An accelerator is a specialized integrated circuit designed to perform specific computations faster than if those were performed by CPU or GPU. A Field-Programmable DNN learning and inference accelerator (FProg-DNN) using hybrid systolic and non-systolic techniques, distributed information-control and deep pipelined structure is proposed and its microarchitecture and operation presented here. Reconfigurability attends diverse DNN designs and allows for different number of workers to be assigned to different layers as a function of the relative difference in computational load among layers. The computational delay per layer is made roughly the same along pipelined accelerator structure. VGG-16 and recently proposed Inception Modules are used for showing the flexibility of the FProg-DNN reconfigurability. Special structures were also added for a combination of convolution layer, map coincidence and feedback for state of the art learning with small set of examples, which is the focus of a companion paper by the author (Franca-Neto, 2018). The accelerator described is able to reconfigure from (1) allocating all a DNN computations to a single worker in one extreme of sub-optimal performance to (2) optimally allocating workers per layer according to computational load in each DNN layer to be realized. Due the pipelined architecture, more than 50x speedup is achieved relative to GPUs or TPUs. This speed-up is consequence of hiding the delay in transporting activation outputs from one layer to the next in a DNN behind the computations in the receiving layer. This FProg-DNN concept has been simulated and validated at behavioral-functional level.
To cope with the increasing demand and computational intensity of deep neural networks (DNNs), industry and academia have turned to accelerator technologies. In particular, FPGAs have been shown to provide a good balance between performance and energy efficiency for accelerating DNNs. While significant research has focused on how to build efficient layer processors, the computational building blocks of DNN accelerators, relatively little attention has been paid to the on-chip interconnects that sit between the layer processors and the FPGA's DRAM controller. We observe a disparity between DNN …
The recent breakthroughs in deep neural networks (DNNs) have spurred a tremendously increased demand for DNN accelerators. However, designing DNN accelerators is non-trivial as it often takes months/years and requires cross-disciplinary knowledge. To enable fast and effective DNN accelerator development, we propose DNN-Chip Predictor, an analytical performance predictor which can accurately predict DNN accelerators' energy, throughput, and latency prior to their actual implementation. Our Predictor features two highlights: (1) its analytical performance formulation of DNN ASIC/FPGA accelerator…
Brno University of Technology(布尔诺理工大学);Technische Universität Wien (TU Wien)(维也纳技术大学)
The state-of-the-art approaches employ approximate computing to reduce the energy consumption of DNN hardware. Approximate DNNs then require extensive retraining afterwards to recover from the accuracy loss caused by the use of approximate operations. However, retraining of complex DNNs does not scale well. In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators while retraining can completely be avoided. ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computi…
The recent breakthroughs and prohibitive complexities of Deep Neural Networks (DNNs) have excited extensive interest in domain-specific DNN accelerators, among which optical DNN accelerators are particularly promising thanks to their unprecedented potential of achieving superior performance-per-watt. However, the development of optical DNN accelerators is much slower than that of electrical DNN accelerators. One key challenge is that while many techniques have been developed to facilitate the development of electrical DNN accelerators, techniques that support or expedite optical DNN accelerato…
Polytechnique Montreal(蒙特利尔综合理工学院);IMT Atlantique(大西洋国立高等矿业电信学校);Mila - Quebec AI Institute(米拉-魁北克人工智能研究所)
Memristors enable the computation of matrix-vector multiplications (MVM) in memory and, therefore, show great potential in highly increasing the energy efficiency of deep neural network (DNN) inference accelerators. However, computations in memristors suffer from hardware non-idealities and are subject to different sources of noise that may negatively impact system performance. In this work, we theoretically analyze the mean squared error of DNNs that use memristor crossbars to compute MVM. We take into account both the quantization noise, due to the necessity of reducing the DNN model size, a…
Southern Illinois University(南伊利诺伊大学);Karlsruhe Institute of Technology(卡尔斯鲁厄理工学院)
