Yu Zhan

Yu Zhan, Fenghai Li, Renliang Weng et al.

In this paper, we propose a novel monocular ray-based 3D (Ray3D) absolute human pose estimation with calibrated camera. Accurate and generalizable absolute 3D human pose estimation from monocular 2D pose input is an ill-posed problem. To address this challenge, we convert the input from pixel space to 3D normalized rays. This conversion makes our approach robust to camera intrinsic parameter changes. To deal with the in-the-wild camera extrinsic parameter variations, Ray3D explicitly takes the camera extrinsic parameters as an input and jointly models the distribution between the 3D pose rays and camera extrinsic parameters. This novel network design is the key to the outstanding generalizability of Ray3D approach. To have a comprehensive understanding of how the camera intrinsic and extrinsic parameter variations affect the accuracy of absolute 3D key-point localization, we conduct in-depth systematic experiments on three single person 3D benchmarks as well as one synthetic benchmark. These experiments demonstrate that our method significantly outperforms existing state-of-the-art models. Our code and the synthetic dataset are available at https://github.com/YxZhxn/Ray3D .

Zhan Yu, Xuanqiang Zhao, Benchi Zhao et al.

Unitary transformations formulate the time evolution of quantum states. How to learn a unitary transformation efficiently is a fundamental problem in quantum machine learning. The most natural and leading strategy is to train a quantum machine learning model based on a quantum dataset. Although the presence of more training data results in better models, using too much data reduces the efficiency of training. In this work, we solve the problem on the minimum size of sufficient quantum datasets for learning a unitary transformation exactly, which reveals the power and limitation of quantum data. First, we prove that the minimum size of a dataset with pure states is $2^n$ for learning an $n$-qubit unitary transformation. To fully explore the capability of quantum data, we introduce a practical quantum dataset consisting of $n+1$ elementary tensor product states that are sufficient for exact training. The main idea is to simplify the structure utilizing decoupling, which leads to an exponential improvement in the size of the datasets with pure states. Furthermore, we show that the size of the quantum dataset with mixed states can be reduced to a constant, which yields an optimal quantum dataset for learning a unitary. We showcase the applications of our results in oracle compiling and Hamiltonian simulation. Notably, to accurately simulate a 3-qubit one-dimensional nearest-neighbor Heisenberg model, our circuit only uses $96$ elementary quantum gates, which is significantly less than $4080$ gates in the circuit constructed by the Trotter-Suzuki product formula.

Zhan Yu, Hongshun Yao, Mujin Li et al.

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.

Chao Hu, Ruishi Yu, Binqi Zeng et al.

Hypergraph neural networks (HGNN) have shown superior performance in various deep learning tasks, leveraging the high-order representation ability to formulate complex correlations among data by connecting two or more nodes through hyperedge modeling. Despite the well-studied adversarial attacks on Graph Neural Networks (GNN), there is few study on adversarial attacks against HGNN, which leads to a threat to the safety of HGNN applications. In this paper, we introduce HyperAttack, the first white-box adversarial attack framework against hypergraph neural networks. HyperAttack conducts a white-box structure attack by perturbing hyperedge link status towards the target node with the guidance of both gradients and integrated gradients. We evaluate HyperAttack on the widely-used Cora and PubMed datasets and three hypergraph neural networks with typical hypergraph modeling techniques. Compared to state-of-the-art white-box structural attack methods for GNN, HyperAttack achieves a 10-20X improvement in time efficiency while also increasing attack success rates by 1.3%-3.7%. The results show that HyperAttack can achieve efficient adversarial attacks that balance effectiveness and time costs.

Zhan Yu, Qiuhao Chen, Yuling Jiao et al.

Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper investigates the expressivity of PQCs for approximating general multivariate function classes. Unlike previous Universal Approximation Theorems for PQCs, which are either nonconstructive or rely on parameterized classical data processing, we explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions. We establish the first non-asymptotic approximation error bounds for these functions in terms of the number of qubits, quantum circuit depth, and number of trainable parameters. Notably, we demonstrate that for approximating functions that satisfy specific smoothness criteria, the quantum circuit size and number of trainable parameters of our proposed PQCs can be smaller than those of deep ReLU neural networks. We further validate the approximation capability of PQCs through numerical experiments. Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.

Yiwen Ying, Hanjing Ye, Senzi Luo et al.

Obstacle avoidance in complex and dynamic environments is a critical challenge for real-time robot navigation. Model-based and learning-based methods often fail in highly dynamic scenarios because traditional methods assume a static environment and cannot adapt to real-time changes, while learning-based methods rely on single-frame observations for motion constraint estimation, limiting their adaptability. To overcome these limitations, this paper proposes a novel framework that leverages multi-frame point constraints, including current and future frames predicted by a dedicated module, to enable proactive end-to-end navigation. By incorporating a prediction module that forecasts the future path of moving obstacles based on multi-frame observations, our method allows the robot to proactively anticipate and avoid potential dangers. This proactive planning capability significantly enhances navigation robustness and efficiency in unknown dynamic environments. Simulations and real-world experiments validate the effectiveness of our approach.

Zhan Yu, Jun Fan, Zhongjie Shi et al.

In recent years, different types of distributed and parallel learning schemes have received increasing attention for their strong advantages in handling large-scale data information. In the information era, to face the big data challenges {that} stem from functional data analysis very recently, we propose a novel distributed gradient descent functional learning (DGDFL) algorithm to tackle functional data across numerous local machines (processors) in the framework of reproducing kernel Hilbert space. Based on integral operator approaches, we provide the first theoretical understanding of the DGDFL algorithm in many different aspects of the literature. On the way of understanding DGDFL, firstly, a data-based gradient descent functional learning (GDFL) algorithm associated with a single-machine model is proposed and comprehensively studied. Under mild conditions, confidence-based optimal learning rates of DGDFL are obtained without the saturation boundary on the regularity index suffered in previous works in functional regression. We further provide a semi-supervised DGDFL approach to weaken the restriction on the maximal number of local machines to ensure optimal rates. To our best knowledge, the DGDFL provides the first divide-and-conquer iterative training approach to functional learning based on data samples of intrinsically infinite-dimensional random functions (functional covariates) and enriches the methodologies for functional data analysis.