Information contraction in noisy binary neural networks and its implications

Neural networks have gained importance as the machine learning models that achieve state-of-the-art performance on large-scale image classification, object detection and natural language processing tasks. In this paper, we consider noisy binary neural networks, where each neuron has a non-zero probability of producing an incorrect output. These noisy models may arise from biological, physical and electronic contexts and constitute an important class of models that are relevant to the physical world. Intuitively, the number of neurons in such systems has to grow to compensate for the noise while maintaining the same level of expressive power and computation reliability. Our key finding is a lower bound for the required number of neurons in noisy neural networks, which is first of its kind. To prove this lower bound, we take an information theoretic approach and obtain a novel strong data processing inequality (SDPI), which not only generalizes the Evans-Schulman results for binary symmetric channels to general channels, but also improves the tightness drastically when applied to estimate end-to-end information contraction in networks. Our SDPI can be applied to various information processing systems, including neural networks and cellular automata. Applying the SPDI in noisy binary neural networks, we obtain our key lower bound and investigate its implications on network depth-width trade-offs, our results suggest a depth-width trade-off for noisy neural networks that is very different from the established understanding regarding noiseless neural networks. Furthermore, we apply the SDPI to study fault-tolerant cellular automata and obtain bounds on the error correction overheads and the relaxation time. This paper offers new understanding of noisy information processing systems through the lens of information theory.

MicroNets: Neural Network Architectures for Deploying TinyML Applications on Commodity Microcontrollers

Executing machine learning workloads locally on resource constrained microcontrollers (MCUs) promises to drastically expand the application space of IoT. However, so-called TinyML presents severe technical challenges, as deep neural network inference demands a large compute and memory budget. To address this challenge, neural architecture search (NAS) promises to help design accurate ML models that meet the tight MCU memory, latency and energy constraints. A key component of NAS algorithms is their latency/energy model, i.e., the mapping from a given neural network architecture to its inference latency/energy on an MCU. In this paper, we observe an intriguing property of NAS search spaces for MCU model design: on average, model latency varies linearly with model operation (op) count under a uniform prior over models in the search space. Exploiting this insight, we employ differentiable NAS (DNAS) to search for models with low memory usage and low op count, where op count is treated as a viable proxy to latency. Experimental results validate our methodology, yielding our MicroNet models, which we deploy on MCUs using Tensorflow Lite Micro, a standard open-source NN inference runtime widely used in the TinyML community. MicroNets demonstrate state-of-the-art results for all three TinyMLperf industry-standard benchmark tasks: visual wake words, audio keyword spotting, and anomaly detection.

Rank and run-time aware compression of NLP Applications

Sequence model based NLP applications can be large. Yet, many applications that benefit from them run on small devices with very limited compute and storage capabilities, while still having run-time constraints. As a result, there is a need for a compression technique that can achieve significant compression without negatively impacting inference run-time and task accuracy. This paper proposes a new compression technique called Hybrid Matrix Factorization that achieves this dual objective. HMF improves low-rank matrix factorization (LMF) techniques by doubling the rank of the matrix using an intelligent hybrid-structure leading to better accuracy than LMF. Further, by preserving dense matrices, it leads to faster inference run-time than pruning or structure matrix based compression technique. We evaluate the impact of this technique on 5 NLP benchmarks across multiple tasks (Translation, Intent Detection, Language Modeling) and show that for similar accuracy values and compression factors, HMF can achieve more than 2.32x faster inference run-time than pruning and 16.77% better accuracy than LMF.

Sparse Systolic Tensor Array for Efficient CNN Hardware Acceleration

Convolutional neural network (CNN) inference on mobile devices demands efficient hardware acceleration of low-precision (INT8) general matrix multiplication (GEMM). Exploiting data sparsity is a common approach to further accelerate GEMM for CNN inference, and in particular, structural sparsity has the advantages of predictable load balancing and very low index overhead. In this paper, we address a key architectural challenge with structural sparsity: how to provide support for a range of sparsity levels while maintaining high utilization of the hardware. We describe a time unrolled formulation of variable density-bound block (VDBB) sparsity that allows for a configurable number of non-zero elements per block, at constant utilization. We then describe a systolic array microarchitecture that implements this scheme, with two data reuse optimizations. Firstly, we increase reuse in both operands and partial products by increasing the number of MACs per PE. Secondly, we introduce a novel approach of moving the IM2COL transform into the hardware, which allows us to achieve a 3x data bandwidth expansion just before the operands are consumed by the datapath, reducing the SRAM power consumption. The optimizations for weight sparsity, activation sparsity and data reuse are all interrelated and therefore the optimal combination is not obvious. Therefore, we perform an design space evaluation to find the pareto-optimal design characteristics. The resulting design achieves 16.8 TOPS/W in 16nm with modest 50% model sparsity and scales with model sparsity up to 55.7TOPS/W at 87.5%. As well as successfully demonstrating the variable DBB technique, this result significantly outperforms previously reported sparse CNN accelerators.

