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Bit-Parallel Vector Composability for Neural Acceleration Soroush Ghodrati Hardik Sharma † Cliff Young ‡ Nam Sung Kim § Hadi Esmaeilzadeh Alternative Computing Technologies (ACT) Lab University of California, San Diego † Bigstream, Inc. ‡ Google Inc. § University of Illinois Urbana-Champaign [email protected] [email protected] [email protected] [email protected] [email protected] Abstract—Conventional neural accelerators rely on isolated self-sufficient functional units that perform an atomic operation while communicating the results through an operand delivery-aggregation logic. Each single unit processes all the bits of their operands atom- ically and produce all the bits of the results in isolation. This paper explores a different design style, where each unit is only responsible for a slice of the bit-level operations to interleave and combine the benefits of bit-level parallelism with the abundant data-level parallelism in deep neural networks. A dynamic collection of these units cooperate at runtime to generate bits of the results, collectively. Such cooperation requires extracting new grouping between the bits, which is only pos- sible if the operands and operations are vectorizable. The abundance of Data-Level Parallelism and mostly repeated execution patterns, provides a unique opportunity to define and leverage this new dimen- sion of Bit-Parallel Vector Composability. This design intersperses bit parallelism within data-level parallelism and dynamically interweaves the two together. As such, the building block of our neural accelerator is a Composable Vector Unit that is a collection of Narrower-Bitwidth Vector Engines, which are dynamically composed or decomposed at the bit granularity. Using six diverse CNN and LSTM deep networks, we evaluate this design style across four design points: with and without algorithmic bitwidth heterogeneity and with and without availability of a high-bandwidth off-chip memory. Across these four design points, Bit-Parallel Vector Composability brings (1.4×to 3.5×) speedup and (1.1×to 2.7×) energy reduction. We also comprehen- sively compare our design style to the Nvidia’s RTX 2080 TI GPU, which also supports INT-4 execution. The benefits range between 28.0×and 33.7×improvement in Performance-per-Watt. Index Terms—Acceleration, neural networks, bit-flexibility I. INTRODUCTION The growing body of neural accelerators [1–3, 6, 7, 9– 11, 15, 17, 20] exploit various forms of Data-Level Parallelism (DLP) that are abundant in Deep Neural Networks. For instance, Google’s TPU [9] extracts data-level parallelism across the lanes of its systolic array, Microsoft’s Brainwave [6] builds a dataflow architecture from vectorized units, and GPUs have been long designed for Single-Instruction Multiple-Data (SIMD) execution model. Nonetheless, these various organization still rely on isolated self-sufficient units that process all the bits of input operands and generate all the bits of the results. These values, packed as atomic words, are then communicated through an operand delivery- aggregation interconnect for further computation. This paper sets out to explore a different design where each unit in vectorized engines is only responsible for processing a bit-slice. This design offers an opening to explore the interleaving of Bit-Level Parallelism with DLP for neural acceleration. Such an interleaving opens a new tradeoff space where the complexity of Narrow-Bitwidth Functional Units needs to be balanced with respect to the overhead of bit-level aggregation as well as the width of vectorization. Additionally, the proposed approach creates a new opportunity for exploring bit-flexibility in the context of vectorized execution. Fig. 1: The landscape of DNN accelerators and how this work fits in the picture. As Figure 1 illustrates, the landscape of neural accelerators can be depicted in the three dimensions of Type of Functional Units (Scalar [1, 2, 7, 9, 15] v.s. Vectorized [3, 6, 17]), Bit Flexibility 1 (Fixed Bitwidth v.s. Flexible Bitwidth), and Composability (Temporal [10, 11, 18] vs. Spatial [20]). This work aims to fill the vacancy for Vectorized Bit-Flexible Spatial Composability. In fact, the interleaving of the bit-level parallelism with DLP creates the new opportunity to explore bit-level composability where a group of bit- parallel vector units dynamically form collaborative groups to carry out SIMD operations. Recent inspiring research investigates bit-level composability for a scalar operation (a single MAC unit) both in spatial and temporal mode. However, the space where composability (bit-level parallelism) meets vectorization (data-level parallelism) is not explored. Our design style opens this space by breaking up the vector units to narrower bitwidth engines. Since the building block is a narrow bitwidth vector engine, another opportunity arises to support execution well below eight bits. That is leveraging the algorithmic insight that heterogenous assignment of bitwidths below eight to DNN layers can reduce their computational complexity while preserving accuracy [4, 5, 8, 13, 16]. Fixed bitwidth designs cannot tap into this level of efficiency where each unit is only processing the fewest number of bits that can preserve the accuracy. We evaluate the proposed concepts with and without availability of algorithmic bitwidth heterogeneity. Experimentation with six real-world DNNs shows that bit-parallel vector composibility provides 40% speedup and energy reduction compared to design with the same architecture (systolic) without support for the proposed composability. When bit flexibility is applicable because of the heterogenous bitwidths in the DNN layers, our design provides 50% speedup and 10% energy reduction compared to BitFusion [20], the state-of-the-art architecture that supports scalar bit-level composability in systolic designs 2 . 1 Bit flexibility can be defined as the capability of a functional unit in reconfiguring itself at runtime to support different bitwidths. 2 We do not compare to BitFusion when algorithmic bitwidth heterogeneity is not available, BitFusion would underperform compared to a non-composable design. arXiv:2004.05333v1 [cs.LG] 11 Apr 2020

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Page 1: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

Bit-Parallel Vector Composability for Neural AccelerationSoroush Ghodrati Hardik Sharma† Cliff Young‡ Nam Sung Kim§ Hadi Esmaeilzadeh

Alternative Computing Technologies (ACT) LabUniversity of California, San Diego †Bigstream, Inc. ‡Google Inc. §University of Illinois Urbana-Champaign

[email protected] [email protected] [email protected] [email protected] [email protected]

