3D point cloud has been widely used in applications such as self-driving cars, robotics, CAD models, etc. To the best of our knowledge, these applications raised the issue of privacy leakage in 3D point clouds, which has not been studied well. Different from the 2D image privacy, which is related to texture and 2D geometric structure, the 3D point cloud is texture-less and only relevant to 3D geometric structure. In this work, we defined the 3D point cloud privacy problem and proposed an efficient privacy-preserving framework named PointFlowGMM that can support downstream classification and segmentation tasks without seeing the original data. Using a flow-based generative model, the point cloud is projected into a latent Gaussian mixture distributed subspace. We further designed a novel angular similarity loss to obfuscate the original geometric structure and reduce the model size from 767MB to 120MB without a decrease in recognition performance. The projected point cloud in the latent space is orthogonally rotated randomly to further protect the original geometric structure, the class-to-class relationship is preserved after rotation, thus, the protected point cloud can support the recognition task. We evaluated our model on multiple datasets and achieved comparable recognition results on encrypted point clouds compared to the original point clouds.

While reasoning and multilingual capabilities in Language Models (LMs) have achieved remarkable progress in recent years, their integration into a unified paradigm, multilingual reasoning, is at a nascent stage. Multilingual reasoning requires language models to handle logical reasoning across languages while addressing misalignment, biases, and challenges in low-resource settings. This survey provides the first in-depth review of multilingual reasoning in LMs. In this survey, we provide a systematic overview of existing methods that leverage LMs for multilingual reasoning, specifically outlining the challenges, motivations, and foundational aspects of applying language models to reason across diverse languages. We provide an overview of the standard data resources used for training multilingual reasoning in LMs and the evaluation benchmarks employed to assess their multilingual capabilities. Next, we analyze various state-of-the-art methods and their performance on these benchmarks. Finally, we explore future research opportunities to improve multilingual reasoning in LMs, focusing on enhancing their ability to handle diverse languages and complex reasoning tasks.

Extracting hepatic vessels from abdominal images is of high interest for clinicians since it allows to divide the liver into functionally-independent Couinaud segments. In this respect, an automated liver blood vessel extraction is widely summoned. Despite the significant growth in performance of semantic segmentation methodologies, preserving the complex multi-scale geometry of main vessels and ramifications remains a major challenge. This paper provides a new deep supervised approach for vessel segmentation, with a strong focus on representations arising from the different scales inherent to the vascular tree geometry. In particular, we propose a new clustering technique to decompose the tree into various scale levels, from tiny to large vessels. Then, we extend standard 3D UNet to multi-task learning by incorporating scale-specific auxiliary tasks and contrastive learning to encourage the discrimination between scales in the shared representation. Promising results, depicted in several evaluation metrics, are revealed on the public 3D-IRCADb dataset.

The attention mechanism is the key to large language models, and the attention matrix serves as an algorithmic and computational bottleneck for such a scheme. In this paper, we define two problems, motivated by designing fast algorithms for proxy of attention matrix and solving regressions against them. Given an input matrix $A\in \mathbb{R}^{n\times d}$ with $n\gg d$ and a response vector $b$, we first consider the matrix exponential of the matrix $A^\top A$ as a proxy, and we in turn design algorithms for two types of regression problems: $\min_{x\in \mathbb{R}^d}\|(A^\top A)^jx-b\|_2$ and $\min_{x\in \mathbb{R}^d}\|A(A^\top A)^jx-b\|_2$ for any positive integer $j$. Studying algorithms for these regressions is essential, as matrix exponential can be approximated term-by-term via these smaller problems. The second proxy is applying exponential entrywise to the Gram matrix, denoted by $\exp(AA^\top)$ and solving the regression $\min_{x\in \mathbb{R}^n}\|\exp(AA^\top)x-b \|_2$. We call this problem the attention kernel regression problem, as the matrix $\exp(AA^\top)$ could be viewed as a kernel function with respect to $A$. We design fast algorithms for these regression problems, based on sketching and preconditioning. We hope these efforts will provide an alternative perspective of studying efficient approximation of attention matrices.

