Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE is not reverse-accurate. Other approaches suffer either from an excessive memory requirement due to deep computational graphs or from limited choices for the time integration scheme, hampering their application to large-scale complex dynamical systems. To achieve accurate gradients without compromising memory efficiency and flexibility, we present a new neural ODE framework, PNODE, based on high-level discrete adjoint algorithmic differentiation. By leveraging discrete adjoint time integrators and advanced checkpointing strategies tailored for these integrators, PNODE can provide a balance between memory and computational costs, while computing the gradients consistently and accurately. We provide an open-source implementation based on PyTorch and PETSc, one of the most commonly used portable, scalable scientific computing libraries. We demonstrate the performance through extensive numerical experiments on image classification and continuous normalizing flow problems. We show that PNODE achieves the highest memory efficiency when compared with other reverse-accurate methods. On the image classification problems, PNODE is up to two times faster than the vanilla neural ODE and up to 2.3 times faster than the best existing reverse-accurate method. We also show that PNODE enables the use of the implicit time integration methods that are needed for stiff dynamical systems.
相關內容
Integration：Integration, the VLSI Journal。
Explanation：集成，VLSI雜志。
Publisher：Elsevier。
SIT：
Datacenters are increasingly becoming heterogeneous, and are starting to include specialized hardware for networking, video processing, and especially deep learning. To leverage the heterogeneous compute capability of modern datacenters, we develop an approach for compiler-level partitioning of deep neural networks (DNNs) onto multiple interconnected hardware devices. We present a general framework for heterogeneous DNN compilation, offering automatic partitioning and device mapping. Our scheduler integrates both an exact solver, through a mixed integer linear programming (MILP) formulation, and a modularity-based heuristic for scalability. Furthermore, we propose a theoretical lower bound formula for the optimal solution, which enables the assessment of the heuristic solutions' quality. We evaluate our scheduler in optimizing both conventional DNNs and randomly-wired neural networks, subject to latency and throughput constraints, on a heterogeneous system comprised of a CPU and two distinct GPUs. Compared to na\"ively running DNNs on the fastest GPU, he proposed framework can achieve more than 3$\times$ times lower latency and up to 2.9$\times$ higher throughput by automatically leveraging both data and model parallelism to deploy DNNs on our sample heterogeneous server node. Moreover, our modularity-based "splitting" heuristic improves the solution runtime up to 395$\times$ without noticeably sacrificing solution quality compared to an exact MILP solution, and outperforms all other heuristics by 30-60% solution quality. Finally, our case study shows how we can extend our framework to schedule large language models across multiple heterogeneous servers by exploiting symmetry in the hardware setup. Our code can be easily plugged in to existing frameworks, and is available at //github.com/abdelfattah-lab/diviml.
Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can improve storage, compute, memory bandwidth, and energy usage. In this paper we propose a novel accurate pruning technique that allows precise control over the output network size. Our method uses an efficient optimal transportation scheme which we make end-to-end differentiable and which automatically tunes the exploration-exploitation behavior of the algorithm to find accurate sparse sub-networks. We show that our method achieves state-of-the-art performance compared to previous pruning methods on 3 different datasets, using 5 different models, across a wide range of pruning ratios, and with two types of sparsity budgets and pruning granularities.
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have been developed to construct dimension-independent algorithms. However, there are three challenges for these infinite-dimensional Bayesian methods: prior measures usually act as regularizers and are not able to incorporate prior information efficiently; complex noises, such as more practical non-i.i.d. distributed noises, are rarely considered; and time-consuming forward PDE solvers are needed to estimate posterior statistical quantities. To address these issues, an infinite-dimensional inference framework has been proposed based on the infinite-dimensional variational inference method and deep generative models. Specifically, by introducing some measure equivalence assumptions, we derive the evidence lower bound in the infinite-dimensional setting and provide possible parametric strategies that yield a general inference framework called the Variational Inverting Network (VINet). This inference framework can encode prior and noise information from learning examples. In addition, relying on the power of deep neural networks, the posterior mean and variance can be efficiently and explicitly generated in the inference stage. In numerical experiments, we design specific network structures that yield a computable VINet from the general inference framework. Numerical examples of linear inverse problems of an elliptic equation and the Helmholtz equation are presented to illustrate the effectiveness of the proposed inference framework.
Artificial intelligence (AI) shows great potential to reduce the huge cost of solving partial differential equations (PDEs). However, it is not fully realized in practice as neural networks are defined and trained on fixed domains and boundaries. Herein, we propose local neural operator (LNO) for solving transient PDEs on varied domains. It comes together with a handy strategy including boundary treatments, enabling one pre-trained LNO to predict solutions on different domains. For demonstration, LNO learns Navier-Stokes equations from randomly generated data samples, and then the pre-trained LNO is used as an explicit numerical time-marching scheme to solve the flow of fluid on unseen domains, e.g., the flow in a lid-driven cavity and the flow across the cascade of airfoils. It is about 1000$\times$ faster than the conventional finite element method to calculate the flow across the cascade of airfoils. The solving process with pre-trained LNO achieves great efficiency, with significant potential to accelerate numerical calculations in practice.
Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches face the data and workload drift problem for a long time. Although both query-driven and hybrid methods are proposed to avoid this problem, even the state-of-the-art of them suffer from high training and estimation costs, limited scalability, instability, and long-tailed distribution problem on high cardinality and high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicates information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduces the inference complexity from O(n) to O(1) compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical and even has a lower inference cost on CPU than that of most learned methods on GPU.
Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.
Fibre orientation distribution (FOD) reconstruction using deep learning has the potential to produce accurate FODs from a reduced number of diffusion-weighted images (DWIs), decreasing total imaging time. Diffusion acquisition invariant representations of the DWI signals are typically used as input to these methods to ensure that they can be applied flexibly to data with different b-vectors and b-values; however, this means the network cannot condition its output directly on the DWI signal. In this work, we propose a spherical deconvolution network, a model-driven deep learning FOD reconstruction architecture, that ensures intermediate and output FODs produced by the network are consistent with the input DWI signals. Furthermore, we implement a fixel classification penalty within our loss function, encouraging the network to produce FODs that can subsequently be segmented into the correct number of fixels and improve downstream fixel-based analysis. Our results show that the model-based deep learning architecture achieves competitive performance compared to a state-of-the-art FOD super-resolution network, FOD-Net. Moreover, we show that the fixel classification penalty can be tuned to offer improved performance with respect to metrics that rely on accurately segmented of FODs. Our code is publicly available at //github.com/Jbartlett6/SDNet .
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191