Abstract—Conventional neural accelerators rely on isolatedself-sufficient functional units that perform an atomic operation whilecommunicating the results through an operand delivery-aggregationlogic. Each single unit processes all the bits of their operands atom-ically and produce all the bits of the results in isolation. This paperexplores a different design style, where each unit is only responsible fora slice of the bit-level operations to interleave and combine the benefitsof bit-level parallelism with the abundant data-level parallelism indeep neural networks. A dynamic collection of these units cooperateat runtime to generate bits of the results, collectively. Such cooperationrequires extracting new grouping between the bits, which is only pos-sible if the operands and operations are vectorizable. The abundanceof Data-Level Parallelism and mostly repeated execution patterns,provides a unique opportunity to define and leverage this new dimen-sion of Bit-Parallel Vector Composability. This design intersperses bitparallelism within data-level parallelism and dynamically interweavesthe two together. As such, the building block of our neural acceleratoris a Composable Vector Unit that is a collection of Narrower-BitwidthVector Engines, which are dynamically composed or decomposed atthe bit granularity. Using six diverse CNN and LSTM deep networks,we evaluate this design style across four design points: with andwithout algorithmic bitwidth heterogeneity and with and withoutavailability of a high-bandwidth off-chip memory. Across these fourdesign points, Bit-Parallel Vector Composability brings (1.4×to 3.5×)speedup and (1.1×to 2.7×) energy reduction. We also comprehen-sively compare our design style to the Nvidia’s RTX 2080 TI GPU,which also supports INT-4 execution. The benefits range between28.0×and 33.7×improvement in Performance-per-Watt.

Index Terms—Acceleration, neural networks, bit-flexibility

I. INTRODUCTION

The growing body of neural accelerators [1–3, 6, 7, 9–11, 15, 17, 20] exploit various forms of Data-Level Parallelism(DLP) that are abundant in Deep Neural Networks. For instance,Google’s TPU [9] extracts data-level parallelism across the lanesof its systolic array, Microsoft’s Brainwave [6] builds a dataflowarchitecture from vectorized units, and GPUs have been longdesigned for Single-Instruction Multiple-Data (SIMD) executionmodel. Nonetheless, these various organization still rely on isolatedself-sufficient units that process all the bits of input operandsand generate all the bits of the results. These values, packed asatomic words, are then communicated through an operand delivery-aggregation interconnect for further computation. This paper sets outto explore a different design where each unit in vectorized enginesis only responsible for processing a bit-slice. This design offers anopening to explore the interleaving of Bit-Level Parallelism withDLP for neural acceleration. Such an interleaving opens a newtradeoff space where the complexity of Narrow-Bitwidth FunctionalUnits needs to be balanced with respect to the overhead of bit-levelaggregation as well as the width of vectorization.

Additionally, the proposed approach creates a new opportunityfor exploring bit-flexibility in the context of vectorized execution.

Fig. 1: The landscape of DNN accelerators and how this work fits in the picture.

As Figure 1 illustrates, the landscape of neural accelerators canbe depicted in the three dimensions of Type of Functional Units(Scalar [1, 2, 7, 9, 15] v.s. Vectorized [3, 6, 17]), Bit Flexibility1

(Fixed Bitwidth v.s. Flexible Bitwidth), and Composability(Temporal [10, 11, 18] vs. Spatial [20]). This work aims to fill thevacancy for Vectorized Bit-Flexible Spatial Composability. In fact,the interleaving of the bit-level parallelism with DLP creates the newopportunity to explore bit-level composability where a group of bit-parallel vector units dynamically form collaborative groups to carryout SIMD operations. Recent inspiring research investigates bit-levelcomposability for a scalar operation (a single MAC unit) both inspatial and temporal mode. However, the space where composability(bit-level parallelism) meets vectorization (data-level parallelism)is not explored. Our design style opens this space by breaking upthe vector units to narrower bitwidth engines. Since the buildingblock is a narrow bitwidth vector engine, another opportunity arisesto support execution well below eight bits. That is leveraging thealgorithmic insight that heterogenous assignment of bitwidths beloweight to DNN layers can reduce their computational complexitywhile preserving accuracy [4, 5, 8, 13, 16]. Fixed bitwidth designscannot tap into this level of efficiency where each unit is onlyprocessing the fewest number of bits that can preserve the accuracy.

We evaluate the proposed concepts with and without availabilityof algorithmic bitwidth heterogeneity. Experimentation with sixreal-world DNNs shows that bit-parallel vector composibilityprovides 40% speedup and energy reduction compared to designwith the same architecture (systolic) without support for theproposed composability. When bit flexibility is applicable becauseof the heterogenous bitwidths in the DNN layers, our designprovides 50% speedup and 10% energy reduction compared toBitFusion [20], the state-of-the-art architecture that supports scalarbit-level composability in systolic designs2.

1Bit flexibility can be defined as the capability of a functional unit in reconfiguringitself at runtime to support different bitwidths.

2We do not compare to BitFusion when algorithmic bitwidth heterogeneity is notavailable, BitFusion would underperform compared to a non-composable design.

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Page 2: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

When a high bandwidth off-chip memory is utilized, the baselinedesign only enjoys 10% speedup and 30% energy reduction, respec-tively. However, bit-parallel vector-composability better utilizes theboosted bandwidth and provides 2.1× speedup and 2.3× energyreduction. With algorithmic bitwidth heterogeneity our design styleprovides 2.4× speedup and 20% energy reduction, compared toBitFusion, while it also utilizes the same high bandwidth memoryFinally, we compare different permutations of our design style withrespect to homogenous/heterogenous bitwidth and off-chip memorybandwidth to the Nvidia’s RTX 2080 TI GPU which also supportsINT-4 execution. Benefits range between 28.0×and 33.7×higherPerformance-per-Watt for four possible design points.

