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### Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference

The rising popularity of intelligent mobile devices and the daunting computational cost of deep learning-based models call for efficient and accurate on-device inference schemes. We propose a quantization scheme that allows inference to be carried out using integer-only arithmetic, which can be implemented more efficiently than floating point inference on commonly available integer-only hardware. We also co-design a training procedure to preserve end-to-end model accuracy post quantization. As a result, the proposed quantization scheme improves the tradeoff between accuracy and on-device latency. The improvements are significant even on MobileNets, a model family known for run-time efficiency, and are demonstrated in ImageNet classification and COCO detection on popular CPUs.

### PocketNN: Integer-only Training and Inference of Neural Networks via Direct Feedback Alignment and Pocket Activations in Pure C++

Standard deep learning algorithms are implemented using floating-point real numbers. This presents an obstacle for implementing them on low-end devices which may not have dedicated floating-point units (FPUs). As a result, researchers in TinyML have considered machine learning algorithms that can train and run a deep neural network (DNN) on a low-end device using integer operations only. In this paper we propose PocketNN, a light and self-contained proof-of-concept framework in pure C++ for the training and inference of DNNs using only integers. Unlike other approaches, PocketNN directly operates on integers without requiring any explicit quantization algorithms or customized fixed-point formats. This was made possible by pocket activations, which are a family of activation functions devised for integer-only DNNs, and an emerging DNN training algorithm called direct feedback alignment (DFA). Unlike the standard backpropagation (BP), DFA trains each layer independently, thus avoiding integer overflow which is a key problem when using BP with integer-only operations. We used PocketNN to train some DNNs on two well-known datasets, MNIST and Fashion-MNIST. Our experiments show that the DNNs trained with our PocketNN achieved 96.98% and 87.7% accuracies on MNIST and Fashion-MNIST datasets, respectively. The accuracies are very close to the equivalent DNNs trained using BP with floating-point real number operations, such that accuracy degradations were just 1.02%p and 2.09%p, respectively. Finally, our PocketNN has high compatibility and portability for low-end devices as it is open source and implemented in pure C++ without any dependencies.

### F8Net: Fixed-Point 8-bit Only Multiplication for Network Quantization

Neural network quantization is a promising compression technique to reduce memory footprint and save energy consumption, potentially leading to real-time inference. However, there is a performance gap between quantized and full-precision models. To reduce it, existing quantization approaches require high-precision INT32 or full-precision multiplication during inference for scaling or dequantization. This introduces a noticeable cost in terms of memory, speed, and required energy. To tackle these issues, we present F8Net, a novel quantization framework consisting of only fixed-point 8-bit multiplication. To derive our method, we first discuss the advantages of fixed-point multiplication with different formats of fixed-point numbers and study the statistical behavior of the associated fixed-point numbers. Second, based on the statistical and algorithmic analysis, we apply different fixed-point formats for weights and activations of different layers. We introduce a novel algorithm to automatically determine the right format for each layer during training. Third, we analyze a previous quantization algorithm -- parameterized clipping activation (PACT) -- and reformulate it using fixed-point arithmetic. Finally, we unify the recently proposed method for quantization fine-tuning and our fixed-point approach to show the potential of our method. We verify F8Net on ImageNet for MobileNet V1/V2 and ResNet18/50. Our approach achieves comparable and better performance, when compared not only to existing quantization techniques with INT32 multiplication or floating-point arithmetic, but also to the full-precision counterparts, achieving state-of-the-art performance.

### Memory-Driven Mixed Low Precision Quantization For Enabling Deep Network Inference On Microcontrollers

This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the inference graph with integer-only operations. Our approach aims at determining the minimum bit precision of every activation and weight tensor given the memory constraints of a device. This is achieved through a rule-based iterative procedure, which cuts the number of bits of the most memory-demanding layers, aiming at meeting the memory constraints. After a quantization-aware retraining step, the fake-quantized graph is converted into an inference integer-only model by inserting the Integer Channel-Normalization (ICN) layers, which introduce a negligible loss as demonstrated on INT4 MobilenetV1 models. We report the latency-accuracy evaluation of mixed-precision MobilenetV1 family networks on a STM32H7 microcontroller. Our experimental results demonstrate an end-to-end deployment of an integer-only Mobilenet network with Top1 accuracy of 68% on a device with only 2MB of FLASH memory and 512kB of RAM, improving by 8% the Top1 accuracy with respect to previously published 8 bit implementations for microcontrollers.

### AdaptivFloat: A Floating-point based Data Type for Resilient Deep Learning Inference

Conventional hardware-friendly quantization methods, such as fixed-point or integer, tend to perform poorly at very low word sizes as their shrinking dynamic ranges cannot adequately capture the wide data distributions commonly seen in sequence transduction models. We present AdaptivFloat, a floating-point inspired number representation format for deep learning that dynamically maximizes and optimally clips its available dynamic range, at a layer granularity, in order to create faithful encoding of neural network parameters. AdaptivFloat consistently produces higher inference accuracies compared to block floating-point, uniform, IEEE-like float or posit encodings at very low precision ($\leq$ 8-bit) across a diverse set of state-of-the-art neural network topologies. And notably, AdaptivFloat is seen surpassing baseline FP32 performance by up to +0.3 in BLEU score and -0.75 in word error rate at weight bit widths that are $\leq$ 8-bit. Experimental results on a deep neural network (DNN) hardware accelerator, exploiting AdaptivFloat logic in its computational datapath, demonstrate per-operation energy and area that is 0.9$\times$ and 1.14$\times$, respectively, that of equivalent bit width integer-based accelerator variants.