Former Defense Department intelligence officer Andrew Badger warns the White House Correspondents' Association Dinner shooting exposed serious security vulnerabilities around Donald Trump.

We provide the first global optimization landscape analysis of Neural Collapse-- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As recently reported in [1], this phenomenon implies that (i) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and (ii) cross-example within-class variability of last-layer activations collapses to zero. We study the problem based on a simplified unconstrained feature model, which isolates the topmost layers from the classifier of the neural network. In this context, we show that the classical cross-entropy loss with weight decay has a benign global landscape, in the sense that the only global minimizers are the Simplex ETFs while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. Our analysis of the simplified model not only explains what kind of features are learned in the last layer, but also shows why they can be efficiently optimized, matching the empirical observations in practical deep network architectures. These findings provide important practical implications. As an example, our experiments demonstrate that one may set the feature dimension equal to the number of classes and fix the last-layer classifier to be a Simplex ETF for network training, which reduces memory cost by over 20% on ResNet18 without sacrificing the generalization performance.

Analysis of neural network optimization in the mean-field regime is important as the setting allows for feature learning. Existing theory has been developed mainly for neural networks in finite dimensions, i.e., each neuron has a finite-dimensional parameter. However, the setting of infinite-dimensional input naturally arises in machine learning problems such as nonparametric functional data analysis and graph classification. In this paper, we develop a new mean-field analysis of two-layer neural network in an infinite-dimensional parameter space. We first give a generalization error bound, which shows that the regularized empirical risk minimizer properly generalizes when the data size is sufficiently large, despite the neurons being infinite-dimensional. Next, we present two gradient-based optimization algorithms for infinite-dimensional mean-field networks, by extending the recently developed particle optimization framework to the infinite-dimensional setting. We show that the proposed algorithms converge to the (regularized) global optimal solution, and moreover, their rates of convergence are of polynomial order in the online setting and exponential order in the finite sample setting, respectively. To our knowledge this is the first quantitative global optimization guarantee of neural network on infinite-dimensional input and in the presence of feature learning.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of taskagnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

We provide concrete rules below for the two competition tracks that comprise DATACOMP: filtering and BYOD . Additionally, we provide a checklist, which encourages participants to specify design decisions, which allows for more granular comparison between submissions. A.1 Filtering track rules Participants can enter submissions for one or many different scales: small, medium, large or xlarge, which represent the raw number of image-text pairs in CommonPool that should be filtered. After choosing a scale, participants generate a list of uids, where each uid refers to a COMMONPOOL sample. The list of uids is used to recover image-text pairs from the pool, which is used for downstream CLIP training.

We provide the supplements of "Contextual Gaussian Process Bandits with Neural Networks" here. Specifically, we discuss alternative acquisition functions that can be incorporated with the neural network-accompanied Gaussian process (NN-AGP) model in Section 6. In Section 7, we discuss the bandit algorithm with NN-AGP, where the neural network approximation error is considered. In Section 8, we provide the detailed proof of theorems. We provide the experimental details and include additional numerical experiments in Section 9. Last we discuss the limitations of NN-AGP and propose the potential approaches to addressing the limitations for future work, including sparse NN-AGP for alleviating computational burdens and transfer learning with NN-AGP to address cold-start issue; see Section 10. In the main text, we employ the upper confidence bound function as the acquisition function in the contextual Bayesian optimization approach. Here, we provide two alternative choices: Thompson sampling (TS) and knowledge gradient (KG). We describe the two procedures of the contextual GP bandit problems with NN-AGP, where the acquisition function is replaced by TS or KG. It chooses the action that maximizes the expected reward with respect to a random belief that is drawn for a posterior distribution. Besides the multi-armed bandit problems, TS has also achieved both theoretical and practical success in BO and Gaussian process regression. For more detailed discussions on TS, we refer to [87, 88]. Specifically, we propose a neural network-accompanied Gaussian process Thompson sampling (NNAGP-TS) approach to address contextual GP bandits. The approach works as follows. In each iteration, NN-AGP-TS first fits an NN-AGP model with the historic data. Then, given the current contextual variable, a realization of the Gaussian process with respect to x X is sampled from the posterior distribution conditional on the historic data1.

This paper studies a new variant of the stochastic multi-armed bandits problem where auxiliary information about the arm rewards is available in the form of control variates. In many applications like queuing and wireless networks, the arm rewards are functions of some exogenous variables. The mean values of these variables are known a priori from historical data and can be used as control variates. Leveraging the theory of control variates, we obtain mean estimates with smaller variance and tighter confidence bounds. We develop an upper confidence bound based algorithm named UCB-CV and characterize the regret bounds in terms of the correlation between rewards and control variates when they follow a multivariate normal distribution. We also extend UCB-CV to other distributions using resampling methods like Jackknifing and Splitting. Experiments on synthetic problem instances validate performance guarantees of the proposed algorithms.

Potential negative societal impacts Although our work improves the performance of text-video retrieval, but may reduce the difficulty of cross-modal retrieval of sensitive information on the network. It may raise challenges to protecting information security. Limitations of our work Iterative approaches are sensitive to initialization and parameters such as the dimensions and the number of subspaces. In our work, although we use the L2 normalization operation to limit the value range of the parameters, the EM algorithm [3] may still converge to bad results. At the same time, the selection of the number of subspaces also has a relatively significant impact on the model effect.