Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work, we introduce an algorithm that removes units and layers of a neural network while not changing the output that is produced, which thus implies a lossless compression. This algorithm, which we denote as LEO (Lossless Expressiveness Optimization), relies on Mixed-Integer Linear Programming (MILP) to identify Rectified Linear Units (ReLUs) with linear behavior over the input domain. By using L1 regularization to induce such behavior, we can benefit from training over a larger architecture than we would later use in the environment where the trained neural network is deployed.
We make the following striking observation: fully convolutional VAE models trained on 32x32 ImageNet can generalize well, not just to 64x64 but also to far larger photographs, with no changes to the model. We use this property, applying fully convolutional models to lossless compression, demonstrating a method to scale the VAE-based 'Bits-Back with ANS' algorithm for lossless compression to large color photographs, and achieving state of the art for compression of full size ImageNet images. We release Craystack, an open source library for convenient prototyping of lossless compression using pr…
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；University College London（伦敦大学学院）
The recently proposed Neural Local Lossless Compression (NeLLoC), which is based on a local autoregressive model, has achieved state-of-the-art (SOTA) out-of-distribution (OOD) generalization performance in the image compression task. In addition to the encouragement of OOD generalization, the local model also allows parallel inference in the decoding stage. In this paper, we propose two parallelization schemes for local autoregressive models. We discuss the practicalities of implementing the schemes and provide experimental evidence of significant gains in compression runtime compared to the …
In this work, we establish an asymptotic limit of almost-lossless compression of a random, finite alphabet tensor which admits a low-rank canonical polyadic decomposition.
ETH Zurich（苏黎世联邦理工学院）；Google Research, Brain Team（谷歌研究院（大脑团队））
We leverage the powerful lossy image compression algorithm BPG to build a lossless image compression system. Specifically, the original image is first decomposed into the lossy reconstruction obtained after compressing it with BPG and the corresponding residual. We then model the distribution of the residual with a convolutional neural network-based probabilistic model that is conditioned on the BPG reconstruction, and combine it with entropy coding to losslessly encode the residual. Finally, the image is stored using the concatenation of the bitstreams produced by BPG and the learned residual…
We introduce a simple and efficient lossless image compression algorithm. We store a low resolution version of an image as raw pixels, followed by several iterations of lossless super-resolution. For lossless super-resolution, we predict the probability of a high-resolution image, conditioned on the low-resolution input, and use entropy coding to compress this super-resolution operator. Super-Resolution based Compression (SReC) is able to achieve state-of-the-art compression rates with practical runtimes on large datasets. Code is available online at https://github.com/caoscott/SReC.
UvA-Bosch Delta Lab（阿姆斯特丹大学-博世德尔塔实验室）；University of Amsterdam（阿姆斯特丹大学）；Google（谷歌）
Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich tr…
We develop a simple and elegant method for lossless compression using latent variable models, which we call 'bits back with asymmetric numeral systems' (BB-ANS). The method involves interleaving encode and decode steps, and achieves an optimal rate when compressing batches of data. We demonstrate it firstly on the MNIST test set, showing that state-of-the-art lossless compression is possible using a small variational autoencoder (VAE) model. We then make use of a novel empirical insight, that fully convolutional generative models, trained on small images, are able to generalize to images of ar…
In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete nature makes them particularly suitable for lossless compression with entropy coding schemes. We start by investigating a recent theoretical claim that states that invertible flows for discrete random variables are less flexible than their continuous counterparts. We demonstrate with a proof that this claim does not hold for integer discrete flows due to the …
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generali…
It is nontrivial to store rapidly growing big data nowadays, which demands high-performance lossless compression techniques. Likelihood-based generative models have witnessed their success on lossless compression, where flow based models are desirable in allowing exact data likelihood optimisation with bijective mappings. However, common continuous flows are in contradiction with the discreteness of coding schemes, which requires either 1) imposing strict constraints on flow models that degrades the performance or 2) coding numerous bijective mapping errors which reduces the efficiency. In thi…
University College London（伦敦大学学院）；University of Edinburgh（爱丁堡大学）
We generalize the 'bits back with ANS' method to time-series models with a latent Markov structure. This family of models includes hidden Markov models (HMMs), linear Gaussian state space models (LGSSMs) and many more. We provide experimental evidence that our method is effective for small scale models, and discuss its applicability to larger scale settings such as video compression.
