Learning convolutional neural networks (CNNs) with low bitwidth is challenging because performance may drop significantly after quantization. Prior arts often discretize the network weights by carefully tuning hyper-parameters of quantization (e.g. non-uniform stepsize and layer-wise bitwidths), which are complicated and sub-optimal because the full-precision and low-precision models have a large discrepancy. This work presents a novel quantization pipeline, Frequency-Aware Transformation (FAT), which has several appealing benefits. (1) Rather than designing complicated quantizers like existing works, FAT learns to transform network weights in the frequency domain before quantization, making them more amenable to training in low bitwidth. (2) With FAT, CNNs can be easily trained in low precision using simple standard quantizers without tedious hyper-parameter tuning. Theoretical analysis shows that FAT improves both uniform and non-uniform quantizers. (3) FAT can be easily plugged into many CNN architectures. When training ResNet-18 and MobileNet-V2 in 4 bits, FAT plus a simple rounding operation already achieves 70.5% and 69.2% top-1 accuracy on ImageNet without bells and whistles, outperforming recent state-of-the-art by reducing 54.9X and 45.7X computations against full-precision models. We hope FAT provides a novel perspective for model quantization. Code is available at \url{https://github.com/ChaofanTao/FAT_Quantization}.
We consider training models on private data that are distributed across user devices. To ensure privacy, we add on-device noise and use secure aggregation so that only the noisy sum is revealed to the server. We present a comprehensive end-to-end system, which appropriately discretizes the data and adds discrete Gaussian noise before performing secure aggregation. We provide a novel privacy analysis for sums of discrete Gaussians and carefully analyze the effects of data quantization and modular summation arithmetic. Our theoretical guarantees highlight the complex tension between communication, privacy, and accuracy. Our extensive experimental results demonstrate that our solution is essentially able to match the accuracy to central differential privacy with less than 16 bits of precision per value.
Many neural network quantization techniques have been developed to decrease the computational and memory footprint of deep learning. However, these methods are evaluated subject to confounding tradeoffs that may affect inference acceleration or resource complexity in exchange for higher accuracy. In this work, we articulate a variety of tradeoffs whose impact is often overlooked and empirically analyze their impact on uniform and mixed-precision post-training quantization, finding that these confounding tradeoffs may have a larger impact on quantized network accuracy than the actual quantization methods themselves. Because these tradeoffs constrain the attainable hardware acceleration for different use-cases, we encourage researchers to explicitly report these design choices through the structure of "quantization cards." We expect quantization cards to help researchers compare methods more effectively and engineers determine the applicability of quantization techniques for their hardware.
Motivation: Single cell RNA sequencing (scRNA-seq) data makes studying the development of cells possible at unparalleled resolution. Given that many cellular differentiation processes are hierarchical, their scRNA-seq data is expected to be approximately tree-shaped in gene expression space. Inference and representation of this tree-structure in two dimensions is highly desirable for biological interpretation and exploratory analysis.Results:Our two contributions are an approach for identifying a meaningful tree structure from high-dimensional scRNA-seq data, and a visualization method respecting the tree-structure. We extract the tree structure by means of a density based minimum spanning tree on a vector quantization of the data and show that it captures biological information well. We then introduce DTAE, a tree-biased autoencoder that emphasizes the tree structure of the data in low dimensional space. We compare to other dimension reduction methods and demonstrate the success of our method both qualitatively and quantitatively on real and toy data.Availability: Our implementation relying on PyTorch and Higra is available at https://github.com/hci-unihd/DTAE.