Deep Neural Networks (DNNs) are being heavily utilized in modern applications and are putting energy-constraint devices to the test. To bypass high energy consumption issues, approximate computing has been employed in DNN accelerators to balance out the accuracy-energy reduction trade-off. However, the approximation-induced accuracy loss can be very high and drastically degrade the performance of the DNN. Therefore, there is a need for a fine-grain mechanism that would assign specific DNN operations to approximation in order to maintain acceptable DNN accuracy, while also achieving low energy …
Hardware accelerators are being increasingly deployed to boost the performance and energy efficiency of deep neural network (DNN) inference. In this paper we propose Thundervolt, a new framework that enables aggressive voltage underscaling of high-performance DNN accelerators without compromising classification accuracy even in the presence of high timing error rates. Using post-synthesis timing simulations of a DNN accelerator modeled on the Google TPU, we show that Thundervolt enables between 34%-57% energy savings on state-of-the-art speech and image recognition benchmarks with less than 1%…
Deep neural networks (DNN) are increasingly being accelerated on application-specific hardware such as the Google TPU designed especially for deep learning. Timing speculation is a promising approach to further increase the energy efficiency of DNN accelerators. Architectural exploration for timing speculation requires detailed gate-level timing simulations that can be time-consuming for large DNNs that execute millions of multiply-and-accumulate (MAC) operations. In this paper we propose FATE, a new methodology for fast and accurate timing simulations of DNN accelerators like the Google TPU. …
Dataflow/mapping decides the compute and energy efficiency of DNN accelerators. Many mappers have been proposed to tackle the intra-layer map-space. However, mappers for inter-layer map-space (aka layer-fusion map-space), have been rarely discussed. In this work, we propose a mapper, DNNFuser, specifically focusing on this layer-fusion map-space. While existing SOTA DNN mapping explorations rely on search-based mappers, this is the first work, to the best of our knowledge, to propose a one-shot inference-based mapper. We leverage Transformer as our DNN architecture to learn layer-fusion optimi…
National Technical University of Athens(雅典国立技术大学);Karlsruhe Institute of Technology(卡尔斯鲁厄理工学院)
Deep Neural Networks (DNNs) are very popular because of their high performance in various cognitive tasks in Machine Learning (ML). Recent advancements in DNNs have brought beyond human accuracy in many tasks, but at the cost of high computational complexity. To enable efficient execution of DNN inference, more and more research works, therefore, exploit the inherent error resilience of DNNs and employ Approximate Computing (AC) principles to address the elevated energy demands of DNN accelerators. This article provides a comprehensive survey and analysis of hardware approximation techniques f…
Karlsruhe Institute of Technology(卡尔斯鲁厄理工学院);Southern Illinois University(南伊利诺伊大学);University of Stuttgart(斯图加特大学)
In this work, we introduce a control variate approximation technique for low error approximate Deep Neural Network (DNN) accelerators. The control variate technique is used in Monte Carlo methods to achieve variance reduction. Our approach significantly decreases the induced error due to approximate multiplications in DNN inference, without requiring time-exhaustive retraining compared to state-of-the-art. Leveraging our control variate method, we use highly approximated multipliers to generate power-optimized DNN accelerators. Our experimental evaluation on six DNNs, for Cifar-10 and Cifar-10…
Carnegie Mellon University(卡内基梅隆大学);The University of Texas at Austin(德克萨斯大学奥斯汀分校)
As the machine learning and systems community strives to achieve higher energy-efficiency through custom DNN accelerators and model compression techniques, there is a need for a design space exploration framework that incorporates quantization-aware processing elements into the accelerator design space while having accurate and fast power, performance, and area models. In this work, we present QAPPA, a highly parameterized quantization-aware power, performance, and area modeling framework for DNN accelerators. Our framework can facilitate the future research on design space exploration of DNN …
University of Tehran(德黑兰大学);Institute for Research in Fundamental Sciences (IPM)(基础科学研究所(IPM));University of Louisiana at Lafayette(路易斯安那大学拉法叶分校);School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran(德黑兰大学电气与计算机工程学院);School of Computer Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran(基础科学研究所(IPM)计算机科学学院);School of Computing and Informatics, University of Louisiana at Lafayette, Lafayette, LA, USA(路易斯安那大学拉法叶分校计算与信息学院)
