The physics-informed neural operator (PINO) is a machine learning architecture that has shown promising empirical results for learning partial differential equations. PINO uses the Fourier neural operator (FNO) architecture to overcome the optimization challenges often faced by physics-informed neural networks. Since the convolution operator in PINO uses the Fourier series representation, its gradient can be computed exactly on the Fourier space. While Fourier series cannot represent nonperiodic functions, PINO and FNO still have the expressivity to learn nonperiodic problems with Fourier extension via padding. However, computing the Fourier extension in the physics-informed optimization requires solving an ill-conditioned system, resulting in inaccurate derivatives which prevent effective optimization. In this work, we present an architecture that leverages Fourier continuation (FC) to apply the exact gradient method to PINO for nonperiodic problems. This paper investigates three different ways that FC can be incorporated into PINO by testing their performance on a 1D blowup problem. Experiments show that FC-PINO outperforms padded PINO, improving equation loss by several orders of magnitude, and it can accurately capture the third order derivatives of nonsmooth solution functions.

In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment the objective with a regularizer to address challenges associated with ill-posedness. The choice of a suitable regularizer is typically driven by prior domain information and computational considerations. Convex regularizers are attractive as they are endowed with certificates of optimality as well as the toolkit of convex analysis, but exhibit a computational scaling that makes them ill-suited beyond moderate-sized problem instances. On the other hand, nonconvex regularizers can often be deployed at scale, but do not enjoy the certification properties associated with convex regularizers. In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what are the optimal regularizers, both convex and nonconvex, for data drawn from the distribution? What properties of a data source govern whether it is amenable to convex regularization? We address these questions for the class of continuous and positively homogenous regularizers for which convex and nonconvex regularizers correspond, respectively, to convex bodies and star bodies. By leveraging dual Brunn-Minkowski theory, we show that a radial function derived from a data distribution is the key quantity for identifying optimal regularizers and for assessing the amenability of a data source to convex regularization. Using tools such as $\Gamma$-convergence, we show that our results are robust in the sense that the optimal regularizers for a sample drawn from a distribution converge to their population counterparts as the sample size grows large. Finally, we give generalization guarantees that recover previous results for polyhedral regularizers (i.e., dictionary learning) and lead to new ones for semidefinite regularizers.

Neural style transfer is a deep learning technique that produces an unprecedentedly rich style transfer from a style image to a content image and is particularly impressive when it comes to transferring style from a painting to an image. It was originally achieved by solving an optimization problem to match the global style statistics of the style image while preserving the local geometric features of the content image. The two main drawbacks of this original approach is that it is computationally expensive and that the resolution of the output images is limited by high GPU memory requirements. Many solutions have been proposed to both accelerate neural style transfer and increase its resolution, but they all compromise the quality of the produced images. Indeed, transferring the style of a painting is a complex task involving features at different scales, from the color palette and compositional style to the fine brushstrokes and texture of the canvas. This paper provides a solution to solve the original global optimization for ultra-high resolution images, enabling multiscale style transfer at unprecedented image sizes. This is achieved by spatially localizing the computation of each forward and backward passes through the VGG network. Extensive qualitative and quantitative comparisons show that our method produces a style transfer of unmatched quality for such high resolution painting styles.

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.

Massive data corpora like WebText, Wikipedia, Conceptual Captions, WebImageText, and LAION have propelled recent dramatic progress in AI. Large neural models trained on such datasets produce impressive results and top many of today's benchmarks. A notable omission within this family of large-scale datasets is 3D data. Despite considerable interest and potential applications in 3D vision, datasets of high-fidelity 3D models continue to be mid-sized with limited diversity of object categories. Addressing this gap, we present Objaverse 1.0, a large dataset of objects with 800K+ (and growing) 3D models with descriptive captions, tags, and animations. Objaverse improves upon present day 3D repositories in terms of scale, number of categories, and in the visual diversity of instances within a category. We demonstrate the large potential of Objaverse via four diverse applications: training generative 3D models, improving tail category segmentation on the LVIS benchmark, training open-vocabulary object-navigation models for Embodied AI, and creating a new benchmark for robustness analysis of vision models. Objaverse can open new directions for research and enable new applications across the field of AI.

