Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure

Neuron-level fuzzy memoization in RNNs

The final publication is available at ACM via http://dx.doi.org/10.1145/3352460.3358309Recurrent Neural Networks (RNNs) are a key technology for applications such as automatic speech recognition or machine translation. Unlike conventional feed-forward DNNs, RNNs remember past information to improve the accuracy of future predictions and, therefore, they are very effective for sequence processing problems. For each application run, each recurrent layer is executed many times for processing a potentially large sequence of inputs (words, images, audio frames, etc.). In this paper, we make the observation that the output of a neuron exhibits small changes in consecutive invocations. We exploit this property to build a neuron-level fuzzy memoization scheme, which dynamically caches the output of each neuron and reuses it whenever it is predicted that the current output will be similar to a previously computed result, avoiding in this way the output computations. The main challenge in this scheme is determining whether the new neuron's output for the current input in the sequence will be similar to a recently computed result. To this end, we extend the recurrent layer with a much simpler Bitwise Neural Network (BNN), and show that the BNN and RNN outputs are highly correlated: if two BNN outputs are very similar, the corresponding outputs in the original RNN layer are likely to exhibit negligible changes. The BNN provides a low-cost and effective mechanism for deciding when fuzzy memoization can be applied with a small impact on accuracy. We evaluate our memoization scheme on top of a state-of-the-art accelerator for RNNs, for a variety of different neural networks from multiple application domains. We show that our technique avoids more than 24.2% of computations, resulting in 18.5% energy savings and 1.35x speedup on average.Peer ReviewedPostprint (author's final draft

