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It is known that for subgraph-closed graph classes the first-order model checking problem is fixed-parameter tractable if and only if the class is nowhere dense [Grohe, Kreutzer, Siebertz, STOC 2014]. However, the dependency on the formula size is non-elementary, and in fact, this is unavoidable even for the class of all trees [Frick and Grohe, LICS 2002]. On the other hand, it is known that the dependency is elementary for classes of bounded degree [Frick and Grohe, LICS 2002] as well as for classes of bounded pathwidth [Lampis, ICALP 2023]. In this paper we generalise these results and almost completely characterise subgraph-closed graph classes for which the model checking problem is fixed-parameter tractable with an elementary dependency on the formula size. Those are the graph classes for which there exists a number $d$ such that for every $r$, some tree of depth $d$ and size bounded by an elementary function of $r$ is avoided as an $({\leq} r)$-subdivision in all graphs in the class. In particular, this implies that if the class in question excludes a fixed tree as a topological minor, then first-order model checking for graphs in the class is fixed-parameter tractable with an elementary dependency on the formula size.

Multi-view stacking is a framework for combining information from different views (i.e. different feature sets) describing the same set of objects. In this framework, a base-learner algorithm is trained on each view separately, and their predictions are then combined by a meta-learner algorithm. In a previous study, stacked penalized logistic regression, a special case of multi-view stacking, has been shown to be useful in identifying which views are most important for prediction. In this article we expand this research by considering seven different algorithms to use as the meta-learner, and evaluating their view selection and classification performance in simulations and two applications on real gene-expression data sets. Our results suggest that if both view selection and classification accuracy are important to the research at hand, then the nonnegative lasso, nonnegative adaptive lasso and nonnegative elastic net are suitable meta-learners. Exactly which among these three is to be preferred depends on the research context. The remaining four meta-learners, namely nonnegative ridge regression, nonnegative forward selection, stability selection and the interpolating predictor, show little advantages in order to be preferred over the other three.

Despite the success of Transformers in self- supervised learning with applications to various downstream tasks, the computational cost of training and inference remains a major challenge for applying these models to a wide spectrum of devices. Several isolated attempts have been made to compress Transformers, but the settings and metrics are different across studies. Trade-off at various compression rates are also largely missing in prior work, making it difficult to compare compression techniques. In this work, we aim to provide context for the isolated results, studying several commonly used compression techniques, including weight pruning, head pruning, low-rank approximation, and knowledge distillation. We report trade- off at various compression rate, including wall-clock time, the number of parameters, and the number of multiply-accumulate operations. Our results show that compared to recent approaches, basic compression techniques are strong baselines. We further present several applications of our results, revealing properties of Transformers, such as the significance of diagonal attention heads. In addition, our results lead to a simple combination of compression techniques that improves trade-off over recent approaches. We hope the results would promote more diverse comparisons among model compression techniques and promote the use of model compression as a tool for analyzing models. Our code of compressing speech self-supervised model is available at //github.com/nervjack2/Speech-SSL-Compression/.

Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects models (NMMs) are commonly (and appropriately) used for models with HDPs. Conversely, in many practical applications of NMM, the random effects (REs) are actually correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. In this paper, we first summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate that this new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, as compared to the existing method based on marginal inference.

We consider the community detection problem in a sparse $q$-uniform hypergraph $G$, assuming that $G$ is generated according to the Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based on the non-backtracking operator for hypergraphs works with high probability down to the generalized Kesten-Stigum detection threshold conjectured by Angelini et al. (2015). We characterize the spectrum of the non-backtracking operator for the sparse HSBM and provide an efficient dimension reduction procedure using the Ihara-Bass formula for hypergraphs. As a result, community detection for the sparse HSBM on $n$ vertices can be reduced to an eigenvector problem of a $2n\times 2n$ non-normal matrix constructed from the adjacency matrix and the degree matrix of the hypergraph. To the best of our knowledge, this is the first provable and efficient spectral algorithm that achieves the conjectured threshold for HSBMs with $r$ blocks generated according to a general symmetric probability tensor.

In the field of robotic manipulation, deep imitation learning is recognized as a promising approach for acquiring manipulation skills. Additionally, learning from diverse robot datasets is considered a viable method to achieve versatility and adaptability. In such research, by learning various tasks, robots achieved generality across multiple objects. However, such multi-task robot datasets have mainly focused on single-arm tasks that are relatively imprecise, not addressing the fine-grained object manipulation that robots are expected to perform in the real world. This paper introduces a dataset of diverse object manipulations that includes dual-arm tasks and/or tasks requiring fine manipulation. To this end, we have generated dataset with 224k episodes (150 hours, 1,104 language instructions) which includes dual-arm fine tasks such as bowl-moving, pencil-case opening or banana-peeling, and this data is publicly available. Additionally, this dataset includes visual attention signals as well as dual-action labels, a signal that separates actions into a robust reaching trajectory and precise interaction with objects, and language instructions to achieve robust and precise object manipulation. We applied the dataset to our Dual-Action and Attention (DAA), a model designed for fine-grained dual arm manipulation tasks and robust against covariate shifts. The model was tested with over 7k total trials in real robot manipulation tasks, demonstrating its capability in fine manipulation. The dataset is available at //sites.google.com/view/multi-task-fine.

Typical pipelines for model geometry generation in computational biomedicine stem from images, which are usually considered to be at rest, despite the object being in mechanical equilibrium under several forces. We refer to the stress-free geometry computation as the reference configuration problem, and in this work we extend such a formulation to the theory of fully nonlinear poroelastic media. The main steps are (i) writing the equations in terms of the reference porosity and (ii) defining a time dependent problem whose steady state solution is the reference porosity. This problem can be computationally challenging as it can require several hundreds of iterations to converge, so we propose the use of Anderson acceleration to speed up this procedure. Our evidence shows that this strategy can reduce the number of iterations up to 80\%. In addition, we note that a primal formulation of the nonlinear mass conservation equations is not consistent due to the presence of second order derivatives of the displacement, which we alleviate through adequate mixed formulations. All claims are validated through numerical simulations in both idealized and realistic scenarios.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

A key requirement for the success of supervised deep learning is a large labeled dataset - a condition that is difficult to meet in medical image analysis. Self-supervised learning (SSL) can help in this regard by providing a strategy to pre-train a neural network with unlabeled data, followed by fine-tuning for a downstream task with limited annotations. Contrastive learning, a particular variant of SSL, is a powerful technique for learning image-level representations. In this work, we propose strategies for extending the contrastive learning framework for segmentation of volumetric medical images in the semi-supervised setting with limited annotations, by leveraging domain-specific and problem-specific cues. Specifically, we propose (1) novel contrasting strategies that leverage structural similarity across volumetric medical images (domain-specific cue) and (2) a local version of the contrastive loss to learn distinctive representations of local regions that are useful for per-pixel segmentation (problem-specific cue). We carry out an extensive evaluation on three Magnetic Resonance Imaging (MRI) datasets. In the limited annotation setting, the proposed method yields substantial improvements compared to other self-supervision and semi-supervised learning techniques. When combined with a simple data augmentation technique, the proposed method reaches within 8% of benchmark performance using only two labeled MRI volumes for training, corresponding to only 4% (for ACDC) of the training data used to train the benchmark.