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Fully-strict fork-join parallelism is a powerful model for shared-memory programming due to its optimal time scaling and strong bounds on memory scaling. The latter is rarely achieved due to the difficulty of implementing continuation stealing in traditional High Performance Computing (HPC) languages -- where it is often impossible without modifying the compiler or resorting to non-portable techniques. We demonstrate how stackless coroutines (a new feature in C++20) can enable fully-portable continuation stealing and present libfork a lock-free fine-grained parallelism library, combining coroutines with user-space, geometric segmented-stacks. We show our approach is able to achieve optimal time/memory scaling, both theoretically and empirically, across a variety of benchmarks. Compared to openMP (libomp), libfork is on average 7.2x faster and consumes 10x less memory. Similarly, compared to Intel's TBB, libfork is on average 2.7x faster and consumes 6.2x less memory. Additionally, we introduce non-uniform memory access (NUMA) optimizations for schedulers that demonstrate performance matching busy-waiting schedulers.

A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method to model weak discontinuities using nonconforming finite-element meshes. The essence of LET is in treating the elements that are cut by an interface as simple laminates of the two phases, and this idea is here extended to propagating interfaces so that the volume fraction of the phases and the lamination orientation vary accordingly. In the proposed LET-PF approach, the phase-field variable (order parameter), which is governed by an evolution equation of the Ginzburg-Landau type, plays the role of a level-set function that implicitly defines the position of the (sharp) interface. The mechanical equilibrium subproblem is then solved using the semisharp LET technique. Performance of LET-PF is illustrated by numerical examples. In particular, it is shown that, for the problems studied, LET-PF exhibits higher accuracy than the conventional phase-field method so that, for instance, qualitatively correct results can be obtained using a significantly coarser mesh, and thus at a lower computational cost.

Phase retrieval (PR) is a fundamental challenge in scientific imaging, enabling nanoscale techniques like coherent diffractive imaging (CDI). Imaging at low radiation doses becomes important in applications where samples are susceptible to radiation damage. However, most PR methods struggle in low dose scenario due to the presence of very high shot noise. Advancements in the optical data acquisition setup, exemplified by in-situ CDI, have shown potential for low-dose imaging. But these depend on a time series of measurements, rendering them unsuitable for single-image applications. Similarly, on the computational front, data-driven phase retrieval techniques are not readily adaptable to the single-image context. Deep learning based single-image methods, such as deep image prior, have been effective for various imaging tasks but have exhibited limited success when applied to PR. In this work, we propose LoDIP which combines the in-situ CDI setup with the power of implicit neural priors to tackle the problem of single-image low-dose phase retrieval. Quantitative evaluations demonstrate the superior performance of LoDIP on this task as well as applicability to real experimental scenarios.

In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Plo\v{s}\v{c}ica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics.

Recently, it has become progressively more evident that classic diagnostic labels are unable to reliably describe the complexity and variability of several clinical phenotypes. This is particularly true for a broad range of neuropsychiatric illnesses (e.g., depression, anxiety disorders, behavioral phenotypes). Patient heterogeneity can be better described by grouping individuals into novel categories based on empirically derived sections of intersecting continua that span across and beyond traditional categorical borders. In this context, neuroimaging data carry a wealth of spatiotemporally resolved information about each patient's brain. However, they are usually heavily collapsed a priori through procedures which are not learned as part of model training, and consequently not optimized for the downstream prediction task. This is because every individual participant usually comes with multiple whole-brain 3D imaging modalities often accompanied by a deep genotypic and phenotypic characterization, hence posing formidable computational challenges. In this paper we design a deep learning architecture based on generative models rooted in a modular approach and separable convolutional blocks to a) fuse multiple 3D neuroimaging modalities on a voxel-wise level, b) convert them into informative latent embeddings through heavy dimensionality reduction, c) maintain good generalizability and minimal information loss. As proof of concept, we test our architecture on the well characterized Human Connectome Project database demonstrating that our latent embeddings can be clustered into easily separable subject strata which, in turn, map to different phenotypical information which was not included in the embedding creation process. This may be of aid in predicting disease evolution as well as drug response, hence supporting mechanistic disease understanding and empowering clinical trials.

We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general measures that are not necessarily discrete. By developing a relaxation scheme in which marginal constraints are replaced by finitely many linear constraints and by proving a specifically tailored duality result for this setting, we approximate the MMOT problem by a linear semi-infinite optimization problem. Moreover, we are able to recover a feasible and approximately optimal solution of the MMOT problem, and its sub-optimality can be controlled to be arbitrarily close to 0 under mild conditions. The developed relaxation scheme leads to a numerical algorithm which can compute a feasible approximate optimizer of the MMOT problem whose theoretical sub-optimality can be chosen to be arbitrarily small. Besides the approximate optimizer, the algorithm is also able to compute both an upper bound and a lower bound on the optimal value of the MMOT problem. The difference between the computed bounds provides an explicit upper bound on the sub-optimality of the computed approximate optimizer. Through a numerical example, we demonstrate that the proposed algorithm is capable of computing a high-quality solution of an MMOT problem involving as many as 50 marginals along with an explicit estimate of its sub-optimality that is much less conservative compared to the theoretical estimate.

Regression analysis is a central topic in statistical modeling, aiming to estimate the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory variables. Linear regression is by far the most popular method for performing this task in several fields of research, such as prediction, forecasting, or causal inference. Beyond various classical methods to solve linear regression problems, such as Ordinary Least Squares, Ridge, or Lasso regressions - which are often the foundation for more advanced machine learning (ML) techniques - the latter have been successfully applied in this scenario without a formal definition of statistical significance. At most, permutation or classical analyses based on empirical measures (e.g., residuals or accuracy) have been conducted to reflect the greater ability of ML estimations for detection. In this paper, we introduce a method, named Statistical Agnostic Regression (SAR), for evaluating the statistical significance of an ML-based linear regression based on concentration inequalities of the actual risk using the analysis of the worst case. To achieve this goal, similar to the classification problem, we define a threshold to establish that there is sufficient evidence with a probability of at least 1-eta to conclude that there is a linear relationship in the population between the explanatory (feature) and the response (label) variables. Simulations in only two dimensions demonstrate the ability of the proposed agnostic test to provide a similar analysis of variance given by the classical $F$ test for the slope parameter.

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.