Chenhan D. Yu

Chenhan D. Yu, William B. March, Bo Xiao et al.

We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N \log^2 N $ work), we can solve linear systems with this matrix with $N \log N $ work. Kernel matrices represent pairwise interactions of points in metric spaces. They appear in machine learning, approximation theory, and computational physics. Kernel matrices are typically dense (matrix multiplication scales quadratically with $N$) and ill-conditioned (solves can require 100s of Krylov iterations). Thus, fast algorithms for matrix multiplication and factorization are critical for scalability. Recently we introduced ASKIT, a new method for approximating a kernel matrix that resembles N-body methods. Here we introduce INV-ASKIT, a factorization scheme based on ASKIT. We describe the new method, derive complexity estimates, and conduct an empirical study of its accuracy and scalability. We report results on real-world datasets including "COVTYPE" ($0.5$M points in 54 dimensions), "SUSY" ($4.5$M points in 8 dimensions) and "MNIST" (2M points in 784 dimensions) using shared and distributed memory parallelism. In our largest run we approximately factorize a dense matrix of size 32M $\times$ 32M (generated from points in 64 dimensions) on 4,096 Sandy-Bridge cores. To our knowledge these results improve the state of the art by several orders of magnitude.

Chenhan D. Yu, William B. March, George Biros

Kernel matrices appear in machine learning and non-parametric statistics. Given $N$ points in $d$ dimensions and a kernel function that requires $\mathcal{O}(d)$ work to evaluate, we present an $\mathcal{O}(dN\log N)$-work algorithm for the approximate factorization of a regularized kernel matrix, a common computational bottleneck in the training phase of a learning task. With this factorization, solving a linear system with a kernel matrix can be done with $\mathcal{O}(N\log N)$ work. Our algorithm only requires kernel evaluations and does not require that the kernel matrix admits an efficient global low rank approximation. Instead our factorization only assumes low-rank properties for the off-diagonal blocks under an appropriate row and column ordering. We also present a hybrid method that, when the factorization is prohibitively expensive, combines a partial factorization with iterative methods. As a highlight, we are able to approximately factorize a dense $11M\times11M$ kernel matrix in 2 minutes on 3,072 x86 "Haswell" cores and a $4.5M\times4.5M$ matrix in 1 minute using 4,352 "Knights Landing" cores.

Linnan Wang, Chenhan Yu, Satish Salian et al.

Customizing Convolution Neural Networks (CNN) for production use has been a challenging task for DL practitioners. This paper intends to expedite the model customization with a model hub that contains the optimized models tiered by their inference latency using Neural Architecture Search (NAS). To achieve this goal, we build a distributed NAS system to search on a novel search space that consists of prominent factors to impact latency and accuracy. Since we target GPU, we name the NAS optimized models as GPUNet, which establishes a new SOTA Pareto frontier in inference latency and accuracy. Within 1$ms$, GPUNet is 2x faster than EfficientNet-X and FBNetV3 with even better accuracy. We also validate GPUNet on detection tasks, and GPUNet consistently outperforms EfficientNet-X and FBNetV3 on COCO detection tasks in both latency and accuracy. All of these data validate that our NAS system is effective and generic to handle different design tasks. With this NAS system, we expand GPUNet to cover a wide range of latency targets such that DL practitioners can deploy our models directly in different scenarios.

Sławomir Kierat, Mateusz Sieniawski, Denys Fridman et al.

We propose three novel pruning techniques to improve the cost and results of inference-aware Differentiable Neural Architecture Search (DNAS). First, we introduce Prunode, a stochastic bi-path building block for DNAS, which can search over inner hidden dimensions with O(1) memory and compute complexity. Second, we present an algorithm for pruning blocks within a stochastic layer of the SuperNet during the search. Third, we describe a novel technique for pruning unnecessary stochastic layers during the search. The optimized models resulting from the search are called PruNet and establishes a new state-of-the-art Pareto frontier for NVIDIA V100 in terms of inference latency for ImageNet Top-1 image classification accuracy. PruNet as a backbone also outperforms GPUNet and EfficientNet on the COCO object detection task on inference latency relative to mean Average Precision (mAP).

Chenhan D. Yu, James Levitt, Severin Reiz et al.

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.