arXiv subjects

Andrew Anderson

Publications and source records attributed to Andrew Anderson.

25 records · Page 2Linked to original sources

arXiv2019

Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural Networks

Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, the performance gain is at the expense of a reduction in floating point (FP) numerical accuracy. In this paper, we analyse the worst case FP error and prove the estimation of norm and conditioning of the algorithm. We show that the bound grows exponentially with the size of the convolution, but the error bound of the \textit{modified} algorithm is smaller than the original one. We propose several methods for reducing FP error. We propose a canonical evaluation ordering based on Huffman coding that reduces summation error. We study the selection of sampling "points" experimentally and find empirically good points for the most important sizes. We identify the main factors associated with good points. In addition, we explore other methods to reduce FP error, including mixed-precision convolution, and pairwise summation across DNN channels. Using our methods we can significantly reduce FP error for a given block size, which allows larger block sizes and reduced computation.

math.NA↗

arXiv2018

Optimal DNN Primitive Selection with Partitioned Boolean Quadratic Programming

Deep Neural Networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. Many different algorithms have been proposed to implement the most computationally expensive layers of DNNs. Further, each of these algorithms has a large number of variants, which offer different trade-offs of parallelism, data locality, memory footprint, and execution time. In addition, specific algorithms operate much more efficiently on specialized data layouts and formats. We state the problem of optimal primitive selection in the presence of data format transformations, and show that it is NP-hard by demonstrating an embedding in the Partitioned Boolean Quadratic Assignment problem (PBQP). We propose an analytic solution via a PBQP solver, and evaluate our approach experimentally by optimizing several popular DNNs using a library of more than 70 DNN primitives, on an embedded platform and a general purpose platform. We show experimentally that significant gains are possible versus the state of the art vendor libraries by using a principled analytic solution to the problem of layout selection in the presence of data format transformations.

cs.PF↗

arXiv2017

Toward Foraging for Understanding of StarCraft Agents: An Empirical Study

Assessing and understanding intelligent agents is a difficult task for users that lack an AI background. A relatively new area, called "Explainable AI," is emerging to help address this problem, but little is known about how users would forage through information an explanation system might offer. To inform the development of Explainable AI systems, we conducted a formative study, using the lens of Information Foraging Theory, into how experienced users foraged in the domain of StarCraft to assess an agent. Our results showed that participants faced difficult foraging problems. These foraging problems caused participants to entirely miss events that were important to them, reluctantly choose to ignore actions they did not want to ignore, and bear high cognitive, navigation, and information costs to access the information they needed.

cs.HC↗

arXiv2017

How the Experts Do It: Assessing and Explaining Agent Behaviors in Real-Time Strategy Games

How should an AI-based explanation system explain an agent's complex behavior to ordinary end users who have no background in AI? Answering this question is an active research area, for if an AI-based explanation system could effectively explain intelligent agents' behavior, it could enable the end users to understand, assess, and appropriately trust (or distrust) the agents attempting to help them. To provide insights into this question, we turned to human expert explainers in the real-time strategy domain, "shoutcaster", to understand (1) how they foraged in an evolving strategy game in real time, (2) how they assessed the players' behaviors, and (3) how they constructed pertinent and timely explanations out of their insights and delivered them to their audience. The results provided insights into shoutcasters' foraging strategies for gleaning information necessary to assess and explain the players; a characterization of the types of implicit questions shoutcasters answered; and implications for creating explanations by using the patterns

cs.HC↗

arXiv2017

Low-memory GEMM-based convolution algorithms for deep neural networks

Deep neural networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. A common approach to implementing DNNs is to recast the most computationally expensive operations as general matrix multiplication (GEMM). However, as we demonstrate in this paper, there are a great many different ways to express DNN convolution operations using GEMM. Although different approaches all perform the same number of operations, the size of temporary data structures differs significantly. Convolution of an input matrix with dimensions $C \times H \times W$, requires $O(K^2CHW)$ additional space using the classical im2col approach. More recently memory-efficient approaches requiring just $O(KCHW)$ auxiliary space have been proposed. We present two novel GEMM-based algorithms that require just $O(MHW)$ and $O(KW)$ additional space respectively, where $M$ is the number of channels in the result of the convolution. These algorithms dramatically reduce the space overhead of DNN convolution, making it much more suitable for memory-limited embedded systems. Experimental evaluation shows that our low-memory algorithms are just as fast as the best patch-building approaches despite requiring just a fraction of the amount of additional memory. Our low-memory algorithms have excellent data locality which gives them a further edge over patch-building algorithms when multiple cores are used. As a result, our low memory algorithms often outperform the best patch-building algorithms using multiple threads.

cs.CV↗

arXiv2017

Parallel Multi Channel Convolution using General Matrix Multiplication

Convolutional neural networks (CNNs) have emerged as one of the most successful machine learning technologies for image and video processing. The most computationally intensive parts of CNNs are the convolutional layers, which convolve multi-channel images with multiple kernels. A common approach to implementing convolutional layers is to expand the image into a column matrix (im2col) and perform Multiple Channel Multiple Kernel (MCMK) convolution using an existing parallel General Matrix Multiplication (GEMM) library. This im2col conversion greatly increases the memory footprint of the input matrix and reduces data locality. In this paper we propose a new approach to MCMK convolution that is based on General Matrix Multiplication (GEMM), but not on im2col. Our algorithm eliminates the need for data replication on the input thereby enabling us to apply the convolution kernels on the input images directly. We have implemented several variants of our algorithm on a CPU processor and an embedded ARM processor. On the CPU, our algorithm is faster than im2col in most cases.

cs.CV↗

arXiv2016

Vectorization of Multibyte Floating Point Data Formats

We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and data transfer volume. We describe how our scheme can be accelerated using existing hardware vector units on a general-purpose processor (GPP). Exploiting native vector hardware allows us to support reduced precision floating point with low overhead. We demonstrate that supporting reduced precision in the compiler as opposed to using a library approach can yield a low overhead solution for GPPs.

cs.MS↗