arXiv subjects

Jiaming Liang

Publications and source records attributed to Jiaming Liang.

67 records · Page 4Linked to original sources

arXiv2023

RITA: Group Attention is All You Need for Timeseries Analytics

Timeseries analytics is of great importance in many real-world applications. Recently, the Transformer model, popular in natural language processing, has been leveraged to learn high quality feature embeddings from timeseries, core to the performance of various timeseries analytics tasks. However, the quadratic time and space complexities limit Transformers' scalability, especially for long timeseries. To address these issues, we develop a timeseries analytics tool, RITA, which uses a novel attention mechanism, named group attention, to address this scalability issue. Group attention dynamically clusters the objects based on their similarity into a small number of groups and approximately computes the attention at the coarse group granularity. It thus significantly reduces the time and space complexity, yet provides a theoretical guarantee on the quality of the computed attention. The dynamic scheduler of RITA continuously adapts the number of groups and the batch size in the training process, ensuring group attention always uses the fewest groups needed to meet the approximation quality requirement. Extensive experiments on various timeseries datasets and analytics tasks demonstrate that RITA outperforms the state-of-the-art in accuracy and is significantly faster -- with speedups of up to 63X.

cs.LG↗

arXiv2023

A unified analysis of a class of proximal bundle methods for solving hybrid convex composite optimization problems

This paper presents a proximal bundle (PB) framework based on a generic bundle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging to it. As a consequence, iteration-complexity bounds for three PB variants based on different bundle update schemes are obtained in the HCCO context for the first time and in a unified manner. While two of the PB variants are universal (i.e., their implementations do not require parameters associated with the HCCO instance), the other newly (as far as the authors are aware of) proposed one is not but has the advantage that it generates simple, namely one-cut, bundle models. The paper also presents a universal adaptive PB variant (which is not necessarily an instance of the framework) based on one-cut models and shows that its iteration-complexity is the same as the two aforementioned universal PB variants.

math.OC↗

arXiv2023

SigVIC: Spatial Importance Guided Variable-Rate Image Compression

Variable-rate mechanism has improved the flexibility and efficiency of learning-based image compression that trains multiple models for different rate-distortion tradeoffs. One of the most common approaches for variable-rate is to channel-wisely or spatial-uniformly scale the internal features. However, the diversity of spatial importance is instructive for bit allocation of image compression. In this paper, we introduce a Spatial Importance Guided Variable-rate Image Compression (SigVIC), in which a spatial gating unit (SGU) is designed for adaptively learning a spatial importance mask. Then, a spatial scaling network (SSN) takes the spatial importance mask to guide the feature scaling and bit allocation for variable-rate. Moreover, to improve the quality of decoded image, Top-K shallow features are selected to refine the decoded features through a shallow feature fusion module (SFFM). Experiments show that our method outperforms other learning-based methods (whether variable-rate or not) and traditional codecs, with storage saving and high flexibility.

eess.IV↗

arXiv2023

A Proximal Algorithm for Sampling from Non-convex Potentials

We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincaré inequality. Rather than smooth, the potentials are assumed to be semi-smooth or the summation of multiple semi-smooth functions. We develop a sampling algorithm that resembles proximal algorithms in optimization for this challenging sampling task. Our algorithm is based on a special case of Gibbs sampling known as the alternating sampling framework (ASF). The key contribution of this work is a practical realization of the ASF based on rejection sampling in the non-convex and semi-smooth setting. This work extends the recent algorithm in \cite{LiaChe21,LiaChe22} for non-smooth/semi-smooth log-concave distribution to the setting with non-convex potentials. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.

cs.LG↗

arXiv2023

Average Curvature FISTA for Nonconvex Smooth Composite Optimization Problems

A previous authors' paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation and two composite resolvent evaluations to compute the next iterate. This paper presents an alternative FISTA-type ACG variant, namely AC-FISTA, which has the following additional features: i) it performs an average of one composite resolvent evaluation per iteration; and ii) it estimates the local upper curvature by using the average of the previously observed upper (instead of upper-Lipschitz) curvatures. These two properties acting together yield a practical AC-FISTA variant which substantially outperforms earlier ACG variants, including the AC-ACG variants discussed in the aforementioned authors' paper.

math.OC↗

arXiv2022

GotFlow3D: Recurrent Graph Optimal Transport for Learning 3D Flow Motion in Particle Tracking

Flow visualization technologies such as particle tracking velocimetry (PTV) are broadly used in understanding the all-pervasiveness three-dimensional (3D) turbulent flow from nature and industrial processes. Despite the advances in 3D acquisition techniques, the developed motion estimation algorithms in particle tracking remain great challenges of large particle displacements, dense particle distributions and high computational cost. By introducing a novel deep neural network based on recurrent Graph Optimal Transport, called GotFlow3D, we present an end-to-end solution to learn the 3D fluid flow motion from double-frame particle sets. The proposed network constructs two graphs in the geometric and feature space and further enriches the original particle representations with the fused intrinsic and extrinsic features learnt from a graph neural network. The extracted deep features are subsequently utilized to make optimal transport plans indicating the correspondences of particle pairs, which are then iteratively and adaptively retrieved to guide the recurrent flow learning. Experimental evaluations, including assessments on numerical experiments and validations on real-world experiments, demonstrate that the proposed GotFlow3D achieves state-of-the-art performance against both recently-developed scene flow learners and particle tracking algorithms, with impressive accuracy, robustness and generalization ability, which can provide deeper insight into the complex dynamics of broad physical and biological systems.