We study the challenging task of neural network quantization without end-to-end retraining, called Post-training Quantization (PTQ). PTQ usually requires a small subset of training data but produces less powerful quantized models than Quantization-Aware Training (QAT). In this work, we propose a novel PTQ framework, dubbed BRECQ, which pushes the limits of bitwidth in PTQ down to INT2 for the first time. BRECQ leverages the basic building blocks in neural networks and reconstructs them one-by-one. In a comprehensive theoretical study of the second-order error, we show that BRECQ achieves a good balance between cross-layer dependency and generalization error. To further employ the power of quantization, the mixed precision technique is incorporated in our framework by approximating the inter-layer and intra-layer sensitivity. Extensive experiments on various handcrafted and searched neural architectures are conducted for both image classification and object detection tasks. And for the first time we prove that, without bells and whistles, PTQ can attain 4-bit ResNet and MobileNetV2 comparable with QAT and enjoy 240 times faster production of quantized models. Codes are available at https://github.com/yhhhli/BRECQ.
The advances in data science and machine learning have resulted in significant improvements regarding the modeling and simulation of nonlinear dynamical systems. It is nowadays possible to make accurate predictions of complex systems such as the weather, disease models or the stock market. Predictive methods are often advertised to be useful for control, but the specifics are frequently left unanswered due to the higher system complexity, the requirement of larger data sets and an increased modeling effort. In other words, surrogate modeling for autonomous systems is much easier than for control systems. In this paper we present the framework QuaSiModO (Quantization-Simulation-Modeling-Optimization) to transform arbitrary predictive models into control systems and thus render the tremendous advances in data-driven surrogate modeling accessible for control. Our main contribution is that we trade control efficiency by autonomizing the dynamics - which yields mixed-integer control problems - to gain access to arbitrary, ready-to-use autonomous surrogate modeling techniques. We then recover the complexity of the original problem by leveraging recent results from mixed-integer optimization. The advantages of QuaSiModO are a linear increase in data requirements with respect to the control dimension, performance guarantees that rely exclusively on the accuracy of the predictive model in use, and little prior knowledge requirements in control theory to solve complex control problems.
Quantization enables efficient acceleration of deep neural networks by reducing model memory footprint and exploiting low-cost integer math hardware units. Quantization maps floating-point weights and activations in a trained model to low-bitwidth integer values using scale factors. Excessive quantization, reducing precision too aggressively, results in accuracy degradation. When scale factors are shared at a coarse granularity across many dimensions of each tensor, effective precision of individual elements within the tensor are limited. To reduce quantization-related accuracy loss, we propose using a separate scale factor for each small vector of ($\approx$16-64) elements within a single dimension of a tensor. To achieve an efficient hardware implementation, the per-vector scale factors can be implemented with low-bitwidth integers when calibrated using a two-level quantization scheme. We find that per-vector scaling consistently achieves better inference accuracy at low precision compared to conventional scaling techniques for popular neural networks without requiring retraining. We also modify a deep learning accelerator hardware design to study the area and energy overheads of per-vector scaling support. Our evaluation demonstrates that per-vector scaled quantization with 4-bit weights and activations achieves 37% area saving and 24% energy saving while maintaining over 75% accuracy for ResNet50 on ImageNet. 4-bit weights and 8-bit activations achieve near-full-precision accuracy for both BERT-base and BERT-large on SQuAD while reducing area by 26% compared to an 8-bit baseline.
Communication of model updates between client nodes and the central aggregating server is a major bottleneck in federated learning, especially in bandwidth-limited settings and high-dimensional models. Gradient quantization is an effective way of reducing the number of bits required to communicate each model update, albeit at the cost of having a higher error floor due to the higher variance of the stochastic gradients. In this work, we propose an adaptive quantization strategy called AdaQuantFL that aims to achieve communication efficiency as well as a low error floor by changing the number of quantization levels during the course of training. Experiments on training deep neural networks show that our method can converge in much fewer communicated bits as compared to fixed quantization level setups, with little or no impact on training and test accuracy.