State-of-the-art brain tumor segmentation is based on deep learning models applied to multi-modal MRIs. Currently, these models are trained on images after a preprocessing stage that involves registration, interpolation, brain extraction (BE, also known as skull-stripping) and manual correction by an expert. However, for clinical practice, this last step is tedious and time-consuming and, therefore, not always feasible, resulting in skull-stripping faults that can negatively impact the tumor segmentation quality. Still, the extent of this impact has never been measured for any of the many different BE methods available. In this work, we propose an automatic brain tumor segmentation pipeline and evaluate its performance with multiple BE methods. Our experiments show that the choice of a BE method can compromise up to 15.7% of the tumor segmentation performance. Moreover, we propose training and testing tumor segmentation models on non-skull-stripped images, effectively discarding the BE step from the pipeline. Our results show that this approach leads to a competitive performance at a fraction of the time. We conclude that, in contrast to the current paradigm, training tumor segmentation models on non-skull-stripped images can be the best option when high performance in clinical practice is desired.

System identification, also known as learning forward models, transfer functions, system dynamics, etc., has a long tradition both in science and engineering in different fields. Particularly, it is a recurring theme in Reinforcement Learning research, where forward models approximate the state transition function of a Markov Decision Process by learning a mapping function from current state and action to the next state. This problem is commonly defined as a Supervised Learning problem in a direct way. This common approach faces several difficulties due to the inherent complexities of the dynamics to learn, for example, delayed effects, high non-linearity, non-stationarity, partial observability and, more important, error accumulation when using bootstrapped predictions (predictions based on past predictions), over large time horizons. Here we explore the use of Reinforcement Learning in this problem. We elaborate on why and how this problem fits naturally and sound as a Reinforcement Learning problem, and present some experimental results that demonstrate RL is a promising technique to solve these kind of problems.

Reinforcement learning is a machine learning approach based on behavioral psychology. It is focused on learning agents that can acquire knowledge and learn to carry out new tasks by interacting with the environment. However, a problem occurs when reinforcement learning is used in critical contexts where the users of the system need to have more information and reliability for the actions executed by an agent. In this regard, explainable reinforcement learning seeks to provide to an agent in training with methods in order to explain its behavior in such a way that users with no experience in machine learning could understand the agent's behavior. One of these is the memory-based explainable reinforcement learning method that is used to compute probabilities of success for each state-action pair using an episodic memory. In this work, we propose to make use of the memory-based explainable reinforcement learning method in a hierarchical environment composed of sub-tasks that need to be first addressed to solve a more complex task. The end goal is to verify if it is possible to provide to the agent the ability to explain its actions in the global task as well as in the sub-tasks. The results obtained showed that it is possible to use the memory-based method in hierarchical environments with high-level tasks and compute the probabilities of success to be used as a basis for explaining the agent's behavior.

Background: Encouraged by the success of pretrained Transformer models in many natural language processing tasks, their use for International Classification of Diseases (ICD) coding tasks is now actively being explored. In this study, we investigate three types of Transformer-based models, aiming to address the extreme label set and long text classification challenges that are posed by automated ICD coding tasks. Methods: The Transformer-based model PLM-ICD achieved the current state-of-the-art (SOTA) performance on the ICD coding benchmark dataset MIMIC-III. It was chosen as our baseline model to be further optimised. XR-Transformer, the new SOTA model in the general extreme multi-label text classification domain, and XR-LAT, a novel adaptation of the XR-Transformer model, were also trained on the MIMIC-III dataset. XR-LAT is a recursively trained model chain on a predefined hierarchical code tree with label-wise attention, knowledge transferring and dynamic negative sampling mechanisms. Results: Our optimised PLM-ICD model, which was trained with longer total and chunk sequence lengths, significantly outperformed the current SOTA PLM-ICD model, and achieved the highest micro-F1 score of 60.8%. The XR-Transformer model, although SOTA in the general domain, did not perform well across all metrics. The best XR-LAT based model obtained results that were competitive with the current SOTA PLM-ICD model, including improving the macro-AUC by 2.1%. Conclusion: Our optimised PLM-ICD model is the new SOTA model for automated ICD coding on the MIMIC-III dataset, while our novel XR-LAT model performs competitively with the previous SOTA PLM-ICD model.

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean \textit{k}-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.