Visual-Spatial Systems has become increasingly essential in concrete crack inspection. However, existing methods often lacks adaptability to diverse scenarios, exhibits limited robustness in image-based approaches, and struggles with curved or complex geometries. To address these limitations, an innovative framework for two-dimensional (2D) crack detection, three-dimensional (3D) reconstruction, and 3D automatic crack measurement was proposed by integrating computer vision technologies and multi-modal Simultaneous localization and mapping (SLAM) in this study. Firstly, building on a base DeepLabv3+ segmentation model, and incorporating specific refinements utilizing foundation model Segment Anything Model (SAM), we developed a crack segmentation method with strong generalization across unfamiliar scenarios, enabling the generation of precise 2D crack masks. To enhance the accuracy and robustness of 3D reconstruction, Light Detection and Ranging (LiDAR) point clouds were utilized together with image data and segmentation masks. By leveraging both image- and LiDAR-SLAM, we developed a multi-frame and multi-modal fusion framework that produces dense, colorized point clouds, effectively capturing crack semantics at a 3D real-world scale. Furthermore, the crack geometric attributions were measured automatically and directly within 3D dense point cloud space, surpassing the limitations of conventional 2D image-based measurements. This advancement makes the method suitable for structural components with curved and complex 3D geometries. Experimental results across various concrete structures highlight the significant improvements and unique advantages of the proposed method, demonstrating its effectiveness, accuracy, and robustness in real-world applications.

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.

Measurement quality assurance (QA) practices play a key role in the safe use of Intensity Modulated Radiation Therapies (IMRT) for cancer treatment. These practices have reduced measurement-based IMRT QA failure below 1%. However, these practices are time and labor intensive which can lead to delays in patient care. In this study, we examine how conformal prediction methodologies can be used to robustly triage plans. We propose a new training-aware conformal risk control method by combining the benefit of conformal risk control and conformal training. We incorporate the decision making thresholds based on the gamma passing rate, along with the risk functions used in clinical evaluation, into the design of the risk control framework. Our method achieves high sensitivity and specificity and significantly reduces the number of plans needing measurement without generating a huge confidence interval. Our results demonstrate the validity and applicability of conformal prediction methods for improving efficiency and reducing the workload of the IMRT QA process.

Stochastic gradient descent with momentum (SGDM), which is defined by adding a momentum term to SGD, has been well studied in both theory and practice. Theoretically investigated results showed that the settings of the learning rate and momentum weight affect the convergence of SGDM. Meanwhile, practical results showed that the setting of batch size strongly depends on the performance of SGDM. In this paper, we focus on mini-batch SGDM with constant learning rate and constant momentum weight, which is frequently used to train deep neural networks in practice. The contribution of this paper is showing theoretically that using a constant batch size does not always minimize the expectation of the full gradient norm of the empirical loss in training a deep neural network, whereas using an increasing batch size definitely minimizes it, that is, increasing batch size improves convergence of mini-batch SGDM. We also provide numerical results supporting our analyses, indicating specifically that mini-batch SGDM with an increasing batch size converges to stationary points faster than with a constant batch size. Python implementations of the optimizers used in the numerical experiments are available at https://anonymous.4open.science/r/momentum-increasing-batch-size-888C/.

Analyzing large-scale datasets, especially involving complex and high-dimensional data like images, is particularly challenging. While self-supervised learning (SSL) has proven effective for learning representations from unlabeled data, it typically focuses on flat, non-hierarchical structures, missing the multi-level relationships present in many realworld datasets. Hierarchical clustering (HC) can uncover these relationships by organizing data into a tree-like structure, but it often relies on rigid similarity metrics that struggle to capture the complexity of diverse data types. To address these we envision InfoHier, a framework that combines SSL with HC to jointly learn robust latent representations and hierarchical structures. This approach leverages SSL to provide adaptive representations, enhancing HC's ability to capture complex patterns. Simultaneously, it integrates HC loss to refine SSL training, resulting in representations that are more attuned to the underlying information hierarchy. InfoHier has the potential to improve the expressiveness and performance of both clustering and representation learning, offering significant benefits for data analysis, management, and information retrieval.

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a noveladaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and datapredictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to otheronline state-of-the-art methods.

What makes untrained deep neural networks (DNNs) different from the trained performant ones? By zooming into the weights in well-trained DNNs, we found that it is the location of weights that holds most of the information encoded by the training. Motivated by this observation, we hypothesized that weights in DNNs trained using stochastic gradient-based methods can be separated into two dimensions: the location of weights, and their exact values. To assess our hypothesis, we propose a novel method called lookahead permutation (LaPerm) to train DNNs by reconnecting the weights. We empirically demonstrate LaPerm's versatility while producing extensive evidence to support our hypothesis: when the initial weights are random and dense, our method demonstrates speed and performance similar to or better than that of regular optimizers, e.g., Adam.

The robust principal component analysis (RPCA) problem seeks to separate low-rank trends from sparse outlierswithin a data matrix, that is, to approximate a n\times d matrix D as the sum of a low-rank matrix L and a sparse matrix S .We examine the robust principal component analysis (RPCA) problem under data compression, wherethe data Y is approximately given by (L S)\cdot C, that is, a low-rank sparse data matrix that has been compressed to size n\times m (with m substantially smaller than the original dimension d) via multiplication witha compression matrix C . We give a convex program for recovering the sparse component S along with the compressed low-rank component L\cdot C, along with upper bounds on the error of this reconstructionthat scales naturally with the compression dimension m and coincides with existing results for the uncompressedsetting m d . Our results can also handle error introduced through additive noise or through missing data.The scaling of dimension, compression, and signal complexity in our theoretical results is verified empirically through simulations, and we also apply our method to a data set measuring chlorine concentration acrossa network of sensors, to test its performance in practice.

In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are K clients whose individually chosen models are aggregated by a central server. The bounds depend on the compressibility of each client's algorithm while keeping other clients' algorithms un-compressed, and leveraging the fact that small changes in each local model change the aggregated model by a factor of only 1/K . Adopting a recently proposed approach by Sefidgaran et al., and extending it suitably to the distributed setting, enables smaller rate-distortion terms which are shown to translate into tighter generalization bounds. The bounds are then applied to the distributed support vector machines (SVM), suggesting that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of \mathcal{O}(\sqrt{\log(K)/K}) .

We propose the Canonical 3D Deformer Map, a new representation of the 3D shape of common object categories that can be learned from a collection of 2D images of independent objects. Our method builds in a novel way on concepts from parametric deformation models, non-parametric 3D reconstruction, and canonical embeddings, combining their individual advantages. In particular, it learns to associate each image pixel with a deformation model of the corresponding 3D object point which is canonical, i.e. intrinsic to the identity of the point and shared across objects of the category. The result is a method that, given only sparse 2D supervision at training time, can, at test time, reconstruct the 3D shape and texture of objects from single views, while establishing meaningful dense correspondences between object instances. It also achieves state-of-the-art results in dense 3D reconstruction on public in-the-wild datasets of faces, cars, and birds.