Low-precision arithmetic trains deep learning models using less energy, less memory and less time. However, we pay a price for the savings: lower precision may yield larger round-off error and hence larger prediction error. As applications proliferate, users must choose which precision to use to train a new model, and chip manufacturers must decide which precisions to manufacture. We view these precision choices as a hyperparameter tuning problem, and borrow ideas from meta-learning to learn the tradeoff between memory and error. In this paper, we introduce Pareto Estimation to Pick the Perfect Precision (PEPPP). We use matrix factorization to find non-dominated configurations (the Pareto frontier) with a limited number of network evaluations. For any given memory budget, the precision that minimizes error is a point on this frontier. Practitioners can use the frontier to trade memory for error and choose the best precision for their goals.
Rice University（莱斯大学）；Texas A&M University（德州农工大学）；UC Santa Barbara（加州大学圣巴巴拉分校）
We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruni…
Agency for Science, Technology and Research（新加坡科技研究局）
Learn in-situ is a growing trend for Edge AI. Training deep neural network (DNN) on edge devices is challenging because both energy and memory are constrained. Low precision training helps to reduce the energy cost of a single training iteration, but that does not necessarily translate to energy savings for the whole training process, because low precision could slows down the convergence rate. One evidence is that most works for low precision training keep an fp32 copy of the model during training, which in turn imposes memory requirements on edge devices. In this work we propose Adaptive Pre…
ELMO: Efficiency via Low-precision and Peak Memory Optimization in Large Output Spaces
Department of Computer Science, Aalto University, Espoo, Finland（艾尔沃斯大学计算机科学系）；Department of Computer Science, University of Bath, Bath, UK（巴斯大学计算机科学系）
WealthNet Advisors（财富网顾问公司）；Advanced Digital Sciences Center（高级数字科学中心）
Financial trading is at the forefront of time-series analysis, and has grown hand-in-hand with it. The advent of electronic trading has allowed complex machine learning solutions to enter the field of financial trading. Financial markets have both long term and short term signals and thus a good predictive model in financial trading should be able to incorporate them together. One of the most sought after forms of electronic trading is high-frequency trading (HFT), typically known for microsecond sensitive changes, which results in a tremendous amount of data. LSTMs are one of the most capable…
National School for Computer Science and Systems analysis（国家计算机科学与系统分析学院）；Mohamed V University（穆罕默德五世大学）
The stock market prediction has always been crucial for stakeholders, traders and investors. We developed an ensemble Long Short Term Memory (LSTM) model that includes two-time frequencies (annual and daily parameters) in order to predict the next-day Closing price (one step ahead). Based on a four-step approach, this methodology is a serial combination of two LSTM algorithms. The empirical experiment is applied to 417 NY stock exchange companies. Based on Open High Low Close metrics and other financial ratios, this approach proves that the stock market prediction can be improved.
University of Padova（帕多瓦大学）；University of Calgary（卡尔加里大学）
Experience has shown that trading in stock and cryptocurrency markets has the potential to be highly profitable. In this light, considerable effort has been recently devoted to investigate how to apply machine learning and deep learning to interpret and predict market behavior. This research introduces a new deep neural network architecture and a novel idea of how to prepare financial data before feeding them to the model. In the data preparation part, the first step is to generate many features using technical indicators and then apply the XGBoost model for feature engineering. Splitting data…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical generalization performance of kernel approximation methods than conventional metrics. An important consequence of this definition is that a kernel approximation matrix must be high rank to attain close approximation. Because storing a high-rank approximation is memory intensive, we propose using a low-precision quantization of random Fourier features (LP-RF…
An automatic program that generates constant profit from the financial market is lucrative for every market practitioner. Recent advance in deep reinforcement learning provides a framework toward end-to-end training of such trading agent. In this paper, we propose an Markov Decision Process (MDP) model suitable for the financial trading task and solve it with the state-of-the-art deep recurrent Q-network (DRQN) algorithm. We propose several modifications to the existing learning algorithm to make it more suitable under the financial trading setting, namely 1. We employ a substantially small re…
