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Attention for transformers is a critical workload that has recently received significant "attention" as a target for custom acceleration. Yet, while prior work succeeds in reducing attention's memory-bandwidth requirements, it creates load imbalance between operators that comprise the attention computation (resulting in severe compute under-utilization) and requires on-chip memory that scales with sequence length (which is expected to grow over time). This paper ameliorates these issues, enabling attention with nearly 100% compute utilization, no off-chip memory traffic bottlenecks, and on-chip buffer size requirements that are independent of sequence length. The main conceptual contribution is to use a recently proposed abstraction -- the cascade of Einsums -- to describe, formalize, and taxonomize the space of attention algorithms that appear in the literature. In particular, we show how Einsum cascades can be used to infer non-trivial lower bounds on the number of passes a kernel must take through its input data, which has implications for either required on-chip buffer capacity or memory traffic. We show how this notion can be used to meaningfully divide the space of attention algorithms into several categories and use these categories to inform our design process. Based on the above characterization, we propose FuseMax -- a novel mapping and binding of attention onto a spatial array-style architecture. On attention, in an iso-area comparison, FuseMax achieves an average 6.7x speedup over the prior state-of-the-art, FLAT, while using 79\% of the energy. Similarly, on full end-to-end transformer inference, FuseMax achieves an average 5.3x speedup over FLAT using 83 of the energy., Comment: 16 pages, 12 figures

Recent large language models (LLMs) employ billions of parameters to enable broad problem-solving capabilities. Such language models also tend to be memory-bound because of the dominance of matrix-vector and matrix-matrix multiplications with low arithmetic intensity. Therefore, optimizing the memory footprint and traffic is an important optimization direction for LLMs today. Model compression methods such as quantization and parameter pruning have been actively explored to achieve memory footprint and traffic optimization. However, the accuracy-efficiency trade-off of rank pruning (i.e., low-rank decomposition) for LLMs is not well-understood yet. Therefore, in this work, we characterize the accuracy-efficiency trade-off of a low-rank decomposition method, specifically Tucker decomposition, on recent language models, including an open-source LLM, Llama 2. We formalize the low-rank decomposition design space and show that the decomposition design space is enormous (e.g., O($2^{39}$) for Llama2-7B). To navigate such a vast design space, we formulate it and perform thorough case studies of accuracy-efficiency trade-offs using six widely used LLM benchmarks on BERT and Llama 2 models. Our results show that we can achieve a 9\% model size reduction with minimal accuracy drops, which range from 4\%p (\%p refers to "percentage point," which refers to the absolute difference between two percentage numbers; 74\% -> 78\% = 4\%p increase) to 10\%p, depending on the difficulty of the benchmark, without any retraining to recover accuracy after decomposition. The results show that low-rank decomposition can be a promising direction for LLM-based applications that require real-time service at scale (e.g., AI agent and real-time coding assistant), where the latency is as important as the model accuracy.

Over the past few years, the explosion in sparse tensor algebra workloads has led to a corresponding rise in domain-specific accelerators to service them. Due to the irregularity present in sparse tensors, these accelerators employ a wide variety of novel solutions to achieve good performance. At the same time, prior work on design-flexible sparse accelerator modeling does not express this full range of design features, making it difficult to understand the impact of each design choice and compare or extend the state-of-the-art. To address this, we propose TeAAL: a language and simulator generator for the concise and precise specification and evaluation of sparse tensor algebra accelerators. We use TeAAL to represent and evaluate four disparate state-of-the-art accelerators -- ExTensor, Gamma, OuterSPACE, and SIGMA -- and verify that it reproduces their performance with high accuracy. Finally, we demonstrate the potential of TeAAL as a tool for designing new accelerators by showing how it can be used to speed up vertex-centric programming accelerators -- achieving $1.9\times$ on BFS and $1.2\times$ on SSSP over GraphDynS., Comment: 17 pages, 13 figures

