In this month’s episode of Functional Futures, our guest is Edward Kmett – Head of Software Engineering at Groq and the author of many widely-used Haskell libraries. In the episode, we dive into his life story – how he went from being broke and in debt to learning category theory and authoring numerous Haskell libraries. We also talk about programming languages and projects beyond Haskell that make Edward excited right now. We hope you’ll enjoy the episode. As […]

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In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this issue in two canonical linear settings: ordinary least squares regression and under-parameterized linear neural networks. For linear regression, we derive exact closed-form expressions for the expected generalization error with bias-variance decomposition, yielding necessary and sufficient conditions for auxiliary tasks to improve generalization on […]

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Across engineering and scientific domains, traditional deep learning (TDL) models perform well when training and test data share the same distribution. However, the dynamic nature of real-world data, broadly termed textit{data shift}, renders TDL models prone to rapid performance degradation, requiring costly relabeling and inefficient retraining. Meta-learning, which enables models to adapt quickly to new data with few examples, offers a promising alternative for mitigating these challenges. Here, we systematically compare TDL with fine-tuning and optimization-based meta-learning algorithms […]

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Test-Time Reinforcement Learning (TTRL) enables Large Language Models (LLMs) to enhance reasoning capabilities on unlabeled test streams by deriving pseudo-rewards from majority voting consensus. However, existing TTRL methods rely exclusively on positive pseudo-labeling strategies. Such reliance becomes vulnerable under challenging scenarios where answer distributions are highly dispersed, resulting in weak consensus that inadvertently reinforces incorrect trajectories as supervision signals. In this paper, we propose SCRL (Selective-Complementary Reinforcement Learning), a robust test-time reinforcement learning framework that effectively mitigates label […]

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Multiphase flow in porous media underpins subsurface energy and environmental technologies, including geological CO$_2$ storage and underground hydrogen storage, yet pore-scale dynamics in realistic three-dimensional materials remain difficult to characterize and predict. Here we introduce a multimodal learning framework that infers multiphase pore-scale flow directly from time-resolved four-dimensional (4D) micro-velocimetry measurements. The model couples a graph network simulator for Lagrangian tracer-particle motion with a 3D U-Net for voxelized interface evolution. The imaged pore geometry serves as a boundary […]

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arXiv:2601.06025v1 Announce Type: new Abstract: We study the discrete-to-continuum consistency of the training of shallow graph convolutional neural networks (GCNNs) on proximity graphs of sampled point clouds under a manifold assumption. Graph convolution is defined spectrally via the graph Laplacian, whose low-frequency spectrum approximates that of the Laplace-Beltrami operator of the underlying smooth manifold, and shallow GCNNs of possibly infinite width are linear functionals on the space of measures on the parameter space. From this functional-analytic perspective, graph […]

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