Emerging intelligent embedded devices rely on Deep Neural Networks (DNNs) to be able to interact with the real-world environment. This interaction comes with the ability to retrain DNNs, since environmental conditions change continuously in time. Stochastic Gradient Descent (SGD) is a widely used algorithm to train DNNs by optimizing the parameters over the training data iteratively. In this work, first we present a novel approach to add the training ability to a baseline DNN accelerator (inference only) by splitting the SGD algorithm into simple computational elements. Then, based on this heu…
Energy efficiency of hardware accelerators of deep neural networks (DNN) can be improved by introducing approximate arithmetic circuits. In order to quantify the error introduced by using these circuits and avoid the expensive hardware prototyping, a software emulator of the DNN accelerator is usually executed on CPU or GPU. However, this emulation is typically two or three orders of magnitude slower than a software DNN implementation running on CPU or GPU and operating with standard floating point arithmetic instructions and common DNN libraries. The reason is that there is no hardware suppor…
Southern Illinois University(南伊利诺伊大学);University of Stuttgart(斯图加特大学);Karlsruhe Institute of Technology(卡尔斯鲁厄理工学院)
Recent Deep Neural Networks (DNNs) managed to deliver superhuman accuracy levels on many AI tasks. Several applications rely more and more on DNNs to deliver sophisticated services and DNN accelerators are becoming integral components of modern systems-on-chips. DNNs perform millions of arithmetic operations per inference and DNN accelerators integrate thousands of multiply-accumulate units leading to increased energy requirements. Approximate computing principles are employed to significantly lower the energy consumption of DNN accelerators at the cost of some accuracy loss. Nevertheless, rec…
National Technical University of Athens(雅典国立技术大学);Aristotle University of Thessaloniki(塞萨洛尼基亚里士多德大学);Karlsruhe Institute of Technology(卡尔斯鲁厄理工学院)
Current state-of-the-art employs approximate multipliers to address the highly increased power demands of DNN accelerators. However, evaluating the accuracy of approximate DNNs is cumbersome due to the lack of adequate support for approximate arithmetic in DNN frameworks. We address this inefficiency by presenting AdaPT, a fast emulation framework that extends PyTorch to support approximate inference as well as approximation-aware retraining. AdaPT can be seamlessly deployed and is compatible with the most DNNs. We evaluate the framework on several DNN models and application fields including C…
Samsung AI(三星人工智能中心);Imperial College London(帝国理工学院);University of Cambridge(剑桥大学)
As the use of AI-powered applications widens across multiple domains, so do increase the computational demands. Primary driver of AI technology are the deep neural networks (DNNs). When focusing either on cloud-based systems that serve multiple AI queries from different users each with their own DNN model, or on mobile robots and smartphones employing pipelines of various models or parallel DNNs for the concurrent processing of multi-modal data, the next generation of AI systems will have multi-DNN workloads at their core. Large-scale deployment of AI services and integration across mobile and…
With proliferation of DNN-based applications, the confidentiality of DNN model is an important commercial goal. Spatial accelerators, that parallelize matrix/vector operations, are utilized for enhancing energy efficiency of DNN computation. Recently, model extraction attacks on simple accelerators, either with a single processing element or running a binarized network, were demonstrated using the methodology derived from differential power analysis (DPA) attack on cryptographic devices. This paper investigates the vulnerability of realistic spatial accelerators using general, 8-bit, number re…
Tallinn University of Technology(塔林理工大学);Mälardalen University(梅拉达伦大学)
While the role of Deep Neural Networks (DNNs) in a wide range of safety-critical applications is expanding, emerging DNNs experience massive growth in terms of computation power. It raises the necessity of improving the reliability of DNN accelerators yet reducing the computational burden on the hardware platforms, i.e. reducing the energy consumption and execution time as well as increasing the efficiency of DNN accelerators. Therefore, the trade-off between hardware performance, i.e. area, power and delay, and the reliability of the DNN accelerator implementation becomes critical and require…
University of Glasgow(格拉斯哥大学);Northeastern University(东北大学)
Edge computing devices inherently face tight resource constraints, which is especially apparent when deploying Deep Neural Networks (DNN) with high memory and compute demands. FPGAs are commonly available in edge devices. Since these reconfigurable circuits can achieve higher throughput and lower power consumption than general purpose processors, they are especially well-suited for DNN acceleration. However, existing solutions for designing FPGA-based DNN accelerators for edge devices come with high development overheads, given the cost of repeated FPGA synthesis passes, reimplementation in a …
