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

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to \infty$ and at least one between $P/D^K$, $N/D^L$ remains finite.

What is the best paradigm to recognize objects -- discriminative inference (fast but potentially prone to shortcut learning) or using a generative model (slow but potentially more robust)? We build on recent advances in generative modeling that turn text-to-image models into classifiers. This allows us to study their behavior and to compare them against discriminative models and human psychophysical data. We report four intriguing emergent properties of generative classifiers: they show a record-breaking human-like shape bias (99% for Imagen), near human-level out-of-distribution accuracy, state-of-the-art alignment with human classification errors, and they understand certain perceptual illusions. Our results indicate that while the current dominant paradigm for modeling human object recognition is discriminative inference, zero-shot generative models approximate human object recognition data surprisingly well.

Evolving virtual creatures is a field with a rich history and recently it has been getting more attention, especially in the soft robotics domain. The compliance of soft materials endows soft robots with complex behavior, but it also makes their design process unintuitive and in need of automated design. Despite the great interest, evolved virtual soft robots lack the complexity, and co-optimization of morphology and control remains a challenging problem. Prior work identifies and investigates a major issue with the co-optimization process -- fragile co-adaptation of brain and body resulting in premature convergence of morphology. In this work, we expand the investigation of this phenomenon by comparing learnable controllers with proprioceptive observations and fixed controllers without any observations, whereas in the latter case, we only have the optimization of the morphology. Our experiments in two morphology spaces and two environments that vary in complexity show, concrete examples of the existence of high-performing regions in the morphology space that are not able to be discovered during the co-optimization of the morphology and control, yet exist and are easily findable when optimizing morphologies alone. Thus this work clearly demonstrates and characterizes the challenges of optimizing morphology during co-optimization. Based on these results, we propose a new body-centric framework to think about the co-optimization problem which helps us understand the issue from a search perspective. We hope the insights we share with this work attract more attention to the problem and help us to enable efficient brain-body co-optimization.

Expander graphs, due to their good mixing properties, are useful in many algorithms and combinatorial constructions. One can produce an expander graph with high probability by taking a random graph. For example, for the case of bipartite graphs of degree $d$ and $n$ vertices in each part we may take independently $d$ permutations of an $n$-element set and use them for edges. This construction is much simpler than all known explicit constructions of expanders and gives graphs with good mixing properties (small second largest eigenvalue) with high probability. However, from the practical viewpoint, it uses too many random bits, so it is difficult to generate and store these bits for reasonably large graphs. The natural idea is to replace the group of all permutations by its small subgroup. Let $n$ be $q^k-1$ for some $k$ and some prime $q$. Then we may interpret vertices as non-zero $k$-dimensional vector over the field $\mathbb{F}_q$, and take random \emph{linear} permutations, i.e., random elements of $GL_k(\mathbb{F}_q)$. In this way the number of random bits used will be polynomial in $k$ (i.e., the logarithm of the graph size, instead of the graph size itself) and the degree. In this paper we provide some experimental data that show that indeed this replacement does not change much the mixing properties (the second eigenvalue) of the random graph that we obtain. These data are provided for several types of graphs (undirected regular and biregular bipartite graphs). We also prove some upper bounds for the second eigenvalue (though it is quite weak compared with the experimental results). Finally, we discuss the possibility to decrease the number of random bits further by using Toeplitz matrices; our experiments show that this change makes the mixing properties of graphs only marginally worse, while the number of random bits decreases significantly.

Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and the Wasserstein distance from the residuals to the set of quantiles, we establish a generalization of the composite quantile regression to the multiple-output settings. Theoretical convergence rates of the proposed estimator are derived both under the setting where the additive error possesses only a finite $\ell$-th moment (for $\ell > 2$) and where it exhibits a sub-Weibull tail. In doing so, we develop novel techniques for analyzing the M-estimation problem that involves Wasserstein-distance in the loss. Numerical studies confirm the practical effectiveness of our proposed procedure.

In the realm of cost-sharing mechanisms, the vulnerability to Sybil strategies -- also known as false-name strategies, where agents create fake identities to manipulate outcomes -- has not yet been studied. In this paper, we delve into the details of different cost-sharing mechanisms proposed in the literature, highlighting their non-Sybil-resistant nature. Furthermore, we prove that a Sybil-proof cost-sharing mechanism for public excludable goods under mild conditions is at least $(n+1)/2-$approximate. This finding reveals an exponential increase in the worst-case social cost in environments where agents are restricted from using Sybil strategies. To circumvent these negative results, we introduce the concept of \textit{Sybil Welfare Invariant} mechanisms, where a mechanism does not decrease its welfare under Sybil-strategies when agents choose weak dominant strategies and have subjective prior beliefs over other players' actions. Finally, we prove that the Shapley value mechanism for symmetric and submodular cost functions holds this property, and so deduce that the worst-case social cost of this mechanism is the $n$th harmonic number $\mathcal H_n$ under equilibrium with Sybil strategies, matching the worst-case social cost bound for cost-sharing mechanisms. This finding suggests that any group of agents, each with private valuations, can fund public excludable goods both permissionless and anonymously, achieving efficiency comparable to that of permissioned and non-anonymous domains, even when the total number of participants is unknown.

This paper discusses the foundation of methods for accurately grasping the interaction effects. Among the existing methods that capture the interaction effects as terms, PD and ALE are known as global modelagnostic methods in the IML field. ALE, among the two, can theoretically provide a functional decomposition of the prediction function, and this study focuses on functional decomposition. Specifically, we mathematically formalize what we consider to be the requirements that must always be met by a decomposition (interaction decomposition, hereafter, ID) that decomposes the prediction function into main and interaction effect terms. We also present a theorem about how to produce a decomposition that meets these requirements. Furthermore, we confirm that while ALE is ID, PD is not, and we present examples of decomposition that meet the requirements of ID using methods other than existing ones (i.e., new methods).

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.

Contextual Bayesian Optimization (CBO) efficiently optimizes black-box functions with respect to design variables, while simultaneously integrating contextual information regarding the environment, such as experimental conditions. However, the relevance of contextual variables is not necessarily known beforehand. Moreover, contextual variables can sometimes be optimized themselves at additional cost, a setting overlooked by current CBO algorithms. Cost-sensitive CBO would simply include optimizable contextual variables as part of the design variables based on their cost. Instead, we adaptively select a subset of contextual variables to include in the optimization, based on the trade-off between their \emph{relevance} and the additional cost incurred by optimizing them compared to leaving them to be determined by the environment. We learn the relevance of contextual variables by sensitivity analysis of the posterior surrogate model while minimizing the cost of optimization by leveraging recent developments on early stopping for BO. We empirically evaluate our proposed Sensitivity-Analysis-Driven Contextual BO (SADCBO) method against alternatives on both synthetic and real-world experiments, together with extensive ablation studies, and demonstrate a consistent improvement across examples.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.