이진 뉴럴 네트워크를 위한 DRAM 기반의 뉴럴 네트워크 가속기 구조

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 컴퓨터공학부, 2021. 2. 유승주.In the convolutional neural network applications, most computations occurred by the multiplication and accumulation of the convolution and fully-connected layers. From the hardware perspective (i.e., in the gate-level circuits), these operations are performed by many dot-products between the feature map and kernel vectors. Since the feature map and kernel have the matrix form, the vector converted from 3D, or 4D matrices is reused many times for the matrix multiplications. As the throughput of the DNN increases, the power consumption and performance bottleneck due to the data movement become a more critical issue. More importantly, power consumption due to off-chip memory accesses dominates total power since off-chip memory access consumes several hundred times greater power than the computation. The accelerators' throughput is about several hundred GOPS~several TOPS, but Memory bandwidth is less than 25.6 or 34 GB/s (with DDR4 or LPDDR4). By reducing the network size and/or data movement size, both data movement power and performance bottleneck problems are improved. Among the algorithms, Quantization is widely used. Binary Neural Networks (BNNs) dramatically reduce precision down to 1 bit. The accuracy is much lower than that of the FP16, but the accuracy is continuously improving through various studies. With the data flow control, there is a method of reducing redundant data movement by increasing data reuse. The above two methods are widely applied in accelerators because they do not need additional computations in the inference computation. In this dissertation, I present 1) a DRAM-based accelerator architecture and 2) a DRAM refresh method to improve performance reduction due to DRAM refresh. Both methods are orthogonal, so can be integrated into the DRAM chip and operate independently. First, we proposed a DRAM-based accelerator architecture capable of massive and large vector dot product operation. In the field of CNN accelerators to which BNN can be applied, a computing-in-memory (CIM) structure that utilizes a cell-array structure of Memory for vector dot product operation is being actively studied. Since DRAM stores all the neural network data, it is advantageous to reduce the amount of data transfer. The proposed architecture operates by utilizing the basic operation of the DRAM. The second method is to reduce the performance degradation and power consumption caused by DRAM refresh. Since the DRAM cannot read and write data while performing a periodic refresh, system performance decreases. The proposed refresh method tests the refresh characteristics inside the DRAM chip during self-refresh and increases the refresh cycle according to the characteristics. Since it operates independently inside DRAM, it can be applied to all systems using DRAM and is the same for deep neural network accelerators. We surveyed system integration with a software stack to use the in-DRAM accelerator in the DL framework. As a result, it is expected to control in-DRAM accelerators with the memory controller implementation method verified in the previous experiment. Also, we have added the performance simulation function of in-DRAM accelerator to PyTorch. When running a neural network in PyTorch, it reports the computation latency and data movement latency occurring in the layer running in the in-DRAM accelerator. It is a significant advantage to predict the performance when running in hardware while co-designing the network.컨볼루셔널 뉴럴 네트워크 (CNN) 어플리케이션에서는, 대부분의 연산이 컨볼루션 레이어와 풀리-커넥티드 레이어에서 발생하는 곱셈과 누적 연산이다. 게이트-로직 레벨에서는, 대량의 벡터 내적으로 실행되며, 입력과 커널 벡터들을 반복해서 사용하여 연산한다. 딥 뉴럴 네트워크 연산에는 범용 연산 유닛보다, 단순한 연산이 가능한 작은 연산 유닛을 대량으로 사용하는 것이 적합하다. 가속기의 성능이 일정 이상 높아지면, 가속기의 성능은 연산에 필요한 데이터 전송에 의해 제한된다. 메모리에서 데이터를 오프-칩으로 전송할 때의 에너지 소모가, 연산 유닛에서 연산에 사용되는 에너지의 수백배로 크다. 또한 연산기의 성능은 초당 수백 기가~수 테라-연산이 가능하지만, 메모리의 데이터 전송은 초당 수십 기가 바이트이다. 데이터 전송에 의한 파워와 성능 문제를 동시에 해결하는 방법은, 전송되는 데이터 크기를 줄이는 것이다. 알고리즘 중에서는 네트워크의 데이터를 양자화하여, 낮은 정밀도로 데이터를 표현하는 방법이 널리 사용된다. 이진 뉴럴 네트워크(BNN)는 정밀도를 1비트까지 극단적으로 낮춘다. 16비트 정밀도보다 네트워크의 정확도가 낮아지는 문제가 있지만, 다양한 연구를 통해 정확도가 지속적으로 개선되고 있다. 또한 구조적으로는, 전송된 데이터를 재사용하여 동일한 데이터의 반복적인 전송을 줄이는 방법이 있다. 위의 두 가지 방법은 추론 과정에서 별도의 연산 없이 적용 가능하여 가속기에서 널리 적용되고 있다. 본 논문에서는, DRAM 기반의 가속기 구조를 제안하고, DRAM refresh에 의한 성능 감소를 개선하는 기술을 제안하였다. 두 방법은 하나의 DRAM 칩으로 집적 가능하며, 독립적으로 구동 가능하다. 첫번째는 대량의 벡터 내적 연산이 가능한 DRAM 기반 가속기에 대한 연구이다. BNN을 적용할 수 있는 CNN가속기 분야에서, 메모리의 셀-어레이 구조를 벡터 내적 연산에 활용하는 컴퓨팅-인-메모리(CIM) 구조가 활발히 연구되고 있다. 특히, DRAM에는 뉴럴 네트워크의 모든 데이터가 있기 때문에, 데이터 전송량의 감소에 유리하다. 우리는 DRAM 셀-어레이의 구조를 바꾸지 않고, DRAM의 기본 동작을 활용하여 연산하는 방법을 제안하였다. 두번째는 DRAM 리프레쉬 주기를 늘려서 성능 열화와 파워 소모를 개선하는 방법이다. DRAM이 리프레쉬를 실행할 때마다, 데이터를 읽고 쓸 수 없기 때문에 시스템 혹은 가속기의 성능 감소가 발생한다. DRAM 칩 내부에서 DRAM의 리프레쉬 특성을 테스트하고, 리프레쉬 주기를 늘리는 방법을 제안하였다. DRAM 내부에서 독립적으로 동작하기 때문에 DRAM을 사용하는 모든 시스템에 적용 가능하며, 딥 뉴럴 네트워크 가속기에서도 동일하다. 또한, 제안된 가속기를 PyTorch와 같이 널리 사용되는 딥러닝 프레임 워크에서도 쉽게 사용할 수 있도록, 소프트웨어 스택을 비롯한 system integration 방법을 조사하였다. 결과적으로, 기존의 TVM compiler와 FPGA로 구현하는 TVM/VTA 가속기에, DRAM refresh 실험에서 검증된 메모리 컨트롤러와 커스텀 컴파일러를 추가하면 in-DRAM 가속기를 제어할 수 있을 것으로 기대된다. 이에 더하여, in-DRAM 가속기와 뉴럴 네트워크의 설계 단계에서 성능을 예측할 수 있도록, 시뮬레이션 기능을 PyTorch에 추가하였다. PyTorch에서 신경망을 실행할 때, DRAM 가속기에서 실행되는 계층에서 발생하는 계산 대기 시간 및 데이터 이동 시간을 확인할 수 있다.Abstract i Contents viii List of Tables x List of Figures xiv Chapter 1 Introduction 1 Chapter 2 Background 6 2.1 Neural Network Operation . . . . . . . . . . . . . . . . 6 2.2 Data Movement Overhead . . . . . . . . . . . . . . . . 7 2.3 Binary Neural Networks . . . . . . . . . . . . . . . . . 10 2.4 Computing-in-Memory . . . . . . . . . . . . . . . . . . 11 2.5 Memory Bottleneck due to Refresh . . . . . . . . . . . . 13 Chapter 3 In-DRAM Neural Network Accelerator 16 3.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.1 DRAM hierarchy . . . . . . . . . . . . . . . . . 18 3.1.2 DRAM Basic Operation . . . . . . . . . . . . . 21 3.1.3 DRAM Commands with Timing Parameters . . . 22 3.1.4 Bit-wise Operation in DRAM . . . . . . . . . . 25 3.2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Proposed architecture . . . . . . . . . . . . . . . . . . . 30 3.3.1 Operation Examples of Row Operator . . . . . . 32 3.3.2 Convolutions on DRAM Chip . . . . . . . . . . 39 3.4 Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4.1 Input Broadcasting in DRAM . . . . . . . . . . 44 3.4.2 Input Data Movement With M2V . . . . . . . . . 47 3.4.3 Internal Data Movement With SiD . . . . . . . . 49 3.4.4 Data Partitioning for Parallel Operation . . . . . 52 3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . 56 3.5.1 Performance Estimation . . . . . . . . . . . . . 56 3.5.2 Configuration of In-DRAM Accelerator . . . . . 58 3.5.3 Improving the Accuracy of BNN . . . . . . . . . 60 3.5.4 Comparison with the Existing Works . . . . . . . 62 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.6.1 Performance Comparison with ASIC Accelerators 67 3.6.2 Challenges of The Proposed Architecture . . . . 70 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 4 Reducing DRAM Refresh Power Consumption by Runtime Profiling of Retention Time and Dualrow Activation 74 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 74 4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Related Works . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 Observations . . . . . . . . . . . . . . . . . . . . . . . . 84 4.5 Solution overview . . . . . . . . . . . . . . . . . . . . . 88 4.6 Runtime profiling . . . . . . . . . . . . . . . . . . . . . 93 4.6.1 Basic Operation . . . . . . . . . . . . . . . . . . 93 4.6.2 Profiling Multiple Rows in Parallel . . . . . . . . 96 4.6.3 Temperature, Data Backup and Error Check . . . 96 4.7 Dual-row Activation . . . . . . . . . . . . . . . . . . . . 98 4.8 Experiments . . . . . . . . . . . . . . . . . . . . . . . . 102 4.8.1 Experimental Setup . . . . . . . . . . . . . . . . 103 4.8.2 Refresh Period Improvement . . . . . . . . . . . 107 4.8.3 Power Reduction . . . . . . . . . . . . . . . . . 110 4.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 116 Chapter 5 System Integration 118 5.1 Integrate The Proposed Methods . . . . . . . . . . . . . 118 5.2 Software Stack . . . . . . . . . . . . . . . . . . . . . . 121 Chapter 6 Conclusion 129 Bibliography 131 국문초록 153Docto