In order to achieve high accuracy for machine learning (ML) applications, it is essential to employ models with a large number of parameters. Certain applications, such as Automatic Speech Recognition (ASR), however, require real-time interactions with users, hence compelling the model to have as low latency as possible. Deploying large scale ML applications thus necessitates model quantization and compression, especially when running ML models on resource constrained devices. For example, by forcing some of the model weight values into zero, it is possible to apply zero-weight compression, which reduces both the model size and model reading time from the memory. In the literature, such methods are referred to as sparse pruning. The fundamental questions are when and which weights should be forced to zero, i.e. be pruned. In this work, we propose a compressed sensing based pruning (CSP) approach to effectively address those questions. By reformulating sparse pruning as a sparsity inducing and compression-error reduction dual problem, we introduce the classic compressed sensing process into the ML model training process. Using ASR task as an example, we show that CSP consistently outperforms existing approaches in the literature.
Researches have demonstrated that low bit-width (e.g., INT8) quantization can be employed to accelerate the inference process. It makes the gradient quantization very promising since the backward propagation requires approximately twice more computation than forward one. Due to the variability and uncertainty of gradient distribution, a lot of methods have been proposed to attain training stability. However, most of them ignore the channel-wise gradient distributions and the impact of gradients with different magnitudes, resulting in the degradation of final accuracy. In this paper, we propose a novel INT8 quantization training framework for convolutional neural network to address the above issues. Specifically, we adopt Gradient Vectorized Quantization to quantize the gradient, based on the observation that layer-wise gradients contain multiple distributions along the channel dimension. Then, Magnitude-aware Clipping Strategy is introduced by taking the magnitudes of gradients into consideration when minimizing the quantization error, and we present a theoretical derivation to solve the quantization parameters of different distributions. Experimental results on broad range of computer vision tasks, such as image classification, object detection and video classification, demonstrate that the proposed Distribution Adaptive INT8 Quantization training method has achieved almost lossless training accuracy for different backbones, including ResNet, MobileNetV2, InceptionV3, VGG and AlexNet, which is superior to the state-of-the-art techniques. Moreover, we further implement the INT8 kernel that can accelerate the training iteration more than 200% under the latest Turing architecture, i.e., our method excels on both training accuracy and speed.
We consider the problem of computing the k-means centers for a large high-dimensional dataset in the context of edge-based machine learning, where data sources offload machine learning computation to nearby edge servers. k-Means computation is fundamental to many data analytics, and the capability of computing provably accurate k-means centers by leveraging the computation power of the edge servers, at a low communication and computation cost to the data sources, will greatly improve the performance of these analytics. We propose to let the data sources send small summaries, generated by joint dimensionality reduction (DR), cardinality reduction (CR), and quantization (QT), to support approximate k-means computation at reduced complexity and communication cost. By analyzing the complexity, the communication cost, and the approximation error of k-means algorithms based on carefully designed composition of DR/CR/QT methods, we show that: (i) it is possible to compute near-optimal k-means centers at a near-linear complexity and a constant or logarithmic communication cost, (ii) the order of applying DR and CR significantly affects the complexity and the communication cost, and (iii) combining DR/CR methods with a properly configured quantizer can further reduce the communication cost without compromising the other performance metrics. Our theoretical analysis has been validated through experiments based on real datasets.
The ever-growing computational demands of increasingly complex machine learning models frequently necessitate the use of powerful cloud-based infrastructure for their training. Binary neural networks are known to be promising candidates for on-device inference due to their extreme compute and memory savings over higher-precision alternatives. However, their existing training methods require the concurrent storage of high-precision activations for all layers, generally making learning on memory-constrained devices infeasible. In this article, we demonstrate that the backward propagation operations needed for binary neural network training are strongly robust to quantization, thereby making on-the-edge learning with modern models a practical proposition. We introduce a low-cost binary neural network training strategy exhibiting sizable memory footprint reductions while inducing little to no accuracy loss vs Courbariaux & Bengio's standard approach. These decreases are primarily enabled through the retention of activations exclusively in binary format. Against the latter algorithm, our drop-in replacement sees memory requirement reductions of 3--5$\times$, while reaching similar test accuracy in comparable time, across a range of small-scale models trained to classify popular datasets. We also demonstrate from-scratch ImageNet training of binarized ResNet-18, achieving a 3.78$\times$ memory reduction. Our work is open-source, and includes the Raspberry Pi-targeted prototype we used to verify our modeled memory decreases and capture the associated energy drops. Such savings will allow for unnecessary cloud offloading to be avoided, reducing latency, increasing energy efficiency, and safeguarding end-user privacy.
