arXiv subjects

Heng Yang

Publications and source records attributed to Heng Yang.

At least 73 records · Page 4Linked to original sources

arXiv2024

CLOSURE: Fast Quantification of Pose Uncertainty Sets

We investigate uncertainty quantification of 6D pose estimation from learned noisy measurements (e.g. keypoints and pose hypotheses). Assuming unknown-but-bounded measurement noises, a pose uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D poses compatible with the measurements. Despite being simple to formulate and its ability to embed uncertainty, the PURSE is difficult to manipulate and interpret due to the many abstract nonconvex polynomial constraints. An appealing simplification of PURSE is to find its minimum enclosing geodesic ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound. We contribute (i) a geometric interpretation of the nonconvex PURSE, and (ii) a fast algorithm to inner approximate the MEGB. Particularly, we show the PURSE corresponds to the feasible set of a constrained dynamical system or the intersection of multiple geodesic balls, and this perspective allows us to design an algorithm to densely sample the boundary of the PURSE through strategic random walks. We then use the miniball algorithm to compute the MEGB of PURSE samples, leading to an inner approximation. Our algorithm is named CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a certificate of approximation tightness by calculating the relative size ratio between the inner approximation and the outer approximation. Running on a single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8% on the LM-O dataset, 91.4% on the 3DMatch dataset and 96.6% on the LM dataset with the average runtime less than 0.3 second. Obtaining comparable worst-case error bound but 398x 833x and 23.6x faster than the outer approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose estimation to be implemented in real-time robot perception applications.

cs.RO↗

arXiv2024

Characterization of BMO spaces via commutators of fractional maximal function on Lorentz spaces

Let $0 \leq α<n$ and $b$ be the locally integrable function. In this paper, we consider the maximal commutator of fractional maximal function $M_{b,α}$ and the nonlinear commutator of fractional maximal function $[b, M_α]$ on Lorentz spaces. We give some necessary and sufficient conditions for the boundedness of the commutators $M_{b,α}$ and $[b, M_α]$ on Lorentz spaces when the function $b$ belongs to BMO spaces, by which some new characterizations of certain subclasses of BMO spaces are obtained.

math.FA↗

arXiv2024

Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid

Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable algorithms to compute simple and tight overapproximations of SME in the form of minimum enclosing ellipsoids (MEE). We first introduce the hierarchy of enclosing ellipsoids proposed by Nie and Demmel (2005), based on sums-of-squares relaxations, that asymptotically converge to the MEE of a basic semialgebraic set. This framework, however, struggles in modern control and perception problems due to computational challenges. We contribute three computational enhancements to make this framework practical, namely constraints pruning, generalized relaxed Chebyshev center, and handling non-Euclidean geometry. We showcase numerical examples on system identification and object pose estimation.

math.OC↗

arXiv2024

On the Nonsmooth Geometry and Neural Approximation of the Optimal Value Function of Infinite-Horizon Pendulum Swing-up

We revisit the inverted pendulum problem with the goal of understanding and computing the true optimal value function. We start with an observation that the true optimal value function must be nonsmooth ($i.e.$, not globally $C^1$) due to the symmetry of the problem. We then give a result that can certify the optimality of a candidate $\textit{piece-wise}$ $C^1$ value function. Further, for a candidate value function obtained via numerical approximation, we provide a bound of suboptimality based on its Hamilton-Jacobi-Bellman (HJB) equation residuals. Inspired by Holzhuter (2004), we then design an algorithm that solves backward the Pontryagin's minimum principle (PMP) ODE from terminal conditions provided by the locally optimal LQR value function. This numerical procedure leads to a piece-wise $C^1$ value function whose nonsmooth region contains periodic $\textit{spiral lines}$ and smooth regions attain HJB residuals about $10^{-4}$, hence certified to be the optimal value function up to minor numerical inaccuracies. This optimal value function checks the power of optimality: (i) it sits above a polynomial lower bound; (ii) its induced controller globally swings up and stabilizes the pendulum, and (iii) attains lower trajectory cost than baseline methods such as energy shaping, model predictive control (MPC), and proximal policy optimization (with MPC attaining almost the same cost). We conclude by distilling the optimal value function into a simple neural network. Our code is avilable in https://github.com/ComputationalRobotics/InvertedPendulumOptimalValue.

