arXiv subjects

Maxim Naumov

Publications and source records attributed to Maxim Naumov.

29 records · Page 2Linked to original sources

arXiv2019

Deep Learning Recommendation Model for Personalization and Recommendation Systems

With the advent of deep learning, neural network-based recommendation models have emerged as an important tool for tackling personalization and recommendation tasks. These networks differ significantly from other deep learning networks due to their need to handle categorical features and are not well studied or understood. In this paper, we develop a state-of-the-art deep learning recommendation model (DLRM) and provide its implementation in both PyTorch and Caffe2 frameworks. In addition, we design a specialized parallelization scheme utilizing model parallelism on the embedding tables to mitigate memory constraints while exploiting data parallelism to scale-out compute from the fully-connected layers. We compare DLRM against existing recommendation models and characterize its performance on the Big Basin AI platform, demonstrating its usefulness as a benchmark for future algorithmic experimentation and system co-design.

cs.IR↗

arXiv2019

Spatial-Winograd Pruning Enabling Sparse Winograd Convolution

Deep convolutional neural networks (CNNs) are deployed in various applications but demand immense computational requirements. Pruning techniques and Winograd convolution are two typical methods to reduce the CNN computation. However, they cannot be directly combined because Winograd transformation fills in the sparsity resulting from pruning. Li et al. (2017) propose sparse Winograd convolution in which weights are directly pruned in the Winograd domain, but this technique is not very practical because Winograd-domain retraining requires low learning rates and hence significantly longer training time. Besides, Liu et al. (2018) move the ReLU function into the Winograd domain, which can help increase the weight sparsity but requires changes in the network structure. To achieve a high Winograd-domain weight sparsity without changing network structures, we propose a new pruning method, spatial-Winograd pruning. As the first step, spatial-domain weights are pruned in a structured way, which efficiently transfers the spatial-domain sparsity into the Winograd domain and avoids Winograd-domain retraining. For the next step, we also perform pruning and retraining directly in the Winograd domain but propose to use an importance factor matrix to adjust weight importance and weight gradients. This adjustment makes it possible to effectively retrain the pruned Winograd-domain network without changing the network structure. For the three models on the datasets of CIFAR10, CIFAR-100, and ImageNet, our proposed method can achieve the Winograd domain sparsities of 63%, 50%, and 74%, respectively.

cs.CV↗

arXiv2019

On the Dimensionality of Embeddings for Sparse Features and Data

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse probability distributions, that can be used to represent sparse features or data, may or not reduce the dimensionality of the item space. However, the embeddings do provide a different and often more meaningful representation of the items for a particular task at hand. Also, we give upper bounds and more precise guidelines for choosing the embedding dimension.

cs.LG↗

arXiv2018

Deep Learning Inference in Facebook Data Centers: Characterization, Performance Optimizations and Hardware Implications

The application of deep learning techniques resulted in remarkable improvement of machine learning models. In this paper provides detailed characterizations of deep learning models used in many Facebook social network services. We present computational characteristics of our models, describe high performance optimizations targeting existing systems, point out their limitations and make suggestions for the future general-purpose/accelerated inference hardware. Also, we highlight the need for better co-design of algorithms, numerics and computing platforms to address the challenges of workloads often run in data centers.

cs.LG↗

arXiv2018

On Periodic Functions as Regularizers for Quantization of Neural Networks

Deep learning models have been successfully used in computer vision and many other fields. We propose an unorthodox algorithm for performing quantization of the model parameters. In contrast with popular quantization schemes based on thresholds, we use a novel technique based on periodic functions, such as continuous trigonometric sine or cosine as well as non-continuous hat functions. We apply these functions component-wise and add the sum over the model parameters as a regularizer to the model loss during training. The frequency and amplitude hyper-parameters of these functions can be adjusted during training. The regularization pushes the weights into discrete points that can be encoded as integers. We show that using this technique the resulting quantized models exhibit the same accuracy as the original ones on CIFAR-10 and ImageNet datasets.

cs.LG↗

arXiv2018

Bandana: Using Non-volatile Memory for Storing Deep Learning Models

Typical large-scale recommender systems use deep learning models that are stored on a large amount of DRAM. These models often rely on embeddings, which consume most of the required memory. We present Bandana, a storage system that reduces the DRAM footprint of embeddings, by using Non-volatile Memory (NVM) as the primary storage medium, with a small amount of DRAM as cache. The main challenge in storing embeddings on NVM is its limited read bandwidth compared to DRAM. Bandana uses two primary techniques to address this limitation: first, it stores embedding vectors that are likely to be read together in the same physical location, using hypergraph partitioning, and second, it decides the number of embedding vectors to cache in DRAM by simulating dozens of small caches. These techniques allow Bandana to increase the effective read bandwidth of NVM by 2-3x and thereby significantly reduce the total cost of ownership.

