arXiv subjects

Pradeep Dubey

Publications and source records attributed to Pradeep Dubey.

34 records · Page 2Linked to original sources

arXiv2017

Ternary Residual Networks

Sub-8-bit representation of DNNs incur some discernible loss of accuracy despite rigorous (re)training at low-precision. Such loss of accuracy essentially makes them equivalent to a much shallower counterpart, diminishing the power of being deep networks. To address this problem of accuracy drop we introduce the notion of \textit{residual networks} where we add more low-precision edges to sensitive branches of the sub-8-bit network to compensate for the lost accuracy. Further, we present a perturbation theory to identify such sensitive edges. Aided by such an elegant trade-off between accuracy and compute, the 8-2 model (8-bit activations, ternary weights), enhanced by ternary residual edges, turns out to be sophisticated enough to achieve very high accuracy ($\sim 1\%$ drop from our FP-32 baseline), despite $\sim 1.6\times$ reduction in model size, $\sim 26\times$ reduction in number of multiplications, and potentially $\sim 2\times$ power-performance gain comparing to 8-8 representation, on the state-of-the-art deep network ResNet-101 pre-trained on ImageNet dataset. Moreover, depending on the varying accuracy requirements in a dynamic environment, the deployed low-precision model can be upgraded/downgraded on-the-fly by partially enabling/disabling residual connections. For example, disabling the least important residual connections in the above enhanced network, the accuracy drop is $\sim 2\%$ (from FP32), despite $\sim 1.9\times$ reduction in model size, $\sim 32\times$ reduction in number of multiplications, and potentially $\sim 2.3\times$ power-performance gain comparing to 8-8 representation. Finally, all the ternary connections are sparse in nature, and the ternary residual conversion can be done in a resource-constraint setting with no low-precision (re)training.

cs.IT↗

arXiv2017

Galactos: Computing the Anisotropic 3-Point Correlation Function for 2 Billion Galaxies

The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random distribution of galaxies. However, the 3PCF's formidable computational expense has prevented its application to astronomical surveys comprising millions to billions of galaxies. We present Galactos, a high-performance implementation of a novel, O(N^2) algorithm that uses a load-balanced k-d tree and spherical harmonic expansions to compute the anisotropic 3PCF. Our implementation is optimized for the Intel Xeon Phi architecture, exploiting SIMD parallelism, instruction and thread concurrency, and significant L1 and L2 cache reuse, reaching 39% of peak performance on a single node. Galactos scales to the full Cori system, achieving 9.8PF (peak) and 5.06PF (sustained) across 9636 nodes, making the 3PCF easily computable for all galaxies in the observable universe.

astro-ph.CO↗

arXiv2017

Deep Learning at 15PF: Supervised and Semi-Supervised Classification for Scientific Data

This paper presents the first, 15-PetaFLOP Deep Learning system for solving scientific pattern classification problems on contemporary HPC architectures. We develop supervised convolutional architectures for discriminating signals in high-energy physics data as well as semi-supervised architectures for localizing and classifying extreme weather in climate data. Our Intelcaffe-based implementation obtains $\sim$2TFLOP/s on a single Cori Phase-II Xeon-Phi node. We use a hybrid strategy employing synchronous node-groups, while using asynchronous communication across groups. We use this strategy to scale training of a single model to $\sim$9600 Xeon-Phi nodes; obtaining peak performance of 11.73-15.07 PFLOP/s and sustained performance of 11.41-13.27 PFLOP/s. At scale, our HEP architecture produces state-of-the-art classification accuracy on a dataset with 10M images, exceeding that achieved by selections on high-level physics-motivated features. Our semi-supervised architecture successfully extracts weather patterns in a 15TB climate dataset. Our results demonstrate that Deep Learning can be optimized and scaled effectively on many-core, HPC systems.

