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We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs to enhance computational efficiency given the computational demands of Bayesian methods. The method we propose is general in nature, providing access to both epistemic and aleatoric uncertainties. It is also capable of generalization to other various basis functions. We validate our method through a series of closure tests, including simple one-dimensional functions and application to the domain of (Stochastic) Partial Differential Equations. Referring to the latter, we demonstrate the method's ability to correctly identify functional dependencies introduced through the inclusion of a stochastic term. The code supporting this work can be found at //github.com/wmdataphys/Bayesian-HR-KAN

This work presents RNAdiffusion, a latent diffusion model for generating and optimizing discrete RNA sequences of variable lengths. RNA is a key intermediary between DNA and protein, exhibiting high sequence diversity and complex three-dimensional structures to support a wide range of functions. We utilize pretrained BERT-type models to encode raw RNA sequences into token-level, biologically meaningful representations. A Query Transformer is employed to compress such representations into a set of fixed-length latent vectors, with an autoregressive decoder trained to reconstruct RNA sequences from these latent variables. We then develop a continuous diffusion model within this latent space. To enable optimization, we integrate the gradients of reward models--surrogates for RNA functional properties--into the backward diffusion process, thereby generating RNAs with high reward scores. Empirical results confirm that RNAdiffusion generates non-coding RNAs that align with natural distributions across various biological metrics. Further, we fine-tune the diffusion model on mRNA 5' untranslated regions (5'-UTRs) and optimize sequences for high translation efficiencies. Our guided diffusion model effectively generates diverse 5'-UTRs with high Mean Ribosome Loading (MRL) and Translation Efficiency (TE), outperforming baselines in balancing rewards and structural stability trade-off. Our findings hold potential for advancing RNA sequence-function research and therapeutic RNA design.

In pseudo-Boolean optimization, a variable interaction graph represents variables as vertices, and interactions between pairs of variables as edges. In black-box optimization, the variable interaction graph may be at least partially discovered by using empirical linkage learning techniques. These methods never report false variable interactions, but they are computationally expensive. The recently proposed local search with linkage learning discovers the partial variable interaction graph as a side-effect of iterated local search. However, information about the strength of the interactions is not learned by the algorithm. We propose local search with linkage learning 2, which builds a weighted variable interaction graph that stores information about the strength of the interaction between variables. The weighted variable interaction graph can provide new insights about the optimization problem and behavior of optimizers. Experiments with NK landscapes, knapsack problem, and feature selection show that local search with linkage learning 2 is able to efficiently build weighted variable interaction graphs. In particular, experiments with feature selection show that the weighted variable interaction graphs can be used for visualizing the feature interactions in machine learning. Additionally, new transformation operators that exploit the interactions between variables can be designed. We illustrate this ability by proposing a new perturbation operator for iterated local search.

Human motion prediction is crucial for human-centric multimedia understanding and interacting. Current methods typically rely on ground truth human poses as observed input, which is not practical for real-world scenarios where only raw visual sensor data is available. To implement these methods in practice, a pre-phrase of pose estimation is essential. However, such two-stage approaches often lead to performance degradation due to the accumulation of errors. Moreover, reducing raw visual data to sparse keypoint representations significantly diminishes the density of information, resulting in the loss of fine-grained features. In this paper, we propose \textit{LiDAR-HMP}, the first single-LiDAR-based 3D human motion prediction approach, which receives the raw LiDAR point cloud as input and forecasts future 3D human poses directly. Building upon our novel structure-aware body feature descriptor, LiDAR-HMP adaptively maps the observed motion manifold to future poses and effectively models the spatial-temporal correlations of human motions for further refinement of prediction results. Extensive experiments show that our method achieves state-of-the-art performance on two public benchmarks and demonstrates remarkable robustness and efficacy in real-world deployments.

Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant. Notable applications include the diagnosis of approximate MCMC samplers and goodness-of-fit tests for unnormalized statistical models. The present work analyzes the convergence control properties of KSDs. We first show that standard KSDs used for weak convergence control fail to control moment convergence. To address this limitation, we next provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence. As an immediate consequence we develop, for each $q > 0$, the first KSDs known to exactly characterize $q$-Wasserstein convergence.

In recent years, Solving partial differential equations has shifted the focus of traditional neural network studies from finite-dimensional Euclidean spaces to generalized functional spaces in research. A novel methodology is to learn an operator as a means of approximating the mapping between outputs. Currently, researchers have proposed a variety of operator architectures. Nevertheless, the majority of these architectures adopt an iterative update architecture, whereby a single operator is learned from the same function space. In practical physical science problems, the numerical solutions of partial differential equations are complex, and a serial single operator is unable to accurately approximate the intricate mapping between input and output. So, We propose a deep parallel operator model (DPNO) for efficiently and accurately solving partial differential equations. DPNO employs convolutional neural networks to extract local features and map data into distinct latent spaces. Designing a parallel block of double Fourier neural operators to solve the iterative error problem. DPNO approximates complex mappings between inputs and outputs by learning multiple operators in different potential spaces in parallel blocks. DPNO achieved the best performance on five of them, with an average improvement of 10.5\%, and ranked second on one dataset.

We propose a method to measure the similarity of papers and authors by simulating a literature search procedure on citation networks, which is an information retrieval inspired conceptualization of similarity. This transition probability (TP) based approach does not require a curated classification system, avoids clustering complications, and provides a continuous measure of similarity. We perform testing scenarios to explore several versions of the general TP concept and the Node2vec machine-learning technique. We found that TP measures outperform Node2vec in mapping the macroscopic structure of fields. The paper provides a general discussion of how to implement TP similarity measurement, with a particular focus on how to utilize publication-level information to approximate the research interest similarity of individual scientists. This paper is accompanied by a Python package capable of calculating all the tested metrics.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.