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Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range, distance-dependent ``interactions'' without assuming a specific form for the underlying probability distribution. Predictions are obtained by means of a fully autonomous learning algorithm which employs equilibrium conditional Monte Carlo simulations. MPRS is able to handle scattered data and arbitrary spatial dimensions. We report tests on various synthetic and real-word data in one, two and three dimensions which demonstrate that the MPRS prediction performance (without parameter tuning) is competitive with standard interpolation methods such as ordinary kriging and inverse distance weighting. In particular, MPRS is a particularly effective gap-filling method for rough and non-Gaussian data (e.g., daily precipitation time series). MPRS shows superior computational efficiency and scalability for large samples. Massive data sets involving millions of nodes can be processed in a few seconds on a standard personal computer.

The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming. The complex cross-scale interactions of processes that produce precipitation are challenging to model, however, inducing potentially strong biases in ESM fields, especially regarding extremes. State-of-the-art bias correction methods only address errors in the simulated frequency distributions locally at every individual grid cell. Improving unrealistic spatial patterns of the ESM output, which would require spatial context, has not been possible so far. Here, we show that a post-processing method based on physically constrained generative adversarial networks (cGANs) can correct biases of a state-of-the-art, CMIP6-class ESM both in local frequency distributions and in the spatial patterns at once. While our method improves local frequency distributions equally well as gold-standard bias-adjustment frameworks, it strongly outperforms any existing methods in the correction of spatial patterns, especially in terms of the characteristic spatial intermittency of precipitation extremes.

We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this line restricts data to follow a hierarchical tree structure and thus lacks inter-span communications. To overcome the problem, we propose a novel contextual inside-outside (CIO) layer that learns contextualized representations of spans through bottom-up and top-down passes, where a bottom-up pass forms representations of high-level spans by composing low-level spans, while a top-down pass combines information inside and outside a span. By stacking several CIO layers between the embedding layer and the attention layers in Transformer, the ReCAT model can perform both deep intra-span and deep inter-span interactions, and thus generate multi-grained representations fully contextualized with other spans. Moreover, the CIO layers can be jointly pre-trained with Transformers, making ReCAT enjoy scaling ability, strong performance, and interpretability at the same time. We conduct experiments on various sentence-level and span-level tasks. Evaluation results indicate that ReCAT can significantly outperform vanilla Transformer models on all span-level tasks and baselines that combine recursive networks with Transformers on natural language inference tasks. More interestingly, the hierarchical structures induced by ReCAT exhibit strong consistency with human-annotated syntactic trees, indicating good interpretability brought by the CIO layers.

We evaluate Julia as a single language and ecosystem paradigm powered by LLVM to develop workflow components for high-performance computing. We run a Gray-Scott, 2-variable diffusion-reaction application using a memory-bound, 7-point stencil kernel on Frontier, the US Department of Energy's first exascale supercomputer. We evaluate the performance, scaling, and trade-offs of (i) the computational kernel on AMD's MI250x GPUs, (ii) weak scaling up to 4,096 MPI processes/GPUs or 512 nodes, (iii) parallel I/O writes using the ADIOS2 library bindings, and (iv) Jupyter Notebooks for interactive analysis. Results suggest that although Julia generates a reasonable LLVM-IR, a nearly 50% performance difference exists vs. native AMD HIP stencil codes when running on the GPUs. As expected, we observed near-zero overhead when using MPI and parallel I/O bindings for system-wide installed implementations. Consequently, Julia emerges as a compelling high-performance and high-productivity workflow composition language, as measured on the fastest supercomputer in the world.

The crossed random effects model is widely used, finding applications in various fields such as longitudinal studies, e-commerce, and recommender systems, among others. However, these models encounter scalability challenges, as the computational time for standard algorithms grows superlinearly with the number N of observations in the data set, commonly $\Omega(N^{3/2})$ or worse. Recent work has developed scalable methods for crossed random effects in linear models and some generalized linear models, but those works only allow for random intercepts. In this paper we devise scalable algorithms for models that include random slopes. This problem brings a substantial difficulty in estimating the random effect covariance matrices in a scalable way. We address that issue by using a variational EM algorithm. In simulations, we see that the proposed method is faster than standard methods. It is also more efficient than ordinary least squares which also has a problem of greatly underestimating the sampling uncertainty in parameter estimates. We illustrate the new method on a large dataset (five million observations) from the online retailer Stitch Fix.

Contemporary practices such as InnerSource and DevOps promote software reuse. This study investigates the implications of using contemporary practices on software reuse. In particular, we investigate the costs, benefits, challenges, and potential improvements in contemporary reuse at Ericsson. We performed the study in two phases: a) the initial data collection based on a combination of data collection methods (e.g., interviews, discussions, company portals), and b) a follow-up group discussion after a year to understand the status of the challenges and improvements identified in the first phase. Our results indicate that developing reusable assets resulted in upfront costs, such as additional effort in ensuring compliance. Furthermore, development with reuse also resulted in additional effort, for example, in integrating and understanding reusable assets. Ericsson perceived the additional effort as an investment resulting in long-term benefits such as improved quality, productivity, customer experience, and way of working. Ericsson's main challenge was increased pressure on the producers of reusable assets, which was mitigated by scaling the InnerSource adoption. InnerSource success is evident from the increase in the contributions to reusable assets. In addition, Ericsson implemented measures such as automating the compliance check, which enhanced the maturity of reusable assets and resulted in increased reuse.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.