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

Quantitative analysis of probabilistic programs aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability, and plays a crucial role in the verification of probabilistic programs. Along this line of research, most existing works consider numerical bounds over the whole state space monolithically and do not consider piecewise bounds. Clearly, monolithic bounds are either conservative, or not expressive and succinct enough in general. To derive more succinct, expressive and precise numerical bounds for probabilistic properties, we propose a novel approach for synthesizing piecewise linear bounds in this work. To this end, we first show how to extract a piecewise feature w.r.t. a given quantitative property from a probabilistic program using latticed $k$-induction that captures a wide and representative class of piecewise bound functions. Second, we develop an algorithmic approach to synthesize piecewise linear upper and lower bounds from the piecewise feature, for which we show that the synthesis of piecewise linear bounds can be reduced to bilinear programming. Third, we implement our approach with the bilinear programming solver Gurobi. The experimental results indicate that our approach is capable of generating tight or even accurate piecewise linear bounds for an extensive set of benchmarks compared with the state of the art.

Dialogue response selection aims to select an appropriate response from several candidates based on a given user and system utterance history. Most existing works primarily focus on post-training and fine-tuning tailored for cross-encoders. However, there are no post-training methods tailored for dense encoders in dialogue response selection. We argue that when the current language model, based on dense dialogue systems (such as BERT), is employed as a dense encoder, it separately encodes dialogue context and response, leading to a struggle to achieve the alignment of both representations. Thus, we propose Dial-MAE (Dialogue Contextual Masking Auto-Encoder), a straightforward yet effective post-training technique tailored for dense encoders in dialogue response selection. Dial-MAE uses an asymmetric encoder-decoder architecture to compress the dialogue semantics into dense vectors, which achieves better alignment between the features of the dialogue context and response. Our experiments have demonstrated that Dial-MAE is highly effective, achieving state-of-the-art performance on two commonly evaluated benchmarks.

Given the Fourier-Legendre expansions of $f$ and $g$, and mild conditions on $f$ and $g$, we derive the Fourier-Legendre expansion of their product in terms of their corresponding Fourier-Legendre coefficients. In this way, expansions of whole number powers of $f$ may be obtained. We establish upper bounds on rates of convergence. We then employ these expansions to solve semi-analytically a class of nonlinear PDEs with a polynomial nonlinearity of degree 2. The obtained numerical results illustrate the efficiency and performance accuracy of this Fourier-Legendre based solution methodology for solving an important class of nonlinear PDEs.

We study the complexity of constructing an optimal parsing $\varphi$ of a string ${\bf s} = s_1 \dots s_n$ under the constraint that given a position $p$ in the original text, and the LZ76-like (Lempel Ziv 76) encoding of $T$ based on $\varphi$, it is possible to identify/decompress the character $s_p$ by performing at most $c$ accesses to the LZ encoding, for a given integer $c.$ We refer to such a parsing $\varphi$ as a $c$-bounded access LZ parsing or $c$-BLZ parsing of ${\bf s}.$ We show that for any constant $c$ the problem of computing the optimal $c$-BLZ parsing of a string, i.e., the one with the minimum number of phrases, is NP-hard and also APX hard, i.e., no PTAS can exist under the standard complexity assumption $P \neq NP.$ We also study the ratio between the sizes of an optimal $c$-BLZ parsing of a string ${\bf s}$ and an optimal LZ76 parsing of ${\bf s}$ (which can be greedily computed in polynomial time).

The pathfinding problem, which aims to identify a collision-free path between two points, is crucial for many applications, such as robot navigation and autonomous driving. Classic methods, such as A$^*$ search, perform well on small-scale maps but face difficulties scaling up. Conversely, data-driven approaches can improve pathfinding efficiency but require extensive data labeling and lack theoretical guarantees, making it challenging for practical applications. To combine the strengths of the two methods, we utilize the imperative learning (IL) strategy and propose a novel self-supervised pathfinding framework, termed imperative learning-based A$^*$ (iA$^*$). Specifically, iA$^*$ is a bilevel optimization process where the lower-level optimization is dedicated to finding the optimal path by a differentiable A$^*$ search module, and the upper-level optimization narrows down the search space to improve efficiency via setting suitable initial values from a data-driven model. Besides, the model within the upper-level optimization is a fully convolutional network, trained by the calculated loss in the lower-level optimization. Thus, the framework avoids extensive data labeling and can be applied in diverse environments. Our comprehensive experiments demonstrate that iA$^*$ surpasses both classical and data-driven methods in pathfinding efficiency and shows superior robustness among different tasks, validated with public datasets and simulation environments.

