RoboKeyGen: Robot Pose and Joint Angles Estimation via Diffusion-based 3D Keypoint Generation

Estimating robot pose and joint angles is significant in advanced robotics, enabling applications like robot collaboration and online hand-eye calibration.However, the introduction of unknown joint angles makes prediction more complex than simple robot pose estimation, due to its higher dimensionality.Previous methods either regress 3D keypoints directly or utilise a render&compare strategy. These approaches often falter in terms of performance or efficiency and grapple with the cross-camera gap problem.This paper presents a novel framework that bifurcates the high-dimensional prediction task into two manageable subtasks: 2D keypoints detection and lifting 2D keypoints to 3D. This separation promises enhanced performance without sacrificing the efficiency innate to keypoint-based techniques.A vital component of our method is the lifting of 2D keypoints to 3D keypoints. Common deterministic regression methods may falter when faced with uncertainties from 2D detection errors or self-occlusions.Leveraging the robust modeling potential of diffusion models, we reframe this issue as a conditional 3D keypoints generation task. To bolster cross-camera adaptability, we introduce theNormalised Camera Coordinate Space (NCCS), ensuring alignment of estimated 2D keypoints across varying camera intrinsics.Experimental results demonstrate that the proposed method outperforms the state-of-the-art render\&compare method and achieves higher inference speed.Furthermore, the tests accentuate our method's robust cross-camera generalisation capabilities.We intend to release both the dataset and code in https://nimolty.github.io/Robokeygen/

GLIME: General, Stable and Local LIME Explanation

As black-box machine learning models grow in complexity and find applications in high-stakes scenarios, it is imperative to provide explanations for their predictions. Although Local Interpretable Model-agnostic Explanations (LIME) [22] is a widely adpoted method for understanding model behaviors, it is unstable with respect to random seeds [35,24,3] and exhibits low local fidelity (i.e., how well the explanation approximates the model's local behaviors) [21,16]. Our study shows that this instability problem stems from small sample weights, leading to the dominance of regularization and slow convergence. Additionally, LIME's sampling neighborhood is non-local and biased towards the reference, resulting in poor local fidelity and sensitivity to reference choice. To tackle these challenges, we introduce GLIME, an enhanced framework extending LIME and unifying several prior methods. Within the GLIME framework, we derive an equivalent formulation of LIME that achieves significantly faster convergence and improved stability. By employing a local and unbiased sampling distribution, GLIME generates explanations with higher local fidelity compared to LIME. GLIME explanations are independent of reference choice. Moreover, GLIME offers users the flexibility to choose a sampling distribution based on their specific scenarios.

OriWheelBot: An origami-wheeled robot

Origami-inspired robots with multiple advantages, such as being lightweight, requiring less assembly, and exhibiting exceptional deformability, have received substantial and sustained attention. However, the existing origami-inspired robots are usually of limited functionalities and developing feature-rich robots is very challenging. Here, we report an origami-wheeled robot (OriWheelBot) with variable width and outstanding sand walking versatility. The OriWheelBot's ability to adjust wheel width over obstacles is achieved by origami wheels made of Miura origami. An improved version, called iOriWheelBot, is also developed to automatically judge the width of the obstacles. Three actions, namely direct pass, variable width pass, and direct return, will be carried out depending on the width of the channel between the obstacles. We have identified two motion mechanisms, i.e., sand-digging and sand-pushing, with the latter being more conducive to walking on the sand. We have systematically examined numerous sand walking characteristics, including carrying loads, climbing a slope, walking on a slope, and navigating sand pits, small rocks, and sand traps. The OriWheelBot can change its width by 40%, has a loading-carrying ratio of 66.7% on flat sand and can climb a 17-degree sand incline. The OriWheelBot can be useful for planetary subsurface exploration and disaster area rescue.

Robot Structure Prior Guided Temporal Attention for Camera-to-Robot Pose Estimation from Image Sequence

In this work, we tackle the problem of online camera-to-robot pose estimation from single-view successive frames of an image sequence, a crucial task for robots to interact with the world.

Koopman neural operator as a mesh-free solver of non-linear partial differential equations

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to series of computational techniques for numerical solutions. In machine learning, numerous latest advances of solver designs are accomplished in developing neural operators, a kind of mesh-free approximators of the infinite-dimensional operators that map between different parameterization spaces of equation solutions. Although neural operators exhibit generalization capacities for learning an entire PDE family simultaneously, they become less accurate and explainable while learning long-term behaviours of non-linear PDE families. In this paper, we propose Koopman neural operator (KNO), a new neural operator, to overcome these challenges. With the same objective of learning an infinite-dimensional mapping between Banach spaces that serves as the solution operator of target PDE family, our approach differs from existing models by formulating a non-linear dynamic system of equation solution. By approximating the Koopman operator, an infinite-dimensional linear operator governing all possible observations of the dynamic system, to act on the flow mapping of dynamic system, we can equivalently learn the solution of an entire non-linear PDE family by solving simple linear prediction problems. In zero-shot prediction and long-term prediction experiments on representative PDEs (e.g., the Navier-Stokes equation), KNO exhibits notable advantages in breaking the tradeoff between accuracy and efficiency (e.g., model size) while previous state-of-the-art models are limited. These results suggest that more efficient PDE solvers can be developed by the joint efforts from physics and machine learning.

