We introduce a novel linear bandit problem with partially observable features, resulting in partial reward information and spurious estimates. Without proper address for latent part, regret possibly grows linearly in decision horizon $T$, as their influence on rewards are unknown. To tackle this, we propose a novel analysis to handle the latent features and an algorithm that achieves sublinear regret. The core of our algorithm involves (i) augmenting basis vectors orthogonal to the observed feature space, and (ii) introducing an efficient doubly robust estimator. Our approach achieves a regret bound of $\tilde{O}(\sqrt{(d + d_h)T})$, where $d$ is the dimension of observed features, and $d_h$ is the unknown dimension of the subspace of the unobserved features. Notably, our algorithm requires no prior knowledge of the unobserved feature space, which may expand as more features become hidden. Numerical experiments confirm that our algorithm outperforms both non-contextual multi-armed bandits and linear bandit algorithms depending solely on observed features.

Dramatic advances in the quality of the latent diffusion models (LDMs) also led to the malicious use of AI-generated images. While current AI-generated image detection methods assume the availability of real/AI-generated images for training, this is practically limited given the vast expressibility of LDMs. This motivates the training-free detection setup where no related data are available in advance. The existing LDM-generated image detection method assumes that images generated by LDM are easier to reconstruct using an autoencoder than real images. However, we observe that this reconstruction distance is overfitted to background information, leading the current method to underperform in detecting images with simple backgrounds. To address this, we propose a novel method called HFI. Specifically, by viewing the autoencoder of LDM as a downsampling-upsampling kernel, HFI measures the extent of aliasing, a distortion of high-frequency information that appears in the reconstructed image. HFI is training-free, efficient, and consistently outperforms other training-free methods in detecting challenging images generated by various generative models. We also show that HFI can successfully detect the images generated from the specified LDM as a means of implicit watermarking. HFI outperforms the best baseline method while achieving magnitudes of

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

We consider the general case where the per-formative risk can be non-convex, for which we develop efficient parameter-free optimistic optimization-based methods. Our algorithms significantly improve upon the existing Lips-chitz bandit-based method in many aspects. In particular, our framework does not require knowledge about the sensitivity parameter of the distribution map and the Lipshitz constant of the loss function. This makes our framework practically favorable, together with the efficient optimistic optimization-based tree-search mechanism. We provide experimental results that demonstrate the numerical superiority of our algorithms over the existing method and other black-box optimistic optimization methods.

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed such structures more accurately, these methods are confined under the message-passing paradigm, making the models vulnerable against side-effects such as oversmoothing and oversquashing. More recent work have proposed global attention-based graph Transformers that can easily model long-range interactions, but their extensions towards non-Euclidean geometry are yet unexplored. To bridge this gap, we propose Fully Product-Stereographic Transformer, a generalization of Transformers towards operating entirely on the product of constant curvature spaces. When combined with tokenized graph Transformers, our model can learn the curvature appropriate for the input graph in an end-to-end fashion, without the need of additional tuning on different curvature initializations. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges while respecting the underlying geometry. Experiments on graph reconstruction and node classification demonstrate the benefits of generalizing Transformers to the non-Euclidean domain.

For realistic talking head generation, creating natural head motion while maintaining accurate lip synchronization is essential. To fulfill this challenging task, we propose DisCoHead, a novel method to disentangle and control head pose and facial expressions without supervision. DisCoHead uses a single geometric transformation as a bottleneck to isolate and extract head motion from a head-driving video. Either an affine or a thin-plate spline transformation can be used and both work well as geometric bottlenecks. We enhance the efficiency of DisCoHead by integrating a dense motion estimator and the encoder of a generator which are originally separate modules. Taking a step further, we also propose a neural mix approach where dense motion is estimated and applied implicitly by the encoder. After applying the disentangled head motion to a source identity, DisCoHead controls the mouth region according to speech audio, and it blinks eyes and moves eyebrows following a separate driving video of the eye region, via the weight modulation of convolutional neural networks. The experiments using multiple datasets show that DisCoHead successfully generates realistic audio-and-video-driven talking heads and outperforms state-of-the-art methods. Project page: https://deepbrainai-research.github.io/discohead/