This paper proposes a vision-based framework for a 7-degree-of-freedom robotic manipulator, with the primary objective of facilitating its capacity to acquire information from human hand demonstrations for the execution of dexterous pick-and-place tasks. Most existing works only focus on the position demonstration without considering the orientations. In this paper, by employing a single depth camera, MediaPipe is applied to generate the three-dimensional coordinates of a human hand, thereby comprehensively recording the hand's motion, encompassing the trajectory of the wrist, orientation of the hand, and the grasp motion. A mean filter is applied during data pre-processing to smooth the raw data. The demonstration is designed to pick up an object at a specific angle, navigate around obstacles in its path and subsequently, deposit it within a sloped container. The robotic system demonstrates its learning capabilities, facilitated by the implementation of Dynamic Movement Primitives, enabling the assimilation of user actions into its trajectories with different start and end poi

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be $O(N^{-2})$ and $O(N^{-b})$, where $N$ is the number of evenly-spaced samples and $b$ is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region $[-1,1]^2$ and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions ($\mathbf{R}$), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.

For a LLM to be trustworthy, its confidence level should be well-calibrated with its actual performance. While it is now common sense that LLM performances are greatly impacted by prompts, the confidence calibration in prompting LLMs has yet to be thoroughly explored. In this paper, we explore how different prompting strategies influence LLM confidence calibration and how it could be improved. We conduct extensive experiments on six prompting methods in the question-answering context and we observe that, while these methods help improve the expected LLM calibration, they also trigger LLMs to be over-confident when responding to some instances. Inspired by human cognition, we propose Fact-and-Reflection (FaR) prompting, which improves the LLM calibration in two steps. First, FaR elicits the known "facts" that are relevant to the input prompt from the LLM. And then it asks the model to "reflect" over them to generate the final answer. Experiments show that FaR prompting achieves significantly better calibration; it lowers the Expected Calibration Error by 23.5% on our multi-purpose QA tasks. Notably, FaR prompting even elicits the capability of verbally expressing concerns in less confident scenarios, which helps trigger retrieval augmentation for solving these harder instances.

In this paper, we propose a novel classification scheme for the remotely sensed hyperspectral image (HSI), namely SP-DLRR, by comprehensively exploring its unique characteristics, including the local spatial information and low-rankness. SP-DLRR is mainly composed of two modules, i.e., the classification-guided superpixel segmentation and the discriminative low-rank representation, which are iteratively conducted. Specifically, by utilizing the local spatial information and incorporating the predictions from a typical classifier, the first module segments pixels of an input HSI (or its restoration generated by the second module) into superpixels. According to the resulting superpixels, the pixels of the input HSI are then grouped into clusters and fed into our novel discriminative low-rank representation model with an effective numerical solution. Such a model is capable of increasing the intra-class similarity by suppressing the spectral variations locally while promoting the inter-class discriminability globally, leading to a restored HSI with more discriminative pixels. Experimental results on three benchmark datasets demonstrate the significant superiority of SP-DLRR over state-of-the-art methods, especially for the case with an extremely limited number of training pixels.

Multimodal learning has achieved great successes in many scenarios. Compared with unimodal learning, it can effectively combine the information from different modalities to improve the performance of learning tasks. In reality, the multimodal data may have missing modalities due to various reasons, such as sensor failure and data transmission error. In previous works, the information of the modality-missing data has not been well exploited. To address this problem, we propose an efficient approach based on maximum likelihood estimation to incorporate the knowledge in the modality-missing data. Specifically, we design a likelihood function to characterize the conditional distribution of the modality-complete data and the modality-missing data, which is theoretically optimal. Moreover, we develop a generalized form of the softmax function to effectively implement maximum likelihood estimation in an end-to-end manner. Such training strategy guarantees the computability of our algorithm capably. Finally, we conduct a series of experiments on real-world multimodal datasets. Our results demonstrate the effectiveness of the proposed approach, even when 95% of the training data has missing modality.