KoopmanLab: machine learning for solving complex physics equations

Numerous physics theories are rooted in partial differential equations (PDEs). However, the increasingly intricate physics equations, especially those that lack analytic solutions or closed forms, have impeded the further development of physics. Computationally solving PDEs by classic numerical approaches suffers from the trade-off between accuracy and efficiency and is not applicable to the empirical data generated by unknown latent PDEs. To overcome this challenge, we present KoopmanLab, an efficient module of the Koopman neural operator family, for learning PDEs without analytic solutions or closed forms. Our module consists of multiple variants of the Koopman neural operator (KNO), a kind of mesh-independent neural-network-based PDE solvers developed following dynamic system theory. The compact variants of KNO can accurately solve PDEs with small model sizes while the large variants of KNO are more competitive in predicting highly complicated dynamic systems govern by unknown, high-dimensional, and non-linear PDEs. All variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier-Stokes equation and the Bateman-Burgers equation in fluid mechanics) and ERA5 (i.e., one of the largest high-resolution global-scale climate data sets in earth physics). These demonstrations suggest the potential of KoopmanLab to be a fundamental tool in diverse physics studies related to equations or dynamic systems.

KoopmanLab: A PyTorch module of Koopman neural operator family for solving partial differential equations

Given the increasingly intricate forms of partial differential equations (PDEs) in physics and related fields, computationally solving PDEs without analytic solutions inevitably suffers from the trade-off between accuracy and efficiency. Recent advances in neural operators, a kind of mesh-independent neural-network-based PDE solvers, have suggested the dawn of overcoming this challenge. In this emerging direction, Koopman neural operator (KNO) is a representative demonstration and outperforms other state-of-the-art alternatives in terms of accuracy and efficiency. Here we present KoopmanLab, a self-contained and user-friendly PyTorch module of the Koopman neural operator family for solving partial differential equations. Beyond the original version of KNO, we develop multiple new variants of KNO based on different neural network architectures to improve the general applicability of our module. These variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier-Stokes equation and the Bateman-Burgers equation) and ERA5 (i.e., one of the largest high-resolution data sets of global-scale climate fields). These demonstrations suggest the potential of KoopmanLab to be considered in diverse applications of partial differential equations.

Statistical Physics of Deep Neural Networks: Initialization toward Optimal Channels

In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information transmission and representation. While considerable efforts are concentrated on realizing optimal channel properties during network optimization, we study a frequently overlooked possibility that neural networks can be initialized toward optimal channels. Our theory, consistent with experimental validation, identifies primary mechanics underlying this unknown possibility and suggests intrinsic connections between statistical physics and deep learning. Unlike the conventional theories that characterize neural networks applying the classic mean-filed approximation, we offer analytic proof that this extensively applied simplification scheme is not valid in studying neural networks as information channels. To fill this gap, we develop a corrected mean-field framework applicable for characterizing the limiting behaviors of information propagation in neural networks without strong assumptions on inputs. Based on it, we propose an analytic theory to prove that mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry, a case where information transmits via norm-preserving mappings. These theoretical predictions are validated by experiments on real neural networks, suggesting the robustness of our theory against finite-size effects. Finally, we analyze our findings with information bottleneck theory to confirm the precise relations among dynamic isometry, mutual information maximization, and optimal channel properties in deep learning.

Video Interpolation by Event-driven Anisotropic Adjustment of Optical Flow

Video frame interpolation is a challenging task due to the ever-changing real-world scene. Previous methods often calculate the bi-directional optical flows and then predict the intermediate optical flows under the linear motion assumptions, leading to isotropic intermediate flow generation. Follow-up research obtained anisotropic adjustment through estimated higher-order motion information with extra frames. Based on the motion assumptions, their methods are hard to model the complicated motion in real scenes. In this paper, we propose an end-to-end training method A^2OF for video frame interpolation with event-driven Anisotropic Adjustment of Optical Flows. Specifically, we use events to generate optical flow distribution masks for the intermediate optical flow, which can model the complicated motion between two frames. Our proposed method outperforms the previous methods in video frame interpolation, taking supervised event-based video interpolation to a higher stage.

A unified theory of information transfer and causal relation

Information transfer between coupled stochastic dynamics, measured by transfer entropy and information flow, is suggested as a physical process underlying the causal relation of systems. While information transfer analysis has booming applications in both science and engineering fields, critical mysteries about its foundations remain unsolved. Fundamental yet difficult questions concern how information transfer and causal relation originate, what they depend on, how they differ from each other, and if they are created by a unified and general quantity. These questions essentially determine the validity of causal relation measurement via information transfer. Here we pursue to lay a complete theoretical basis of information transfer and causal relation. Beyond the well-known relations between these concepts that conditionally hold, we demonstrate that information transfer and causal relation universally originate from specific information synergy and redundancy phenomena characterized by high-order mutual information. More importantly, our theory analytically explains the mechanisms for information transfer and causal relation to originate, vanish, and differ from each other. Moreover, our theory naturally defines the effect sizes of information transfer and causal relation based on high-dimensional coupling events. These results may provide a unified view of information, synergy, and causal relation to bridge Pearl's causal inference theory in computer science and information transfer analysis in physics.