cs.LG↗

arXiv2018

AdaBatch: Adaptive Batch Sizes for Training Deep Neural Networks

Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer more parallelism and hence better computational efficiency. We have developed a new training approach that, rather than statically choosing a single batch size for all epochs, adaptively increases the batch size during the training process. Our method delivers the convergence rate of small batch sizes while achieving performance similar to large batch sizes. We analyse our approach using the standard AlexNet, ResNet, and VGG networks operating on the popular CIFAR-10, CIFAR-100, and ImageNet datasets. Our results demonstrate that learning with adaptive batch sizes can improve performance by factors of up to 6.25 on 4 NVIDIA Tesla P100 GPUs while changing accuracy by less than 1% relative to training with fixed batch sizes.

cs.LG↗

arXiv2017

Parallel Complexity of Forward and Backward Propagation

We show that the forward and backward propagation can be formulated as a solution of lower and upper triangular systems of equations. For standard feedforward (FNNs) and recurrent neural networks (RNNs) the triangular systems are always block bi-diagonal, while for a general computation graph (directed acyclic graph) they can have a more complex triangular sparsity pattern. We discuss direct and iterative parallel algorithms that can be used for their solution and interpreted as different ways of performing model parallelism. Also, we show that for FNNs and RNNs with $k$ layers and $τ$ time steps the backward propagation can be performed in parallel in O($\log k$) and O($\log k \log τ$) steps, respectively. Finally, we outline the generalization of this technique using Jacobians that potentially allows us to handle arbitrary layers.

cs.LG↗

arXiv2017

Feedforward and Recurrent Neural Networks Backward Propagation and Hessian in Matrix Form

In this paper we focus on the linear algebra theory behind feedforward (FNN) and recurrent (RNN) neural networks. We review backward propagation, including backward propagation through time (BPTT). Also, we obtain a new exact expression for Hessian, which represents second order effects. We show that for $t$ time steps the weight gradient can be expressed as a rank-$t$ matrix, while the weight Hessian is as a sum of $t^{2}$ Kronecker products of rank-$1$ and $W^{T}AW$ matrices, for some matrix $A$ and weight matrix $W$. Also, we show that for a mini-batch of size $r$, the weight update can be expressed as a rank-$rt$ matrix. Finally, we briefly comment on the eigenvalues of the Hessian matrix.

cs.LG↗

arXiv2010

Exact Calculation of Entanglement in a 19-site 2D Spin System

Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-1/2 particles in a two dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter $λ$ = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $λ$ shows that the system exhibits a quantum phase transition at about $λ_c$ = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.

quant-ph↗

arXiv2009

Multimillion Atom Simulations with NEMO 3-D

The rapid progress in nanofabrication technologies has led to the emergence of new classes of nanodevices and structures. At the atomic scale of novel nanostructured semiconductors the distinction between new device and new material is blurred and device physics and material science meet. The quantum mechanical effects in the electronic states of the device and the granular, atomistic representation of the underlying material become important. The variety of geometries, materials, and doping configurations in semiconductor devices at the nanoscale suggests that a general nanoelectronic modeling tool is needed. The Nanoelectronic Modeling tool (NEMO 3-D) has been developed to address these needs. Based on the atomistic valence-force field (VFF) method and a variety of nearest-neighbor tight-binding models, NEMO 3-D enables the computation of strain for over 64 million atoms and of electronic structure for over 52 million atoms, corresponding to volumes of (110nmx110nmx110nm) and (101nmx101nmx101nm), respectively. This article discusses the theoretical models, essential algorithmic and computational components, and optimization methods that have been used in the development and the deployment of NEMO 3-D. Also, successful applications of NEMO 3-D are demonstrated in the atomistic calculation of single-particle electronic states of (1) self-assembled quantum dots including long-range strain and piezoelectricity; (2) stacked quantum dots ; (3) Phosphorus impurities in Silicon used in quantum computation; (4) Si on SiGe quantum wells (QWs); and (5) SiGe nanowires.

physics.comp-ph↗