HPC applications are critical in various scientific domains ranging from molecular dynamics to chemistry to fluid dynamics. Conjugate Gradient (CG) is a popular application kernel used in iterative linear HPC solvers and has applications in numerous scientific domains. However, the HPCG benchmark shows that the peformance achieved by Top500 HPC systems on CG is a small fraction of the performance achieved on Linpack. While CG applications have significant portions of computations that are dense and sparse matrix multiplications, skewed SpMMs/GEMMs in the HPC solvers have poor arithmetic intensities which makes their execution highly memory bound unlike GEMMs in DNNs which have high arithmetic intensity. The problem of low intensity individual skewed GEMMs also exists in various emerging workloads from other domains like Graph Neural Networks, Transformers etc. In this work we identify various reuse opportunities between the tensors in these solver applications to extract reuse in the entire Directed Acyclic Graph of the tensor operations rather than individual tensor operations. These opportunities essentially depend on the dimensions of the tensors and the structure of the tensor dependency graph. We propose a systematic methodology to determine various kinds of reuse opportunities in the graph of operations and determine the loop order and tiling in the interdependent operations. As a result, we propose a novel mapping strategy GOGETA that improves reuse of HPC applications on spatial accelerators. We also propose a data organization strategy in the buffer. Our mapping achieves geomean 6.7x reduction in memory accesses.

Sparsity is a growing trend in modern DNN models. Existing Sparse-Sparse Matrix Multiplication (SpMSpM) accelerators are tailored to a particular SpMSpM dataflow (i.e., Inner Product, Outer Product or Gustavsons), that determines their overall efficiency. We demonstrate that this static decision inherently results in a suboptimal dynamic solution. This is because different SpMSpM kernels show varying features (i.e., dimensions, sparsity pattern, sparsity degree), which makes each dataflow better suited to different data sets. In this work we present Flexagon, the first SpMSpM reconfigurable accelerator that is capable of performing SpMSpM computation by using the particular dataflow that best matches each case. Flexagon accelerator is based on a novel Merger-Reduction Network (MRN) that unifies the concept of reducing and merging in the same substrate, increasing efficiency. Additionally, Flexagon also includes a 3-tier memory hierarchy, specifically tailored to the different access characteristics of the input and output compressed matrices. Using detailed cycle-level simulation of contemporary DNN models from a variety of application domains, we show that Flexagon achieves average performance benefits of 4.59x, 1.71x, and 1.35x with respect to the state-of-the-art SIGMA-like, Sparch-like and GAMMA-like accelerators (265% , 67% and 18%, respectively, in terms of average performance/area efficiency)., Comment: To appear on ASPLOS 2023

The high efficiency of domain-specific hardware accelerators for machine learning (ML) has come from specialization, with the trade-off of less configurability/ flexibility. There is growing interest in developing flexible ML accelerators to make them future-proof to the rapid evolution of Deep Neural Networks (DNNs). However, the notion of accelerator flexibility has always been used in an informal manner, restricting computer architects from conducting systematic apples-to-apples design-space exploration (DSE) across trillions of choices. In this work, we formally define accelerator flexibility and show how it can be integrated for DSE. Specifically, we capture DNN accelerator flexibility across four axes: tiling, ordering, parallelization, and array shape. We categorize existing accelerators into 16 classes based on their axes of flexibility support, and define a precise quantification of the degree of flexibility of an accelerator across each axis. We leverage these to develop a novel flexibility-aware DSE framework. We demonstrate how this can be used to perform first-of-their-kind evaluations, including an isolation study to identify the individual impact of the flexibility axes. We demonstrate that adding flexibility features to a hypothetical DNN accelerator designed in 2014 improves runtime on future (i.e., present-day) DNNs by 11.8x geomean.

The design of DNN accelerators includes two key parts: HW resource configuration and mapping strategy. Intensive research has been conducted to optimize each of them independently. Unfortunately, optimizing for both together is extremely challenging due to the extremely large cross-coupled search space. To address this, in this paper, we propose a HW-Mapping co-optimization framework, an efficient encoding of the immense design space constructed by HW and Mapping, and a domain-aware genetic algorithm, named DiGamma, with specialized operators for improving search efficiency. We evaluate DiGamma with seven popular DNNs models with different properties. Our evaluations show DiGamma can achieve (geomean) 3.0x and 10.0x speedup, comparing to the best-performing baseline optimization algorithms, in edge and cloud settings.

Recently, numerous sparse hardware accelerators for Deep Neural Networks (DNNs), Graph Neural Networks (GNNs), and scientific computing applications have been proposed. A common characteristic among all of these accelerators is that they target tensor algebra (typically matrix multiplications); yet dozens of new accelerators are proposed for every new application. The motivation is that the size and sparsity of the workloads heavily influence which architecture is best for memory and computation efficiency. To satisfy the growing demand of efficient computations across a spectrum of workloads on large data centers, we propose deploying a flexible 'heterogeneous' accelerator, which contains many 'sub-accelerators' (smaller specialized accelerators) working together. To this end, we propose: (1) HARD TACO, a quick and productive C++ to RTL design flow to generate many types of sub-accelerators for sparse and dense computations for fair design-space exploration, (2) AESPA, a heterogeneous sparse accelerator design template constructed with the sub-accelerators generated from HARD TACO, and (3) a suite of scheduling strategies to map tensor kernels onto heterogeneous sparse accelerators with high efficiency and utilization. AESPA with optimized scheduling achieves 1.96X higher performance, and 7.9X better energy-delay product (EDP) than a Homogeneous EIE-like accelerator with our diverse workload suite.

