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We consider optimal experimental design (OED) for nonlinear Bayesian inverse problems governed by large-scale partial differential equations (PDEs). For the optimality criteria of Bayesian OED, we consider both expected information gain and summary statistics including the trace and determinant of the information matrix that involves the evaluation of the parameter-to-observable (PtO) map and its derivatives. However, it is prohibitive to compute and optimize these criteria when the PDEs are very expensive to solve, the parameters to estimate are high-dimensional, and the optimization problem is combinatorial, high-dimensional, and non-convex. To address these challenges, we develop an accurate, scalable, and efficient computational framework to accelerate the solution of Bayesian OED. In particular, the framework is developed based on derivative-informed neural operator (DINO) surrogates with proper dimension reduction techniques and a modified swapping greedy algorithm. We demonstrate the high accuracy of the DINO surrogates in the computation of the PtO map and the optimality criteria compared to high-fidelity finite element approximations. We also show that the proposed method is scalable with increasing parameter dimensions. Moreover, we demonstrate that it achieves high efficiency with over 1000X speedup compared to a high-fidelity Bayesian OED solution for a three-dimensional PDE example with tens of thousands of parameters, including both online evaluation and offline construction costs of the surrogates.

Automated machine learning (AutoML) systems propose an end-to-end solution to a given machine learning problem, creating either fixed or flexible pipelines. Fixed pipelines are task independent constructs: their general composition remains the same, regardless of the data. In contrast, the structure of flexible pipelines varies depending on the input, making them finely tailored to individual tasks. However, flexible pipelines can be structurally overcomplicated and have poor explainability. We propose the EVOSA approach that compensates for the negative points of flexible pipelines by incorporating a sensitivity analysis which increases the robustness and interpretability of the flexible solutions. EVOSA quantitatively estimates positive and negative impact of an edge or a node on a pipeline graph, and feeds this information to the evolutionary AutoML optimizer. The correctness and efficiency of EVOSA was validated in tabular, multimodal and computer vision tasks, suggesting generalizability of the proposed approach across domains.

State-of-the-art techniques in weakly-supervised semantic segmentation (WSSS) using image-level labels exhibit severe performance degradation on driving scene datasets such as Cityscapes. To address this challenge, we develop a new WSSS framework tailored to driving scene datasets. Based on extensive analysis of dataset characteristics, we employ Contrastive Language-Image Pre-training (CLIP) as our baseline to obtain pseudo-masks. However, CLIP introduces two key challenges: (1) pseudo-masks from CLIP lack in representing small object classes, and (2) these masks contain notable noise. We propose solutions for each issue as follows. (1) We devise Global-Local View Training that seamlessly incorporates small-scale patches during model training, thereby enhancing the model's capability to handle small-sized yet critical objects in driving scenes (e.g., traffic light). (2) We introduce Consistency-Aware Region Balancing (CARB), a novel technique that discerns reliable and noisy regions through evaluating the consistency between CLIP masks and segmentation predictions. It prioritizes reliable pixels over noisy pixels via adaptive loss weighting. Notably, the proposed method achieves 51.8\% mIoU on the Cityscapes test dataset, showcasing its potential as a strong WSSS baseline on driving scene datasets. Experimental results on CamVid and WildDash2 demonstrate the effectiveness of our method across diverse datasets, even with small-scale datasets or visually challenging conditions. The code is available at //github.com/k0u-id/CARB.

Large language models (LLMs) have recently attracted considerable interest for their ability to perform complex reasoning tasks, such as chain-of-thought reasoning. However, most of the existing approaches to enhance this ability rely heavily on data-driven methods, while neglecting the structural aspects of the model's reasoning capacity. We find that while LLMs can manage individual reasoning steps well, they struggle with maintaining consistency across an entire reasoning chain. To solve this, we introduce 'planning tokens' at the start of each reasoning step, serving as a guide for the model. These token embeddings are then fine-tuned along with the rest of the model parameters. Our approach requires a negligible increase in trainable parameters (just 0.001%) and can be applied through either full fine-tuning or a more parameter-efficient scheme. We demonstrate our method's effectiveness by applying it to three different LLMs, showing notable accuracy improvements across three math word problem datasets w.r.t. plain chain-of-thought fine-tuning baselines.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.

Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.

This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at //explained.ai

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.