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The ray casting operation in the Monte Carlo ray tracing algorithm usually adopts a bounding volume hierarchy (BVH) to accelerate the process of finding intersections to evaluate visibility. However, its characteristics are irregular, with divergence in memory access and branch execution, so it cannot achieve maximum efficiency on GPUs. This paper proposes a novel Neural Intersection Function based on a multilayer perceptron whose core operation contains only dense matrix multiplication with predictable memory access. Our method is the first solution integrating the neural network-based approach and BVH-based ray tracing pipeline into one unified rendering framework. We can evaluate the visibility and occlusion of secondary rays without traversing the most irregular and time-consuming part of the BVH and thus accelerate ray casting. The experiments show the proposed method can reduce the secondary ray casting time for direct illumination by up to 35% compared to a BVH-based implementation and still preserve the image quality.

It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate functions from few samples. So far, theoretical guarantees are missing. The goal of this paper is twofold. On the one hand, we give such guarantees and briefly describe the difficulties of the involved proof. On the other hand, we combine these periodization strategies with recent novel constructive methods for the efficient subsampling of finite frames in $\mathbb{C}$. As a result we are able to reconstruct non-periodic multivariate functions from very few samples. The used sampling nodes are the result of a two-step procedure. Firstly, a random draw with respect to the Chebychev measure provides an initial node set. A further sparsification technique selects a significantly smaller subset of these nodes with equal approximation properties. This set of sampling nodes scales linearly in the dimension of the subspace on which we project and works universally for the whole class of functions. The method is based on principles developed by Batson, Spielman, and Srivastava and can be numerically implemented. Samples on these nodes are then used in a (plain) least-squares sampling recovery step on a suitable hyperbolic cross subspace of functions resulting in a near-optimal behavior of the sampling error. Numerical experiments indicate the applicability of our results.

In sim-to-real Reinforcement Learning (RL), a policy is trained in a simulated environment and then deployed on the physical system. The main challenge of sim-to-real RL is to overcome the reality gap - the discrepancies between the real world and its simulated counterpart. Using general geometric representations, such as convex decomposition, triangular mesh, signed distance field can improve simulation fidelity, and thus potentially narrow the reality gap. Common to these approaches is that many contact points are generated for geometrically-complex objects, which slows down simulation and may cause numerical instability. Contact reduction methods address these issues by limiting the number of contact points, but the validity of these methods for sim-to-real RL has not been confirmed. In this paper, we present a contact reduction method with bounded stiffness to improve the simulation accuracy. Our experiments show that the proposed method critically enables training RL policy for a tight-clearance double pin insertion task and successfully deploying the policy on a rigid, position-controlled physical robot.

In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the planted matrices are disjoint, and their row and column indices can be arbitrary. Inspired by scientific applications, the second model restricts the row and column indices to be consecutive. In the detection problem, under the null hypothesis, the observed matrix is a realization of independent and identically distributed standard normal entries. Under the alternative, there exists a set of hidden submatrices with elevated means inside the same standard normal matrix. Recovery refers to the task of locating the hidden submatrices. For both problems, and for both models, we characterize the statistical and computational barriers by deriving information-theoretic lower bounds, designing and analyzing algorithms matching those bounds, and proving computational lower bounds based on the low-degree polynomials conjecture. In particular, we show that the space of the model parameters (i.e., number of planted submatrices, their dimensions, and elevated mean) can be partitioned into three regions: the impossible regime, where all algorithms fail; the hard regime, where while detection or recovery are statistically possible, we give some evidence that polynomial-time algorithm do not exist; and finally the easy regime, where polynomial-time algorithms exist.

Over the past decade, the techniques of topological data analysis (TDA) have grown into prominence to describe the shape of data. In recent years, there has been increasing interest in developing statistical methods and in particular hypothesis testing procedures for TDA. Under the statistical perspective, persistence diagrams -- the central multi-scale topological descriptors of data provided by TDA -- are viewed as random observations sampled from some population or process. In this context, one of the earliest works on hypothesis testing focuses on the two-group permutation-based approach where the associated loss function is defined in terms of within-group pairwise bottleneck or Wasserstein distances between persistence diagrams (Robinson and Turner, 2017). However, in situations where persistence diagrams are large in size and number, the permutation test in question gets computationally more costly to apply. To address this limitation, we instead consider pairwise distances between vectorized functional summaries of persistence diagrams for the loss function. In the present work, we explore the utility of the Betti function in this regard, which is one of the simplest function summaries of persistence diagrams. We introduce an alternative vectorization method for the Betti function based on integration and prove stability results with respect to the Wasserstein distance. Moreover, we propose a new shuffling technique of group labels to increase the power of the test. Through several experimental studies, on both synthetic and real data, we show that the vectorized Betti function leads to competitive results compared to the baseline method involving the Wasserstein distances for the permutation test.

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desired. In absence of the governing equations describing the dynamics, we need to construct the parametric reduced-order surrogate model in a non-intrusive fashion. In this setting, the usual residual-based error estimate for optimal parameter sampling associated with the reduced basis method is not directly available. Our work provides a non-intrusive optimality criterion to efficiently populate the parameter snapshots, thereby, enabling us to effectively construct a parametric surrogate model. We consider separate parameter-specific proper orthogonal decomposition (POD) subspaces and propose an active-learning-driven surrogate model using kernel-based shallow neural networks, abbreviated as ActLearn-POD-KSNN surrogate model. To demonstrate the validity of our proposed ideas, we present numerical experiments using two physical models, namely Burgers' equation and shallow water equations. Both the models have mixed -- convective and diffusive -- effects within their respective parameter domains, with each of them dominating in certain regions. The proposed ActLearn-POD-KSNN surrogate model efficiently predicts the solution at new parameter locations, even for a setting with multiple interacting shock profiles.

In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.

The proliferation of automated data collection schemes and the advances in sensorics are increasing the amount of data we are able to monitor in real-time. However, given the high annotation costs and the time required by quality inspections, data is often available in an unlabeled form. This is fostering the use of active learning for the development of soft sensors and predictive models. In production, instead of performing random inspections to obtain product information, labels are collected by evaluating the information content of the unlabeled data. Several query strategy frameworks for regression have been proposed in the literature but most of the focus has been dedicated to the static pool-based scenario. In this work, we propose a new strategy for the stream-based scenario, where instances are sequentially offered to the learner, which must instantaneously decide whether to perform the quality check to obtain the label or discard the instance. The approach is inspired by the optimal experimental design theory and the iterative aspect of the decision-making process is tackled by setting a threshold on the informativeness of the unlabeled data points. The proposed approach is evaluated using numerical simulations and the Tennessee Eastman Process simulator. The results confirm that selecting the examples suggested by the proposed algorithm allows for a faster reduction in the prediction error.

Humans naturally exploit haptic feedback during contact-rich tasks like loading a dishwasher or stocking a bookshelf. Current robotic systems focus on avoiding unexpected contact, often relying on strategically placed environment sensors. Recently, contact-exploiting manipulation policies have been trained in simulation and deployed on real robots. However, they require some form of real-world adaptation to bridge the sim-to-real gap, which might not be feasible in all scenarios. In this paper we train a contact-exploiting manipulation policy in simulation for the contact-rich household task of loading plates into a slotted holder, which transfers without any fine-tuning to the real robot. We investigate various factors necessary for this zero-shot transfer, like time delay modeling, memory representation, and domain randomization. Our policy transfers with minimal sim-to-real gap and significantly outperforms heuristic and learnt baselines. It also generalizes to plates of different sizes and weights. Demonstration videos and code are available at //sites.google.com/view/compliant-object-insertion.

In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.