Recent neural compression methods have been based on the popular hyperprior framework. It relies on Scalar Quantization and offers a very strong compression performance. This contrasts from recent advances in image generation and representation learning, where Vector Quantization is more commonly employed. In this work, we attempt to bring these lines of research closer by revisiting vector quantization for image compression. We build upon the VQ-VAE framework and introduce several modifications. First, we replace the vanilla vector quantizer by a product quantizer. This intermediate solution between vector and scalar quantization allows for a much wider set of rate-distortion points: It implicitly defines high-quality quantizers that would otherwise require intractably large codebooks. Second, inspired by the success of Masked Image Modeling (MIM) in the context of self-supervised learning and generative image models, we propose a novel conditional entropy model which improves entropy coding by modelling the co-dependencies of the quantized latent codes. The resulting PQ-MIM model is surprisingly effective: its compression performance on par with recent hyperprior methods. It also outperforms HiFiC in terms of FID and KID metrics when optimized with perceptual losses (e.g. adversarial). Finally, since PQ-MIM is compatible with image generation frameworks, we show qualitatively that it can operate under a hybrid mode between compression and generation, with no further training or finetuning. As a result, we explore the extreme compression regime where an image is compressed into 200 bytes, i.e., less than a tweet.
Although considerable progress has been obtained in neural network quantization for efficient inference, existing methods are not scalable to heterogeneous devices as one dedicated model needs to be trained, transmitted, and stored for one specific hardware setting, incurring considerable costs in model training and maintenance. In this paper, we study a new vertical-layered representation of neural network weights for encapsulating all quantized models into a single one. With this representation, we can theoretically achieve any precision network for on-demand service while only needing to train and maintain one model. To this end, we propose a simple once quantization-aware training (QAT) scheme for obtaining high-performance vertical-layered models. Our design incorporates a cascade downsampling mechanism which allows us to obtain multiple quantized networks from one full precision source model by progressively mapping the higher precision weights to their adjacent lower precision counterparts. Then, with networks of different bit-widths from one source model, multi-objective optimization is employed to train the shared source model weights such that they can be updated simultaneously, considering the performance of all networks. By doing this, the shared weights will be optimized to balance the performance of different quantized models, thus making the weights transferable among different bit widths. Experiments show that the proposed vertical-layered representation and developed once QAT scheme are effective in embodying multiple quantized networks into a single one and allow one-time training, and it delivers comparable performance as that of quantized models tailored to any specific bit-width. Code will be available.
Embedding tables are usually huge in click-through rate (CTR) prediction models. To train and deploy the CTR models efficiently and economically, it is necessary to compress their embedding tables at the training stage. To this end, we formulate a novel quantization training paradigm to compress the embeddings from the training stage, termed low-precision training (LPT). Also, we provide theoretical analysis on its convergence. The results show that stochastic weight quantization has a faster convergence rate and a smaller convergence error than deterministic weight quantization in LPT. Further, to reduce the accuracy degradation, we propose adaptive low-precision training (ALPT) that learns the step size (i.e., the quantization resolution) through gradient descent. Experiments on two real-world datasets confirm our analysis and show that ALPT can significantly improve the prediction accuracy, especially at extremely low bit widths. For the first time in CTR models, we successfully train 8-bit embeddings without sacrificing prediction accuracy. The code of ALPT is publicly available.
Quantization has become a predominant approach for model compression, enabling deployment of large models trained on GPUs onto smaller form-factor devices for inference. Quantization-aware training (QAT) optimizes model parameters with respect to the end task while simulating quantization error, leading to better performance than post-training quantization. Approximation of gradients through the non-differentiable quantization operator is typically achieved using the straight-through estimator (STE) or additive noise. However, STE-based methods suffer from instability due to biased gradients, whereas existing noise-based methods cannot reduce the resulting variance. In this work, we incorporate exponentially decaying quantization-error-aware noise together with a learnable scale of task loss gradient to approximate the effect of a quantization operator. We show this method combines gradient scale and quantization noise in a better optimized way, providing finer-grained estimation of gradients at each weight and activation layer's quantizer bin size. Our controlled noise also contains an implicit curvature term that could encourage flatter minima, which we show is indeed the case in our experiments. Experiments training ResNet architectures on the CIFAR-10, CIFAR-100 and ImageNet benchmarks show that our method obtains state-of-the-art top-1 classification accuracy for uniform (non mixed-precision) quantization, out-performing previous methods by 0.5-1.2% absolute.