This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite network. The proposed approach is based on the notion of alternating simulation functions. This notion relates a concrete network to its symbolic model with guaranteed mismatch bounds between their output behaviors. We propose a compositional approach to construct a symbolic model for an infinite network, together with an alternating simulation function, by composing symbolic models and alternating simulation functions constructed for subsystems. Assuming that each subsystem is incrementally input-to-state stable and under some small-gain type conditions, we present an algorithm for orderly constructing local symbolic models with properly designed quantization parameters. In this way, the proposed compositional approach can provide us a guideline for constructing an overall symbolic model with any desired approximation accuracy. A compositional controller synthesis scheme is also provided to enforce safety properties on the infinite network in a decentralized fashion. The effectiveness of our result is illustrated through a road traffic network consisting of infinitely many road cells.
We present PLONQ, a progressive neural image compression scheme which pushes the boundary of variable bitrate compression by allowing quality scalable coding with a single bitstream. In contrast to existing learned variable bitrate solutions which produce separate bitstreams for each quality, it enables easier rate-control and requires less storage. Leveraging the latent scaling based variable bitrate solution, we introduce nested quantization, a method that defines multiple quantization levels with nested quantization grids, and progressively refines all latents from the coarsest to the finest quantization level. To achieve finer progressiveness in between any two quantization levels, latent elements are incrementally refined with an importance ordering defined in the rate-distortion sense. To the best of our knowledge, PLONQ is the first learning-based progressive image coding scheme and it outperforms SPIHT, a well-known wavelet-based progressive image codec.
Deep learning approaches have achieved unprecedented performance in visual recognition tasks such as object detection and pose estimation. However, state-of-the-art models have millions of parameters represented as floats which make them computationally expensive and constrain their deployment on hardware such as mobile phones and IoT nodes. Most commonly, activations of deep neural networks tend to be sparse thus proving that models are over parametrized with redundant neurons. Model compression techniques, such as pruning and quantization, have recently shown promising results by improving model complexity with little loss in performance. In this work, we extended pruning, a compression technique that discards unnecessary model connections, and weight sharing techniques for the task of object detection. With our approach, we are able to compress a state-of-the-art object detection model by 30.0% without a loss in performance. We also show that our compressed model can be easily initialized with existing pre-trained weights, and thus is able to fully utilize published state-of-the-art model zoos.
Traditional low bit-rate speech coding approach only handles narrowband speech at 8kHz, which limits further improvements in speech quality. Motivated by recent successful exploration of deep learning methods for image and speech compression, this paper presents a new approach through vector quantization (VQ) of mel-frequency cepstral coefficients (MFCCs) and using a deep generative model called WaveGlow to provide efficient and high-quality speech coding. The coding feature is sorely an 80-dimension MFCCs vector for 16kHz wideband speech, then speech coding at the bit-rate throughout 1000-2000 bit/s could be scalably implemented by applying different VQ schemes for MFCCs vector. This new deep generative network based codec works fast as the WaveGlow model abandons the sample-by-sample autoregressive mechanism. We evaluated this new approach over the multi-speaker TIMIT corpus, and experimental results demonstrate that it provides better speech quality compared with the state-of-the-art classic MELPe codec at lower bit-rate.