Max Planck Institute for Informatics(马克斯·普朗克信息学研究所);IBM T. J. Watson Research Center(IBM托马斯·J·沃森研究中心);University of Tübingen(图宾根大学)
Deep neural network (DNN) accelerators received considerable attention in recent years due to the potential to save energy compared to mainstream hardware. Low-voltage operation of DNN accelerators allows to further reduce energy consumption, however, causes bit-level failures in the memory storing the quantized weights. Furthermore, DNN accelerators are vulnerable to adversarial attacks on voltage controllers or individual bits. In this paper, we show that a combination of robust fixed-point quantization, weight clipping, as well as random bit error training (RandBET) or adversarial bit error…
Reconfigurable accelerators for deep neural networks (DNNs) promise to improve performance such as inference latency. STONNE is the first cycle-accurate simulator for reconfigurable DNN inference accelerators which allows for the exploration of accelerator designs and configuration space. However, preparing models for evaluation and exploring configuration space in STONNE is a manual developer-timeconsuming process, which is a barrier for research. This paper introduces Bifrost, an end-to-end framework for the evaluation and optimization of reconfigurable DNN inference accelerators. Bifrost op…
Shanghai Jiao Tong University(上海交通大学);University of Rochester(罗切斯特大学);Institute of Computing Technology, Chinese Academy of Sciences(中国科学院计算技术研究所)
The research interest in specialized hardware accelerators for deep neural networks (DNN) spikes recently owing to their superior performance and efficiency. However, today's DNN accelerators primarily focus on accelerating specific "kernels" such as convolution and matrix multiplication, which are vital but only part of an end-to-end DNN-enabled application. Meaningful speedups over the entire application often require supporting computations that are, while massively parallel, ill-suited to DNN accelerators. Integrating a general-purpose processor such as a CPU or a GPU incurs significant da…
Max Planck Institute for Informatics(马克斯·普朗克信息学研究所);IBM T. J. Watson Research Center(IBM T. J. Watson 研究中心);University of Tübingen(蒂宾根大学)
Deep neural network (DNN) accelerators received considerable attention in past years due to saved energy compared to mainstream hardware. Low-voltage operation of DNN accelerators allows to further reduce energy consumption significantly, however, causes bit-level failures in the memory storing the quantized DNN weights. In this paper, we show that a combination of robust fixed-point quantization, weight clipping, and random bit error training (RandBET) improves robustness against random bit errors in (quantized) DNN weights significantly. This leads to high energy savings from both low-voltag…
Deep neural networks (DNNs) have the advantage that they can take into account a large number of parameters, which enables them to solve complex tasks. In computer vision and speech recognition, they have a better accuracy than common algorithms, and in some tasks, they boast an even higher accuracy than human experts. With the progress of DNNs in recent years, many other fields of application such as diagnosis of diseases and autonomous driving are taking advantage of them. The trend at DNNs is clear: The network size is growing exponentially, which leads to an exponential increase in computa…
Carnegie Mellon University(卡内基梅隆大学);The University of Texas at Austin(德克萨斯大学奥斯汀分校)
As the machine learning and systems communities strive to achieve higher energy-efficiency through custom deep neural network (DNN) accelerators, varied bit precision or quantization levels, there is a need for design space exploration frameworks that incorporate quantization-aware processing elements (PE) into the accelerator design space while having accurate and fast power, performance, and area models. In this work, we present QADAM, a highly parameterized quantization-aware power, performance, and area modeling framework for DNN accelerators. Our framework can facilitate future research o…
The use of lower precision has emerged as a popular technique to optimize the compute and storage requirements of complex Deep Neural Networks (DNNs). In the quest for lower precision, recent studies have shown that ternary DNNs (which represent weights and activations by signed ternary values) represent a promising sweet spot, achieving accuracy close to full-precision networks on complex tasks. We propose TiM-DNN, a programmable in-memory accelerator that is specifically designed to execute ternary DNNs. TiM-DNN supports various ternary representations including unweighted {-1,0,1}, symmetri…
Exploration of Activation Fault Reliability in Quantized Systolic Array-Based DNN Accelerators
Tallinn University of Technology(塔林理工大学);University of Alberta(阿尔伯塔大学);Shahid Bahonar University of Kerman(克尔曼沙希德·巴霍纳尔大学);York University(约克大学);Mälardalen University(梅拉达伦大学)