II. BIT-PARALLEL VECTOR COMPOSABILITY

This paper builds upon the fundamental property of vectordot-product operation – the most common operation in DNNs – thatvector dot-product with wide-bitwidth data types can be decomposedand reformulated as a summation of several dot-products withnarrow-bitwidth data types. The element-wise multiplication invector dot-product can be performed independently, exposing data-level parallelism. This work explores another degree of parallelism– bit-level parallelism (BLP) – wherein individual multiplicationscan be broken down at bit-level and written as a summation ofnarrower bitwidth multiplications. Leveraging this insight, thiswork studies the interleaving of both data-level parallelism in vectordot-product with bit-level parallelism in individual multiplicationsto introduce the notion of bit-parallel vector composability. Thisdesign style can also be exploited to support runtime-flexiblebitwidths on the underlying hardware. The rest of this section detailsthe mathematical formulation for bit-parallel vector composability.Fixed-Bitwidth bit-parallel vector composability. Digital valuescan be expressed as the summation of individual bits multipliedby powers of two. Hence, a vector dot-product operation betweentwo vectors, ~X, ~W can be expressed as follows:

~X• ~W=∑i(xi×wi)=

∑i((

∑bwx−1j=0 2j×xi[j])×(

∑bww−1k=0 2k×wi[k]))

(1)Variables bwx and bww represent the bitwidths of the elementsin ~X and ~W , respectively. Expanding the bitwise multiplicationsbetween the elements of the two vectors yields:

~X• ~W=∑i(∑bwx−1j=0

∑bww−1k=0 2j+k×xi[j]×wi[k]) (2)

Conventional architectures rely on compute units that operate on allbits of individual operands, and require complex left-shift operationsfollowed by wide-bitwidth additions as shown with an underlinein Equation 2. By leveraging the associativity property of themultiplication and addition, we can cluster the bit-wise operationsthat share the same significance position together and factor outthe power of two multiplications. In other words, this clustering canbe realized by swapping the order of

∑i and

∑j

∑k operators.

~X• ~W=∑bwx−1j=0

∑bww−1k=0 2j+k×(

∑ixi[j]×wi[k]) (3)

Leveraging this insight enables the use of significantly less complex,narrow-bitwidth, compute units (1-bit in the equation), exploitingbit-level parallelism, amortizing the cost of left-shift and wide-bitwidth addition. Breaking down the dot-product is not limited

to single bit and elements of the vectors can be bit-sliced withdifferent sizes. As such, Equation 3 can be further generalized as:

=∑ bwx

α −1j=0

∑ bwwβ −1

k=0 2αj+βk×(∑ixi[αj :(α+1)j]×wi[βk :(β+1)k])

(4)Here, α and β are the bit-slices for operands xi and wi forthe narrow-bitwidth compute units, respectively. Figure 2-(a)graphically illustrates bit-parallel vector composability using anexample of a vector dot-product operation (~X • ~W =

∑ixi×wi)

between two vectors of ~X and ~W , each of which constitutes two4-bit elements. As it is shown with different shades, each elementcan be bit-sliced and broken down into two 2-bit slices. With thisbit-slicing scheme, the original element (xi or wi) can be writtenas 22× bslMSB+20× bslLSB, where bsls are the bit-slices andthey are multiplied by powers of two based on their significanceposition. With the aforementioned bit-slicing scheme, performinga product operation between an element from ~X and another from~W requires four multiplications between the slices, each of whichis also multiplied by the corresponding significance position factor.However, because of the associativity property of the multiply-add,we cluster the bit-sliced multiplications that share the samesignificance position and apply the power of two multiplicands byshifting the accumulated result of the bit-sliced multiplications.Flexible-Bitwidth vector composability. The bit-parallel vectorcomposable design style can enable flexible-bitwidth support atruntime. Figure 2-(b) shows an example of flexible-bitwidth vectordot-product operation considering the same number of computeresources (2-bit multipliers, adders, and shifters) as Figure 2. InFigure 2-(b), a vector dot-product operation between a vector ofinputs (~X) that has four 4-bit elements and a vector of weights ( ~W )that has four 2-bit elements is illustrated. Using the same bit-slicingscheme, the original vector ~X is broken down to two sub-vectorsthat are required to go under dot-product with ~W and then getshifted and aggregated. However, exploiting 2-bit datatypes forweights compared to 4-bit in the example given in Figure 2-(a),provides 2× boost in compute performance. Bit-parallel vectorcomposability enables maximum utilization of the computeresources, resulting in computing a vector dot-product operationwith 2× more elements using the same amount of resources.

The next section discusses the acceleration using this design style.

2b 2b 2b 2b 2b 2b 2b 2b~X

~W 2b 2b 2b 2b

+2b 2b

2b 2b

2b

2b

+2b

2b

2b

2b

+2b

2b

2b

2b

+2b

2b

( ( ( (

( ( ( (

+<< 2+0 << 2+0

<< 0+0 << 0+0

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2b 2b 2b 2b

2b 2b 2b 2b

2b 2b

+( ( 2+2<<

2b 2b

+( ( 2+0<<

2b 2b

+( (

2b 2b

+ 0+2<<2b 2b

+(2b 2b

+ (

0+0<<

+~X

~W

Dot-product of two vectors with four elements

2b

2b

2b

2b

2bx2b multiplier

+ Adder << Shifter

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w0<latexit sha1_base64="5/lQsLQlQibisCKoQouFooaz9j0=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9R3++WKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAIpo2e</latexit><latexit sha1_base64="5/lQsLQlQibisCKoQouFooaz9j0=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9R3++WKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAIpo2e</latexit><latexit sha1_base64="5/lQsLQlQibisCKoQouFooaz9j0=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9R3++WKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAIpo2e</latexit><latexit sha1_base64="5/lQsLQlQibisCKoQouFooaz9j0=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9R3++WKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAIpo2e</latexit>

