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We consider the task of estimating functions belonging to a specific class of nonsmooth functions, namely so-called tame functions. These functions appear in a wide range of applications: training deep learning, value functions of mixed-integer programs, or wave functions of small molecules. We show that tame functions are approximable by piecewise polynomials on any full-dimensional cube. We then present the first ever mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.

The semantic segmentation of pelvic organs via MRI has important clinical significance. Recently, deep learning-enabled semantic segmentation has facilitated the three-dimensional geometric reconstruction of pelvic floor organs, providing clinicians with accurate and intuitive diagnostic results. However, the task of labeling pelvic floor MRI segmentation, typically performed by clinicians, is labor-intensive and costly, leading to a scarcity of labels. Insufficient segmentation labels limit the precise segmentation and reconstruction of pelvic floor organs. To address these issues, we propose a semi-supervised framework for pelvic organ segmentation. The implementation of this framework comprises two stages. In the first stage, it performs self-supervised pre-training using image restoration tasks. Subsequently, fine-tuning of the self-supervised model is performed, using labeled data to train the segmentation model. In the second stage, the self-supervised segmentation model is used to generate pseudo labels for unlabeled data. Ultimately, both labeled and unlabeled data are utilized in semi-supervised training. Upon evaluation, our method significantly enhances the performance in the semantic segmentation and geometric reconstruction of pelvic organs, Dice coefficient can increase by 2.65% averagely. Especially for organs that are difficult to segment, such as the uterus, the accuracy of semantic segmentation can be improved by up to 3.70%.

The simulation of geological facies in an unobservable volume is essential in various geoscience applications. Given the complexity of the problem, deep generative learning is a promising approach to overcome the limitations of traditional geostatistical simulation models, in particular their lack of physical realism. This research aims to investigate the application of generative adversarial networks and deep variational inference for conditionally simulating meandering channels in underground volumes. In this paper, we review the generative deep learning approaches, in particular the adversarial ones and the stabilization techniques that aim to facilitate their training. The proposed approach is tested on 2D and 3D simulations generated by the stochastic process-based model Flumy. Morphological metrics are utilized to compare our proposed method with earlier iterations of generative adversarial networks. The results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions. Moreover, we demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.

Navigating the challenges of data-driven speech processing, one of the primary hurdles is accessing reliable pathological speech data. While public datasets appear to offer solutions, they come with inherent risks of potential unintended exposure of patient health information via re-identification attacks. Using a comprehensive real-world pathological speech corpus, with over n=3,800 test subjects spanning various age groups and speech disorders, we employed a deep-learning-driven automatic speaker verification (ASV) approach. This resulted in a notable mean equal error rate (EER) of 0.89% with a standard deviation of 0.06%, outstripping traditional benchmarks. Our comprehensive assessments demonstrate that pathological speech overall faces heightened privacy breach risks compared to healthy speech. Specifically, adults with dysphonia are at heightened re-identification risks, whereas conditions like dysarthria yield results comparable to those of healthy speakers. Crucially, speech intelligibility does not influence the ASV system's performance metrics. In pediatric cases, particularly those with cleft lip and palate, the recording environment plays a decisive role in re-identification. Merging data across pathological types led to a marked EER decrease, suggesting the potential benefits of pathological diversity in ASV, accompanied by a logarithmic boost in ASV effectiveness. In essence, this research sheds light on the dynamics between pathological speech and speaker verification, emphasizing its crucial role in safeguarding patient confidentiality in our increasingly digitized healthcare era.

This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of characteristics. The approach is simple to implement, generates entropic solutions, and avoids solving Riemann problems. A diffusion control parameter is introduced to increase the accuracy of the scheme. Numerical examples are presented for the Euler equation for an ideal gas. The results demonstrate the method's ability to capture contact discontinuity and shock wave profiles with high accuracy and low cost as well as its robustness.

In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various alignments of executions. Seemingly more flexible alignments can be expressed in terms of product automata based on program transition relations. A single degenerate alignment rule (self-composition), atop a complete Hoare logic, comprises a RHL for $\forall\forall$ properties that is complete in the ordinary logical sense. The notion of alignment completeness was previously proposed as a more satisfactory measure, and some rules were shown to be alignment complete with respect to a few ad hoc forms of alignment automata. This paper proves alignment completeness with respect to a general class of $\forall\forall$ alignment automata, for a RHL comprised of standard rules together with a rule of semantics-preserving rewrites based on Kleene algebra with tests. A new logic for $\forall\exists$ properties is introduced and shown to be alignment complete. The $\forall\forall$ and $\forall\exists$ automata are shown to be semantically complete. Thus the logics are both complete in the ordinary sense.

The weak Galerkin (WG) finite element method has shown great potential in solving various type of partial differential equations. In this paper, we propose an arbitrary order locking-free WG method for solving linear elasticity problems, with the aid of an appropriate $H(div)$-conforming displacement reconstruction operator. Optimal order locking-free error estimates in both the $H^1$-norm and the $L^2$-norm are proved, i.e., the error is independent of the $Lam\acute{e}$ constant $\lambda$. Moreover, the term $\lambda\|\nabla\cdot \mathbf{u}\|_k$ does not need to be bounded in order to achieve these estimates. We validate the accuracy and the robustness of the proposed locking-free WG algorithm by numerical experiments.

We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to other robots. In this paper, we propose a method to learn correspondences among two or more robots that may have different morphologies. To be specific, besides robots with similar morphologies with different degrees of freedom, we show that a fixed-based manipulator robot with joint control and a differential drive mobile robot can be addressed within the proposed framework. To set up the correspondence among the robots considered, an initial base task is demonstrated to the robots to achieve the same goal. Then, a common latent representation is learned along with the individual robot policies for achieving the goal. After the initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robots to achieve the same task. We verified our system in a set of experiments where the correspondence between robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.