arXiv subjects

Tao Luo

Publications and source records attributed to Tao Luo.

At least 163 records · Page 9Linked to original sources

arXiv2022

Quasi-periodic oscillations of the X-ray burst from the magnetar SGR J1935+2154 and associated with the fast radio burst FRB 200428

The origin(s) and mechanism(s) of fast radio bursts (FRBs), which are short radio pulses from cosmological distances, have remained a major puzzle since their discovery. We report a strong Quasi-Periodic Oscillation(QPO) of 40 Hz in the X-ray burst from the magnetar SGR J1935+2154 and associated with FRB 200428, significantly detected with the Hard X-ray Modulation Telescope (Insight-HXMT) and also hinted by the Konus-Wind data. QPOs from magnetar bursts have only been rarely detected; our 3.4 sigma (p-value is 2.9e-4) detection of the QPO reported here reveals the strongest QPO signal observed from magnetars (except in some very rare giant flares), making this X-ray burst unique among magnetar bursts. The two X-ray spikes coinciding with the two FRB pulses are also among the peaks of the QPO. Our results suggest that at least some FRBs are related to strong oscillation processes of neutron stars. We also show that we may overestimate the significance of the QPO signal and underestimate the errors of QPO parameters if QPO exists only in a fraction of the time series of a X-ray burst which we use to calculate the Leahy-normalized periodogram.

astro-ph.HE↗

arXiv2022

Winograd Convolution: A Perspective from Fault Tolerance

Winograd convolution is originally proposed to reduce the computing overhead by converting multiplication in neural network (NN) with addition via linear transformation. Other than the computing efficiency, we observe its great potential in improving NN fault tolerance and evaluate its fault tolerance comprehensively for the first time. Then, we explore the use of fault tolerance of winograd convolution for either fault-tolerant or energy-efficient NN processing. According to our experiments, winograd convolution can be utilized to reduce fault-tolerant design overhead by 27.49\% or energy consumption by 7.19\% without any accuracy loss compared to that without being aware of the fault tolerance

cs.LG↗

arXiv2022

Embedding Principle of Loss Landscape of Deep Neural Networks

Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN "contains" all the critical points of all the narrower DNNs. More precisely, we propose a critical embedding such that any critical point, e.g., local or global minima, of a narrower DNN can be embedded to a critical point/hyperplane of the target DNN with higher degeneracy and preserving the DNN output function. The embedding structure of critical points is independent of loss function and training data, showing a stark difference from other nonconvex problems such as protein-folding. Empirically, we find that a wide DNN is often attracted by highly-degenerate critical points that are embedded from narrow DNNs. The embedding principle provides an explanation for the general easy optimization of wide DNNs and unravels a potential implicit low-complexity regularization during the training. Overall, our work provides a skeleton for the study of loss landscape of DNNs and its implication, by which a more exact and comprehensive understanding can be anticipated in the near

cs.LG↗

arXiv2021

MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator representation with regularization from data. For linear PDEs, we use a DNN to parameterize the Green's function and obtain the neural operator to approximate the solution according to the Green's method. To train the DNN, the empirical risk consists of the mean squared loss with the least square formulation or the variational formulation of the governing equation and boundary conditions. For complicated problems, the empirical risk also includes a few labels, which are computed on coarse grid points with cheap computation cost and significantly improves the model accuracy. Intuitively, the labeled dataset works as a regularization in addition to the model constraints. The MOD-Net solves a family of PDEs rather than a specific one and is much more efficient than original neural operator because few expensive labels are required. We numerically show MOD-Net is very efficient in solving Poisson equation and one-dimensional radiative transfer equation. For nonlinear PDEs, the nonlinear MOD-Net can be similarly used as an ansatz for solving nonlinear PDEs, exemplified by solving several nonlinear PDE problems, such as the Burgers equation.

math.NA↗

arXiv2021

Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks

In an attempt to better understand structural benefits and generalization power of deep neural networks, we firstly present a novel graph theoretical formulation of neural network models, including fully connected, residual network (ResNet) and densely connected networks (DenseNet). Secondly, we extend the error analysis of the population risk for two layer network \cite{ew2019prioriTwo} and ResNet \cite{e2019prioriRes} to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained. These estimates are a priori in nature since they depend sorely on the information prior to the training process, in particular, the bounds for the estimation errors are independent of the input dimension.

