Fan Cheng

Zhantao Yang, Ruili Feng, Han Zhang et al. · tsinghua

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we explore a perplexing tendency of diffusion models: they often display the infinite Lipschitz property of the network with respect to time variable near the zero point. We provide theoretical proofs to illustrate the presence of infinite Lipschitz constants and empirical results to confirm it. The Lipschitz singularities pose a threat to the stability and accuracy during both the training and inference processes of diffusion models. Therefore, the mitigation of Lipschitz singularities holds great potential for enhancing the performance of diffusion models. To address this challenge, we propose a novel approach, dubbed E-TSDM, which alleviates the Lipschitz singularities of the diffusion model near the zero point of timesteps. Remarkably, our technique yields a substantial improvement in performance. Moreover, as a byproduct of our method, we achieve a dramatic reduction in the Fréchet Inception Distance of acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. Extensive experiments on diverse datasets validate our theory and method. Our work may advance the understanding of the general diffusion process, and also provide insights for the design of diffusion models.

Fan L. Cheng, Nikolaus Kriegeskorte

Prompting steers large language models (LLMs) and vision-language models (VLMs) without weight updates, but it remains unclear how instruction changes reshape internal representations to produce behavior. We introduce a nested geometric decomposition framework that treats prompting as a transformation of the representational geometry of the content following the prompt. For each prompt pair, we align representations of the same stimuli under two prompts using increasingly expressive stimulus-invariant maps: translation, rigid transformation with uniform scaling, sequential axis scaling, affine transformation, and nonlinear transformation. We then causally test each map by replacing a single layer's prompt-A hidden state for held-out stimuli with its mapped counterpart and measuring recovery of prompt-B representational geometry and behavior. Across three LLMs, three VLMs, and six text or image datasets spanning style, emotion, scene content, and number, prompts consistently reshape representations toward the instructed task structure. Cross-validated variance decomposition shows that much prompt-induced activation change is captured by shape-preserving maps, especially translation and rigid transformation with uniform scaling, while tier profiles reveal model- and task-specific routing strategies across layers. Crucially, although translation and rigid tiers already improve behavioral agreement, affine transformation is the first tier to nearly recover target-prompt task geometry and yields corresponding behavioral gains. This suggests that cross-dimensional linear mixing is a key mechanism by which prompts reorganize representations toward instructed task structure. Our framework decomposes prompt-induced representational change into interpretable geometric components and reveals how models route task-relevant structure to produce prompt-driven behavior.

Zhize Wu, Changjiang Du, Le Zou et al.

A good feature representation is the key to image classification. In practice, image classifiers may be applied in scenarios different from what they have been trained on. This so-called domain shift leads to a significant performance drop in image classification. Unsupervised domain adaptation (UDA) reduces the domain shift by transferring the knowledge learned from a labeled source domain to an unlabeled target domain. We perform feature disentanglement for UDA by distilling category-relevant features and excluding category-irrelevant features from the global feature maps. This disentanglement prevents the network from overfitting to category-irrelevant information and makes it focus on information useful for classification. This reduces the difficulty of domain alignment and improves the classification accuracy on the target domain. We propose a coarse-to-fine domain adaptation method called Domain Adaptation via Feature Disentanglement~(DAFD), which has two components: (1)the Category-Relevant Feature Selection (CRFS) module, which disentangles the category-relevant features from the category-irrelevant features, and (2)the Dynamic Local Maximum Mean Discrepancy (DLMMD) module, which achieves fine-grained alignment by reducing the discrepancy within the category-relevant features from different domains. Combined with the CRFS, the DLMMD module can align the category-relevant features properly. We conduct comprehensive experiment on four standard datasets. Our results clearly demonstrate the robustness and effectiveness of our approach in domain adaptive image classification tasks and its competitiveness to the state of the art.

Isabella Elaine Rosario, Fan L. Cheng, Zitang Sun et al.

Understanding human motion processing is essential for building reliable, human-centered computer vision systems. Although deep neural networks (DNNs) achieve strong performance in optical flow estimation, they remain less robust than humans and rely on fundamentally different computational strategies. Visual motion illusions provide a powerful probe into these mechanisms, revealing how human and machine vision align or diverge. While recent DNN-based motion models can reproduce dynamic illusions such as reverse-phi, it remains unclear whether they can perceive illusory motion in static images, exemplified by the Rotating Snakes illusion. We evaluate several representative optical flow models on Rotating Snakes and show that most fail to generate flow fields consistent with human perception. Under simulated conditions mimicking saccadic eye movements, only the human-inspired Dual-Channel model exhibits the expected rotational motion, with the closest correspondence emerging during the saccade simulation. Ablation analyses further reveal that both luminance-based and higher-order color--feature--based motion signals contribute to this behavior and that a recurrent attention mechanism is critical for integrating local cues. Our results highlight a substantial gap between current optical-flow models and human visual motion processing, and offer insights for developing future motion-estimation systems with improved correspondence to human perception and human-centric AI.

Pinyuan Feng, Hossein Adeli, Wenxuan Guo et al.

Recent work has demonstrated that complex visual stimuli can be decoded from human brain activity using deep generative models, helping brain science researchers interpret how the brain represents real-world scenes. However, most current approaches leverage mapping brain signals into intermediate image or text feature spaces before guiding the generative process, masking the effect of contributions from different brain areas on the final reconstruction output. In this work, we propose NeuroAdapter, a visual decoding framework that directly conditions a latent diffusion model on brain representations, bypassing the need for intermediate feature spaces. Our method demonstrates competitive visual reconstruction quality on public fMRI datasets compared to prior work, while providing greater transparency into how brain signals shape the generation process. To this end, we contribute an Image-Brain BI-directional interpretability framework (IBBI) which investigates cross-attention mechanisms across diffusion denoising steps to reveal how different cortical areas influence the unfolding generative trajectory. Our results highlight the potential of end-to-end brain-to-image decoding and establish a path toward interpreting diffusion models through the lens of visual neuroscience.

Zhoujun Cheng, Haoyu Dong, Ran Jia et al.

Tables store rich numerical data, but numerical reasoning over tables is still a challenge. In this paper, we find that the spreadsheet formula, which performs calculations on numerical values in tables, is naturally a strong supervision of numerical reasoning. More importantly, large amounts of spreadsheets with expert-made formulae are available on the web and can be obtained easily. FORTAP is the first method for numerical-reasoning-aware table pretraining by leveraging large corpus of spreadsheet formulae. We design two formula pretraining tasks to explicitly guide FORTAP to learn numerical reference and calculation in semi-structured tables. FORTAP achieves state-of-the-art results on two representative downstream tasks, cell type classification and formula prediction, showing great potential of numerical-reasoning-aware pretraining.

Fan Cheng, Anastasios Panagiotelis, Rob J Hyndman

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of probability distributions rather than vector-valued variables are available or when data size is large. We resolve this problem by proposing a new method for approximation in statistical manifold learning. The novelty of our approximation is the strongly consistent distance estimators based on independent and identically distributed samples from probability distributions. By exploiting the connection between Hellinger/total variation distance for discrete distributions and the L2/L1 norm, we demonstrate that the proposed distance estimators, combined with approximate nearest neighbor searching, could largely improve the computational efficiency with little to no loss in the accuracy of manifold embedding. The result is robust to different manifold learning algorithms and different approximate nearest neighbor algorithms. The proposed method is applied to learning statistical manifolds of electricity usage. This application demonstrates how underlying structures in high dimensional data, including anomalies, can be visualized and identified, in a way that is scalable to large datasets.