Federated learning enables cooperative training among massively distributed clients by sharing their learned local model parameters. However, with increasing model size, deploying federated learning requires a large communication bandwidth, which limits its deployment in wireless networks. To address this bottleneck, we introduce a residual-based federated learning framework (ResFed), where residuals rather than model parameters are transmitted in communication networks for training. In particular, we integrate two pairs of shared predictors for the model prediction in both server-to-client and client-to-server communication. By employing a common prediction rule, both locally and globally updated models are always fully recoverable in clients and the server. We highlight that the residuals only indicate the quasi-update of a model in a single inter-round, and hence contain more dense information and have a lower entropy than the model, comparing to model weights and gradients. Based on this property, we further conduct lossy compression of the residuals by sparsification and quantization and encode them for efficient communication. The experimental evaluation shows that our ResFed needs remarkably less communication costs and achieves better accuracy by leveraging less sensitive residuals, compared to standard federated learning. For instance, to train a 4.08 MB CNN model on CIFAR-10 with 10 clients under non-independent and identically distributed (Non-IID) setting, our approach achieves a compression ratio over 700X in each communication round with minimum impact on the accuracy. To reach an accuracy of 70%, it saves around 99% of the total communication volume from 587.61 Mb to 6.79 Mb in up-streaming and to 4.61 Mb in down-streaming on average for all clients.
There has been an explosion of interest in designing various Knowledge Graph Neural Networks (KGNNs), which achieve state-of-the-art performance and provide great explainability for recommendation. The promising performance is mainly resulting from their capability of capturing high-order proximity messages over the knowledge graphs. However, training KGNNs at scale is challenging due to the high memory usage. In the forward pass, the automatic differentiation engines (\textsl{e.g.}, TensorFlow/PyTorch) generally need to cache all intermediate activation maps in order to compute gradients in the backward pass, which leads to a large GPU memory footprint. Existing work solves this problem by utilizing multi-GPU distributed frameworks. Nonetheless, this poses a practical challenge when seeking to deploy KGNNs in memory-constrained environments, especially for industry-scale graphs. Here we present TinyKG, a memory-efficient GPU-based training framework for KGNNs for the tasks of recommendation. Specifically, TinyKG uses exact activations in the forward pass while storing a quantized version of activations in the GPU buffers. During the backward pass, these low-precision activations are dequantized back to full-precision tensors, in order to compute gradients. To reduce the quantization errors, TinyKG applies a simple yet effective quantization algorithm to compress the activations, which ensures unbiasedness with low variance. As such, the training memory footprint of KGNNs is largely reduced with negligible accuracy loss. To evaluate the performance of our TinyKG, we conduct comprehensive experiments on real-world datasets. We found that our TinyKG with INT2 quantization aggressively reduces the memory footprint of activation maps with $7 \times$, only with $2\%$ loss in accuracy, allowing us to deploy KGNNs on memory-constrained devices.
Zero-shot quantization is a promising approach for developing lightweight deep neural networks when data is inaccessible owing to various reasons, including cost and issues related to privacy. By exploiting the learned parameters ($\mu$ and $\sigma$) of batch normalization layers in an FP32-pre-trained model, zero-shot quantization schemes focus on generating synthetic data. Subsequently, they distill knowledge from the pre-trained model (teacher) to the quantized model (student) such that the quantized model can be optimized with the synthetic dataset. However, thus far, zero-shot quantization has primarily been discussed in the context of quantization-aware training methods, which require task-specific losses and long-term optimization as much as retraining. We thus introduce a post-training quantization scheme for zero-shot quantization that produces high-quality quantized networks within a few hours. Furthermore, we propose a framework called Genie~that generates data suited for quantization. With the data synthesized by Genie, we can produce robust quantized models without real datasets, which is comparable to few-shot quantization. We also propose a post-training quantization algorithm to enhance the performance of quantized models. By combining them, we can bridge the gap between zero-shot and few-shot quantization while significantly improving the quantization performance compared to that of existing approaches. In other words, we can obtain a unique state-of-the-art zero-shot quantization approach. The code is available at \url{https://github.com/SamsungLabs/Genie}.