In recommendation systems, practitioners observed that increase in the number of embedding tables and their sizes often leads to significant improvement in model performances. Given this and the business importance of these models to major internet companies, embedding tables for personalization tasks have grown to terabyte scale and continue to grow at a significant rate. Meanwhile, these large-scale models are often trained with GPUs where high-performance memory is a scarce resource, thus motivating numerous work on embedding table compression during training. We propose a novel change to e…
Universita’ di Bologna（博洛尼亚大学）；ETH Zurich（苏黎世联邦理工学院）
This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the inference graph with integer-only operations. Our approach aims at determining the minimum bit precision of every activation and weight tensor given the memory constraints of a device. This is achieved through a rule-based iterative procedure, which cuts the number of bits of the …
University of Toronto（多伦多大学）；University of British Columbia（不列颠哥伦比亚大学）
This work investigates how using reduced precision data in Convolutional Neural Networks (CNNs) affects network accuracy during classification. More specifically, this study considers networks where each layer may use different precision data. Our key result is the observation that the tolerance of CNNs to reduced precision data not only varies across networks, a well established observation, but also within networks. Tuning precision per layer is appealing as it could enable energy and performance improvements. In this paper we study how error tolerance across layers varies and propose a meth…
For computer vision applications, prior works have shown the efficacy of reducing numeric precision of model parameters (network weights) in deep neural networks. Activation maps, however, occupy a large memory footprint during both the training and inference step when using mini-batches of inputs. One way to reduce this large memory footprint is to reduce the precision of activations. However, past works have shown that reducing the precision of activations hurts model accuracy. We study schemes to train networks from scratch using reduced-precision activations without hurting accuracy. We re…
Low-precision training has become a popular approach to reduce compute requirements, memory footprint, and energy consumption in supervised learning. In contrast, this promising approach has not yet enjoyed similarly widespread adoption within the reinforcement learning (RL) community, partly because RL agents can be notoriously hard to train even in full precision. In this paper we consider continuous control with the state-of-the-art SAC agent and demonstrate that a naïve adaptation of low-precision methods from supervised learning fails. We propose a set of six modifications, all straightfo…
When Quantization Breaks Memory: Recurrent-State Write-Back in Low-Precision Temporal Inference
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Center for Modeling, Simulation, and Imaging in Medicine（医学建模、仿真与成像中心）；Department of Biomedical Engineering（生物医学工程系）
Università di Bologna（博洛尼亚大学）；Greenwaves Technologies；Università di Modena e Reggio Emilia（摩德纳雷焦艾米利亚大学）；IIS ETH Zurich（苏黎世联邦理工学院集成系统研究所）
The severe on-chip memory limitations are currently preventing the deployment of the most accurate Deep Neural Network (DNN) models on tiny MicroController Units (MCUs), even if leveraging an effective 8-bit quantization scheme. To tackle this issue, in this paper we present an automated mixed-precision quantization flow based on the HAQ framework but tailored for the memory and computational characteristics of MCU devices. Specifically, a Reinforcement Learning agent searches for the best uniform quantization levels, among 2, 4, 8 bits, of individual weight and activation tensors, under the t…
The excellent performance of modern deep neural networks (DNNs) comes at an often prohibitive training cost, limiting the rapid development of DNN innovations and raising various environmental concerns. To reduce the dominant data movement cost of training, process in-memory (PIM) has emerged as a promising solution as it alleviates the need to access DNN weights. However, state-of-the-art PIM DNN training accelerators employ either analog/mixed signal computing which has limited precision or digital computing based on a memory technology that supports limited logic functions and thus requires…
We formalize the problem of trading-off DNN training time and memory requirements as the tensor rematerialization optimization problem, a generalization of prior checkpointing strategies. We introduce Checkmate, a system that solves for optimal rematerialization schedules in reasonable times (under an hour) using off-the-shelf MILP solvers or near-optimal schedules with an approximation algorithm, then uses these schedules to accelerate millions of training iterations. Our method scales to complex, realistic architectures and is hardware-aware through the use of accelerator-specific, profile-b…