The Variational Auto-Encoder (VAE) is a simple, efficient, and popular deep maximum likelihood model. Though usage of VAEs is widespread, the derivation of the VAE is not as widely understood. In this tutorial, we will provide an overview of the VAE and a tour through various derivations and interpretations of the VAE objective. From a probabilistic standpoint, we will examine the VAE through the lens of Bayes' Rule, importance sampling, and the change-of-variables formula. From an information theoretic standpoint, we will examine the VAE through the lens of lossless compression and transmissi…
Deep latent variable models have seen recent success in many data domains. Lossless compression is an application of these models which, despite having the potential to be highly useful, has yet to be implemented in a practical manner. We present `Bits Back with ANS' (BB-ANS), a scheme to perform lossless compression with latent variable models at a near optimal rate. We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model (VAE), achieving compression rates superior to standard methods with only a simple VAE. Given that the scheme is highly am…
In this paper, the problem of optimal gradient lossless compression in Deep Neural Network (DNN) training is considered. Gradient compression is relevant in many distributed DNN training scenarios, including the recently popular federated learning (FL) scenario in which each remote users are connected to the parameter server (PS) through a noiseless but rate limited channel. In distributed DNN training, if the underlying gradient distribution is available, classical lossless compression approaches can be used to reduce the number of bits required for communicating the gradient entries. Mean fi…
JPEG images can be further compressed to enhance the storage and transmission of large-scale image datasets. Existing learned lossless compressors for RGB images cannot be well transferred to JPEG images due to the distinguishing distribution of DCT coefficients and raw pixels. In this paper, we propose a novel framework for learned lossless compression of JPEG images that achieves end-to-end optimized prediction of the distribution of decoded DCT coefficients. To enable learning in the frequency domain, DCT coefficients are partitioned into groups to utilize implicit local redundancy. An auto…
In recent years, several point cloud geometry compression methods that utilize advanced deep learning techniques have been proposed, but there are limited works on attribute compression, especially lossless compression. In this work, we build an end-to-end multiscale point cloud attribute coding method (MNeT) that progressively projects the attributes onto multiscale latent spaces. The multiscale architecture provides an accurate context for the attribute probability modeling and thus minimizes the coding bitrate with a single network prediction. Besides, our method allows scalable coding that…
This work is motivated by the necessity to automate the discovery of structure in vast and evergrowing collection of relational data commonly represented as graphs, for example genomic networks. A novel algorithm, dubbed Graphitour, for structure induction by lossless graph compression is presented and illustrated by a clear and broadly known case of nested structure in a DNA molecule. This work extends to graphs some well established approaches to grammatical inference previously applied only to strings. The bottom-up graph compression problem is related to the maximum cardinality (non-bipart…
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Tel Aviv University（特拉维夫大学）
Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of the dataset. This phenomenon results in an increasing demand for storage space, which may be very costly. This problem mostly manifests in a subscriber based environment, where a user-specific ensemble needs to be stored on a personal device with strict storage limitations (such as a cellular device). In this work we introduce a novel method for lossless compr…
It was estimated that the world produced $59 ZB$ ($5.9 \times 10^{13} GB$) of data in 2020, resulting in the enormous costs of both data storage and transmission. Fortunately, recent advances in deep generative models have spearheaded a new class of so-called "neural compression" algorithms, which significantly outperform traditional codecs in terms of compression ratio. Unfortunately, the application of neural compression garners little commercial interest due to its limited bandwidth; therefore, developing highly efficient frameworks is of critical practical importance. In this paper, we dis…
Nokia Technologies（诺基亚科技）；Tampere University（坦佩雷大学）
Lossless image compression is an important technique for image storage and transmission when information loss is not allowed. With the fast development of deep learning techniques, deep neural networks have been used in this field to achieve a higher compression rate. Methods based on pixel-wise autoregressive statistical models have shown good performance. However, the sequential processing way prevents these methods to be used in practice. Recently, multi-scale autoregressive models have been proposed to address this limitation. Multi-scale approaches can use parallel computing systems effic…
UCLA（加州大学洛杉矶分校）；University of California, Irvine（加州大学欧文分校）
Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This overhead can only be partially eliminated with elaborate schemes such as bits-back coding, often resulting in poor single-sample compression rates. To overcome such problems, we establish a new class of tractable lossless compression models that permit efficient encoding and decoding: Probabilistic Circuits (PCs). These are a class of neural networks involving $|p|…
Lossless Compression: A New Benchmark for Time Series Model Evaluation
