Yuqian Zhang

Hao Ding, Yuqian Zhang, Tuxun Lu et al.

Surgical data science has seen rapid advancement due to the excellent performance of end-to-end deep neural networks (DNNs) for surgical video analysis. Despite their successes, end-to-end DNNs have been proven susceptible to even minor corruptions, substantially impairing the model's performance. This vulnerability has become a major concern for the translation of cutting-edge technology, especially for high-stakes decision-making in surgical data science. We introduce SegSTRONG-C, a benchmark and challenge in surgical data science dedicated, aiming to better understand model deterioration under unforeseen but plausible non-adversarial corruption and the capabilities of contemporary methods that seek to improve it. Through comprehensive baseline experiments and participating submissions from widespread community engagement, SegSTRONG-C reveals key themes for model failure and identifies promising directions for improving robustness. The performance of challenge winners, achieving an average 0.9394 DSC and 0.9301 NSD across the unreleased test sets with corruption types: bleeding, smoke, and low brightness, shows inspiring improvement of 0.1471 DSC and 0.2584 NSD in average comparing to strongest baseline methods with UNet architecture trained with AutoAugment. In conclusion, the SegSTRONG-C challenge has identified some practical approaches for enhancing model robustness, yet most approaches relied on conventional techniques that have known, and sometimes quite severe, limitations. Looking ahead, we advocate for expanding intellectual diversity and creativity in non-adversarial robustness beyond data augmentation or training scale, calling for new paradigms that enhance universal robustness to corruptions and may enable richer applications in surgical data science.

Hao Ding, Yuqian Zhang, Wenzheng Cheng et al.

Surgical phase recognition (SPR) is an integral component of surgical data science, enabling high-level surgical analysis. End-to-end trained neural networks that predict surgical phase directly from videos have shown excellent performance on benchmarks. However, these models struggle with robustness due to non-causal associations in the training set. Our goal is to improve model robustness to variations in the surgical videos by leveraging the digital twin (DT) paradigm -- an intermediary layer to separate high-level analysis (SPR) from low-level processing. As a proof of concept, we present a DT representation-based framework for SPR from videos. The framework employs vision foundation models with reliable low-level scene understanding to craft DT representation. We embed the DT representation in place of raw video inputs in the state-of-the-art SPR model. The framework is trained on the Cholec80 dataset and evaluated on out-of-distribution (OOD) and corrupted test samples. Contrary to the vulnerability of the baseline model, our framework demonstrates strong robustness on both OOD and corrupted samples, with a video-level accuracy of 80.3 on a highly corrupted Cholec80 test set, 67.9 on the challenging CRCD dataset, and 99.8 on an internal robotic surgery dataset, outperforming the baseline by 3.9, 16.8, and 90.9 respectively. We also find that using DT representation as an augmentation to the raw input can significantly improve model robustness. Our findings lend support to the thesis that DT representations are effective in enhancing model robustness. Future work will seek to improve the feature informativeness and incorporate interpretability for a more comprehensive framework.

Yudong Chen, Dogyoon Song, Xumei Xi et al.

We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is non-convex, there can be multiple local minima that are not globally optimal, even for well-separated mixture models. Our study reveals that all local minima share a common structure that partially identifies the cluster centers (i.e., means of the Gaussian components) of the true location mixture. Specifically, each local minimum can be represented as a non-overlapping combination of two types of sub-configurations: fitting a single mean estimate to multiple Gaussian components or fitting multiple estimates to a single true component. These results apply to settings where the true mixture components satisfy a certain separation condition, and are valid even when the number of components is over- or under-specified. We also present a more fine-grained analysis for the setting of one-dimensional GMMs with three components, which provide sharper approximation error bounds with improved dependence on the separation.

Wei Qian, Yuqian Zhang, Yudong Chen

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide applicability, a theoretical understanding of the $k$-means problem has not been completely satisfactory. Existing algorithms with theoretical performance guarantees often rely on sophisticated (sometimes artificial) algorithmic techniques and restricted assumptions on the data. The main challenge lies in the non-convex nature of the problem; in particular, there exist additional local solutions other than the global optimum. Moreover, the simplest and most popular algorithm for $k$-means, namely Lloyd's algorithm, generally converges to such spurious local solutions both in theory and in practice. In this paper, we approach the $k$-means problem from a new perspective, by investigating the structures of these spurious local solutions under a probabilistic generative model with $k$ ground truth clusters. As soon as $k=3$, spurious local minima provably exist, even for well-separated and balanced clusters. One such local minimum puts two centers at one true cluster, and the third center in the middle of the other two true clusters. For general $k$, one local minimum puts multiple centers at a true cluster, and one center in the middle of multiple true clusters. Perhaps surprisingly, we prove that this is essentially the only type of spurious local minima under a separation condition. Our results pertain to the $k$-means formulation for mixtures of Gaussians or bounded distributions. Our theoretical results corroborate existing empirical observations and provide justification for several improved algorithms for $k$-means clustering.