Xingyu Zhu

Xingyu Zhu, Zixuan Wang, Xiang Wang et al. · princeton, uw

Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold $2/η$ (where $η$ is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below $2/η$. While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and $2/η$. In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the final converging point has sharpness close to $2/η$. Globally we observe that the training dynamics for our example has an interesting bifurcating behavior, which was also observed in the training of neural nets.

Xingyu Zhu, Beier Zhu, Yunfan Li et al.

Image clustering is a classic problem in computer vision, which categorizes images into different groups. Recent studies utilize nouns as external semantic knowledge to improve clus- tering performance. However, these methods often overlook the inherent ambiguity of nouns, which can distort semantic representations and degrade clustering quality. To address this issue, we propose a hierarChical semAntic alignmEnt method for image clustering, dubbed CAE, which improves cluster- ing performance in a training-free manner. In our approach, we incorporate two complementary types of textual seman- tics: caption-level descriptions, which convey fine-grained attributes of image content, and noun-level concepts, which represent high-level object categories. We first select relevant nouns from WordNet and descriptions from caption datasets to construct a semantic space aligned with image features. Then, we align image features with selected nouns and captions via optimal transport to obtain a more discriminative semantic space. Finally, we combine the enhanced semantic and image features to perform clustering. Extensive experiments across 8 datasets demonstrate the effectiveness of our method, notably surpassing the state-of-the-art training-free approach with a 4.2% improvement in accuracy and a 2.9% improvement in adjusted rand index (ARI) on the ImageNet-1K dataset.

Yuchen Wang, Xingyu Zhu, Guanhui Ye et al.

DNN-based watermarking methods are rapidly developing and delivering impressive performances. Recent advances achieve resolution-agnostic image watermarking by reducing the variant resolution watermarking problem to a fixed resolution watermarking problem. However, such a reduction process can potentially introduce artifacts and low robustness. To address this issue, we propose the first, to the best of our knowledge, Resolution-Agnostic Image WaterMarking (RAIMark) framework by watermarking the implicit neural representation (INR) of image. Unlike previous methods, our method does not rely on the previous reduction process by directly watermarking the continuous signal instead of image pixels, thus achieving resolution-agnostic watermarking. Precisely, given an arbitrary-resolution image, we fit an INR for the target image. As a continuous signal, such an INR can be sampled to obtain images with variant resolutions. Then, we quickly fine-tune the fitted INR to get a watermarked INR conditioned on a binary secret message. A pre-trained watermark decoder extracts the hidden message from any sampled images with arbitrary resolutions. By directly watermarking INR, we achieve resolution-agnostic watermarking with increased robustness. Extensive experiments show that our method outperforms previous methods with significant improvements: averagely improved bit accuracy by 7%$\sim$29%. Notably, we observe that previous methods are vulnerable to at least one watermarking attack (e.g. JPEG, crop, resize), while ours are robust against all watermarking attacks.