gate Inverter Arrays

ENOS: Energy-Aware Network Operator Search in Deep Neural Networks

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MC²RAM: Markov Chain Monte Carlo Sampling in SRAM for Fast Bayesian Inference