cs.LG↗

arXiv2021

Optimizing for In-memory Deep Learning with Emerging Memory Technology

In-memory deep learning computes neural network models where they are stored, thus avoiding long distance communication between memory and computation units, resulting in considerable savings in energy and time. In-memory deep learning has already demonstrated orders of magnitude higher performance density and energy efficiency. The use of emerging memory technology promises to increase the gains in density, energy, and performance even further. However, emerging memory technology is intrinsically unstable, resulting in random fluctuations of data reads. This can translate to non-negligible accuracy loss, potentially nullifying the gains. In this paper, we propose three optimization techniques that can mathematically overcome the instability problem of emerging memory technology. They can improve the accuracy of the in-memory deep learning model while maximizing its energy efficiency. Experiments show that our solution can fully recover most models' state-of-the-art accuracy, and achieves at least an order of magnitude higher energy efficiency than the state-of-the-art.

cs.LG↗

arXiv2021

Embedding Principle: a hierarchical structure of loss landscape of deep neural networks

We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i.e., loss landscape of an NN contains all critical points of all the narrower NNs. This result is obtained by constructing a class of critical embeddings which map any critical point of a narrower NN to a critical point of the target NN with the same output function. By discovering a wide class of general compatible critical embeddings, we provide a gross estimate of the dimension of critical submanifolds embedded from critical points of narrower NNs. We further prove an irreversiblility property of any critical embedding that the number of negative/zero/positive eigenvalues of the Hessian matrix of a critical point may increase but never decrease as an NN becomes wider through the embedding. Using a special realization of general compatible critical embedding, we prove a stringent necessary condition for being a "truly-bad" critical point that never becomes a strict-saddle point through any critical embedding. This result implies the commonplace of strict-saddle points in wide NNs, which may be an important reason underlying the easy optimization of wide NNs widely observed in practice.

cs.LG↗

arXiv2021

E3NE: An End-to-End Framework for Accelerating Spiking Neural Networks with Emerging Neural Encoding on FPGAs

Compiler frameworks are crucial for the widespread use of FPGA-based deep learning accelerators. They allow researchers and developers, who are not familiar with hardware engineering, to harness the performance attained by domain-specific logic. There exists a variety of frameworks for conventional artificial neural networks. However, not much research effort has been put into the creation of frameworks optimized for spiking neural networks (SNNs). This new generation of neural networks becomes increasingly interesting for the deployment of AI on edge devices, which have tight power and resource constraints. Our end-to-end framework E3NE automates the generation of efficient SNN inference logic for FPGAs. Based on a PyTorch model and user parameters, it applies various optimizations and assesses trade-offs inherent to spike-based accelerators. Multiple levels of parallelism and the use of an emerging neural encoding scheme result in an efficiency superior to previous SNN hardware implementations. For a similar model, E3NE uses less than 50% of hardware resources and 20% less power, while reducing the latency by an order of magnitude. Furthermore, scalability and generality allowed the deployment of the large-scale SNN models AlexNet and VGG.

cs.NE↗

arXiv2021

Privacy Budget Scheduling

Machine learning (ML) models trained on personal data have been shown to leak information about users. Differential privacy (DP) enables model training with a guaranteed bound on this leakage. Each new model trained with DP increases the bound on data leakage and can be seen as consuming part of a global privacy budget that should not be exceeded. This budget is a scarce resource that must be carefully managed to maximize the number of successfully trained models. We describe PrivateKube, an extension to the popular Kubernetes datacenter orchestrator that adds privacy as a new type of resource to be managed alongside other traditional compute resources, such as CPU, GPU, and memory. The abstractions we design for the privacy resource mirror those defined by Kubernetes for traditional resources, but there are also major differences. For example, traditional compute resources are replenishable while privacy is not: a CPU can be regained after a model finishes execution while privacy budget cannot. This distinction forces a re-design of the scheduler. We present DPF (Dominant Private Block Fairness) -- a variant of the popular Dominant Resource Fairness (DRF) algorithm -- that is geared toward the non-replenishable privacy resource but enjoys similar theoretical properties as DRF. We evaluate PrivateKube and DPF on microbenchmarks and an ML workload on Amazon Reviews data. Compared to existing baselines, DPF allows training more models under the same global privacy guarantee. This is especially true for DPF over Rényi DP, a highly composable form of DP.