cs.PF↗

arXiv2017

Faster CNNs with Direct Sparse Convolutions and Guided Pruning

Phenomenally successful in practical inference problems, convolutional neural networks (CNN) are widely deployed in mobile devices, data centers, and even supercomputers. The number of parameters needed in CNNs, however, are often large and undesirable. Consequently, various methods have been developed to prune a CNN once it is trained. Nevertheless, the resulting CNNs offer limited benefits. While pruning the fully connected layers reduces a CNN's size considerably, it does not improve inference speed noticeably as the compute heavy parts lie in convolutions. Pruning CNNs in a way that increase inference speed often imposes specific sparsity structures, thus limiting the achievable sparsity levels. We present a method to realize simultaneously size economy and speed improvement while pruning CNNs. Paramount to our success is an efficient general sparse-with-dense matrix multiplication implementation that is applicable to convolution of feature maps with kernels of arbitrary sparsity patterns. Complementing this, we developed a performance model that predicts sweet spots of sparsity levels for different layers and on different computer architectures. Together, these two allow us to demonstrate 3.1--7.3$\times$ convolution speedups over dense convolution in AlexNet, on Intel Atom, Xeon, and Xeon Phi processors, spanning the spectrum from mobile devices to supercomputers. We also open source our project at https://github.com/IntelLabs/SkimCaffe.

cs.CV↗

arXiv2017

Ternary Neural Networks with Fine-Grained Quantization

We propose a novel fine-grained quantization (FGQ) method to ternarize pre-trained full precision models, while also constraining activations to 8 and 4-bits. Using this method, we demonstrate a minimal loss in classification accuracy on state-of-the-art topologies without additional training. We provide an improved theoretical formulation that forms the basis for a higher quality solution using FGQ. Our method involves ternarizing the original weight tensor in groups of $N$ weights. Using $N=4$, we achieve Top-1 accuracy within $3.7\%$ and $4.2\%$ of the baseline full precision result for Resnet-101 and Resnet-50 respectively, while eliminating $75\%$ of all multiplications. These results enable a full 8/4-bit inference pipeline, with best-reported accuracy using ternary weights on ImageNet dataset, with a potential of $9\times$ improvement in performance. Also, for smaller networks like AlexNet, FGQ achieves state-of-the-art results. We further study the impact of group size on both performance and accuracy. With a group size of $N=64$, we eliminate $\approx99\%$ of the multiplications; however, this introduces a noticeable drop in accuracy, which necessitates fine tuning the parameters at lower precision. We address this by fine-tuning Resnet-50 with 8-bit activations and ternary weights at $N=64$, improving the Top-1 accuracy to within $4\%$ of the full precision result with $<30\%$ additional training overhead. Our final quantized model can run on a full 8-bit compute pipeline using 2-bit weights and has the potential of up to $15\times$ improvement in performance compared to baseline full-precision models.

cs.LG↗

arXiv2016

Parallelizing Word2Vec in Multi-Core and Many-Core Architectures

Word2vec is a widely used algorithm for extracting low-dimensional vector representations of words. State-of-the-art algorithms including those by Mikolov et al. have been parallelized for multi-core CPU architectures, but are based on vector-vector operations with "Hogwild" updates that are memory-bandwidth intensive and do not efficiently use computational resources. In this paper, we propose "HogBatch" by improving reuse of various data structures in the algorithm through the use of minibatching and negative sample sharing, hence allowing us to express the problem using matrix multiply operations. We also explore different techniques to distribute word2vec computation across nodes in a compute cluster, and demonstrate good strong scalability up to 32 nodes. The new algorithm is particularly suitable for modern multi-core/many-core architectures, especially Intel's latest Knights Landing processors, and allows us to scale up the computation near linearly across cores and nodes, and process hundreds of millions of words per second, which is the fastest word2vec implementation to the best of our knowledge.

cs.DC↗

arXiv2016

Parallelizing Word2Vec in Shared and Distributed Memory

Word2Vec is a widely used algorithm for extracting low-dimensional vector representations of words. It generated considerable excitement in the machine learning and natural language processing (NLP) communities recently due to its exceptional performance in many NLP applications such as named entity recognition, sentiment analysis, machine translation and question answering. State-of-the-art algorithms including those by Mikolov et al. have been parallelized for multi-core CPU architectures but are based on vector-vector operations that are memory-bandwidth intensive and do not efficiently use computational resources. In this paper, we improve reuse of various data structures in the algorithm through the use of minibatching, hence allowing us to express the problem using matrix multiply operations. We also explore different techniques to distribute word2vec computation across nodes in a compute cluster, and demonstrate good strong scalability up to 32 nodes. In combination, these techniques allow us to scale up the computation near linearly across cores and nodes, and process hundreds of millions of words per second, which is the fastest word2vec implementation to the best of our knowledge.