math.OC↗

arXiv2024

Characterization of Lipschitz functions via commutators of maximal operators on slice spaces

Let $0 \leq α<n$, $M_α$ be the fractional maximal operator, $M^{\sharp}$ be the sharp maximal operator and $b$ be the locally integrable function. Denote by $[b, M_α]$ and $[b, M^{\sharp}]$ be the commutators of the fractional maximal operator $M_α$ and the sharp maximal operator $M^{\sharp}$. In this paper, we show some necessary and sufficient conditions for the boundedness of the commutators $[b, M_α]$ and $[b, M^{\sharp}]$ on slice spaces when the function $b$ is the Lipschitz function, by which some new characterizations of the non-negative Lipschitz function are obtained

math.FA↗

arXiv2024

Discounted Adaptive Online Learning: Towards Better Regularization

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing good regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs and Candès, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees.

cs.LG↗

arXiv2024

Integrated Sensing and Communication Channel Modeling: A Survey

Integrated sensing and communication (ISAC) is expected to play a crucial role in the sixth-generation (6G) mobile communication systems, offering potential applications in the scenarios of intelligent transportation, smart factories, etc. The performance of radar sensing in ISAC systems is closely related to the characteristics of radar sensing and communication channels. Therefore, ISAC channel modeling serves as a fundamental cornerstone for evaluating and optimizing ISAC systems. This article provides a comprehensive survey on the ISAC channel modeling methods. Furthermore, the methods of target radar cross section (RCS) modeling and clutter RCS modeling are summarized. Finally, we discuss the future research trends related to ISAC channel modeling in various scenarios.

cs.NI↗

arXiv2024

LSA: Modeling Aspect Sentiment Coherency via Local Sentiment Aggregation

Aspect sentiment coherency is an intriguing yet underexplored topic in the field of aspect-based sentiment classification. This concept reflects the common pattern where adjacent aspects often share similar sentiments. Despite its prevalence, current studies have not fully recognized the potential of modeling aspect sentiment coherency, including its implications in adversarial defense. To model aspect sentiment coherency, we propose a novel local sentiment aggregation (LSA) paradigm based on constructing a differential-weighted sentiment aggregation window. We have rigorously evaluated our model through experiments, and the results affirm the proficiency of LSA in terms of aspect coherency prediction and aspect sentiment classification. For instance, it outperforms existing models and achieves state-of-the-art sentiment classification performance across five public datasets. Furthermore, we demonstrate the promising ability of LSA in ABSC adversarial defense, thanks to its sentiment coherency modeling. To encourage further exploration and application of this concept, we have made our code publicly accessible. This will provide researchers with a valuable tool to delve into sentiment coherency modeling in future research.

cs.CL↗

arXiv2024

BootAug: Boosting Text Augmentation via Hybrid Instance Filtering Framework

Text augmentation is an effective technique for addressing the problem of insufficient data in natural language processing. However, existing text augmentation methods tend to focus on few-shot scenarios and usually perform poorly on large public datasets. Our research indicates that existing augmentation methods often generate instances with shifted feature spaces, which leads to a drop in performance on the augmented data (for example, EDA generally loses $\approx 2\%$ in aspect-based sentiment classification). To address this problem, we propose a hybrid instance-filtering framework (BootAug) based on pre-trained language models that can maintain a similar feature space with natural datasets. BootAug is transferable to existing text augmentation methods (such as synonym substitution and back translation) and significantly improves the augmentation performance by $\approx 2-3\%$ in classification accuracy. Our experimental results on three classification tasks and nine public datasets show that BootAug addresses the performance drop problem and outperforms state-of-the-art text augmentation methods. Additionally, we release the code to help improve existing augmentation methods on large datasets.