cs.CR↗

arXiv2021

Global Solutions to an initial boundary problem for the compressible 3-D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains

An initial boundary value problem for compressible Magnetohydrodynamics (MHD) is considered on an exterior domain (with the first Betti number vanishes) in $R^3$ in this paper. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established. Moreover the explicit decay rate is given. In particular, the results obtained in this paper also imply the global existence of classical solutions for the full compressible Navier-Stokes equations with Navier-slip boundary conditions on exterior domains in three dimensions, which is not available in literature, to the best of knowledge of the authors'.

math.AP↗

arXiv2021

DTNN: Energy-efficient Inference with Dendrite Tree Inspired Neural Networks for Edge Vision Applications

Deep neural networks (DNN) have achieved remarkable success in computer vision (CV). However, training and inference of DNN models are both memory and computation intensive, incurring significant overhead in terms of energy consumption and silicon area. In particular, inference is much more cost-sensitive than training because training can be done offline with powerful platforms, while inference may have to be done on battery powered devices with constrained form factors, especially for mobile or edge vision applications. In order to accelerate DNN inference, model quantization was proposed. However previous works only focus on the quantization rate without considering the efficiency of operations. In this paper, we propose Dendrite-Tree based Neural Network (DTNN) for energy-efficient inference with table lookup operations enabled by activation quantization. In DTNN both costly weight access and arithmetic computations are eliminated for inference. We conducted experiments on various kinds of DNN models such as LeNet-5, MobileNet, VGG, and ResNet with different datasets, including MNIST, Cifar10/Cifar100, SVHN, and ImageNet. DTNN achieved significant energy saving (19.4X and 64.9X improvement on ResNet-18 and VGG-11 with ImageNet, respectively) with negligible loss of accuracy. To further validate the effectiveness of DTNN and compare with state-of-the-art low energy implementation for edge vision, we design and implement DTNN based MLP image classifiers using off-the-shelf FPGAs. The results show that DTNN on the FPGA, with higher accuracy, could achieve orders of magnitude better energy consumption and latency compared with the state-of-the-art low energy approaches reported that use ASIC chips.

cs.CV↗

arXiv2021

RCT: Resource Constrained Training for Edge AI

Neural networks training on edge terminals is essential for edge AI computing, which needs to be adaptive to evolving environment. Quantised models can efficiently run on edge devices, but existing training methods for these compact models are designed to run on powerful servers with abundant memory and energy budget. For example, quantisation-aware training (QAT) method involves two copies of model parameters, which is usually beyond the capacity of on-chip memory in edge devices. Data movement between off-chip and on-chip memory is energy demanding as well. The resource requirements are trivial for powerful servers, but critical for edge devices. To mitigate these issues, We propose Resource Constrained Training (RCT). RCT only keeps a quantised model throughout the training, so that the memory requirements for model parameters in training is reduced. It adjusts per-layer bitwidth dynamically in order to save energy when a model can learn effectively with lower precision. We carry out experiments with representative models and tasks in image application and natural language processing. Experiments show that RCT saves more than 86\% energy for General Matrix Multiply (GEMM) and saves more than 46\% memory for model parameters, with limited accuracy loss. Comparing with QAT-based method, RCT saves about half of energy on moving model parameters.

cs.LG↗

arXiv2021

QROSS: QUBO Relaxation Parameter Optimisation via Learning Solver Surrogates

An increasingly popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this relaxation introduces hyper-parameters that balance the objective and penalty terms for the constraints, and their chosen values significantly impact performance. Hence, tuning these parameters is an important problem. Existing generic hyper-parameter tuning methods require multiple expensive calls to a QUBO solver, making them impractical for performance critical applications when repeated solutions of similar combinatorial optimisation problems are required. In this paper, we propose the QROSS method, in which we build surrogate models of QUBO solvers via learning from solver data on a collection of instances of a problem. In this way, we are able capture the common structure of the instances and their interactions with the solver, and produce good choices of penalty parameters with fewer number of calls to the QUBO solver. We take the Traveling Salesman Problem (TSP) as a case study, where we demonstrate that our method can find better solutions with fewer calls to QUBO solver compared with conventional hyper-parameter tuning techniques. Moreover, with simple adaptation methods, QROSS is shown to generalise well to out-of-distribution datasets and different types of QUBO solvers.

