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In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied with some confidence indication. Two popular post-processing approaches for that aim are: 1) calibration: modifying the classifier's softmax values such that their maximum (associated with the prediction) better estimates the correctness probability; and 2) conformal prediction (CP): devising a score (based on the softmax values) from which a set of predictions with theoretically guaranteed marginal coverage of the correct class is produced. While in practice both types of indications can be desired, so far the interplay between them has not been investigated. Toward filling this gap, in this paper we study the effect of temperature scaling, arguably the most common calibration technique, on prominent CP methods. We start with an extensive empirical study that among other insights shows that, surprisingly, calibration has a detrimental effect on popular adaptive CP methods: it frequently leads to larger prediction sets. Then, we turn to theoretically analyze this behavior. We reveal several mathematical properties of the procedure, according to which we provide a reasoning for the phenomenon. Our study suggests that it may be worthwhile to utilize adaptive CP methods, chosen for their enhanced conditional coverage, based on softmax values prior to (or after canceling) temperature scaling calibration.

We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},\sigma_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $\lambda^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, \sigma_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts. This problem arises from the goodness-of-fit test when we would like to test whether the data are generated from $g_{0}(Y|X)$ (null hypothesis) or they are generated from the whole mixture (alternative hypothesis). Based on the algebraic structure of the expert functions and the distinguishability between $g_0$ and the mixture part, we construct novel Voronoi-based loss functions to capture the convergence rates of maximum likelihood estimation (MLE) for our models. We further demonstrate that our proposed loss functions characterize the local convergence rates of parameter estimation more accurately than the generalized Wasserstein, a loss function being commonly used for estimating parameters in the Gaussian mixture of experts.

In this critical survey, we analyze typical claims on the relationship between explainable AI (XAI) and fairness to disentangle the multidimensional relationship between these two concepts. Based on a systematic literature review and a subsequent qualitative content analysis, we identify seven archetypal claims from 175 papers on the alleged fairness benefits of XAI. We present crucial caveats with respect to these claims and provide an entry point for future discussions around the potentials and limitations of XAI for specific fairness desiderata. Importantly, we notice that claims are often (i) vague and simplistic, (ii) lacking normative grounding, or (iii) poorly aligned with the actual capabilities of XAI. We encourage to conceive XAI not as an ethical panacea but as one of many tools to approach the multidimensional, sociotechnical challenge of algorithmic fairness. Moreover, when making a claim about XAI and fairness, we emphasize the need to be more specific about what kind of XAI method is used and which fairness desideratum it refers to, how exactly it enables fairness, and who is the stakeholder that benefits from XAI.

The probabilistic formal verification (PFV) of AI systems is in its infancy. So far, approaches have been limited to ad-hoc algorithms for specific classes of models and/or properties. We propose a unifying framework for the PFV of AI systems based onWeighted Model Integration (WMI), which allows to frame the problem in very general terms. Crucially, this reduction enables the verification of many properties of interest, like fairness, robustness or monotonicity, over a wide range of machine learning models, without making strong distributional assumptions. We support the generality of the approach by solving multiple verification tasks with a single, off-the-shelf WMI solver, then discuss the scalability challenges and research directions related to this promising framework.

This study investigates the asymptotic dynamics of alternating minimization applied to optimize a bilinear non-convex function with normally distributed covariates. We employ the replica method from statistical physics in a multi-step approach to precisely trace the algorithm's evolution. Our findings indicate that the dynamics can be described effectively by a two--dimensional discrete stochastic process, where each step depends on all previous time steps, revealing a memory dependency in the procedure. The theoretical framework developed in this work is broadly applicable for the analysis of various iterative algorithms, extending beyond the scope of alternating minimization.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.