Block orthogonal sparse superposition (BOSS) code is a class of joint coded modulation methods, which can closely achieve the finite-blocklength capacity with a low-complexity decoder at a few coding rates under Gaussian channels. However, for fading channels, the code performance degrades considerably because coded symbols experience different channel fading effects. In this paper, we put forth novel joint demodulation and decoding methods for BOSS codes under fading channels. For a fast fading channel, we present a minimum mean square error approximate maximum a posteriori (MMSE-A-MAP) algorithm for the joint demodulation and decoding when channel state information is available at the receiver (CSIR). We also propose a joint demodulation and decoding method without using CSIR for a block fading channel scenario. We refer to this as the non-coherent sphere decoding (NSD) algorithm. Simulation results demonstrate that BOSS codes with MMSE-A-MAP decoding outperform CRC-aided polar codes, while NSD decoding achieves comparable performance to quasi-maximum likelihood decoding with significantly reduced complexity. Both decoding algorithms are suitable for parallelization, satisfying low-latency constraints. Additionally, real-time simulations on a software-defined radio testbed validate the feasibility of using BOSS codes for low-power transmission.

This paper proposes to develop a new variant of the two-time-scale stochastic approximation to find the roots of two coupled nonlinear operators, assuming only noisy samples of these operators can be observed. Our key idea is to leverage the classic Ruppert-Polyak averaging technique to dynamically estimate the operators through their samples. The estimated values of these averaging steps will then be used in the two-time-scale stochastic approximation updates to find the desired solution. Our main theoretical result is to show that under the strongly monotone condition of the underlying nonlinear operators the mean-squared errors of the iterates generated by the proposed method converge to zero at an optimal rate $O(1/k)$, where $k$ is the number of iterations. Our result significantly improves the existing result of two-time-scale stochastic approximation, where the best known finite-time convergence rate is $O(1/k^{2/3})$. We illustrate this result by applying the proposed method to develop new reinforcement learning algorithms with improved performance.

We prove that the single-site Glauber dynamics for sampling proper $q$-colorings mixes in $O_\Delta(n\log n)$ time on line graphs with $n$ vertices and maximum degree $\Delta$ when $q>(1+o(1))\Delta$. The main tool in our proof is the matrix trickle-down theorem developed by Abdolazimi, Liu and Oveis Gharan (FOCS, 2021).

Chatterjee's rank correlation coefficient $\xi_n$ is an empirical index for detecting functional dependencies between two variables $X$ and $Y$. It is an estimator for a theoretical quantity $\xi$ that is zero for independence and one if $Y$ is a measurable function of $X$. Based on an equivalent characterization of sorted numbers, we derive an upper bound for $\xi_n$ and suggest a simple normalization aimed at reducing its bias for small sample size $n$. In Monte Carlo simulations of various cases, the normalization reduced the bias in all cases. The mean squared error was reduced, too, for values of $\xi$ greater than about 0.4. Moreover, we observed that non-parametric confidence intervals for $\xi$ based on bootstrapping $\xi_n$ in the usual n-out-of-n way have a coverage probability close to zero. This is remedied by an m-out-of-n bootstrap without replacement in combination with our normalization method.

We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its distributional assumption by using a quasi-likelihood setup. By parameterizing the mean-variance relationship on data entries, we additionally introduce a dispersion parameter and entry-wise weights to model large variations and missing values. The resulting model is thus not only robust to distribution misspecification but also more flexible and able to capture non-Gaussian covariance structures of the data matrix. Our main focus is on efficient computational approaches to perform the factor analysis. Previous modeling frameworks rely on simulated maximum likelihood (SML) to find the factorization solution, but this method was shown to lead to asymptotic bias when the simulated sample size grows slower than the square root of the sample size $n$, eliminating its practical application for data matrices with large $n$. Borrowing from expectation-maximization (EM) and stochastic gradient descent (SGD), we investigate three estimation procedures based on iterative factorization updates. Our proposed solution does not show asymptotic biases, and scales even better for large matrix factorizations with error $O(1/p)$. To support our findings, we conduct simulation experiments and discuss its application in three case studies.