Convolutional Neural Networks (CNNs) have proven to be a powerful state-of-the-art method for image classification tasks. One drawback however is the high computational complexity and high memory consumption of CNNs which makes them unfeasible for execution on embedded platforms which are constrained on physical resources needed to support CNNs. Quantization has often been used to efficiently optimize CNNs for memory and computational complexity at the cost of a loss of prediction accuracy. We therefore propose a method to optimally quantize the weights, biases and activations of each layer of a pre-trained CNN while controlling the loss in inference accuracy to enable quantized inference. We quantize the 32-bit floating-point precision parameters to low bitwidth fixed-point representations thereby finding optimal bitwidths and fractional offsets for parameters of each layer of a given CNN. We quantize parameters of a CNN post-training without re-training it. Our method is designed to quantize parameters of a CNN taking into account how other parameters are quantized because ignoring quantization errors due to other quantized parameters leads to a low precision CNN with accuracy losses of up to 50% which is far beyond what is acceptable. Our final method therefore gives a low precision CNN with accuracy losses of less than 1%. As compared to a method used by commercial tools that quantize all parameters to 8-bits, our approach provides quantized CNN with averages of 53% lower memory consumption and 77.5% lower cost of executing multiplications for the two CNNs trained on the four datasets that we tested our work on. We find that layer-wise quantization of parameters significantly helps in this process.
Detection of inconsistencies of double JPEG artefacts across different image regions is often used to detect local image manipulations, like image splicing, and to localize them. In this paper, we move one step further, proposing an end-to-end system that, in addition to detecting and localizing spliced regions, can also distinguish regions coming from different donor images. We assume that both the spliced regions and the background image have undergone a double JPEG compression, and use a local estimate of the primary quantization matrix to distinguish between spliced regions taken from different sources. To do so, we cluster the image blocks according to the estimated primary quantization matrix and refine the result by means of morphological reconstruction. The proposed method can work in a wide variety of settings including aligned and non-aligned double JPEG compression, and regardless of whether the second compression is stronger or weaker than the first one. We validated the proposed approach by means of extensive experiments showing its superior performance with respect to baseline methods working in similar conditions.
The ever-growing cost of both training and inference for state-of-the-art neural networks has brought literature to look upon ways to cut off resources used with a minimal impact on accuracy. Using lower precision comes at the cost of negligible loss in accuracy. While training neural networks may require a powerful setup, deploying a network must be possible on low-power and low-resource hardware architectures. Reconfigurable architectures have proven to be more powerful and flexible than GPUs when looking at a specific application. This article aims to assess the impact of mixed-precision when applied to neural networks deployed on FPGAs. While several frameworks exist that create tools to deploy neural networks using reduced-precision, few of them assess the importance of quantization and the framework quality. FINN and Brevitas, two frameworks from Xilinx labs, are used to assess the impact of quantization on neural networks using 2 to 8 bit precisions and weights with several parallelization configurations. Equivalent accuracy can be obtained using lower-precision representation and enough training. However, the compressed network can be better parallelized allowing the deployed network throughput to be 62 times faster. The benchmark set up in this work is available in a public repository (https://github.com/QDucasse/nn benchmark).
Federated Learning marks a turning point in the implementation of decentralized machine learning (especially deep learning) for wireless devices by protecting users' privacy and safeguarding raw data from third-party access. It assigns the learning process independently to each client. First, clients locally train a machine learning model based on local data. Next, clients transfer local updates of model weights and biases (training data) to a server. Then, the server aggregates updates (received from clients) to create a global learning model. However, the continuous transfer between clients and the server increases communication costs and is inefficient from a resource utilization perspective due to the large number of parameters (weights and biases) used by deep learning models. The cost of communication becomes a greater concern when the number of contributing clients and communication rounds increases. In this work, we propose a novel framework, FedZip, that significantly decreases the size of updates while transferring weights from the deep learning model between clients and their servers. FedZip implements Top-z sparsification, uses quantization with clustering, and implements compression with three different encoding methods. FedZip outperforms state-of-the-art compression frameworks and reaches compression rates up to 1085x, and preserves up to 99% of bandwidth and 99% of energy for clients during communication.