cs.LG↗

arXiv2021

Convergence from Atomistic Model to Peierls-Nabarro Model for Dislocations in Bilayer System with Complex Lattice

In this paper, we prove the convergence from the atomistic model to the Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex lattice. We show that the displacement field of the dislocation solution of the PN model converges to the dislocation solution of the atomistic model with second-order accuracy. The consistency of PN model and the stability of atomistic model are essential in our proof. The main idea of our approach is to use several low-degree polynomials to approximate the energy due to atomistic interactions of different groups of atoms of the complex lattice.

math.AP↗

arXiv2021

Insight-HXMT observations of jet-like corona in a black hole X-ray binary MAXI J1820+070

A black hole X-ray binary produces hard X-ray radiation from its corona and disk when the accreting matter heats up. During an outburst, the disk and corona co-evolves with each other. However, such an evolution is still unclear in both its geometry and dynamics. Here we report the unusual decrease of the reflection fraction in MAXI J1820+070, which is the ratio of the coronal intensity illuminating the disk to the coronal intensity reaching the observer, as the corona is observed to contrast during the decay phase. We postulate a jet-like corona model, in which the corona can be understood as a standing shock where the material flowing through. In this dynamical scenario, the decrease of the reflection fraction is a signature of the corona's bulk velocity. Our findings suggest that as the corona is observed to get closer to the black hole, the coronal material might be outflowing faster.

astro-ph.HE↗

arXiv2021

Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle (LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore, through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to a LFP model with quantitative prediction power.

cs.LG↗

arXiv2021

Improving "Fast Iterative Shrinkage-Thresholding Algorithm": Faster, Smarter and Greedier

The "fast iterative shrinkage-thresholding algorithm", a.k.a. FISTA, is one of the most well-known first-order optimisation scheme in the literature, as it achieves the worst-case $O(1/k^2)$ optimal convergence rate in terms of objective function value. However, despite such an optimal theoretical convergence rate, in practice the (local) oscillatory behaviour of FISTA often damps its efficiency. Over the past years, various efforts are made in the literature to improve the practical performance of FISTA, such as monotone FISTA, restarting FISTA and backtracking strategies. In this paper, we propose a simple yet effective modification to the original FISTA scheme which has two advantages: it allows us to 1) prove the convergence of generated sequence; 2) design a so-called "lazy-start" strategy which can up to an order faster than the original scheme. Moreover, by exploring the properties of FISTA scheme, we propose novel adaptive and greedy strategies which probes the limit of the algorithm. The advantages of the proposed schemes are tested through problems arising from inverse problem, machine learning and signal/image processing.

math.OC↗

arXiv2021

A comprehensive study on the semileptonic decay of heavy flavor mesons

The semileptonic decay of heavy flavor mesons offers a clean environment for extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, which describes the CP-violating and flavor changing process in the Standard Model. The involved form factors where the dynamical information is encoded play an essential role in achieving any conclusive statement. That is, the knowledge of the form factors should be under good control, requiring one to examine more observables in addition to the branching fraction. In this paper, we provide the mean value and the $q^2$-dependent shape for further observables [differential decay distribution ($dΓ/dq^2$), forward-backward asymmetry ($\mathcal{A}_{FB}^l$), longitudinal ($P_L^l$) and transverse ($P_T^l$) polarization of a charged lepton, longitudinal polarization of a vector meson in the final state ($F_L^l(V)$), leptonic convexity parameter ($C_F^l$), and trigonometric moments ($W_i^l$) in the decay of $D_{(s)}$ and $B_{(s)}$ to $P/V l^+ ν_l$ ($l=e$, $μ$ or $τ$)], based on the predictions of the relevant form factors from the covariant light-front quark model. $P$ and $V$ denote the pseudoscalar and vector meson, respectively. As a comparison, we find a good agreement with the results from the covariant confining quark model and the relativistic quark model in the literature. As it has been observed that the $P_L^l$ and $F_L^l(V)$ are crucial quantities to discriminate various New Physics models, the reexamination of these observables from a different method is also essential and necessary.

hep-ph↗