High Throughput Matrix-Matrix Multiplication between Asymmetric Bit-Width Operands

Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD matrix multiplication instructions for symmetric bit-width operands can support operands of mixed precision by zero- or sign-extending the narrow operand to match the size of the other operands, they cannot exploit the benefit of narrow bit-width of one of the operands. We propose a new SIMD matrix multiplication instruction that uses mixed precision on its inputs (8- and 4-bit operands) and accumulates product values into narrower 16-bit output accumulators, in turn allowing the SIMD operation at 128-bit vector width to process a greater number of data elements per instruction to improve processing throughput and memory bandwidth utilization without increasing the register read- and write-port bandwidth in CPUs. The proposed asymmetric-operand-size SIMD instruction offers 2x improvement in throughput of matrix multiplication in comparison to throughput obtained using existing symmetric-operand-size instructions while causing negligible (0.05%) overflow from 16-bit accumulators for representative machine learning workloads. The asymmetric-operand-size instruction not only can improve matrix multiplication throughput in CPUs, but also can be effective to support multiply-and-accumulate (MAC) operation between 8- and 4-bit operands in state-of-the-art DNN hardware accelerators (e.g., systolic array microarchitecture in Google TPU, etc.) and offer similar improvement in matrix multiply performance seamlessly without violating the various implementation constraints. We demonstrate how a systolic array architecture designed for symmetric-operand-size instructions could be modified to support an asymmetric-operand-sized instruction.

Efficient Residue Number System Based Winograd Convolution

Prior research has shown that Winograd algorithm can reduce the computational complexity of convolutional neural networks (CNN) with weights and activations represented in floating point. However it is difficult to apply the scheme to the inference of low-precision quantized (e.g. INT8) networks. Our work extends the Winograd algorithm to Residue Number System (RNS). The minimal complexity convolution is computed precisely over large transformation tile (e.g. 10 x 10 to 16 x 16) of filters and activation patches using the Winograd transformation and low cost (e.g. 8-bit) arithmetic without degrading the prediction accuracy of the networks during inference. The arithmetic complexity reduction is up to 7.03x while the performance improvement is up to 2.30x to 4.69x for 3 x 3 and 5 x 5 filters respectively.

TinyLSTMs: Efficient Neural Speech Enhancement for Hearing Aids

Modern speech enhancement algorithms achieve remarkable noise suppression by means of large recurrent neural networks (RNNs). However, large RNNs limit practical deployment in hearing aid hardware (HW) form-factors, which are battery powered and run on resource-constrained microcontroller units (MCUs) with limited memory capacity and compute capability. In this work, we use model compression techniques to bridge this gap. We define the constraints imposed on the RNN by the HW and describe a method to satisfy them. Although model compression techniques are an active area of research, we are the first to demonstrate their efficacy for RNN speech enhancement, using pruning and integer quantization of weights/activations. We also demonstrate state update skipping, which reduces the computational load. Finally, we conduct a perceptual evaluation of the compressed models to verify audio quality on human raters. Results show a reduction in model size and operations of 11.9$\times$ and 2.9$\times$, respectively, over the baseline for compressed models, without a statistical difference in listening preference and only exhibiting a loss of 0.55dB SDR. Our model achieves a computational latency of 2.39ms, well within the 10ms target and 351$\times$ better than previous work.

Systolic Tensor Array: An Efficient Structured-Sparse GEMM Accelerator for Mobile CNN Inference

Convolutional neural network (CNN) inference on mobile devices demands efficient hardware acceleration of low-precision (INT8) general matrix multiplication (GEMM). The systolic array (SA) is a pipelined 2D array of processing elements (PEs), with very efficient local data movement, well suited to accelerating GEMM, and widely deployed in industry. In this work, we describe two significant improvements to the traditional SA architecture, to specifically optimize for CNN inference. Firstly, we generalize the traditional scalar PE, into a Tensor-PE, which gives rise to a family of new Systolic Tensor Array (STA) microarchitectures. The STA family increases intra-PE operand reuse and datapath efficiency, resulting in circuit area and power dissipation reduction of as much as 2.08x and 1.36x respectively, compared to the conventional SA at iso-throughput with INT8 operands. Secondly, we extend this design to support a novel block-sparse data format called density-bound block (DBB). This variant (STA-DBB) achieves a 3.14x and 1.97x improvement over the SA baseline at iso-throughput in area and power respectively, when processing specially-trained DBB-sparse models, while remaining fully backwards compatible with dense models.

Searching for Winograd-aware Quantized Networks

Lightweight architectural designs of Convolutional Neural Networks (CNNs) together with quantization have paved the way for the deployment of demanding computer vision applications on mobile devices. Parallel to this, alternative formulations to the convolution operation such as FFT, Strassen and Winograd, have been adapted for use in CNNs offering further speedups. Winograd convolutions are the fastest known algorithm for spatially small convolutions, but exploiting their full potential comes with the burden of numerical error, rendering them unusable in quantized contexts. In this work we propose a Winograd-aware formulation of convolution layers which exposes the numerical inaccuracies introduced by the Winograd transformations to the learning of the model parameters, enabling the design of competitive quantized models without impacting model size. We also address the source of the numerical error and propose a relaxation on the form of the transformation matrices, resulting in up to 10% higher classification accuracy on CIFAR-10. Finally, we propose wiNAS, a neural architecture search (NAS) framework that jointly optimizes a given macro-architecture for accuracy and latency leveraging Winograd-aware layers. A Winograd-aware ResNet-18 optimized with wiNAS for CIFAR-10 results in 2.66x speedup compared to im2row, one of the most widely used optimized convolution implementations, with no loss in accuracy.