Low-Rank Adaptation (LoRA) offers a cost-effective solution for fine-tuning large language models (LLMs), but it often produces overconfident predictions in data-scarce few-shot settings. To address this issue, several classical statistical learning approaches have been repurposed for scalable uncertainty-aware LoRA fine-tuning. However, these approaches neglect how input characteristics affect the predictive uncertainty estimates. To address this limitation, we propose Contextual Low-Rank Adaptation (**C-LoRA**) as a novel uncertainty-aware and parameter efficient fine-tuning approach, by developing new lightweight LoRA modules contextualized to each input data sample to dynamically adapt uncertainty estimates. Incorporating data-driven contexts into the parameter posteriors, C-LoRA mitigates overfitting, achieves well-calibrated uncertainties, and yields robust predictions. Extensive experiments on LLaMA2-7B models demonstrate that C-LoRA consistently outperforms the state-of-the-art uncertainty-aware LoRA methods in both uncertainty quantification and model generalization. Ablation studies further confirm the critical role of our contextual modules in capturing sample-specific uncertainties. C-LoRA sets a new standard for robust, uncertainty-aware LLM fine-tuning in few-shot regimes. Although our experiments are limited to 7B models, our method is architecture-agnostic and, in principle, applies beyond this scale; studying its scaling to larger models remains an open problem. Our code is available at https://github.com/ahra99/c_lora.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints, leading to inaccuracies in representing critical processes like thunderstorms that occur on the sub-resolution scale. Hybrid methods combining physics with machine learning (ML) offer faster, higher fidelity climate simulations by outsourcing compute-hungry, high-resolution simulations to ML emulators. However, these hybrid physics-ML simulations require domain-specific data and workflows that have been inaccessible to many ML experts. This paper is an extended version of our NeurIPS award-winning ClimSim dataset paper. The ClimSim dataset includes 5.7 billion pairs of multivariate input/output vectors spanning ten years at high temporal resolution, capturing the influence of high-resolution, high-fidelity physics on a host climate simulator's macro-scale state. In this extended version, we introduce a significant new contribution in Section 5, which provides a cross-platform, containerized pipeline to integrate ML models into operational climate simulators for hybrid testing. We also implement various baselines of ML models and hybrid simulators to highlight the ML challenges of building stable, skillful emulators. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res, also in a low-resolution version at https://huggingface.co/datasets/LEAP/ClimSim_low-res and an aquaplanet version at https://huggingface.co/datasets/LEAP/ClimSim_low-res_aqua-planet) and code (https://leap-stc.github.io/ClimSim and https://github.com/leap-stc/climsim-online) are publicly released to support the development of hybrid physics-ML and high-fidelity climate simulations.

Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by reducing heavily overparameterized deep neural networks. Specifically, deep neural architectures compressed via structured sparsity (e.g., node sparsity) provide low-latency inference, higher data throughput, and reduced energy consumption. In this article, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks (BNNs). To this end, we propose structurally sparse BNNs, which systematically prune excessive nodes with the following: 1) spike-and-slab group Lasso (SS-GL) and 2) SS group Horseshoe (SS-GHS) priors, and develop computationally tractable variational inference, including continuous relaxation of Bernoulli variables. We establish the contraction rates of the variational posterior of our proposed models as a function of the network topology, layerwise node cardinalities, and bounds on the network weights. We empirically demonstrate the competitive performance of our models compared with the baseline models in prediction accuracy, model compression, and inference latency.

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters–referred to as an active subspace–by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore's Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator's macro-scale physical state.The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res) and code (https://leap-stc.github.io/ClimSim) are released openly to support the development of hybrid ML-physics and high-fidelity climate simulations for the benefit of science and society.

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing high-dimensional data because of the underexploration of the underlying structure. In this work, we propose to apply tensor-based regression model to perform tomographic reconstruction. Furthermore, we explore the low-rank structure embedded in the corresponding tensor form. As a result, our proposed method efficiently reduces the dimensionality of the unknown parameters, which is particularly beneficial for ill-posed inverse problem suffering from insufficient data. We demonstrate the robustness of our proposed approach on synthetic noise-free as well as on Gaussian noise-added data.