cs.CL↗

arXiv2024

The Best Defense is Attack: Repairing Semantics in Textual Adversarial Examples

Recent studies have revealed the vulnerability of pre-trained language models to adversarial attacks. Existing adversarial defense techniques attempt to reconstruct adversarial examples within feature or text spaces. However, these methods struggle to effectively repair the semantics in adversarial examples, resulting in unsatisfactory performance and limiting their practical utility. To repair the semantics in adversarial examples, we introduce a novel approach named Reactive Perturbation Defocusing (Rapid). Rapid employs an adversarial detector to identify fake labels of adversarial examples and leverage adversarial attackers to repair the semantics in adversarial examples. Our extensive experimental results conducted on four public datasets, convincingly demonstrate the effectiveness of Rapid in various adversarial attack scenarios. To address the problem of defense performance validation in previous works, we provide a demonstration of adversarial detection and repair based on our work, which can be easily evaluated at https://tinyurl.com/22ercuf8.

cs.CL↗

arXiv2024

Improving Adaptive Online Learning Using Refined Discretization

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and ($ii$) the comparator norm adaptivity also known as "parameter freeness" in the literature. In particular, - our algorithm does not employ the impractical doubling trick, and does not require an a priori estimate of the time-uniform Lipschitz constant; - the associated regret bound has the optimal $O(\sqrt{V_T})$ dependence on the gradient variance $V_T$, without the typical logarithmic multiplicative factor; - the leading constant in the regret bound is "almost" optimal. Central to these results is a continuous time approach to online learning. We first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.

cs.LG↗

arXiv2024

Sparse Polynomial Optimization with Unbounded Sets

This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one extra auxiliary variable for each variable clique according to the correlative sparsity pattern. Under the running intersection property, we prove that this hierarchy has asymptotic convergence. Furthermore, we provide two alternative sparse hierarchies to remove perturbations while preserving asymptotic convergence. As byproducts, new Positivstellensätze are obtained for sparse positive polynomials on unbounded sets. Extensive numerical experiments demonstrate the power of our approach in solving sparse polynomial optimization problems on unbounded sets with up to thousands of variables. Finally, we apply our approach to tackle two trajectory optimization problems (block-moving with minimum work and optimal control of Van der Pol).

math.OC↗

arXiv2023

PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

cs.LG↗

arXiv2023

InstOptima: Evolutionary Multi-objective Instruction Optimization via Large Language Model-based Instruction Operators

Instruction-based language modeling has received significant attention in pretrained language models. However, the efficiency of instruction engineering remains low and hinders the development of instruction studies. Recent studies have focused on automating instruction generation, but they primarily aim to improve performance without considering other crucial objectives that impact instruction quality, such as instruction length and perplexity. Therefore, we propose a novel approach (i.e., InstOptima) that treats instruction generation as an evolutionary multi-objective optimization problem. In contrast to text edition-based methods, our approach utilizes a large language model (LLM) to simulate instruction operators, including mutation and crossover. Furthermore, we introduce an objective-guided mechanism for these operators, allowing the LLM to comprehend the objectives and enhance the quality of the generated instructions. Experimental results demonstrate improved fine-tuning performance and the generation of a diverse set of high-quality instructions.

cs.CL↗

arXiv2023

Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints

We consider a category-level perception problem, where one is given 2D or 3D sensor data picturing an object of a given category (e.g., a car), and has to reconstruct the 3D pose and shape of the object despite intra-class variability (i.e., different car models have different shapes). We consider an active shape model, where -- for an object category -- we are given a library of potential CAD models describing objects in that category, and we adopt a standard formulation where pose and shape are estimated from 2D or 3D keypoints via non-convex optimization. Our first contribution is to develop PACE3D* and PACE2D*, the first certifiably optimal solvers for pose and shape estimation using 3D and 2D keypoints, respectively. Both solvers rely on the design of tight (i.e., exact) semidefinite relaxations. Our second contribution is to develop outlier-robust versions of both solvers, named PACE3D# and PACE2D#. Towards this goal, we propose ROBIN, a general graph-theoretic framework to prune outliers, which uses compatibility hypergraphs to model measurements' compatibility. We show that in category-level perception problems these hypergraphs can be built from the winding orders of the keypoints (in 2D) or their convex hulls (in 3D), and many outliers can be filtered out via maximum hyperclique computation. The last contribution is an extensive experimental evaluation. Besides providing an ablation study on simulated datasets and on the PASCAL3D+ dataset, we combine our solver with a deep keypoint detector, and show that PACE3D# improves over the state of the art in vehicle pose estimation in the ApolloScape datasets, and its runtime is compatible with practical applications. We release our code at https://github.com/MIT-SPARK/PACE.