DyCL: Dynamic Neural Network Compilation Via Program Rewriting and Graph Optimization

DL compiler's primary function is to translate DNN programs written in high-level DL frameworks such as PyTorch and TensorFlow into portable executables. These executables can then be flexibly executed by the deployed host programs. However, existing DL compilers rely on a tracing mechanism, which involves feeding a runtime input to a neural network program and tracing the program execution paths to generate the computational graph necessary for compilation. Unfortunately, this mechanism falls short when dealing with modern dynamic neural networks (DyNNs) that possess varying computational graphs depending on the inputs. Consequently, conventional DL compilers struggle to accurately compile DyNNs into executable code. To address this limitation, we propose \tool, a general approach that enables any existing DL compiler to successfully compile DyNNs. \tool tackles the dynamic nature of DyNNs by introducing a compilation mechanism that redistributes the control and data flow of the original DNN programs during the compilation process. Specifically, \tool develops program analysis and program transformation techniques to convert a dynamic neural network into multiple sub-neural networks. Each sub-neural network is devoid of conditional statements and is compiled independently. Furthermore, \tool synthesizes a host module that models the control flow of the DyNNs and facilitates the invocation of the sub-neural networks. Our evaluation demonstrates the effectiveness of \tool, achieving a 100\% success rate in compiling all dynamic neural networks. Moreover, the compiled executables generated by \tool exhibit significantly improved performance, running between $1.12\times$ and $20.21\times$ faster than the original DyNNs executed on general-purpose DL frameworks.Comment: This paper has been accepted to ISSTA 202