w1<latexit sha1_base64="x3+vf06QaiZbytuTgzZc+MW2BGw=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9T3+uWKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAKKo2f</latexit><latexit sha1_base64="x3+vf06QaiZbytuTgzZc+MW2BGw=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9T3+uWKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAKKo2f</latexit><latexit sha1_base64="x3+vf06QaiZbytuTgzZc+MW2BGw=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9T3+uWKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAKKo2f</latexit><latexit sha1_base64="x3+vf06QaiZbytuTgzZc+MW2BGw=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48V7Qe0oWy2k3bpZhN2N0oJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4Zua3H1FpHssHM0nQj+hQ8pAzaqx0/9T3+uWKW3XnIKvEy0kFcjT65a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi2VNELtZ/NTp+TMKgMSxsqWNGSu/p7IaKT1JApsZ0TNSC97M/E/r5ua8MrPuExSg5ItFoWpICYms7/JgCtkRkwsoUxxeythI6ooMzadkg3BW355lbQuqp5b9e4uK/XrPI4inMApnIMHNajDLTSgCQyG8Ayv8OYI58V5dz4WrQUnnzmGP3A+fwAKKo2f</latexit>

(a)

(b)

2b2b

2b

2bx2b multiplier

2b2b 2b 2b2b2b

2b 2b 2b 2b2b 2b

2b 2b

2b 2b 2b 2b

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2b 2b

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Fig. 2: (a) Fixed-bitwidth bit-parallel vector composability with 2-bit slicing and (b)Bit-Flexible vector composability for 4-b inputs and 2-b weights; 2x improvementin performance compared to fixed 4-bit dot-product.

Page 3: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

(c) Heterogenous quantized bitwidth mode, conceptual view; four clusters of NBVEs work in parallel and then cooperate together to perform an 8-bit 2-bit dot-product with length of 4 L

(b) Homogenous 8-bit mode, conceptual view; All the NBVEs cooperate together and perform an 8-bit 8-bit dot product with length of L

<<+

<<+ <<+

<<+ <<+

2-bit multiplier<<+ Combinational shift-add

NBVE

Logical composition

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<<+ <<+

2b2b 2b2b2b2b 2b2b2b2bw0

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2b 2b 2b 2b2b 2b

<<

2b 2b 2b 2b

<<

2b 2b 2b 2b

<<

2b 2b 2b 2b

<<

2b 2b 2b 2b

(a) Hardware realization of CVU for the example in Figure 2-(a)

NBVE NBVE

NBVE NBVE

Fig. 3: Composable Vector Unit.

III. ARCHITECTUREDESIGN FOR BIT-PARALLEL VECTOR COMPOSABILITY

To enable hardware realization for the insight of bit-parallel vectorcomposability, the main building block of our design becomesa Composable Vector Unit (CVU), which performs the vectordot-product operation by splitting it into multiple narrow-bitwidthdot-products. As such, the CVU consists of several Narrow-Bitwidth Vector Engines (NBVE) that calculate the dot-productof bit-sliced sub-vectors from the original vectors. The CVU thencombines the results from NBVEs according to the bitwidth ofeach DNN layer. Below, we discuss the micro-architecture.

A. Composable Vector Unit (CVU)Figure 3-(a) illustrates an instance of the hardware realization

of CVU for the vector dot-product example given in Figure 2-(a).In this example, CVU encapsulates 4 Narrow-Bitwidth VectorEngines (NBVE). The number of NBVEs inside a CVU is basedon the size of bit-slicing and maximum bitwidth of datatypes (inputsand weights) that have been selected as two and four in thisexample, respectively. A spatial array of narrow-bitwidth multipliers,connected through an adder-tree, constitute each NBVE. Eachnarrow-bitwidth multiplier performs a 2-bit×2-bit multiplicationwith a 2-bit-slice of inputs and weights, the result of which thengoes to the adder-tree to get aggregated with the outputs of othermultipliers inside an NBVE. As such, the NBVE generates a singlescalar that is the result of the dot-product operation between twobit-sliced sub-vectors. The CVU then shifts the outputs of NBVEsbased on the significance position of their bit-sliced operands and

aggregates the shifted values across all the NBVEs to generatethe final result of the vector dot-product operation. In our design,we consider 8-bit as the maximum bitwidth of inputs and weights,commensurate with prior work [9], and 2-bit slicing for the CVU.As such, CVU encapsulates 16 NBVEs that work in parallel.Below, we discuss how the CVU operates when homogenous andheterogenous bitwidths are exploited.Homogeneous 8-bit mode of operation. Figure 3(b) illustrates theconceptual view of CVU when 8-bit datatypes are homogeneouslyexploited for DNN layers. Each NBVE performs a bit-paralleldot-product on 2-bit-sliced sub-vectors of the original 8-bit×8-bitdot-product between vectors of length L, generating a scalar. TheNBVEs are equipped with shifters to shift their scalar outputs.Finally, to generate the final scalar of the 8-bit dot-product, allthe NBVEs in a CVU, globally cooperate together and CVUaggregates their outputs.Heterogeneous quantized bitwidth mode of operation. Whenthe DNN uses heterogeneous bitwidths (less than 8-bit datatypes)across its layers, the CVU can be dynamically reconfigured to matchthe bitwidths of the DNN layers at runtime. This includes both thereconfigurations of the shifters and the NBVEs composition scheme.For instance, Figure 3 (c) illustrates a case when 8-bit inputs and 2-bit weights are used, the 16 NBVEs will be clustered as four groups,each of which encapsulates four NBVEs. In this mode, the CVUcomposes the NBVEs in two levels. At the first level, all the fourNBVEs in each cluster are privately composed together by applyingthe shift-add logic to complete a dot-product operation with a lengthof L. At the second level, the CVU globally aggregates the outputsof all four clusters and produces the scalar result of dot-productoperation between vectors of length 4×L. As another example, if2-bit datatypes are used for both inputs and weights, each NBVEperforms an independent dot-product, providing 16× higher perfor-mance compared to the homogenous 8-bit mode. To evaluate thebenefits of the bit-parallel vector composability and its design trade-offs, we perform a design space exploration for different number ofmultipliers in an NBVE (L) and choice of bit-slicing and analyze thesensitivity of the CVU’s power/area to these parameters, as follows.