Computer Network Information Center, Chinese Academy of Sciences（中国科学院计算机网络信息中心）；University of Science and Technology Beijing（北京科技大学）；North China Electric Power University（华北电力大学）；Software Institute of Chinaunicom（中国unicom软件学院）
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Facebook AI Research（脸书人工智能研究院）；University College London（伦敦大学学院）；University of Oxford（牛津大学）
Latent variable models have been successfully applied in lossless compression with the bits-back coding algorithm. However, bits-back suffers from an increase in the bitrate equal to the KL divergence between the approximate posterior and the true posterior. In this paper, we show how to remove this gap asymptotically by deriving bits-back coding algorithms from tighter variational bounds. The key idea is to exploit extended space representations of Monte Carlo estimators of the marginal likelihood. Naively applied, our schemes would require more initial bits than the standard bits-back coder,…
University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）；TECNUN, University of Navarra（纳瓦拉大学TECNUN）；Stanford University（斯坦福大学）
We consider lossless compression based on statistical data modeling followed by prediction-based encoding, where an accurate statistical model for the input data leads to substantial improvements in compression. We propose DZip, a general-purpose compressor for sequential data that exploits the well-known modeling capabilities of neural networks (NNs) for prediction, followed by arithmetic coding. Dzip uses a novel hybrid architecture based on adaptive and semi-adaptive training. Unlike most NN based compressors, DZip does not require additional training data and is not restricted to specific …
Vector Institute（向量研究所）；The University of British Columbia（英属哥伦比亚大学）；Facebook AI Research（脸书人工智能研究院）；University of Toronto（多伦多大学）
Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1000\times$…
Benchmarking Language Modeling for Lossless Compression of Full-Fidelity Audio
University of California, San Diego, Computer Science and Engineering Department（加州大学圣地亚哥分校计算机科学与工程系）；Carnegie Mellon University, School of Computer Science（卡内基梅隆大学计算机科学学院）
Explicit deep generative models (DGMs), e.g., VAEs and Normalizing Flows, have shown to offer an effective data modelling alternative for lossless compression. However, DGMs themselves normally require large storage space and thus contaminate the advantage brought by accurate data density estimation. To eliminate the requirement of saving separate models for different target datasets, we propose a novel setting that starts from a pretrained deep generative model and compresses the data batches while adapting the model with a dynamical system for only one epoch. We formalise this setting as tha…
We propose the first practical learned lossless image compression system, L3C, and show that it outperforms the popular engineered codecs, PNG, WebP and JPEG 2000. At the core of our method is a fully parallelizable hierarchical probabilistic model for adaptive entropy coding which is optimized end-to-end for the compression task. In contrast to recent autoregressive discrete probabilistic models such as PixelCNN, our method i) models the image distribution jointly with learned auxiliary representations instead of exclusively modeling the image distribution in RGB space, and ii) only requires …
NeuralZip: Reusable Setup for Fast Lossless Compression
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；University of Chile（智利大学）；National Center for Artificial Intelligence (CENIA)（国家人工智能中心（CENIA））
ENEC: A Lossless AI Model Compression Method Enabling Fast Inference on Ascend NPUs
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Huawei Technologies Co., Ltd.（华为技术有限公司）
City University of Hong Kong（香港城市大学）；National Taiwan University（台湾大学）
Deep-learning-based compressor has received interests recently due to much improved compression ratio. However, modern approaches suffer from long execution time. To ease this problem, this paper targets on cutting down the execution time of deep-learning-based compressors. Building history-dependencies sequentially (e.g., recurrent neural networks) is responsible for long inference latency. Instead, we introduce transformer into deep learning compressors to build history-dependencies in parallel. However, existing transformer is too heavy in computation and incompatible to compression tasks. …
Université Paris-Saclay（巴黎-萨克雷大学）；CNRS（法国国家科学研究中心）；CentraleSupelec（中央理工-高等电力学院）；Laboratoire des Signaux et Systèmes（信号与系统实验室）
We propose a practical deep generative approach for lossless point cloud geometry compression, called MSVoxelDNN, and show that it significantly reduces the rate compared to the MPEG G-PCC codec. Our previous work based on autoregressive models (VoxelDNN) has a fast training phase, however, inference is slow as the occupancy probabilities are predicted sequentially, voxel by voxel. In this work, we employ a multiscale architecture which models voxel occupancy in coarse-to-fine order. At each scale, MSVoxelDNN divides voxels into eight conditionally independent groups, thus requiring a single n…
Tsinghua University（清华大学）；Peng Cheng Laboratory（鹏城实验室）；Renmin University of China（中国人民大学）
By applying entropy codecs with learned data distributions, neural compressors have significantly outperformed traditional codecs in terms of compression ratio. However, the high inference latency of neural networks hinders the deployment of neural compressors in practical applications. In this work, we propose Integer-only Discrete Flows (IODF), an efficient neural compressor with integer-only arithmetic. Our work is built upon integer discrete flows, which consists of invertible transformations between discrete random variables. We propose efficient invertible transformations with integer-on…
