Video Anomaly Detection (VAD) finds widespread applications in security surveillance, traffic monitoring, industrial monitoring, and healthcare. Despite extensive research efforts, there remains a lack of concise reviews that provide insightful guidance for researchers. Such reviews would serve as quick references to grasp current challenges, research trends, and future directions.

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

Subspace learning is a critical endeavor in contemporary machine learning, particularly given the vast dimensions of modern datasets.

This paper introduces CoFie, a novel local geometry-aware neural surface representation. CoFie is motivated by the theoretical analysis of local SDFs with quadratic approximation. We find that local shapes are highly compressive in an aligned coordinate frame defined by the normal and tangent directions of local shapes. Accordingly, we introduce Coordinate Field, which is a composition of coordinate frames of all local shapes. The Coordinate Field is optimizable and is used to transform the local shapes from the world coordinate frame to the aligned shape coordinate frame. It largely reduces the complexity of local shapes and benefits the learning of MLP-based implicit representations.

In this section, we provide more details on the apparatus necessary to perform a posteriori conditional sampling in the presence of a linear constraint. Eq. (6) suggests that the SDE drift corresponding to the score may be broken down into 3 steps: 1. However, in practice this modification creates a "discontinuity" between the constrained and unconstrained components, leading to erroneous correlations between them in the generated samples. This is the post-processed denoiser function Eq. (7) in the main text. Thus it needs to be tuned empirically. The correction in Eq. (16) is equivalent to imposing a Gaussian likelihood on x It is worth noting that both the mean and variance here have direct correspondence to estimations of statistical moments using Tweedie's formulas [29]: E[x However, the Gaussian assumption is good at early stages of denoising (t 0) when the signal-to-noise ratio (SNR) is low. Remark 2. The post-processing presented in this section is similar to [17], who propose to apply a correction proportional to In practice, we found that including this scaling contributes greatly to the numerical stability and efficiency of continuous-time sampling. B.1 Training The training of our denoiser-based diffusion models largely follows the methodology proposed in [45]. In this section, we present the most relevant components for completeness and better reproducibility.

Diffusion models generate new samples by progressively decreasing the noise from the initially provided random distribution. This inference procedure generally utilizes a trained neural network numerous times to obtain the final output, creating significant latency and energy consumption on digital electronic hardware such as GPUs. In this study, we demonstrate that the propagation of a light beam through a semi-transparent medium can be programmed to implement a denoising diffusion model on image samples. This framework projects noisy image patterns through passive diffractive optical layers, which collectively only transmit the predicted noise term in the image. The optical transparent layers, which are trained with an online training approach, backpropagating the error to the analytical model of the system, are passive and kept the same across different steps of denoising. Hence this method enables high-speed image generation with minimal power consumption, benefiting from the bandwidth and energy efficiency of optical information processing.

Diffusion models have garnered widespread attention in Reinforcement Learning (RL) for their powerful expressiveness and multimodality. It has been verified that utilizing diffusion policies can significantly improve the performance of RL algorithms in continuous control tasks by overcoming the limitations of unimodal policies, such as Gaussian policies. Furthermore, the multimodality of diffusion policies also shows the potential of providing the agent with enhanced exploration capabilities. However, existing works mainly focus on applying diffusion policies in offline RL, while their incorporation into online RL has been less investigated. The diffusion model's training objective, known as the variational lower bound, cannot be applied directly in online RL due to the unavailability of'good' samples (actions).

We consider the problem of minimizing a smooth convex function by reducing the optimization to computing the Nash equilibrium of a particular zero-sum convexconcave game. Zero-sum games can be solved using online learning dynamics, where a classical technique involves simulating two no-regret algorithms that play against each other and, after T rounds, the average iterate is guaranteed to solve the original optimization problem with error decaying as O(log T/T).

Average-link is widely recognized as one of the most popular and effective methods for building hierarchical agglomerative clustering. The available theoretical analyses show that this method has a much better approximation than other popular heuristics, as single-linkage and complete-linkage, regarding variants of Dasgupta's cost function [STOC 2016]. However, these analyses do not separate average-link from a random hierarchy and they are not appealing for metric spaces since every hierarchical clustering has a 1/2 approximation with regard to the variant of Dasgupta's function that is employed for dissimilarity measures [Moseley and Yang 2020]. In this paper, we present a comprehensive study of the performance of average-link in metric spaces, regarding several natural criteria that capture separability and cohesion, and are more interpretable than Dasgupta's cost function and its variants. We also present experimental results with real datasets that, together with our theoretical analyses, suggest that average-link is a better choice than other related methods when both cohesion and separability are important goals.

Recent advances in diffusion-based Large Restoration Models (LRMs) have significantly improved photo-realistic image restoration by leveraging the internal knowledge embedded within model weights. However, existing LRMs often suffer from the hallucination dilemma, i.e., producing incorrect contents or textures when dealing with severe degradations, due to their heavy reliance on limited internal knowledge. In this paper, we propose an orthogonal solution called the Retrieval-augmented Framework for Image Restoration (ReFIR), which incorporates retrieved images as external knowledge to extend the knowledge boundary of existing LRMs in generating details faithful to the original scene. Specifically, we first introduce the nearest neighbor lookup to retrieve content-relevant high-quality images as reference, after which we propose the cross-image injection to modify existing LRMs to utilize high-quality textures from retrieved images. Thanks to the additional external knowledge, our ReFIR can well handle the hallucination challenge and facilitate faithfully results. Extensive experiments demonstrate that ReFIR can achieve not only high-fidelity but also realistic restoration results. Importantly, our ReFIR requires no training and is adaptable to various LRMs.