亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure of covariances by means of the Bures-Wasserstein metric geometry. We make use of the Riemmanian-like structure induced by this metric to define a notion of mean and covariance of a random flow, and develop an associated Karhunen-Lo\`eve expansion. We then treat the problem of estimation and construction of functional principal components from a finite collection of covariance flows, observed fully or irregularly. Our theoretical results are motivated by modern problems in functional data analysis, where one observes operator-valued random processes -- for instance when analysing dynamic functional connectivity and fMRI data, or when analysing multiple functional time series in the frequency domain. Nevertheless, our framework is also novel in the finite-dimensions (matrix case), and we demonstrate what simplifications can be afforded then. We illustrate our methodology by means of simulations and data analyses.

We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and Kripke frames, where the quantifiers range over all sets of worlds. We show that any normal propositionally quantified modal logic containing all instances of the Barcan scheme is strongly complete with respect to the class of quantifiable general frames validating it. We also provide a sufficient condition for the truth of all formulas, possibly with quantifiers, to be preserved under passing from a quantifiable general frame to its underlying Kripke frame. This is reminiscent of both the idea of elementary submodel in model theory and the persistence concepts in propositional modal logic. The key to this condition is the concept of finite diversity (Fritz 2023), and with it, we show that if $\Theta$ is a set of Sahlqvist formulas whose class of Kripke frames has finite diversity, then the smallest normal propositionally quantified modal logic containing $\Theta$, Barcan, a formula stating the existence of world propositions, and a formula stating the definability of successor sets, is Kripke complete. As a special case, we have a simple finite axiomatization of the logic of Euclidean Kripke frames.

Today, three-dimensional reconstruction of objects has many applications in various fields, and therefore, choosing a suitable method for high resolution three-dimensional reconstruction is an important issue and displaying high-level details in three-dimensional models is a serious challenge in this field. Until now, active methods have been used for high-resolution three-dimensional reconstruction. But the problem of active three-dimensional reconstruction methods is that they require a light source close to the object. Shape from polarization (SfP) is one of the best solutions for high-resolution three-dimensional reconstruction of objects, which is a passive method and does not have the drawbacks of active methods. The changes in polarization of the reflected light from an object can be analyzed by using a polarization camera or locating polarizing filter in front of the digital camera and rotating the filter. Using this information, the surface normal can be reconstructed with high accuracy, which will lead to local reconstruction of the surface details. In this paper, an end-to-end deep learning approach has been presented to produce the surface normal of objects. In this method a benchmark dataset has been used to train the neural network and evaluate the results. The results have been evaluated quantitatively and qualitatively by other methods and under different lighting conditions. The MAE value (Mean-Angular-Error) has been used for results evaluation. The evaluations showed that the proposed method could accurately reconstruct the surface normal of objects with the lowest MAE value which is equal to 18.06 degree on the whole dataset, in comparison to previous physics-based methods which are between 41.44 and 49.03 degree.

We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.

Sequential recommender systems aims to predict the users' next interaction through user behavior modeling with various operators like RNNs and attentions. However, existing models generally fail to achieve the three golden principles for sequential recommendation simultaneously, i.e., training efficiency, low-cost inference, and strong performance. To this end, we propose RecBLR, an Efficient Sequential Recommendation Model based on Behavior-Dependent Linear Recurrent Units to accomplish the impossible triangle of the three principles. By incorporating gating mechanisms and behavior-dependent designs into linear recurrent units, our model significantly enhances user behavior modeling and recommendation performance. Furthermore, we unlock the parallelizable training as well as inference efficiency for our model by designing a hardware-aware scanning acceleration algorithm with a customized CUDA kernel. Extensive experiments on real-world datasets with varying lengths of user behavior sequences demonstrate RecBLR's remarkable effectiveness in simultaneously achieving all three golden principles - strong recommendation performance, training efficiency, and low-cost inference, while exhibiting excellent scalability to datasets with long user interaction histories.

Inductive conformal predictors (ICPs) are algorithms that are able to generate prediction sets, instead of point predictions, which are valid at a user-defined confidence level, only assuming exchangeability. These algorithms are useful for reliable machine learning and are increasing in popularity. The ICP development process involves dividing development data into three parts: training, calibration and test. With access to limited or expensive development data, it is an open question regarding the most efficient way to divide the data. This study provides several experiments to explore this question and consider the case for allowing overlap of examples between training and calibration sets. Conclusions are drawn that will be of value to academics and practitioners planning to use ICPs.

We present a new framework for solving general topology optimization (TO) problems that find an optimal material distribution within a design space to maximize the performance of a structure while satisfying design constraints. These problems involve state variables that nonlinearly depend on the design variables, with objective functions that can be convex or non-convex, and may include multiple candidate materials. The framework is designed to greatly enhance computational efficiency, primarily by diminishing optimization iteration counts and thereby reducing the solving of associated state-equilibrium partial differential equations (PDEs). It maintains binary design variables and addresses the large-scale mixed integer nonlinear programming (MINLP) problem that arises from discretizing the design space and PDEs. The core of this framework is the integration of the generalized Benders' decomposition and adaptive trust regions. The trust-region radius adapts based on a merit function. To mitigate ill-conditioning due to extreme parameter values, we further introduce a parameter relaxation scheme where two parameters are relaxed in stages at different paces. Numerical tests validate the framework's superior performance, including minimum compliance and compliant mechanism problems in single-material and multi-material designs. We compare our results with those of other methods and demonstrate significant reductions in optimization iterations by about one order of magnitude, while maintaining comparable optimal objective function values. As the design variables and constraints increase, the framework maintains consistent solution quality and efficiency, underscoring its good scalability. We anticipate this framework will be especially advantageous for TO applications involving substantial design variables and constraints and requiring significant computational resources for PDE solving.

We give a new coalgebraic semantics for intuitionistic modal logic with $\Box$. In particular, we provide a colagebraic representation of intuitionistic descriptive modal frames and of intuitonistic modal Kripke frames based on image-finite posets. This gives a solution to a problem in the area of coalgebaic logic for these classes of frames, raised explicitly by Litak (2014) and de Groot and Pattinson (2020). Our key technical tool is a recent generalization of a construction by Ghilardi, in the form of a right adjoint to the inclusion of the category of Esakia spaces in the category of Priestley spaces. As an application of these results, we study bisimulations of intuitionistic modal frames, describe dual spaces of free modal Heyting algebras, and provide a path towards a theory of coalgebraic intuitionistic logics.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.