cs.DC↗

arXiv2016

PANDA: Extreme Scale Parallel K-Nearest Neighbor on Distributed Architectures

Computing $k$-Nearest Neighbors (KNN) is one of the core kernels used in many machine learning, data mining and scientific computing applications. Although kd-tree based $O(\log n)$ algorithms have been proposed for computing KNN, due to its inherent sequentiality, linear algorithms are being used in practice. This limits the applicability of such methods to millions of data points, with limited scalability for Big Data analytics challenges in the scientific domain. In this paper, we present parallel and highly optimized kd-tree based KNN algorithms (both construction and querying) suitable for distributed architectures. Our algorithm includes novel approaches for pruning search space and improving load balancing and partitioning among nodes and threads. Using TB-sized datasets from three science applications: astrophysics, plasma physics, and particle physics, we show that our implementation can construct kd-tree of 189 billion particles in 48 seconds on utilizing $\sim$50,000 cores. We also demonstrate computation of KNN of 19 billion queries in 12 seconds. We demonstrate almost linear speedup both for shared and distributed memory computers. Our algorithms outperforms earlier implementations by more than order of magnitude; thereby radically improving the applicability of our implementation to state-of-the-art Big Data analytics problems. In addition, we showcase performance and scalability on the recently released Intel Xeon Phi processor showing that our algorithm scales well even on massively parallel architectures.

cs.DC↗

arXiv2016

BlackOut: Speeding up Recurrent Neural Network Language Models With Very Large Vocabularies

We propose BlackOut, an approximation algorithm to efficiently train massive recurrent neural network language models (RNNLMs) with million word vocabularies. BlackOut is motivated by using a discriminative loss, and we describe a new sampling strategy which significantly reduces computation while improving stability, sample efficiency, and rate of convergence. One way to understand BlackOut is to view it as an extension of the DropOut strategy to the output layer, wherein we use a discriminative training loss and a weighted sampling scheme. We also establish close connections between BlackOut, importance sampling, and noise contrastive estimation (NCE). Our experiments, on the recently released one billion word language modeling benchmark, demonstrate scalability and accuracy of BlackOut; we outperform the state-of-the art, and achieve the lowest perplexity scores on this dataset. Moreover, unlike other established methods which typically require GPUs or CPU clusters, we show that a carefully implemented version of BlackOut requires only 1-10 days on a single machine to train a RNNLM with a million word vocabulary and billions of parameters on one billion words. Although we describe BlackOut in the context of RNNLM training, it can be used to any networks with large softmax output layers.

cs.LG↗

arXiv2016

Distributed Deep Learning Using Synchronous Stochastic Gradient Descent

We design and implement a distributed multinode synchronous SGD algorithm, without altering hyper parameters, or compressing data, or altering algorithmic behavior. We perform a detailed analysis of scaling, and identify optimal design points for different networks. We demonstrate scaling of CNNs on 100s of nodes, and present what we believe to be record training throughputs. A 512 minibatch VGG-A CNN training run is scaled 90X on 128 nodes. Also 256 minibatch VGG-A and OverFeat-FAST networks are scaled 53X and 42X respectively on a 64 node cluster. We also demonstrate the generality of our approach via best-in-class 6.5X scaling for a 7-layer DNN on 16 nodes. Thereafter we attempt to democratize deep-learning by training on an Ethernet based AWS cluster and show ~14X scaling on 16 nodes.

cs.DC↗

arXiv2015

Money as Minimal Complexity

We consider mechanisms that provide traders the opportunity to exchange commodity $i$ for commodity $j$, for certain ordered pairs $ij$. Given any connected graph $G$ of opportunities, we show that there is a unique mechanism $M_{G}$ that satisfies some natural conditions of "fairness" and "convenience". Let $\mathfrak{M}(m)$ denote the class of mechanisms $M_{G}$ obtained by varying $G$ on the commodity set $\left\{1,\ldots,m\right\} $. We define the complexity of a mechanism $M$ in $\mathfrak{M(m)}$ to be a certain pair of integers $τ(M),π(M)$ which represent the time required to exchange $i$ for $j$ and the information needed to determine the exchange ratio (each in the worst case scenario, across all $i\neq j$). This induces a quasiorder $\preceq$ on $\mathfrak{M}(m)$ by the rule \[ M\preceq M^{\prime}\text{if}τ(M)\leqτ(M^{\prime})\text{and}π(M)\leqπ(M^{\prime}). \] We show that, for $m>3$, there are precisely three $\preceq$-minimal mechanisms $M_{G}$ in $\mathfrak{M}(m)$, where $G$ corresponds to the star, cycle and complete graphs. The star mechanism has a distinguished commodity -- the money -- that serves as the sole medium of exchange and mediates trade between decentralized markets for the other commodities. Our main result is that, for any weights $λ,μ>0,$ the star mechanism is the unique minimizer of $λτ(M)+μπ(M)$ on $\mathfrak{M}(m)$ for large enough $m$.