B. Design Space Exploration and TradeoffsFigure 4 shows the design space exploration for 1-bit and 2-bit

slicing, in addition to different lengths of vectors for NBVE fromL=1 toL=16. All the design points in this analysis are synthesizedin 500 Mhz and 45 nm node. Y-Axis shows the power and area perone 8-bit × 8-bit MAC operation performed by CVU normalized tothe power/area of a conventional digital 8-bit MAC unit. We sweepthe L parameter for 1-bit slicing and 2-bit slicing in the X-axis.Figure 4 also shows the breakdown of power and area across four dif-ferent hardware logics; multiplication, addition, shifting, and register-ing. Inspecting this analysis leads us to following key observations:

(1) Adder-tree consumes the most power/area and mightbottleneck the efficiency. As we observe in both 1-bit and 2-bitslicing, across all the hardware components adder-tree ranks first inpower/area consumption. Bit-parallel vector composability imposestwo levels of add-tree logic: (a) An adder-tree private to eachNBVE that sums the results of narrow-bitwidth multiplications.(b) A global adder-tree that aggregates the outputs of NBVEs togenerate the final scalar result. Hence, to gain power/area efficiency,the cost of add-tree requires to be minimized.

Page 4: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

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1.5x

2.0x

2.5x

3.0x

Energy BreakdownPlatform Multiplic

ationAddition Shifting Register

Bit-partitioning

Bit-partitioning 0.10496 3.29314 0.06016 0.138

Bit-partitioning

Bit-partitioning 0.092 0.89284918090.061189663910.1379766931

Spatial Vectorized+Bit_partitioning

Spatial Vectorized+Bit_partitioning 0.10496 2.01618 0.06304 0.069

Spatial Vectorized+Bit_partitioning

Spatial Vectorized+Bit_partitioning 0.092 0.54795570.0580144 0.069

Temporal Vectorized+Bit_partitioning

Temporal Vectorized+Bit_partitioning 0.10496 1.38162 0.06304 0.0345

Temporal Vectorized+Bit_partitioning

Temporal Vectorized+Bit_partitioning 0.092 0.4058981 0.0290072 0.0345

Spatio-Temporal Vectorized+Bit_partitioning

Spatio-Temporal Vectorized+Bit_partitioning 0.10496 1.1589 0.03152 0.01725

Spatio-Temporal Vectorized+Bit_partitioning

Spatio-Temporal Vectorized+Bit_partitioning 0.092 0.37964320.02102 0.01725

0.10496 1.0278 0.0288 0.008625

0.092 0.3783618750.01254 0.008625

0.0x

0.5x

1.0x

1.5x

2.0x

2.5x

3.0x

Multiplication Addition Shifting Register

Lower Is Better

1-Bi

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ing

3.6x 3.5x2.3x 2.3x

1.6x 1.5x1.3x 1.2x1.2x 1.0x

L = 1 L = 2 L = 4 L = 8 L = 16

1.4x

0.8x1.1x

0.6x 0.8x0.5x

0.7x0.5x 0.6x

L = 1 L = 2 L = 4 L = 8 L = 16

Power/op Area/op

Energy Breakdown-1Platform Multiplic

ationAddition Shifting Register

Bit-partitioning

Bit-partitioning 0.092 0.89284918090.061189663910.1379766931

Bit-partitioning

Bit-partitioning 0.29378980890.82087261940.2134777070.0724522293

Spatial Vectorized+Bit_partitioning

Spatial Vectorized+Bit_partitioning 0.092 0.54795570.0580144 0.069

Spatial Vectorized+Bit_partitioning

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(2) Integrating more narrow bitwidth multipliers withinNBVEs (exploiting DLP within BLP) minimizes the cost of add-treelogic. Encapsulating a larger number of narrow-bitwidth multipliersin an NBVE leads to amortizing the cost of add-tree logic acrossa wider array of multipliers and yields power/area efficiency. As itis shown in Figure 4, increasing L from 1 to 16 improves the pow-er/area by≈3× in 1-bit slicing and≈2.5× in 2-bit slicing. However,this improvement in power/area gradually saturates. As such,increasing L beyond 16 does not provide further significant benefits.

(3) The 2-bit slicing strikes a better balance between thecomplexity of the narrow-bitwidth multipliers and the cost ofaggregation and operand delivery in CVUs. 1-bit slicing requires1-bit multipliers (merely AND gates), that also generates 1-bit valuesas the inputs of the adder-trees in NBVEs. However, slicing 8-bitoperands to 1-bit require 8×8=64 NBVEs for a CVU, imposinga costly 64-input global adder-tree to CVUs. Consequently, as itis shown in Figure 4, 1-bit slicing does not provide any benefitscompared to the conventional design. On the other hand, although2-bit slicing results in generating 4-bit values by the multipliersas inputs to adder-trees in NBVEs, it quadratically decreases thetotal number of NBVEs in a CVU from 64 to 16. This quadraticdecrease trumps using wider-bitwidth values as the inputs of adder-trees in NBVEs, significantly lowering add-tree cost. In conclusion,the optimal design choice for a digital CVU comes with 2-bit slicingand length of L=16. Compared to a conventional digital design,this design point provides 2.0× and 1.7× improvement in powerand area respectively, for an 8-bit × 8-bit MAC operation. Note that4-bit slicing provides lower power/area for CVU design, however, itleads to underutilization of compute resources when DNNs with lessthan 4-bits are being processed. As such, 2-bit slicing strikes a betterbalance between the efficiency of CVUs and their overall utilization.