Performing data-intensive tasks in the von Neumann architecture is challenging to achieve both high performance and power efficiency due to the memory wall bottleneck. Computing-in-memory (CiM) is a promising mitigation approach by enabling parallel in-situ multiply-accumulate (MAC) operations within the memory with support from the peripheral interface and datapath. SRAM-based charge-domain CiM (CD-CiM) has shown its potential of enhanced power efficiency and computing accuracy. However, existing SRAM-based CD-CiM faces scaling challenges to meet the throughput requirement of high-performance multi-bit-quantization applications. This paper presents an SRAM-based high-throughput ReLU-optimized CD-CiM macro. It is capable of completing MAC and ReLU of two signed 8b vectors in one CiM cycle with only one A/D conversion. Along with non-linearity compensation for the analog computing and A/D conversion interfaces, this work achieves 51.2GOPS throughput and 10.3TOPS/W energy efficiency, while showing 88.6% accuracy in the CIFAR-10 dataset.
In recent years, the task of Automatic Music Transcription (AMT), whereby various attributes of music notes are estimated from audio, has received increasing attention. At the same time, the related task of Multi-Pitch Estimation (MPE) remains a challenging but necessary component of almost all AMT approaches, even if only implicitly. In the context of AMT, pitch information is typically quantized to the nominal pitches of the Western music scale. Even in more general contexts, MPE systems typically produce pitch predictions with some degree of quantization. In certain applications of AMT, such as Guitar Tablature Transcription (GTT), it is more meaningful to estimate continuous-valued pitch contours. Guitar tablature has the capacity to represent various playing techniques, some of which involve pitch modulation. Contemporary approaches to AMT do not adequately address pitch modulation, and offer only less quantization at the expense of more model complexity. In this paper, we present a GTT formulation that estimates continuous-valued pitch contours, grouping them according to their string and fret of origin. We demonstrate that for this task, the proposed method significantly improves the resolution of MPE and simultaneously yields tablature estimation results competitive with baseline models.
Mixed-precision quantization has been widely applied on deep neural networks (DNNs) as it leads to significantly better efficiency-accuracy tradeoffs compared to uniform quantization. Meanwhile, determining the exact precision of each layer remains challenging. Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. In this work, we propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability. CSQ stabilizes the bit-level mixed-precision training process with a bi-level gradual continuous sparsification on both the bit values of the quantized weights and the bit selection in determining the quantization precision of each layer. The continuous sparsification scheme enables fully-differentiable training without gradient approximation while achieving an exact quantized model in the end.A budget-aware regularization of total model size enables the dynamic growth and pruning of each layer's precision towards a mixed-precision quantization scheme of the desired size. Extensive experiments show CSQ achieves better efficiency-accuracy tradeoff than previous methods on multiple models and datasets.
The post-training quantization (PTQ) challenge of bringing quantized neural net accuracy close to original has drawn much attention driven by industry demand. Many of the methods emphasize optimization of a specific degree-of-freedom (DoF), such as quantization step size, preconditioning factors, bias fixing, often chained to others in multi-step solutions. Here we rethink quantized network parameterization in HW-aware fashion, towards a unified analysis of all quantization DoF, permitting for the first time their joint end-to-end finetuning. Our single-step simple and extendable method, dubbed quantization-aware finetuning (QFT), achieves 4-bit weight quantization results on-par with SoTA within PTQ constraints of speed and resource.
