As the size and complexity of models and datasets grow, so does the need for communication-efficient variants of stochastic gradient descent that can be deployed on clusters to perform model fitting in parallel. Alistarh et al. (2017) describe two variants of data-parallel SGD that quantize and encode gradients to lessen communication costs. For the first variant, QSGD, they provide strong theoretical guarantees. For the second variant, which we call QSGDinf, they demonstrate impressive empirical gains for distributed training of large neural networks. Building on their work, we propose an alternative scheme for quantizing gradients and show that it yields stronger theoretical guarantees than exist for QSGD while matching the empirical performance of QSGDinf.
We tackle the problem of unsupervised visual descriptors compression, which is a key ingredient of large-scale image retrieval systems. While the deep learning machinery has benefited literally all computer vision pipelines, the existing state-of-the-art compression methods employ shallow architectures, and we aim to close this gap by our paper. In more detail, we introduce a DNN architecture for the unsupervised compressed-domain retrieval, based on multi-codebook quantization. The proposed architecture is designed to incorporate both fast data encoding and efficient distances computation via lookup tables. We demonstrate the exceptional advantage of our scheme over existing quantization approaches on several datasets of visual descriptors via outperforming the previous state-of-the-art by a large margin.
Model quantization is leveraged to reduce the memory consumption and the computation time of deep neural networks. This is achieved by representing weights and activations with a lower bit resolution when compared to their high precision floating point counterparts. The suitable level of quantization is directly related to the model performance. Lowering the quantization precision (e.g. 2 bits), reduces the amount of memory required to store model parameters and the amount of logic required to implement computational blocks, which contributes to reducing the power consumption of the entire system. These benefits typically come at the cost of reduced accuracy. The main challenge is to quantize a network as much as possible, while maintaining the performance accuracy. In this work, we present a quantization method for the U-Net architecture, a popular model in medical image segmentation. We then apply our quantization algorithm to three datasets: (1) the Spinal Cord Gray Matter Segmentation (GM), (2) the ISBI challenge for segmentation of neuronal structures in Electron Microscopic (EM), and (3) the public National Institute of Health (NIH) dataset for pancreas segmentation in abdominal CT scans. The reported results demonstrate that with only 4 bits for weights and 6 bits for activations, we obtain 8 fold reduction in memory requirements while loosing only 2.21%, 0.57% and 2.09% dice overlap score for EM, GM and NIH datasets respectively. Our fixed point quantization provides a flexible trade off between accuracy and memory requirement which is not provided by previous quantization methods for U-Net such as TernaryNet.
The increasing use of machine learning in practice and legal regulations like EU's GDPR cause the necessity to be able to explain the prediction and behavior of machine learning models. A prominent example of particularly intuitive explanations of AI models in the context of decision making are counterfactual explanations. Yet, it is still an open research problem how to efficiently compute counterfactual explanations for many models. We investigate how to efficiently compute counterfactual explanations for an important class of models, prototype-based classifiers such as learning vector quantization models. In particular, we derive specific convex and non-convex programs depending on the used metric.
Existing data-dependent hashing methods usually learn hash functions from pairwise or triplet data relationships, which only capture the data similarity locally, and often suffer from low learning efficiency and low collision rate. In this work, we propose a new \emph{global} similarity metric, termed as \emph{central similarity}, with which the hash codes of similar data pairs are encouraged to approach a common center and those for dissimilar pairs to converge to different centers, to improve hash learning efficiency and retrieval accuracy. We principally formulate the computation of the proposed central similarity metric by introducing a new concept, i.e., \emph{hash center} that refers to a set of data points scattered in the Hamming space with a sufficient mutual distance between each other. We then provide an efficient method to construct well separated hash centers by leveraging the Hadamard matrix and Bernoulli distributions. Finally, we propose the Central Similarity Quantization (CSQ) that optimizes the central similarity between data points w.r.t.\ their hash centers instead of optimizing the local similarity. CSQ is generic and applicable to both image and video hashing scenarios. Extensive experiments on large-scale image and video retrieval tasks demonstrate that CSQ can generate cohesive hash codes for similar data pairs and dispersed hash codes for dissimilar pairs, achieving a noticeable boost in retrieval performance, i.e. 3\%-20\% in mAP over the previous state-of-the-arts. The code is at: \url{https://github.com/yuanli2333/Hadamard-Matrix-for-hashing}
The field of video compression has developed some of the most sophisticated and efficient compression algorithms known in the literature, enabling very high compressibility for little loss of information. Whilst some of these techniques are domain specific, many of their underlying principles are universal in that they can be adapted and applied for compressing different types of data. In this work we present DeepCABAC, a compression algorithm for deep neural networks that is based on one of the state-of-the-art video coding techniques. Concretely, it applies a Context-based Adaptive Binary Arithmetic Coder (CABAC) to the network's parameters, which was originally designed for the H.264/AVC video coding standard and became the state-of-the-art for lossless compression. Moreover, DeepCABAC employs a novel quantization scheme that minimizes the rate-distortion function while simultaneously taking the impact of quantization onto the accuracy of the network into account. Experimental results show that DeepCABAC consistently attains higher compression rates than previously proposed coding techniques for neural network compression. For instance, it is able to compress the VGG16 ImageNet model by x63.6 with no loss of accuracy, thus being able to represent the entire network with merely 8.7MB. The source code for encoding and decoding can be found at https://github.com/fraunhoferhhi/DeepCABAC.
