Zihan Deng

Junjie Yu, Zhuoli Ouyang, Haotian Deng et al.

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned embeddings controls predictive performance for a fixed trained model. We show that population risk can be bounded by two factors: (i) the intrinsic dimension of the embedding distribution, which determines the convergence rate of empirical embedding distribution to the population distribution in Wasserstein distance, and (ii) the sensitivity of the downstream mapping from embeddings to predictions, characterized by Lipschitz constants. Together, these yield an embedding-dependent error bound that does not rely on parameter counts or hypothesis class complexity. At the final embedding layer, architectural sensitivity vanishes and the bound is dominated by embedding dimension, explaining its strong empirical correlation with generalization performance. Experiments across architectures and datasets validate the theory and demonstrate the utility of embedding-based diagnostics.

Junjie Yu, Wenxiao Ma, Chen Wei et al.

Recent work has found that neural networks with stronger generalization tend to exhibit higher representational alignment with one another across architectures and training paradigms. In this work, we show that models with stronger generalization also align more strongly with human neural activity. Moreover, generalization performance, model--model alignment, and model--brain alignment are all significantly correlated with each other. We further show that these relationships can be explained by a single geometric property of learned representations: the local intrinsic dimension of embeddings. Lower local dimension is consistently associated with stronger model--model alignment, stronger model--brain alignment, and better generalization, whereas global dimension measures fail to capture these effects. Finally, we find that increasing model capacity and training data scale systematically reduces local intrinsic dimension, providing a geometric account of the benefits of scaling. Together, our results identify local intrinsic dimension as a unifying descriptor of representational convergence in artificial and biological systems.

Chuanzhi Xu, Boyu Wei, Haoxian Zhou et al.

As 3D Gaussian Splatting (3DGS) gains attention in immersive media and digital content creation, assessing the aesthetics of 3D scenes becomes important in helping creators build more visually compelling 3D content. However, existing evaluation methods for 3D scenes primarily emphasize reconstruction fidelity and perceptual realism, largely overlooking higher-level aesthetic attributes such as composition, harmony, and visual appeal. This limitation comes from two key challenges: (1) the absence of general 3DGS datasets with aesthetic annotations, and (2) the intrinsic nature of 3DGS as a low-level primitive representation, which makes it difficult to capture high-level aesthetic features. To address these challenges, we propose Aes3D, the first systematic framework for assessing the aesthetics of 3D neural rendering scenes. Aes3D includes Aesthetic3D, the first dataset dedicated to 3D scene aesthetic assessment, built on our proposed annotation strategy for 3D scene aesthetics. In addition, we present Aes3DGSNet, a lightweight model that directly predicts scene-level aesthetic scores from 3DGS representations. Notably, our model operates solely on 3D Gaussian primitives, eliminating the need for rendering multi-view images and thus reducing computational cost and hardware requirements. Through aesthetics-supervised learning on multi-view 3DGS scene representations, Aes3DGSNet effectively captures high-level aesthetic cues and accurately regresses aesthetic scores. Experimental results demonstrate that our approach achieves strong performance while maintaining a lightweight design, establishing a new benchmark for 3D scene aesthetic assessment. Code and datasets will be made available in a future version.