To alleviate the practical constraints for deploying deep neural networks (DNNs) on edge devices, quantization is widely regarded as one promising technique. It reduces the resource requirements for computational power and storage space by quantizing the weights and/or activation tensors of a DNN into lower bit-width fixed-point numbers, resulting in quantized neural networks (QNNs). While it has been empirically shown to introduce minor accuracy loss, critical verified properties of a DNN might become invalid once quantized. Existing verification methods focus on either individual neural networks (DNNs or QNNs) or quantization error bound for partial quantization. In this work, we propose a quantization error bound verification method, named QEBVerif, where both weights and activation tensors are quantized. QEBVerif consists of two parts, i.e., a differential reachability analysis (DRA) and a mixed-integer linear programming (MILP) based verification method. DRA performs difference analysis between the DNN and its quantized counterpart layer-by-layer to compute a tight quantization error interval efficiently. If DRA fails to prove the error bound, then we encode the verification problem into an equivalent MILP problem which can be solved by off-the-shelf solvers. Thus, QEBVerif is sound, complete, and reasonably efficient. We implement QEBVerif and conduct extensive experiments, showing its effectiveness and efficiency.
Optimal Transport (OT) provides a useful geometric framework to estimate the permutation matrix under unsupervised cross-lingual word embedding (CLWE) models that pose the alignment task as a Wasserstein-Procrustes problem. However, linear programming algorithms and approximate OT solvers via Sinkhorn for computing the permutation matrix come with a significant computational burden since they scale cubically and quadratically, respectively, in the input size. This makes it slow and infeasible to compute OT distances exactly for a larger input size, resulting in a poor approximation quality of the permutation matrix and subsequently a less robust learned transfer function or mapper. This paper proposes an unsupervised projection-based CLWE model called quantized Wasserstein Procrustes (qWP). qWP relies on a quantization step of both the source and target monolingual embedding space to estimate the permutation matrix given a cheap sampling procedure. This approach substantially improves the approximation quality of empirical OT solvers given fixed computational cost. We demonstrate that qWP achieves state-of-the-art results on the Bilingual lexicon Induction (BLI) task.
The tradeoff between performance and inference speed is critical for practical applications. Architecture reparameterization obtains better tradeoffs and it is becoming an increasingly popular ingredient in modern convolutional neural networks. Nonetheless, its quantization performance is usually too poor to deploy (more than 20% top-1 accuracy drop on ImageNet) when INT8 inference is desired. In this paper, we dive into the underlying mechanism of this failure, where the original design inevitably enlarges quantization error. We propose a simple, robust, and effective remedy to have a quantization-friendly structure that also enjoys reparameterization benefits. Our method greatly bridges the gap between INT8 and FP32 accuracy for RepVGG. Without bells and whistles, the top-1 accuracy drop on ImageNet is reduced within 2% by standard post-training quantization. Moreover, our method also achieves similar FP32 performance as RepVGG. Extensive experiments on detection and semantic segmentation tasks verify its generalization.
Learning-based image compression has improved to a level where it can outperform traditional image codecs such as HEVC and VVC in terms of coding performance. In addition to good compression performance, device interoperability is essential for a compression codec to be deployed, i.e., encoding and decoding on different CPUs or GPUs should be error-free and with negligible performance reduction. In this paper, we present a method to solve the device interoperability problem of a state-of-the-art image compression network. We implement quantization to entropy networks which output entropy parameters. We suggest a simple method which can ensure cross-platform encoding and decoding, and can be implemented quickly with minor performance deviation, of 0.3% BD-rate, from floating point model results.
Multiple-input multiple-output (MIMO) systems exploit spatial diversity to facilitate multi-user communications with high spectral efficiency by beamforming. As MIMO systems utilize multiple antennas and radio frequency (RF) chains, they are typically costly to implement and consume high power. A common method to reduce the cost of MIMO receivers is utilizing less RF chains than antennas by employing hybrid analog/digital beamforming (HBF). However, the added analog circuitry involves active components whose consumed power may surpass that saved in RF chain reduction. An additional method to realize power-efficient MIMO systems is to use low-resolution analog-to-digital converters (ADCs), which typically compromises signal recovery accuracy. In this work, we propose a power-efficient hybrid MIMO receiver with low-quantization rate ADCs, by jointly optimizing the analog and digital processing in a hardware-oriented manner using task-specific quantization techniques. To mitigate power consumption on the analog front-end, we utilize efficient analog hardware architecture comprised of sparse low-resolution vector modulators, while accounting for their properties in design to maintain recovery accuracy and mitigate interferers in congested environments. To account for common mismatches induced by non-ideal hardware and inaccurate channel state information, we propose a robust mismatch aware design. Supported by numerical simulations and power analysis, our power-efficient MIMO receiver achieves comparable signal recovery performance to power-hungry fully-digital MIMO receivers using high-resolution ADCs. Furthermore, our receiver outperforms the task-agnostic HBF receivers with low-rate ADCs in recovery accuracy at lower power and successfully copes with hardware mismatches.