Training deep neural networks (DNNs) is a computationally expensive job, which can take weeks or months even with high performance GPUs. As a remedy for this challenge, community has started exploring the use of more efficient data representations in the training process, e.g., block floating point (BFP). However, prior work on BFP-based DNN accelerators rely on a specific BFP representation making them less versatile. This paper builds upon an algorithmic observation that we can accelerate the training by leveraging multiple BFP precisions without compromising the finally achieved accuracy. B…
University of Missouri(密苏里大学);The University of Texas at Dallas(德克萨斯大学达拉斯分校)
Systolic array-based deep neural network (DNN) accelerators have recently gained prominence for their low computational cost. However, their high energy consumption poses a bottleneck to their deployment in energy-constrained devices. To address this problem, approximate computing can be employed at the cost of some tolerable accuracy loss. However, such small accuracy variations may increase the sensitivity of DNNs towards undesired subtle disturbances, such as permanent faults. The impact of permanent faults in accurate DNNs has been thoroughly investigated in the literature. Conversely, the…
The University of British Columbia(英属哥伦比亚大学);Microsoft Corporation(微软公司)
The success of DNN pruning has led to the development of energy-efficient inference accelerators that support pruned models with sparse weight and activation tensors. Because the memory layouts and dataflows in these architectures are optimized for the access patterns during $\mathit{inference}$, however, they do not efficiently support the emerging sparse $\mathit{training}$ techniques. In this paper, we demonstrate (a) that accelerating sparse training requires a co-design approach where algorithms are adapted to suit the constraints of hardware, and (b) that hardware for sparse DNN training…
Carnegie Mellon University(卡内基梅隆大学);The University of Texas at Austin(德克萨斯大学奥斯汀分校)
As the machine learning and systems communities strive to achieve higher energy-efficiency through custom deep neural network (DNN) accelerators, varied precision or quantization levels, and model compression techniques, there is a need for design space exploration frameworks that incorporate quantization-aware processing elements into the accelerator design space while having accurate and fast power, performance, and area models. In this work, we present QUIDAM, a highly parameterized quantization-aware DNN accelerator and model co-exploration framework. Our framework can facilitate future re…
Duke University(杜克大学);University of Southern California(南加州大学)
With the rise of artificial intelligence in recent years, Deep Neural Networks (DNNs) have been widely used in many domains. To achieve high performance and energy efficiency, hardware acceleration (especially inference) of DNNs is intensively studied both in academia and industry. However, we still face two challenges: large DNN models and datasets, which incur frequent off-chip memory accesses; and the training of DNNs, which is not well-explored in recent accelerator designs. To truly provide high throughput and energy efficient acceleration for the training of deep and large models, we ine…
The excellent performance of modern deep neural networks (DNNs) comes at an often prohibitive training cost, limiting the rapid development of DNN innovations and raising various environmental concerns. To reduce the dominant data movement cost of training, process in-memory (PIM) has emerged as a promising solution as it alleviates the need to access DNN weights. However, state-of-the-art PIM DNN training accelerators employ either analog/mixed signal computing which has limited precision or digital computing based on a memory technology that supports limited logic functions and thus requires…
Dedicated accelerators are being designed to address the huge resource requirement of the deep neural network (DNN) applications. The power, performance and area (PPA) constraints limit the number of MACs available in these accelerators. The convolution layers which require huge number of MACs are often partitioned into multiple iterative sub-tasks. This puts huge pressure on the available system resources such as interconnect and memory bandwidth. The optimal partitioning of the feature maps for these sub-tasks can reduce the bandwidth requirement substantially. Some accelerators avoid off-ch…
University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校);Advanced Digital Sciences Center(高级数字科学中心);IBM T. J. Watson Research Center(IBM T. J.沃森研究中心)
High quality AI solutions require joint optimization of AI algorithms, such as deep neural networks (DNNs), and their hardware accelerators. To improve the overall solution quality as well as to boost the design productivity, efficient algorithm and accelerator co-design methodologies are indispensable. In this paper, we first discuss the motivations and challenges for the Algorithm/Accelerator co-design problem and then provide several effective solutions. Especially, we highlight three leading works of effective co-design methodologies: 1) the first simultaneous DNN/FPGA co-design method; 2)…
