Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation
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A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and re-purposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION 5B dataset.Keywords:
Chaining
Generative model
The speed of simulation of power system dynamics has been one of the topics most concerned with on-line security assessment. This paper proposes a new method for forming the constant Jacobian matrix for enhancing the speed of system simulation. By using the constant Jacobian matrix approach in system simulations, both for post-fault and fault-on duration, simulation efficiency is greatly enhanced. Techniques for speeding up the constant Jacobian matrix approach are discussed. Theoretical analysis is presented to demonstrate how the constant Jacobian matrix approach can be extended to a power system with generator controls. Simulation results with the constant Jacobian matrix approach in the 10-generator New England test system and the North China power system are compared with the results obtained by the use of commercial software BPA.
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Visual Servoing
Epipolar geometry
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An efficient method for Jacobian evaluations in multimode hierarchical circuit simulation is presented. The method evaluates the Jacobian matrix based on the block Jacobian contributions which can be evaluated by various methods for different types of blocks to achieve both accuracy and efficiency. Comparison of the method with the forward-difference method shows considerable improvement in simulation efficiency and convergence.
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The Jacobian matrix is the core part of power flow analysis, which is the basis for power system planning and operations. This paper estimates the Jacobian matrix in high dimensional space. Firstly, theoretical analysis and model-based calculation of the Jacobian matrix are introduced to obtain the benchmark value. Then, the estimation algorithms based on least-squared errors and the deviation estimation based on the neural network are studied in detail, including the theories, equations, derivations, codes, advantages and disadvantages, and application scenes. The proposed algorithms are data-driven and sensitive to up-to-date topology parameters and state variables. The efforts are validate by comparing the results to benchmark values.
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S ummary . The experiment was concerned with teaching two types of chain or serial task. The chain types were paper‐folding, regarded as a motor assembly task, and numerical procedures. The aim of the experiment was to investigate the effect of chain length (short, medium and long) and teaching strategy (backward chaining, forward chaining and whole method) on the acquisition and retention of the two types of chain. 176 women students were randomly assigned to nine groups (3 × 3) defined by chain length and teaching strategy. Within each group a motor and a number chain were taught by means of self‐instructional programmes and followed by practice to a criterion of one promptless trial. One week later the tasks were relearned to the same criterion. No advantage was found for backward chaining in the case of the motor chains and the short and medium number chains. However, for the long number chain there was some indication that backward chaining was superior to forward chaining. Both methods were in general inferior to the whole method.
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The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.
Matrix (chemical analysis)
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This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.
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The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system's Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.
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