We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3.5 times better compression performance than the algorithms based on a neural-network autoencoder and principal component analysis. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.
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In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the alternative hypothesis is a mixture of products of either iid distributions or finite order Markov distributions with stationary transition kernels. The problem is studied under the Neyman-Pearson framework in which our main interest is the maximum error exponent of the second type of error. We derive the optimal achievable error exponent and under a further sufficient condition establish the maximum $\epsilon$-achievable error exponent. It is shown that to obtain the latter, the study of the exponentially strong converse is needed. Using a simple code transfer argument we also establish new results for the Wyner-Ahlswede-K{\"o}rner problem in which the source distribution is a mixture of iid components.
Error-bounded lossy compression is one of the most effective techniques for scientific data reduction. However, the traditional trial-and-error approach used to configure lossy compressors for finding the optimal trade-off between reconstructed data quality and compression ratio is prohibitively expensive. To resolve this issue, we develop a general-purpose analytical ratio-quality model based on the prediction-based lossy compression framework, which can effectively foresee the reduced data quality and compression ratio, as well as the impact of the lossy compressed data on post-hoc analysis quality. Our analytical model significantly improves the prediction-based lossy compression in three use-cases: (1) optimization of predictor by selecting the best-fit predictor; (2) memory compression with a target ratio; and (3) in-situ compression optimization by fine-grained error-bound tuning of various data partitions. We evaluate our analytical model on 10 scientific datasets, demonstrating its high accuracy (93.47% accuracy on average) and low computational cost (up to 18.7X lower than the trial-and-error approach) for estimating the compression ratio and the impact of lossy compression on post-hoc analysis quality. We also verified the high efficiency of our ratio-quality model using different applications across the three use-cases. In addition, the experiment demonstrates that our modeling based approach reduces the time to store the 3D Reverse Time Migration data by up to 3.4X over the traditional solution using 128 CPU cores from 8 compute nodes.
The method of types presented by Csiszar and Korner is a central tool used to develop and analyze the basic properties and constraints on sequences of data over finite alphabets. A central problem considered using these tools is that of data compression, and specifically lossy data compression. In this work we consider this very problem, however, instead of sequences of data we consider directed graphs. We show that given a more natural distortion measure, fitting the data structure of a directed graph, the method of types cannot be applied. The suggested distortion measure aims to preserves the local structure of a directed graph. We build on the recent work of Barvinok and extend the method of types to the two dimensional setting of directed graphs. We see that the extension is quite natural in many ways. Given this extension we provide a lower and upper bound on the rate-distortion problem of lossy compression given the suggested distortion measure.
Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no known bound for the upper limit on lossy compressibility. Correlation structures in the data, choice of compressor and error bound are factors allowing larger compression ratios and improved quality metrics. Analyzing these three factors provides one direction towards quantifying lossy compressibility. As a first step, we explore statistical methods to characterize the correlation structures present in the data and their relationships, through functional models, to compression ratios. We observed a relationship between compression ratios and statistics summarizing correlation structure of the data, which are a first step towards evaluating the theoretical limits of lossy compressibility used to eventually predict compression performance and adapt compressors to correlation structures present in the data.
We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of the generating curves of the axisymmetric surfaces. The proposed numerical methods are based on piecewise linear parametric finite elements. The constructed fully practical schemes satisfy the conservation of the enclosed volume. In addition, we prove the unconditional stability and consider the distribution of vertices for the discretized schemes. The introduced methods are implicit and the resulting nonlinear systems of equations can be solved very efficiently and accurately via the Newton's iterative method. Numerical results are presented to show the accuracy and efficiency of the introduced schemes for computing the considered axisymmetric geometric flows.
We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (I) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proof-of-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems.
We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equation with general equation of state. The method, which is based on an $h-$adaptive Discontinuos Galerkin spatial discretization and on an Additive Runge Kutta IMEX method for time discretization, is tailored for low Mach number applications and allows to simulate low Mach regimes at a significantly reduced computational cost, while maintaining full second order accuracy also for higher Mach number regimes. The method has been implemented in the framework of the deal.II numerical library, whose adaptive mesh refinement capabilities are employed to enhance efficiency. Refinement indicators appropriate for real gas phenomena have been introduced. A number of numerical experiments on classical benchmarks for compressible flows and their extension to real gases demonstrate the properties of the proposed method.
Background: Recently, an extensive amount of research has been focused on compressing and accelerating Deep Neural Networks (DNNs). So far, high compression rate algorithms required the entire training dataset, or its subset, for fine-tuning and low precision calibration process. However, this requirement is unacceptable when sensitive data is involved as in medical and biometric use-cases. Contributions: We present three methods for generating synthetic samples from trained models. Then, we demonstrate how these samples can be used to fine-tune or to calibrate quantized models with negligible accuracy degradation compared to the original training set --- without using any real data in the process. Furthermore, we suggest that our best performing method, leveraging intrinsic batch normalization layers' statistics of a trained model, can be used to evaluate data similarity. Our approach opens a path towards genuine data-free model compression, alleviating the need for training data during deployment.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
Like any large software system, a full-fledged DBMS offers an overwhelming amount of configuration knobs. These range from static initialisation parameters like buffer sizes, degree of concurrency, or level of replication to complex runtime decisions like creating a secondary index on a particular column or reorganising the physical layout of the store. To simplify the configuration, industry grade DBMSs are usually shipped with various advisory tools, that provide recommendations for given workloads and machines. However, reality shows that the actual configuration, tuning, and maintenance is usually still done by a human administrator, relying on intuition and experience. Recent work on deep reinforcement learning has shown very promising results in solving problems, that require such a sense of intuition. For instance, it has been applied very successfully in learning how to play complicated games with enormous search spaces. Motivated by these achievements, in this work we explore how deep reinforcement learning can be used to administer a DBMS. First, we will describe how deep reinforcement learning can be used to automatically tune an arbitrary software system like a DBMS by defining a problem environment. Second, we showcase our concept of NoDBA at the concrete example of index selection and evaluate how well it recommends indexes for given workloads.
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