Model compression has become necessary when applying neural networks (NN) into many real application tasks that can accept slightly-reduced model accuracy with strict tolerance to model complexity. Recently, Knowledge Distillation, which distills the knowledge from well-trained and highly complex teacher model into a compact student model, has been widely used for model compression. However, under the strict requirement on the resource cost, it is quite challenging to achieve comparable performance with the teacher model, essentially due to the drastically-reduced expressiveness ability of the compact student model. Inspired by the nature of the expressiveness ability in Neural Networks, we propose to use multi-segment activation, which can significantly improve the expressiveness ability with very little cost, in the compact student model. Specifically, we propose a highly efficient multi-segment activation, called Light Multi-segment Activation (LMA), which can rapidly produce multiple linear regions with very few parameters by leveraging the statistical information. With using LMA, the compact student model is capable of achieving much better performance effectively and efficiently, than the ReLU-equipped one with same model scale. Furthermore, the proposed method is compatible with other model compression techniques, such as quantization, which means they can be used jointly for better compression performance. Experiments on state-of-the-art NN architectures over the real-world tasks demonstrate the effectiveness and extensibility of the LMA.
In this paper, we address the problem of reducing the memory footprint of convolutional network architectures. We introduce a vector quantization method that aims at preserving the quality of the reconstruction of the network outputs rather than its weights. The principle of our approach is that it minimizes the loss reconstruction error for in-domain inputs. Our method only requires a set of unlabelled data at quantization time and allows for efficient inference on CPU by using byte-aligned codebooks to store the compressed weights. We validate our approach by quantizing a high performing ResNet-50 model to a memory size of 5MB (20x compression factor) while preserving a top-1 accuracy of 76.1% on ImageNet object classification and by compressing a Mask R-CNN with a 26x factor.
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware for rapid random projections which leverages the propagation of light in random media. A signal of interest $\mathbf{\xi} \in \mathbb{R}^N$ is mixed by a random scattering medium to compute the projection $\mathbf{y} = \mathbf{A} \mathbf{\xi}$, with $\mathbf{A} \in \mathbb{C}^{M \times N}$ being a realization of a standard complex Gaussian iid random matrix. Such optics-based matrix multiplications can be much faster and energy-efficient than their CPU or GPU counterparts, yet two difficulties must be resolved: only the intensity ${|\mathbf{y}|}^2$ can be recorded by the camera, and the transmission matrix $\mathbf{A}$ is unknown. We show that even without knowing $\mathbf{A}$, we can recover the unknown phase of $\mathbf{y}$ for some equivalent transmission matrix with the same distribution as $\mathbf{A}$. Our method is based on two observations: first, conjugating or changing the phase of any row of $\mathbf{A}$ does not change its distribution; and second, since we control the input we can interfere $\mathbf{\xi}$ with arbitrary reference signals. We show how to leverage these observations to cast the measurement phase retrieval problem as a Euclidean distance geometry problem. We demonstrate appealing properties of the proposed algorithm in both numerical simulations and real hardware experiments. Not only does our algorithm accurately recover the missing phase, but it mitigates the effects of quantization and the sensitivity threshold, thus improving the measured magnitudes.
In this work, a deep learning-based quantization scheme for log-likelihood ratio (L-value) storage is introduced. We analyze the dependency between the average magnitude of different L-values from the same quadrature amplitude modulation (QAM) symbol and show they follow a consistent ordering. Based on this we design a deep autoencoder that jointly compresses and separately reconstructs each L-value, allowing the use of a weighted loss function that aims to more accurately reconstructs low magnitude inputs. Our method is shown to be competitive with state-of-the-art maximum mutual information quantization schemes, reducing the required memory footprint by a ratio of up to two and a loss of performance smaller than 0.1 dB with less than two effective bits per L-value or smaller than 0.04 dB with 2.25 effective bits. We experimentally show that our proposed method is a universal compression scheme in the sense that after training on an LDPC-coded Rayleigh fading scenario we can reuse the same network without further training on other channel models and codes while preserving the same performance benefits.