Special Session: Approximation and Fault Resiliency of DNN Accelerators
Tallinn University of Technology(塔林理工大学);University of Naples Federico II(那不勒斯费德里科二世大学);Ecole Centrale de Lyon(里昂中央理工学院);Mälardalen University(马拉达伦大学);Politecnico di Torino(都灵理工大学)
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 inference operators have been proposed to improve the computational efficiency of a DNN. Augmenting the operators, their corresponding novel computing modes have also been explored. However, simplification of DNN operators invariably comes at the cost of lower accuracy, especially on complex processing tasks. Our proposed ENOS framework allows an optimal layer-wise integration of inference operators and comp…
MAx-DNN: Multi-Level Arithmetic Approximation for Energy-Efficient DNN Hardware Accelerators
National Technical University of Athens, School of Electrical and Computer Engineering(希腊雅典国家技术大学电气与计算机工程学院);Harokopio University of Athens, Department of Informatics and Telematics(雅典霍罗科波利斯大学信息与电信学院)
Deep neural networks (DNNs) have been proving the effectiveness in various computing fields. To provide more efficient computing platforms for DNN applications, it is essential to have evaluation environments that include assorted benchmark workloads. Though a few DNN benchmark suites have been recently released, most of them require to install proprietary DNN libraries or resource-intensive DNN frameworks, which are hard to run on resource-limited mobile platforms or architecture simulators. To provide a more scalable evaluation environment, we propose a new DNN benchmark suite that can run o…
The efficiency of a spatial DNN accelerator depends heavily on the compiler and its cost model ability to generate optimized mappings for various operators of DNN models on to the accelerator's compute and memory resources. But, existing cost models lack a formal boundary over the operators for precise and tractable analysis, which poses adaptability challenges for new DNN operators. To address this challenge, we leverage the recently introduced Maestro Data-Centric (MDC) notation. We develop a formal understanding of DNN operators whose mappings can be described in the MDC notation, because a…
School of Electrical and Computer Engineering, Georgia Institute of Technology(佐治亚理工学院电气与计算机工程学院)
DNN+NeuroSim is an integrated framework to benchmark compute-in-memory (CIM) accelerators for deep neural networks, with hierarchical design options from device-level, to circuit-level and up to algorithm-level. A python wrapper is developed to interface NeuroSim with a popular machine learning platform: Pytorch, to support flexible network structures. The framework provides automatic algorithm-to-hardware mapping, and evaluates chip-level area, energy efficiency and throughput for training or inference, as well as training/inference accuracy with hardware constraints. Our prior work (DNN+Neur…
Recent advances in Deep Neural Networks (DNNs) have led to active development of specialized DNN accelerators, many of which feature a large number of processing elements laid out spatially, together with a multi-level memory hierarchy and flexible interconnect. While DNN accelerators can take advantage of data reuse and achieve high peak throughput, they also expose a large number of runtime parameters to the programmers who need to explicitly manage how computation is scheduled both spatially and temporally. In fact, different scheduling choices can lead to wide variations in performance and…
DNN accelerators provide efficiency by leveraging reuse of activations/weights/outputs during the DNN computations to reduce data movement from DRAM to the chip. The reuse is captured by the accelerator's dataflow. While there has been significant prior work in exploring and comparing various dataflows, the strategy for assigning on-chip hardware resources (i.e., compute and memory) given a dataflow that can optimize for performance/energy while meeting platform constraints of area/power for DNN(s) of interest is still relatively unexplored. The design-space of choices for balancing compute an…
This paper presents a programmable in-memory-computing processor, demonstrated in a 65nm CMOS technology. For data-centric workloads, such as deep neural networks, data movement often dominates when implemented with today's computing architectures. This has motivated spatial architectures, where the arrangement of data-storage and compute hardware is distributed and explicitly aligned to the computation dataflow, most notably for matrix-vector multiplication. In-memory computing is a spatial architecture where processing elements correspond to dense bit cells, providing local storage and compu…