(4) Bit-parallel vector composability amortizes the cost offlexibility across the elements of vectors. Prior bit-flexible works,both spatial (e.g., BitFusion [20]) and temporal (e.g., Stripes andLoom [10, 18]), enable supporting deep quantized DNNs withheterogenous bitwidths at the cost of extra area overheads. BitFu-sion [20] exploits spatial bit-parallel composability for a scalar. Thisdesign can be assumed as one possible configuration of bit-parallelvector composability with 2-bit slicing and L = 1. As shown inFigure 4, this design point imposes 40% area overhead as comparedto conventional design, while our design provides 40% reduction inarea. Also our proposed CVU provides 2.4× improvement in poweras compared to Fusion Units in BitFusion. This result seems counterintuitive at the first glance as flexibility often comes with an over-head. In fact, the cost of bit-level flexibility stems from aggregationlogic that puts the results back together. Our proposed bit-parallel

TABLE I:EVALUATED DNN MODELS.

DNN Models Type Model Size (INT8)

Multiply-Adds(GOps)

Heterogenous Bitwidths

AlexNet CNN 56.1 MB 2,678 First and last layer 8-bit, the rest 4-bitInception-v1 CNN 8.6 MB 1,860 First and last layer 8-bit, the rest 4-bitResNet-18 CNN 11.1 MB 4,269 First and last layer 8-bit, the rest 4-bitResNet-50 CNN 24.4 MB 8,030 All layers with 4-bit

RNN RNN 16.0 MB 17 All layers with 4-bitLSTM RNN 12.3 MB 13 All layers with 4-bit

TABLE II:EVALUATED HARDWARE PLATFORMS.

Chip TPU-Like Baseline

BitFusion BPVeC Chip RTX 2080 TI

# of MACs 512 448 1024 # of Tensor Cores 544Architecture Systolic Systolic Systolic Architecture Turing

On-chip memory 112 KB 112 KB 112 KB Memory 11 GB (GDDR6)Frequency 500 Mhz 500 Mhz 500 Mhz Frequency 1545 Mhz

Technology Node 45 nm 45 nm 45 nm Technology Node 12 nm

ASIC Platforms GPU Platform

vector-level composability amortizes this cost across the elementsof the vector. Moreover, since it reduces the complexity of the co-operating narrower bitwidth units, it leads to even further reduction.

C. Overall ArchitectureConceptually, bit-parallel vector composability is orthogonal

to the architectural organization of the CVUs. We explore thisdesign style using a 2D systolic array architecture, which is efficientfor matrix-multiplications and convolutions, as explored by priorworks [9]. In this architecture, called BPVEC, each CVU readsa vector of weights from its private scratchpad, while a vector ofinputs is shared across columns of CVUs in each row of the 2Darray. The scalar outputs of CVUs aggregate across columns ofthe array in a systolic fashion and accumulate using 64-bit registers.

IV. EVALUATION

A. Methodology

Workloads. Table I details the specification of the evaluated models.We evaluate our proposal using these neural models in two cases ofhomogenous and heterogenous bitwidths. For the former one we use8-bit datatypes for all the activations and weights and for the laterwe use the bitwidths reported in the results of the literature [4, 8, 13]that maintains the full-precision accuracy of the models.ASIC baselines. For the experiments with homogeneous fixedbitwidths, we use a TPU-like accelerator with a systolic architecture.For the case of heterogeneous bitwidths, we use BitFusion [20], astate-of-the-art spatial bit-flexible DNN accelerator, as the compar-ison point. In all setups, we use 250 mW core power budget forall the baselines and the proposed accelerator in 45 nm technologynode and with 500 Mhz frequency. Table II details the specificationsof the evaluated platforms. We modify the open-source simulation

Page 5: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

Improvement over EyerissConvention

al DigitalVector-

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infrastructure in [20] to obtain end-to-end performance and energymetrics for the TPU-like baseline accelerator, baseline BitFusionaccelerator, as well as the proposed BPVEC accelerator.GPU baseline. We also compare BPVEC to the Nvidia’sRTX 2080 TI GPU, equipped with tensor cores that are specializedfor deep learning inference. Table II shows the architecturalparameters of this GPU. For the sake of fairness, we use 8-bitexecution for the case of homogenous bitwidths and 4-bit executionfor heterogenous bitwidths using the Nvidia’s TensorRT 5.1compiled with CUDA 10.1 and cuDNN 7.5.Hardware measurements. We implement the proposed acceleratorusing Verilog RTL. We use Synopsis Design Compiler (L-2016.03-SP5) for synthesis and measuring energy/area. All the synthesis forthe design space exploration presented in Figure 4 are performed in45 nm technology node and 500 Mhz frequency and all the designpoints meet the frequency criteria. The on-chip scratchpads forASIC designs are modeled with CACTI-P [12].Off-chip memory. We evaluate our design style with both a mod-erate and high bandwidth off-chip memory system to assess its sen-sitivity to the off-chip bandwidth. For moderate bandwidth, we useDDR4 with 16 GB/sec bandwidth and 15 pJ/bit energy for data ac-cesses. We model the high bandwidth memory based on HBM2 with256 GB/sec bandwidth and 1.2 pJ/bit energy for data accesses [14].