Quantization has been an effective technology in ANN (approximate nearest neighbour) search due to its high accuracy and fast search speed. To meet the requirement of different applications, there is always a trade-off between retrieval accuracy and speed, reflected by variable code lengths. However, to encode the dataset into different code lengths, existing methods need to train several models, where each model can only produce a specific code length. This incurs a considerable training time cost, and largely reduces the flexibility of quantization methods to be deployed in real applications. To address this issue, we propose a Deep Recurrent Quantization (DRQ) architecture which can generate sequential binary codes. To the end, when the model is trained, a sequence of binary codes can be generated and the code length can be easily controlled by adjusting the number of recurrent iterations. A shared codebook and a scalar factor is designed to be the learnable weights in the deep recurrent quantization block, and the whole framework can be trained in an end-to-end manner. As far as we know, this is the first quantization method that can be trained once and generate sequential binary codes. Experimental results on the benchmark datasets show that our model achieves comparable or even better performance compared with the state-of-the-art for image retrieval. But it requires significantly less number of parameters and training times. Our code is published online: https://github.com/cfm-uestc/DRQ.
Product Quantization (PQ) has long been a mainstream for generating an exponentially large codebook at very low memory/time cost. Despite its success, PQ is still tricky for the decomposition of high-dimensional vector space, and the retraining of model is usually unavoidable when the code length changes. In this work, we propose a deep progressive quantization (DPQ) model, as an alternative to PQ, for large scale image retrieval. DPQ learns the quantization codes sequentially and approximates the original feature space progressively. Therefore, we can train the quantization codes with different code lengths simultaneously. Specifically, we first utilize the label information for guiding the learning of visual features, and then apply several quantization blocks to progressively approach the visual features. Each quantization block is designed to be a layer of a convolutional neural network, and the whole framework can be trained in an end-to-end manner. Experimental results on the benchmark datasets show that our model significantly outperforms the state-of-the-art for image retrieval. Our model is trained once for different code lengths and therefore requires less computation time. Additional ablation study demonstrates the effect of each component of our proposed model. Our code is released at https://github.com/cfm-uestc/DPQ.
Homomorphic Encryption (HE) is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). Leveled-HE (LHE)-enabled Convolutional Neural Networks (LHECNNs) are proposed to implement MLaaS to avoid large bootstrapping overhead. However, prior LHECNNs have to pay significant computing overhead but achieve only low inference accuracy, due to their polynomial approximation activations and poolings. Stacking many polynomial approximation activation layers in a network greatly reduces inference accuracy, since the polynomial approximation activation errors lead to a low distortion of the output distribution of the next batch normalization layer. So the polynomial approximation activations and poolings have become the obstacle to a fast and accurate LHECNN model. In this paper, we propose a Shift-accumulation-based LHE-enabled deep neural network (SHE) for fast and accurate inferences on encrypted data. We use the binary-operation-friendly Leveled Fast Homomorphic Encryption over Torus (LTFHE) encryption scheme to implement ReLU activations and max poolings. We also adopt the logarithmic quantization to accelerate inferences by replacing expensive LTFHE multiplications with cheap LTFHE shifts. We propose a mixed bitwidth accumulator to accelerate accumulations. Since the LTFHE ReLU activations, max poolings, shifts and accumulations have small multiplicative depth overhead, SHE can implement much deeper network architectures with more convolutional and activation layers. Our experimental results show SHE achieves the state-of-the-art inference accuracy and reduces the inference latency by 76.21% ~ 94.23% over prior LHECNNs on MNIST and CIFAR-10. The source code of SHE is available at https://github.com/qianlou/SHE.
The `Internet of Things' has brought increased demand for AI-based edge computing in applications ranging from healthcare monitoring systems to autonomous vehicles. Quantization is a powerful tool to address the growing computational cost of such applications, and yields significant compression over full-precision networks. However, quantization can result in substantial loss of performance for complex image classification tasks. To address this, we propose a Principal Component Analysis (PCA) driven methodology to identify the important layers of a binary network, and design mixed-precision networks. The proposed Hybrid-Net achieves a more than 10% improvement in classification accuracy over binary networks such as XNOR-Net for ResNet and VGG architectures on CIFAR-100 and ImageNet datasets while still achieving up to 94% of the energy-efficiency of XNOR-Nets. This work furthers the feasibility of using highly compressed neural networks for energy-efficient neural computing in edge devices.
