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Implicit regularization is an important way to interpret neural networks. Recent theory starts to explain implicit regularization with the model of deep matrix factorization (DMF) and analyze the trajectory of discrete gradient dynamics in the optimization process. These discrete gradient dynamics are relatively small but not infinitesimal, thus fitting well with the practical implementation of neural networks. Currently, discrete gradient dynamics analysis has been successfully applied to shallow networks but encounters the difficulty of complex computation for deep networks. In this work, we introduce another discrete gradient dynamics approach to explain implicit regularization, i.e. landscape analysis. It mainly focuses on gradient regions, such as saddle points and local minima. We theoretically establish the connection between saddle point escaping (SPE) stages and the matrix rank in DMF. We prove that, for a rank-R matrix reconstruction, DMF will converge to a second-order critical point after R stages of SPE. This conclusion is further experimentally verified on a low-rank matrix reconstruction problem. This work provides a new theory to analyze implicit regularization in deep learning.

Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. The observed data often contains both amplitude ($y$-axis) and phase ($x$-axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this paper, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its non-elastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt.\ Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt.\ Pinatubo, with most detected changepoints occurring in the tropics as expected.

Medical image segmentation is an important step in medical image analysis, especially as a crucial prerequisite for efficient disease diagnosis and treatment. The use of deep learning for image segmentation has become a prevalent trend. The widely adopted approach currently is U-Net and its variants. Additionally, with the remarkable success of pre-trained models in natural language processing tasks, transformer-based models like TransUNet have achieved desirable performance on multiple medical image segmentation datasets. In this paper, we conduct a survey of the most representative four medical image segmentation models in recent years. We theoretically analyze the characteristics of these models and quantitatively evaluate their performance on two benchmark datasets (i.e., Tuberculosis Chest X-rays and ovarian tumors). Finally, we discuss the main challenges and future trends in medical image segmentation. Our work can assist researchers in the related field to quickly establish medical segmentation models tailored to specific regions.

Learning disentangled representations with variational autoencoders (VAEs) is often attributed to the regularisation component of the loss. In this work, we highlight the interaction between data and the reconstruction term of the loss as the main contributor to disentanglement in VAEs. We show that standard benchmark datasets have unintended correlations between their subjective ground-truth factors and perceived axes in the data according to typical VAE reconstruction losses. Our work exploits this relationship to provide a theory for what constitutes an adversarial dataset under a given reconstruction loss. We verify this by constructing an example dataset that prevents disentanglement in state-of-the-art frameworks while maintaining human-intuitive ground-truth factors. Finally, we re-enable disentanglement by designing an example reconstruction loss that is once again able to perceive the ground-truth factors. Our findings demonstrate the subjective nature of disentanglement and the importance of considering the interaction between the ground-truth factors, data and notably, the reconstruction loss, which is under-recognised in the literature.

Group sequential designs in clinical trials allow for interim efficacy and futility monitoring. Adjustment for baseline covariates can increase power and precision of estimated effects. However, inconsistently applying covariate adjustment throughout the stages of a group sequential trial can result in inflation of type I error, biased point estimates, and anti-conservative confidence intervals. We propose methods for performing correct interim monitoring, estimation, and inference in this setting that avoid these issues. We focus on two-arm trials with simple, balanced randomization and continuous outcomes. We study the performance of our boundary, estimation, and inference adjustments in simulation studies. We end with recommendations about the application of covariate adjustment in group sequential designs.

Many segmentation networks have been proposed for 3D volumetric segmentation of tumors and organs at risk. Hospitals and clinical institutions seek to accelerate and minimize the efforts of specialists in image segmentation. Still, in case of errors generated by these networks, clinicians would have to manually edit the generated segmentation maps. Given a 3D volume and its putative segmentation map, we propose an approach to identify and measure erroneous regions in the segmentation map. Our method can estimate error at any point or node in a 3D mesh generated from a possibly erroneous volumetric segmentation map, serving as a Quality Assurance tool. We propose a graph neural network-based transformer based on the Nodeformer architecture to measure and classify the segmentation errors at any point. We have evaluated our network on a high-resolution micro-CT dataset of the human inner-ear bony labyrinth structure by simulating erroneous 3D segmentation maps. Our network incorporates a convolutional encoder to compute node-centric features from the input micro-CT data, the Nodeformer to learn the latent graph embeddings, and a Multi-Layer Perceptron (MLP) to compute and classify the node-wise errors. Our network achieves a mean absolute error of ~0.042 over other Graph Neural Networks (GNN) and an accuracy of 79.53% over other GNNs in estimating and classifying the node-wise errors, respectively. We also put forth vertex-normal prediction as a custom pretext task for pre-training the CNN encoder to improve the network's overall performance. Qualitative analysis shows the efficiency of our network in correctly classifying errors and reducing misclassifications.

Novel view synthesis and 3D modeling using implicit neural field representation are shown to be very effective for calibrated multi-view cameras. Such representations are known to benefit from additional geometric and semantic supervision. Most existing methods that exploit additional supervision require dense pixel-wise labels or localized scene priors. These methods cannot benefit from high-level vague scene priors provided in terms of scenes' descriptions. In this work, we aim to leverage the geometric prior of Manhattan scenes to improve the implicit neural radiance field representations. More precisely, we assume that only the knowledge of the indoor scene (under investigation) being Manhattan is known -- with no additional information whatsoever -- with an unknown Manhattan coordinate frame. Such high-level prior is used to self-supervise the surface normals derived explicitly in the implicit neural fields. Our modeling allows us to cluster the derived normals and exploit their orthogonality constraints for self-supervision. Our exhaustive experiments on datasets of diverse indoor scenes demonstrate the significant benefit of the proposed method over the established baselines. The source code will be available at //github.com/nikola3794/normal-clustering-nerf.

Even though the analysis of unsteady 2D flow fields is challenging, fluid mechanics experts generally have an intuition on where in the simulation domain specific features are expected. Using this intuition, showing similar regions enables the user to discover flow patterns within the simulation data. When focusing on similarity, a solid mathematical framework for a specific flow pattern is not required. We propose a technique that visualizes similar and dissimilar regions with respect to a region selected by the user. Using infinitesimal strain theory, we capture the strain and rotation progression and therefore the dynamics of fluid parcels along pathlines, which we encode as distributions. We then apply the Jensen-Shannon divergence to compute the (dis)similarity between pathline dynamics originating in a user-defined flow region and the pathline dynamics of the flow field. We validate our method by applying it to two simulation datasets of two-dimensional unsteady flows. Our results show that our approach is suitable for analyzing the similarity of time-dependent flow fields.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

Designing and generating new data under targeted properties has been attracting various critical applications such as molecule design, image editing and speech synthesis. Traditional hand-crafted approaches heavily rely on expertise experience and intensive human efforts, yet still suffer from the insufficiency of scientific knowledge and low throughput to support effective and efficient data generation. Recently, the advancement of deep learning induces expressive methods that can learn the underlying representation and properties of data. Such capability provides new opportunities in figuring out the mutual relationship between the structural patterns and functional properties of the data and leveraging such relationship to generate structural data given the desired properties. This article provides a systematic review of this promising research area, commonly known as controllable deep data generation. Firstly, the potential challenges are raised and preliminaries are provided. Then the controllable deep data generation is formally defined, a taxonomy on various techniques is proposed and the evaluation metrics in this specific domain are summarized. After that, exciting applications of controllable deep data generation are introduced and existing works are experimentally analyzed and compared. Finally, the promising future directions of controllable deep data generation are highlighted and five potential challenges are identified.