Zhiyuan Zhan

Liuzhuozheng Li, Zhiyuan Zhan, Shuhong Liu et al.

Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to significant performance degradation. However, other deterministic sampling approaches, such as flow matching, can generate high-quality content without this conditioning, raising the question of its necessity. In this work, we revisit the role of time conditioning from a geometric perspective. We analyze the evolution of noisy data distributions under the forward diffusion process and demonstrate that, in high-dimensional spaces, these distributions concentrate on low-dimensional hyper-cylinder-like manifolds embedded within the input space. Successful generation, we argue, stems from the disentanglement of these manifolds in high-dimensional space. Based on this insight, we modify the forward process of DDIM to align the noisy data manifold with the flow-matching approach, proving that DDIM can generate high-quality content without time conditioning, provided the noisy manifold evolves according to the flow-matching method. Additionally, we extend our framework to class-conditioned generation by decoupling classes into distinct time spaces, enabling class-conditioned synthesis with a class-unconditional denoising model. Extensive experiments validate our theoretical analysis and show that high-quality generation is achievable without explicit conditional embeddings.

Qi Wang, Li Chen, Zhiyuan Zhan et al.

This paper presents a generic approach for applying the cognitive workload recognizer by exploiting common electroencephalogram (EEG) patterns across different human-machine tasks and individual sets. We propose a neural network called SCVCNet, which eliminates task- and individual-set-related interferences in EEGs by analyzing finer-grained frequency structures in the power spectral densities. The SCVCNet utilizes a sliding cross-vector convolution (SCVC) operation, where paired input layers representing the theta and alpha power are employed. By extracting the weights from a kernel matrix's central row and column, we compute the weighted sum of the two vectors around a specified scalp location. Next, we introduce an inter-frequency-point feature integration module to fuse the SCVC feature maps. Finally, we combined the two modules with the output-channel pooling and classification layers to construct the model. To train the SCVCNet, we employ the regularized least-square method with ridge regression and the extreme learning machine theory. We validate its performance using three databases, each consisting of distinct tasks performed by independent participant groups. The average accuracy (0.6813 and 0.6229) and F1 score (0.6743 and 0.6076) achieved in two different validation paradigms show partially higher performance than the previous works. All features and algorithms are available on website:https://github.com/7ohnKeats/SCVCNet.

Zhiyuan Zhan, Masashi Sugiyama

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations (SDEs) on manifolds, which raises the need for convergence theory of numerical schemes for manifold-valued SDEs. In Euclidean space, the Euler--Maruyama (EM) scheme achieves strong convergence with order $1/2$, but an analogous result for manifold discretizations is less understood in general settings. In this work, we study a geometric version of the EM scheme for SDEs on Riemannian manifolds and prove strong convergence with order $1/2$ under geometric and regularity conditions. As an application, we obtain a Wasserstein bound for sampling on manifolds via the geometric EM discretization of Riemannian Langevin dynamics.