cs.GT↗

arXiv2015

Graphical Exchange Mechanisms

Consider an exchange mechanism which accepts diversified offers of various commodities and redistributes everything it receives. We impose certain conditions of fairness and convenience on such a mechanism and show that it admits unique prices, which equalize the value of offers and returns for each individual. We next define the complexity of a mechanism in terms of certain integers $τ_{ij},π_{ij}$ and $k_{i}$ that represent the time required to exchange $i$ for $j$, the difficulty in determining the exchange ratio, and the dimension of the message space. We show that there are a finite number of minimally complex mechanisms, in each of which all trade is conducted through markets for commodity pairs. Finally we consider minimal mechanisms with smallest worst-case complexities $τ=\maxτ_{ij}$ and $π=\maxπ_{ij}$. For $m>3$ commodities, there are precisely three such mechanisms, one of which has a distinguished commodity -- the money -- that serves as the sole medium of exchange. As $m\rightarrow \infty$ the money mechanism is the only one with bounded $\left( π,τ\right) $.

cs.GT↗

arXiv2015

GraphMat: High performance graph analytics made productive

Given the growing importance of large-scale graph analytics, there is a need to improve the performance of graph analysis frameworks without compromising on productivity. GraphMat is our solution to bridge this gap between a user-friendly graph analytics framework and native, hand-optimized code. GraphMat functions by taking vertex programs and mapping them to high performance sparse matrix operations in the backend. We get the productivity benefits of a vertex programming framework without sacrificing performance. GraphMat is in C++, and we have been able to write a diverse set of graph algorithms in this framework with the same effort compared to other vertex programming frameworks. GraphMat performs 1.2-7X faster than high performance frameworks such as GraphLab, CombBLAS and Galois. It achieves better multicore scalability (13-15X on 24 cores) than other frameworks and is 1.2X off native, hand-optimized code on a variety of different graph algorithms. Since GraphMat performance depends mainly on a few scalable and well-understood sparse matrix operations, GraphMatcan naturally benefit from the trend of increasing parallelism on future hardware.

cs.PF↗

arXiv2015

Decentralization of a Machine: Some Definitions

We define some notions of the decentralization of a deterministic input-output machine. This opens the possibility for introducing game-theoretic elements -- such as strategic players -- inside the machine, as part of its design.

cs.CC↗

arXiv2014

Lattice QCD with Domain Decomposition on Intel Xeon Phi Co-Processors

The gap between the cost of moving data and the cost of computing continues to grow, making it ever harder to design iterative solvers on extreme-scale architectures. This problem can be alleviated by alternative algorithms that reduce the amount of data movement. We investigate this in the context of Lattice Quantum Chromodynamics and implement such an alternative solver algorithm, based on domain decomposition, on Intel Xeon Phi co-processor (KNC) clusters. We demonstrate close-to-linear on-chip scaling to all 60 cores of the KNC. With a mix of single- and half-precision the domain-decomposition method sustains 400-500 Gflop/s per chip. Compared to an optimized KNC implementation of a standard solver [1], our full multi-node domain-decomposition solver strong-scales to more nodes and reduces the time-to-solution by a factor of 5.

hep-lat↗

arXiv2011

Fast Updates on Read-Optimized Databases Using Multi-Core CPUs

Read-optimized columnar databases use differential updates to handle writes by maintaining a separate write-optimized delta partition which is periodically merged with the read-optimized and compressed main partition. This merge process introduces significant overheads and unacceptable downtimes in update intensive systems, aspiring to combine transactional and analytical workloads into one system. In the first part of the paper, we report data analyses of 12 SAP Business Suite customer systems. In the second half, we present an optimized merge process reducing the merge overhead of current systems by a factor of 30. Our linear-time merge algorithm exploits the underlying high compute and bandwidth resources of modern multi-core CPUs with architecture-aware optimizations and efficient parallelization. This enables compressed in-memory column stores to handle the transactional update rate required by enterprise applications, while keeping properties of read-optimized databases for analytic-style queries.

cs.DB↗