B. Experimental Results1) Without Bitwidth HeterogeneityFigure 5 evaluates the performance and energy benefits of

BPVEC across a range of DNNs with homogenous btiwidths (8-bit). The baseline uses the same systolic-array architecture as theBPVEC accelerator, but with conventional compute units thatoperate on individual operands and not bit-slices. Both designsuse a DRR4 memory system. Bit-parallel vector composabilityenables our accelerator to integrate ≈2.0× more compute resourcescompared to the baseline design under the same core power budget.On average, BPVEC provides 40% speedup and energy reduction.Across the evaluated workloads, CNN models enjoy more benefitscompared to RNN ones. Unlike the CNNs that have significantdata-reuse, the vector-matrix multiplications in RNNs have limiteddata-reuse and require extensive off-chip data accesses. As such,the limited bandwidth of the DDR4 memory leads to starvation ofthe copious on-chip compute resources in BPVEC.

Improvement over BitFusion2D-

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flexivecAlexNet 1.00 1.96 1.00 1.2

Inception-v1 1.00 1.62 1.00 1.1ResNet-18 1.00 1.77 1.00 1.1

ResNet-50 1.00 1.32 1.00 1.1RNN 1.00 1.13 1.00 1.2LSTM 1.00 1.11 1.00 1.1GEOMEAN 1.00 1.45 1.00 1.13

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Improvement over BitFusion2D-

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flexivecAlexNet 1.10 3.0 2.00 2.6

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(HBM2) for the baseline and BPVEC, normalized to the baselinewith DDR4. While benefits from high bandwidth memory arelimited for the baseline design, our BPVEC enjoys a 2.1×and2.3×speedup and energy reduction, respectively. Results suggestthat BPVEC is better able to exploit the increased bandwidthand reduced energy cost from HBM2 memory system. Whileall benchmarks see improved efficiency, benefits are highest forbandwidth-hungry RNN and LSTM.

2) With Bitwidth HeterogeneityFigure 7 evaluates the performance and energy benefits for

quantized DNNs with heterogenous bitwidths. The baseline inFigure 7 is BitFusion [20], a state-of-the-art accelerator thatalso supports flexible bitwidths, but at the scalar level. In thisexperiment, the baseline BitFusion and BPVEC use DDR4 memory.Bit-parallel vector composability enables our design to integrate≈ 2.3× more compute resources compared to BitFusion underthe same core power budget. On average, BPVEC provides 50%speedup and 10% energy reduction over BitFusion. Across theevaluated workloads, CNN models enjoy more benefits comparedto bandwidth-hungry RNN and LSTM.

Figure 8 studies the interplay of high off-chip bandwidth withflexible-bitwidth acceleration. The speedup and energy reductionnumbers are normalized to BitFusion with moderate bandwidthDDR4. BPVEC provides 2.5×speedup and 20% energy reductionover BitFusion with HBM2 memory (3.5× speedup and 2.7×energy reduction over the baseline 2D BitFusion). RNN andLSTM, see the highest performance benefits (4.5×), since thesebenchmarks can take advantage of both the increased compute unitsin BPVEC design, as well as the increased bandwidth form HBM2.

3) GPU ComparisonFigure 9 compares the Performance-per-Watt of BPVEC design

with DDR4 and HBM2 memory and with homogenous (Figure 9(a)) and heterogenous (Figure 9) bitwidths for DNN layers,respectively as compared to the Nvidia’s RTX 2080 TI GPU. Withhomogenous bitwidths (Figure 9 (a)), BPVEC achieves 33.7× and31.1× improvements on average with DDR4 and HBM2 memory,respectively. Across the evaluated workloads, the RNN modelssee the most benefits. These models require a large amount ofvector-matrix multiplications, which particularly suitable for theproposed bit-parallel vector composability design style. In the caseof heterogenous bitwidths, the benefits go to 28.0× and 29.8×

Page 6: Bit-ParallelVectorComposabilityforNeuralAcceleration · Alternative Computing Technologies (ACT) Lab University of California, San Diego yBigstream, Inc. zGoogle Inc. xUniversity

Improvement over BitFusion2D-Digital 3D-Digital

AlexNet 18.7 20.4Inception-v1 30.2 19.6

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AlexNet 11.1062058125.7818885313.5286432336.29489933Inception-v1 12.3030382929.7658645813.3143510332.15200925

ResNet-18 7.35684743417.219117597.85132005218.07949549ResNet-50 10.9614585819.9003557111.5613914623.56475497

RNN 194.5817981277.1861474192.1282374472.2213324LSTM 225.3392439307.6262149221.806863532.9532664GEOMEAN 28.0121346953.1027041529.7748010970.72228434

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AlexNet 18.7 36.34 20.4 50.54Inception-v1 30.2 34.26 19.6 38.13

ResNet-18 12.0 16.34 11.7 24.79ResNet-50 9.0 11.52 8.8 16.90

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AlexNet 11.1062058125.7818885313.5286432336.29489933Inception-v1 12.3030382929.7658645813.3143510332.15200925

ResNet-18 7.35684743417.219117597.85132005218.07949549ResNet-50 10.9614585819.9003557111.5613914623.56475497

RNN 194.5817981277.1861474192.1282374472.2213324LSTM 225.3392439307.6262149221.806863532.9532664GEOMEAN 28.0121346953.1027041529.7748010970.72228434

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heterogenous bitwidths

Fig. 9: Performance-Per-Watt comparison to RTX 2080 TI GPU.

with DDR4 and HBM2, respectively. The trends look similar tothe homogenous 8-bit mode, since both the design points and theGPU baseline exploit the deep quantized mode of operations.