Reducing the precision of weights and activation functions in neural network training, with minimal impact on performance, is essential for the deployment of these models in resource-constrained environments. We apply mean-field techniques to networks with quantized activations in order to evaluate the degree to which quantization degrades signal propagation at initialization. We derive initialization schemes which maximize signal propagation in such networks and suggest why this is helpful for generalization. Building on these results, we obtain a closed form implicit equation for $L_{\max}$, the maximal trainable depth (and hence model capacity), given $N$, the number of quantization levels in the activation function. Solving this equation numerically, we obtain asymptotically: $L_{\max}\propto N^{1.82}$.
The high computation, memory, and power budgets of inferring convolutional neural networks (CNNs) are major bottlenecks of model deployment to edge computing platforms, e.g., mobile devices and IoT. Moreover, training CNNs is time and energy-intensive even on high-grade servers. Convolution layers and fully connected layers, because of their intense use of multiplications, are the dominant contributor to this computation budget. We propose to alleviate this problem by introducing two new operations: convolutional shifts and fully-connected shifts which replace multiplications with bitwise shift and sign flipping during both training and inference. During inference, both approaches require only 5 bits (or less) to represent the weights. This family of neural network architectures (that use convolutional shifts and fully connected shifts) is referred to as DeepShift models. We propose two methods to train DeepShift models: DeepShift-Q which trains regular weights constrained to powers of 2, and DeepShift-PS that trains the values of the shifts and sign flips directly. Very close accuracy, and in some cases higher accuracy, to baselines are achieved. Converting pre-trained 32-bit floating-point baseline models of ResNet18, ResNet50, VGG16, and GoogleNet to DeepShift and training them for 15 to 30 epochs, resulted in Top-1/Top-5 accuracies higher than that of the original model. Last but not least, we implemented the convolutional shifts and fully connected shift GPU kernels and showed a reduction in latency time of 25% when inferring ResNet18 compared to unoptimized multiplication-based GPU kernels. The code can be found at https://github.com/mostafaelhoushi/DeepShift.
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.
Efficient deep neural network (DNN) inference on mobile or embedded devices typically involves quantization of the network parameters and activations. In particular, mixed precision networks achieve better performance than networks with homogeneous bitwidth for the same size constraint. Since choosing the optimal bitwidths is not straight forward, training methods, which can learn them, are desirable. Differentiable quantization with straight-through gradients allows to learn the quantizer's parameters using gradient methods. We show that a suited parametrization of the quantizer is the key to achieve a stable training and a good final performance. Specifically, we propose to parametrize the quantizer with the step size and dynamic range. The bitwidth can then be inferred from them. Other parametrizations, which explicitly use the bitwidth, consistently perform worse. We confirm our findings with experiments on CIFAR-10 and ImageNet and we obtain mixed precision DNNs with learned quantization parameters, achieving state-of-the-art performance.
We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in particular that any Lipschitz-continuous map defined on a hypercube can be uniformly approximated by a quantized neural network. We then focus on the regularization effect of additive noise on the arguments of multi-step functions inherent to the quantization of continuous variables. In particular, when the expectation operator is applied to a non-differentiable multi-step random function, and if the underlying probability density is differentiable (in either classical or weak sense), then a differentiable function is retrieved, with explicit bounds on its Lipschitz constant. Based on these results, we propose a novel gradient-based training algorithm for quantized neural networks that generalizes the straight-through estimator, acting on noise applied to the network's parameters. We evaluate our algorithm on the CIFAR-10 and ImageNet image classification benchmarks, showing state-of-the-art performance on AlexNet and MobileNetV2 for ternary networks.
Communication overhead is a major bottleneck hampering the scalability of distributed machine learning systems. Recently, there has been a surge of interest in using gradient compression to improve the communication efficiency of distributed neural network training. Using 1-bit quantization, signSGD with majority vote achieves a 32x reduction on communication cost. However, its convergence is based on unrealistic assumptions and can diverge in practice. In this paper, we propose a general distributed compressed SGD with Nesterov's momentum. We consider two-way compression, which compresses the gradients both to and from workers. Convergence analysis on nonconvex problems for general gradient compressors is provided. By partitioning the gradient into blocks, a blockwise compressor is introduced such that each gradient block is compressed and transmitted in 1-bit format with a scaling factor, leading to a nearly 32x reduction on communication. Experimental results show that the proposed method converges as fast as full-precision distributed momentum SGD and achieves the same testing accuracy. In particular, on distributed ResNet training with 7 workers on the ImageNet, the proposed algorithm achieves the same testing accuracy as momentum SGD using full-precision gradients, but with $46\%$ less wall clock time.