cs.CV↗

arXiv2023

Optimal Pose and Shape Estimation for Category-level 3D Object Perception

We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given category (e.g. a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e. different car models have different shapes). We consider an active shape model, where -- for an object category -- we are given a library of potential CAD models describing objects in that category, and we adopt a standard formulation where pose and shape estimation are formulated as a non-convex optimization. Our first contribution is to provide the first certifiably optimal solver for pose and shape estimation. In particular, we show that rotation estimation can be decoupled from the estimation of the object translation and shape, and we demonstrate that (i) the optimal object rotation can be computed via a tight (small-size) semidefinite relaxation, and (ii) the translation and shape parameters can be computed in closed-form given the rotation. Our second contribution is to add an outlier rejection layer to our solver, hence making it robust to a large number of misdetections. Towards this goal, we wrap our optimal solver in a robust estimation scheme based on graduated non-convexity. To further enhance robustness to outliers, we also develop the first graph-theoretic formulation to prune outliers in category-level perception, which removes outliers via convex hull and maximum clique computations; the resulting approach is robust to 70%-90% outliers. Our third contribution is an extensive experimental evaluation. Besides providing an ablation study on a simulated dataset and on the PASCAL3D+ dataset, we combine our solver with a deep-learned keypoint detector, and show that the resulting approach improves over the state of the art in vehicle pose estimation in the ApolloScape datasets.

cs.CV↗

arXiv2023

SIM-Sync: From Certifiably Optimal Synchronization over the 3D Similarity Group to Scene Reconstruction with Learned Depth

This paper presents SIM-Sync, a certifiably optimal algorithm that estimates camera trajectory and 3D scene structure directly from multiview image keypoints. SIM-Sync fills the gap between pose graph optimization and bundle adjustment; the former admits efficient global optimization but requires relative pose measurements and the latter directly consumes image keypoints but is difficult to optimize globally (due to camera projective geometry). The bridge to this gap is a pretrained depth prediction network. Given a graph with nodes representing monocular images taken at unknown camera poses and edges containing pairwise image keypoint correspondences, SIM-Sync first uses a pretrained depth prediction network to lift the 2D keypoints into 3D scaled point clouds, where the scaling of the per-image point cloud is unknown due to the scale ambiguity in monocular depth prediction. SIM-Sync then seeks to synchronize jointly the unknown camera poses and scaling factors (i.e., over the 3D similarity group). The SIM-Sync formulation, despite nonconvex, allows designing an efficient certifiably optimal solver that is almost identical to the SE-Sync algorithm. We demonstrate the tightness, robustness, and practical usefulness of SIM-Sync in both simulated and real experiments. In simulation, we show (i) SIM-Sync compares favorably with SE-Sync in scale-free synchronization, and (ii) SIM-Sync can be used together with robust estimators to tolerate a high amount of outliers. In real experiments, we show (a) SIM-Sync achieves similar performance as Ceres on bundle adjustment datasets, and (b) SIM-Sync performs on par with ORB-SLAM3 on the TUM dataset with zero-shot depth prediction.

cs.RO↗

arXiv2023

PyABSA: A Modularized Framework for Reproducible Aspect-based Sentiment Analysis

The advancement of aspect-based sentiment analysis (ABSA) has urged the lack of a user-friendly framework that can largely lower the difficulty of reproducing state-of-the-art ABSA performance, especially for beginners. To meet the demand, we present \our, a modularized framework built on PyTorch for reproducible ABSA. To facilitate ABSA research, PyABSA supports several ABSA subtasks, including aspect term extraction, aspect sentiment classification, and end-to-end aspect-based sentiment analysis. Concretely, PyABSA integrates 29 models and 26 datasets. With just a few lines of code, the result of a model on a specific dataset can be reproduced. With a modularized design, PyABSA can also be flexibly extended to considered models, datasets, and other related tasks. Besides, PyABSA highlights its data augmentation and annotation features, which significantly address data scarcity. All are welcome to have a try at \url{https://github.com/yangheng95/PyABSA}.

cs.CL↗