V. RELATED WORK

A large body of inspiring work has explored hardwareacceleration for DNNs by exploiting their algorithmic propertiessuch as data-level parallelism, tolerance for reduced precisionand sparsification, and redundancy in computations. To realizethe hardware accelerators, prior efforts have built upon isolatedcompute units that operate on all the bits of individual operands,and have used multiple compute units operating together to extractdata-level parallelism. This work introduces a different designstyle that explores the interleaving of bit-level operations acrosscompute units in the context of vectors and combine the benefitsfrom bit-level parallelism and data-level parallelism, both of whichare abundant in DNNs. Below, we discuss the most related works.Design without support for bit-level composability. Prior worksin TPU [9] and Eyeriss [2] design hardware accelerators toextract data-level parallelism in DNNs. SCNN [15], EIE [7], andCnvlutin [1] use both zero-skipping and data-level parallelism forefficient DNN execution. Brainwave [6] also uses SIMD vectorizedexecution to extract data-level parallelism on FPGAs, however withfixed-bitwidth execution whose bitwidth is decided before synthesiz-ing the FPGA on the design. ISAAC [17] and PRIME [3] build uponResistiveRam(ReRam) technology to provide high energy efficiency.Further, ISAAC and PRIME operate on vectors of data in the analog(current) domain to mitigate the high cost of ADC. In contrast, wefocus on interleaving of the bit-level and data-level parallelism in vec-tor units, in addition to hardware support for bitwidth heterogeneity.Design with support for bit-level flexibility through bit-serialcomputation. Stripes [10], Loom [18], UNPU [11] exploit thetolerance to reduced bitwidth in DNNs to yield performance benefitsby exploring bit-bit serial compute units. The data-level parallelismcompensates for bit-serial individual operations. Our design incontrast interleaves bit-level parallelism with data-level parallelism.Designs with support for bit-level composability BitFusion [20]uses bit-level parallelism with a spatial design. We provide

a head-to-head comparison with BitFusion in Section IV-B2.Laconic [19] combines spatial bit-level composability with temporalexecution to support for bit-sparsity and reduce the ineffectualcomputations. These inspiring efforts do not focus on bit-parallelvector composability that breaks the calculations across spatialcomposable units that cooperate at the level of vectors.

VI. CONCLUSIONTraditionally, neural accelerators have relied on extracting DLP

using isolated and self-sufficient compute units that process allthe bits of operands. This work introduced a different design style,bit-parallel vector-composability, that operates on operand bit-slicesto interleave and combine the traditional data-level parallelism withbit-level parallelism. Across a range of deep models the resultsshow that the proposed design style offers significant performanceand efficiency compared to even bit-flexible accelerators.

VII. ACKNOWLEDGEMENT

This work was in part supported by the National Science Founda-tion (NSF) awards CNS#1703812, ECCS#1609823, CCF#1553192,Air Force Office of Scientific Research (AFOSR) YoungInvestigator Program (YIP) award #FA9550-17-1-0274, NationalInstitute of Health (NIH) award #R01EB028350, and AirForceResearch Laboratory (AFRL) and Defense Advanced ResearchProject Agency (DARPA) under agreement number #FA8650-20-2-7009 and #HR0011-18-C-0020. The U.S. Government is authorizedto reproduce and distribute reprints for Governmental purposesnot withstanding any copyright notation thereon. The views andconclusions contained herein are those of the authors and shouldnot be interpreted as necessarily representing the official policiesor endorsements, either expressed or implied of Google, Samsung,NSF, AFSOR, NIH, AFRL, DARPA or the U.S. Government.

REFERENCES[1] J. Albericio et al., “Cnvlutin: ineffectual-neuron-free deep neural network computing,” in

ISCA, 2016.[2] Y.-H. Chen et al., “Eyeriss: A spatial architecture for energy-efficient dataflow for

convolutional neural networks,” in ISCA, 2016.[3] P. Chi et al., “Prime: A novel processing-in-memory architecture for neural network

computation in reram-based main memory,” in ISCA, 2016.[4] J. Choi et al., “Pact: Parameterized clipping activation for quantized neural networks,”

arXiv preprint arXiv:1805.06085, 2018.[5] A. T. Elthakeb et al., “Releq: an automatic reinforcement learning approach for deep

quantization of neural networks,” arXiv preprint arXiv:1811.01704, 2018.[6] J. Fowers et al., “A configurable cloud-scale dnn processor for real-time ai,” in ISCA, 2018.[7] S. Han et al., “Eie: efficient inference engine on compressed deep neural network,” in

ISCA, 2016.[8] I. Hubara et al., “Quantized neural networks: Training neural networks with low precision

weights and activations,” arXiv, 2016.[9] N. P. Jouppi et al., “In-datacenter performance analysis of a tensor processing unit,” in

ISCA, 2017.[10] P. Judd et al., “Stripes: Bit-serial deep neural network computing,” in MICRO, 2016.[11] J. Lee et al., “Unpu: A 50.6 tops/w unified deep neural network accelerator with

1b-to-16b fully-variable weight bit-precision,” in ISSCC, 2018.[12] S. Li et al., “CACTI-P: Architecture-level Modeling for SRAM-based Structures with

Advanced Leakage Reduction Techniques,” in ICCAD, 2011.[13] A. K. Mishra et al., “WRPN: wide reduced-precision networks,” arXiv, 2017.[14] M. OâAZConnor et al., “Fine-grained dram: energy-efficient dram for extreme bandwidth

systems,” in MICRO. IEEE, 2017, pp. 41–54.[15] A. Parashar et al., “SCNN: An Accelerator for Compressed-sparse Convolutional Neural

Networks,” in ISCA, 2017.[16] M. Samragh et al., “Codex: Bit-flexible encoding for streaming-based fpga acceleration

of dnns,” arXiv preprint arXiv:1901.05582, 2019.[17] A. Shafiee et al., “Isaac: A convolutional neural network accelerator with in-situ analog

arithmetic in crossbars,” in ISCA, 2016.[18] S. Sharify et al., “Loom: Exploiting weight and activation precisions to accelerate

convolutional neural networks,” arXiv, 2017.[19] S. Sharify et al., “Laconic deep learning inference acceleration,” in ISCA, 2019.[20] H. Sharma et al., “Bit fusion: Bit-level dynamically composable architecture for

accelerating deep neural network,” in ISCA. IEEE, 2018, pp. 764–775.


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