physics.flu-dyn↗

arXiv2022

STDC-MA Network for Semantic Segmentation

Semantic segmentation is applied extensively in autonomous driving and intelligent transportation with methods that highly demand spatial and semantic information. Here, an STDC-MA network is proposed to meet these demands. First, the STDC-Seg structure is employed in STDC-MA to ensure a lightweight and efficient structure. Subsequently, the feature alignment module (FAM) is applied to understand the offset between high-level and low-level features, solving the problem of pixel offset related to upsampling on the high-level feature map. Our approach implements the effective fusion between high-level features and low-level features. A hierarchical multiscale attention mechanism is adopted to reveal the relationship among attention regions from two different input sizes of one image. Through this relationship, regions receiving much attention are integrated into the segmentation results, thereby reducing the unfocused regions of the input image and improving the effective utilization of multiscale features. STDC- MA maintains the segmentation speed as an STDC-Seg network while improving the segmentation accuracy of small objects. STDC-MA was verified on the verification set of Cityscapes. The segmentation result of STDC-MA attained 76.81% mIOU with the input of 0.5x scale, 3.61% higher than STDC-Seg.

cs.CV↗

arXiv2022

A Proximal Algorithm for Sampling from Non-smooth Potentials

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a polynomial-time complexity $\tilde {\cal O}(d\varepsilon^{-1})$ to obtain $\varepsilon$ total variation distance to the target density, better than most existing results under the same assumptions. Our method is based on the proximal bundle method and an alternating sampling framework. This framework requires the so-called restricted Gaussian oracle, which can be viewed as a sampling counterpart of the proximal mapping in convex optimization. One key contribution of this work is a fast algorithm that realizes the restricted Gaussian oracle for any convex non-smooth potential with bounded Lipschitz constant.

cs.LG↗

arXiv2021

A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes

This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle subproblems whose objective functions are regularized composite cutting-plane models. Moreover, RPB uses a novel condition to decide whether to perform a serious or null iteration which does not necessarily yield a function value decrease. Optimal iteration-complexity bounds for RPB are established for a large range of prox stepsizes, both in the convex and strongly convex settings. To the best of our knowledge, this is the first time that a proximal bundle variant is shown to be optimal for a large range of prox stepsizes. Finally, iteration-complexity results for RPB to obtain iterates satisfying practical termination criteria, rather than near optimal solutions, are also derived.

math.OC↗

arXiv2021

A Semantic-based Method for Unsupervised Commonsense Question Answering

Unsupervised commonsense question answering is appealing since it does not rely on any labeled task data. Among existing work, a popular solution is to use pre-trained language models to score candidate choices directly conditioned on the question or context. However, such scores from language models can be easily affected by irrelevant factors, such as word frequencies, sentence structures, etc. These distracting factors may not only mislead the model to choose a wrong answer but also make it oversensitive to lexical perturbations in candidate answers. In this paper, we present a novel SEmantic-based Question Answering method (SEQA) for unsupervised commonsense question answering. Instead of directly scoring each answer choice, our method first generates a set of plausible answers with generative models (e.g., GPT-2), and then uses these plausible answers to select the correct choice by considering the semantic similarity between each plausible answer and each choice. We devise a simple, yet sound formalism for this idea and verify its effectiveness and robustness with extensive experiments. We evaluate the proposed method on four benchmark datasets, and our method achieves the best results in unsupervised settings. Moreover, when attacked by TextFooler with synonym replacement, SEQA demonstrates much less performance drops than baselines, thereby indicating stronger robustness.

cs.CL↗

arXiv2021

A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems

In this paper, we describe and establish iteration-complexity of two accelerated composite gradient (ACG) variants to solve a smooth nonconvex composite optimization problem whose objective function is the sum of a nonconvex differentiable function $ f $ with a Lipschitz continuous gradient and a simple nonsmooth closed convex function $ h $. When $f$ is convex, the first ACG variant reduces to the well-known FISTA for a specific choice of the input, and hence the first one can be viewed as a natural extension of the latter one to the nonconvex setting. The first variant requires an input pair $(M,m)$ such that $f$ is $m$-weakly convex, $\nabla f$ is $M$-Lipschitz continuous, and $m \le M$ (possibly $m<M$), which is usually hard to obtain or poorly estimated. The second variant on the other hand can start from an arbitrary input pair $(M,m)$ of positive scalars and its complexity is shown to be not worse, and better in some cases, than that of the first variant for a large range of the input pairs. Finally, numerical results are provided to illustrate the efficiency of the two ACG variants.

math.OC↗

arXiv2020

An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems

This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known Lipschitz gradient constant or a sequence of maximum observed curvatures, the current one is based on the average of all past observed curvatures. More specifically, AC-ACG uses a positive multiple of the average of all observed curvatures until the previous iteration as a way to estimate the "function curvature" at the current point and then two resolvent evaluations to compute the next iterate. In contrast to other variable Lipschitz estimation variants, e.g., the ones based on the maximum curvature, AC-ACG always accepts the aforementioned iterate regardless how poor the Lipschitz estimation turns out to be. Finally, computational results are presented to illustrate the efficiency of AC-ACG on both randomly generated and real-world problem instances.

math.OC↗

arXiv2018

A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems

This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form $f+h$ where $f$ is a (possibly nonconvex) differentiable function whose gradient is Lipschitz continuous and $h$ is a closed convex function with bounded domain. D-AIPP performs two types of iterations, namely, inner and outer ones. Its outer iterations correspond to the ones of the accelerated inexact proximal point scheme. Its inner iterations are the ones performed by an accelerated composite gradient method for inexactly solving the convex proximal subproblems generated during the outer iterations. Thus, D-AIPP employs both inner and outer accelerations.

math.OC↗