With increasing diversity in Deep Neural Network(DNN) models in terms of layer shapes and sizes, the research community has been investigating flexible/reconfigurable accelerator substrates. This line of research has opened up two challenges. The first is to determine the appropriate amount of flexibility within an accelerator array that that can trade-off the performance benefits versus the area overheads of the reconfigurability. The second is being able to determine the right configuration of the array for the current DNN model and/or layer and reconfigure the accelerator at runtime. This work introduces a new class of accelerators that we call Self Adaptive Reconfigurable Array (SARA). SARA architectures comprise of both a reconfigurable array and a hardware unit capable of determining an optimized configuration for the array at runtime. We demonstrate an instance of SARA with an accelerator we call SAGAR, which introduces a novel reconfigurable systolic array that can be configured to work as a distributed collection of smaller arrays of various sizes or as a single array with flexible aspect ratios. We also develop a novel recommendation neural network called ADAPTNET which recommends an array configuration and dataflow for the current layer parameters. ADAPTNET runs on an integrated custom hardware ADAPTNETX that runs ADAPTNET at runtime and reconfigures the array, making the entire accelerator self-sufficient. SAGAR is capable of providing the same mapping flexibility as a collection of 1024 4x4 arrays working as a distributed system while achieving 3.5x more power efficiency and 3.2x higher compute density Furthermore, the runtime achieved on the recommended parameters from ADAPTNET is 99.93% of the best achievable runtime.

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 any mapping adhering to the notation is always analyzable by the MDC's cost model. Furthermore, we introduce a transformation for translating mappings into the MDC notation for exploring the mapping space. Searching for the optimal mappings is challenging because of the large space of mappings, and this challenge gets exacerbated with new operators and diverse accelerator configurations.To address this challenge, we propose a decoupled off-chip/on-chip approach that decomposes the mapping space into off-chip and on-chip subspaces, and first optimizes the off-chip subspace followed by the on-chip subspace. The motivation for this decomposition is to reduce the size of the search space dramatically and also to prioritize the optimization of off-chip data movement, which is 2-3 orders of magnitude more compared to the on-chip data movement. We implemented our approach in a tool called {\em Marvel}, and another major benefit of our approach is that it is applicable to any DNN operator conformable with the MDC notation.

Emerging AI-enabled applications such as augmented/virtual reality (AR/VR) leverage multiple deep neural network (DNN) models for sub-tasks such as object detection, hand tracking, and so on. Because of the diversity of the sub-tasks, the layers within and across the DNN models are highly heterogeneous in operation and shape. Such layer heterogeneity is a challenge for a fixed dataflow accelerator (FDA) that employs a fixed dataflow on a single accelerator substrate since each layer prefers different dataflows (computation order and parallelization) and tile sizes. Reconfigurable DNN accelerators (RDAs) have been proposed to adapt their dataflows to diverse layers to address the challenge. However, the dataflow flexibility in RDAs is enabled at the area and energy costs of expensive hardware structures (switches, controller, etc.) and per-layer reconfiguration. Alternatively, this work proposes a new class of accelerators, heterogeneous dataflow accelerators (HDAs), which deploys multiple sub-accelerators each supporting a different dataflow. HDAs enable coarser-grained dataflow flexibility than RDAs with higher energy efficiency and lower area cost comparable to FDAs. To exploit such benefits, hardware resource partitioning across sub-accelerators and layer execution schedule need to be carefully optimized. Therefore, we also present Herald, which co-optimizes hardware partitioning and layer execution schedule. Using Herald on a suite of AR/VR and MLPerf workloads, we identify a promising HDA architecture, Maelstrom, which demonstrates 65.3% lower latency and 5.0% lower energy than the best FDAs and 22.0% lower energy at the cost of 20.7% higher latency than a state-of-the-art RDA. The results suggest that HDA is an alternative class of Pareto-optimal accelerators to RDA with strength in energy, which can be a better choice than RDAs depending on the use cases., Comment: This paper is accepted at HPCA 2021