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with fewer degrees of freedom, on the dataset. We introduce the frameworks of semiclassical and microlocal analysis to data analysis and develop a novel, yet natural uncertainty principle for extracting fine-scale features of this geometric structure in data, crucially dependent on data-driven approximations to quantum mechanical processes underlying geometric optics. This leads to the first tractable algorithm for approximation of wave dynamics and geodesics on data manifolds with rigorous probabilistic convergence rates under the manifold hypothesis. We demonstrate our algorithm on real-world datasets, including an analysis of population mobility information during the COVID-19 pandemic to achieve four-fold improvement in dimensionality reduction over existing state-of-the-art and reveal anomalous behavior exhibited by less than 1.2% of the entire dataset. Our work initiates the study of data-driven quantum dynamics for analyzing datasets, and we outline several future directions for research.
Transformer language models such as GPT-2 are difficult to quantize because of outliers in activations leading to a large quantization error. To adapt to the error, one must use quantization-aware training, which entails a fine-tuning process based on the dataset and the training pipeline identical to those for the original model. Pretrained language models, however, often do not grant access to their datasets and training pipelines, forcing us to rely on arbitrary ones for fine-tuning. In that case, it is observed that quantization-aware training overfits the model to the fine-tuning data. For quantization without overfitting, we introduce a quantization adapter (Quadapter), a small set of parameters that are learned to make activations quantization-friendly by scaling them channel-wise. It keeps the model parameters unchanged. By applying our method to the challenging task of quantizing GPT-2, we demonstrate that it effectively prevents the overfitting and improves the quantization performance.
We consider the problems of computing the average degree and the size of a given network in a distributed fashion under quantized communication. We present two distributed algorithms which rely on quantized operation (i.e., nodes process and transmit quantized messages), and are able to calculate the exact solutions in a finite number of steps. Furthermore, during the operation of our algorithms, each node is able to determine in a distributed manner whether convergence has been achieved and thus terminate its operation. To the best of the authors' knowledge these algorithms are the first to find the exact solutions under quantized communication (i.e., there is no error in the final calculation). Additionally, note that our network size calculation algorithm is the first in the literature which calculates the exact size of a network in a finite number of steps without introducing a final error. This error in other algorithms can be either due to quantization or asymptotic convergence. In our case, no error is introduced since the desired result is calculated in the form of a fraction involving a quantized numerator and a quantized denominator. Finally, we demonstrate the operation of our algorithms and their potential advantages.
We study the problem of training and certifying adversarially robust quantized neural networks (QNNs). Quantization is a technique for making neural networks more efficient by running them using low-bit integer arithmetic and is therefore commonly adopted in industry. Recent work has shown that floating-point neural networks that have been verified to be robust can become vulnerable to adversarial attacks after quantization, and certification of the quantized representation is necessary to guarantee robustness. In this work, we present quantization-aware interval bound propagation (QA-IBP), a novel method for training robust QNNs. Inspired by advances in robust learning of non-quantized networks, our training algorithm computes the gradient of an abstract representation of the actual network. Unlike existing approaches, our method can handle the discrete semantics of QNNs. Based on QA-IBP, we also develop a complete verification procedure for verifying the adversarial robustness of QNNs, which is guaranteed to terminate and produce a correct answer. Compared to existing approaches, the key advantage of our verification procedure is that it runs entirely on GPU or other accelerator devices. We demonstrate experimentally that our approach significantly outperforms existing methods and establish the new state-of-the-art for training and certifying the robustness of QNNs.