The data partitioning and scheduling strategies used by DNN accelerators to leverage reuse and perform staging are known as dataflow, and they directly impact the performance and energy efficiency of DNN accelerator designs. An accelerator microarchitecture dictates the dataflow(s) that can be employed to execute a layer or network. Selecting an optimal dataflow for a layer shape can have a large impact on utilization and energy efficiency, but there is a lack of understanding on the choices and consequences of dataflows, and of tools and methodologies to help architects explore the co-optimization design space. In this work, we first introduce a set of data-centric directives to concisely specify the space of DNN dataflows in a compilerfriendly form. We then show how these directives can be analyzed to infer various forms of reuse and to exploit them using hardware capabilities. We codify this analysis into an analytical cost model, MAESTRO (Modeling Accelerator Efficiency via Spatio-Temporal Reuse and Occupancy), that estimates various cost-benefit tradeoffs of a dataflow including execution time and energy efficiency for a DNN model and hardware configuration. We demonstrate the use of MAESTRO to drive a hardware design space exploration (DSE) experiment, which searches across 480M designs to identify 2.5M valid designs at an average rate of 0.17M designs per second, including Pareto-optimal throughput- and energy-optimized design points.

Convolutional Neural Networks (CNNs) have begun to permeate all corners of electronic society (from voice recognition to scene generation) due to their high accuracy and machine efficiency per operation. At their core, CNN computations are made up of multi-dimensional dot products between weight and input vectors. This paper studies how weight repetition ---when the same weight occurs multiple times in or across weight vectors--- can be exploited to save energy and improve performance during CNN inference. This generalizes a popular line of work to improve efficiency from CNN weight sparsity, as reducing computation due to repeated zero weights is a special case of reducing computation due to repeated weights. To exploit weight repetition, this paper proposes a new CNN accelerator called the Unique Weight CNN Accelerator (UCNN). UCNN uses weight repetition to reuse CNN sub-computations (e.g., dot products) and to reduce CNN model size when stored in off-chip DRAM ---both of which save energy. UCNN further improves performance by exploiting sparsity in weights. We evaluate UCNN with an accelerator-level cycle and energy model and with an RTL implementation of the UCNN processing element. On three contemporary CNNs, UCNN improves throughput-normalized energy consumption by 1.2x - 4x, relative to a similarly provisioned baseline accelerator that uses Eyeriss-style sparsity optimizations. At the same time, the UCNN processing element adds only 17-24% area overhead relative to the same baseline., Comment: Appears in the proceedings of the 45th International Symposium on Computer Architecture~(ISCA), 2018

The C and C++ high-level languages provide programmers with atomic operations for writing high-performance concurrent code. At the assembly language level, C and C++ atomics get mapped down to individual instructions or combinations of instructions by compilers, depending on the ordering guarantees and synchronization instructions provided by the underlying architecture. These compiler mappings must uphold the ordering guarantees provided by C/C++ atomics or the compiled program will not behave according to the C/C++ memory model. In this paper we discuss two counterexamples to the well-known trailing-sync compiler mappings for the Power and ARMv7 architectures that were previously thought to be proven correct. In addition to the counterexamples, we discuss the loophole in the proof of the mappings that allowed the incorrect mappings to be proven correct. We also discuss the current state of compilers and architectures in relation to the bug.

Memory consistency models (MCMs) which govern inter-module interactions in a shared memory system, are a significant, yet often under-appreciated, aspect of system design. MCMs are defined at the various layers of the hardware-software stack, requiring thoroughly verified specifications, compilers, and implementations at the interfaces between layers. Current verification techniques evaluate segments of the system stack in isolation, such as proving compiler mappings from a high-level language (HLL) to an ISA or proving validity of a microarchitectural implementation of an ISA. This paper makes a case for full-stack MCM verification and provides a toolflow, TriCheck, capable of verifying that the HLL, compiler, ISA, and implementation collectively uphold MCM requirements. The work showcases TriCheck's ability to evaluate a proposed ISA MCM in order to ensure that each layer and each mapping is correct and complete. Specifically, we apply TriCheck to the open source RISC-V ISA, seeking to verify accurate, efficient, and legal compilations from C11. We uncover under-specifications and potential inefficiencies in the current RISC-V ISA documentation and identify possible solutions for each. As an example, we find that a RISC-V-compliant microarchitecture allows 144 outcomes forbidden by C11 to be observed out of 1,701 litmus tests examined. Overall, this paper demonstrates the necessity of full-stack verification for detecting MCM-related bugs in the hardware-software stack., Comment: Proceedings of the Twenty-Second International Conference on Architectural Support for Programming Languages and Operating Systems