The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a single pixel. To address this, we develop a scalable Bayesian framework that leverages natural sparsity in spatial signal patterns to recover relative rates for each molecule across the entire image. Our method relies on the use of a heavy-tailed variant of the graphical lasso prior and a novel hierarchical variational family, enabling efficient inference via automatic differentiation variational inference. Simulation results show that our approach outperforms state-of-the-practice point estimate methodologies in IMS, and has superior posterior coverage than mean-field variational inference techniques. Results on real IMS data demonstrate that our approach better recovers the true anatomical structure of known tissue, removes artifacts, and detects active regions missed by the standard analysis approach.

In this work, we introduce a novel approach for optimizing LLM training by adjusting learning rates across weights of different components in Transformer models. Traditional methods often apply a uniform learning rate across all network layers, potentially overlooking the unique dynamics of each part. Remarkably, our introduced relative learning rates, RLRS, method accelerates the training process by up to $23\%$, particularly in complex models such as Mixture of Experts (MoE). Hyperparameters of RLRS can be efficiently tuned on smaller models and then effectively reused on models up to $27\times$ larger. This simple and effective method results in a substantial reduction in training time and computational resources, offering a practical and scalable solution for optimizing large-scale neural networks.

Multi-task learning (MTL) has achieved great success in various research domains, such as CV, NLP and IR etc. Due to the complex and competing task correlation, naive training all tasks may lead to inequitable learning, i.e. some tasks are learned well while others are overlooked. Multi-task optimization (MTO) aims to improve all tasks at same time, but conventional methods often perform poor when tasks with large loss scale or gradient norm magnitude difference. To solve the issue, we in-depth investigate the equity problem for MTL and find that regularizing relative contribution of different tasks (i.e. value of task-specific loss divides its raw gradient norm) in updating shared parameter can improve generalization performance of MTL. Based on our theoretical analysis, we propose a novel multi-task optimization method, named EMTL, to achieve equitable MTL. Specifically, we efficiently add variance regularization to make different tasks' relative contribution closer. Extensive experiments have been conduct to evaluate EMTL, our method stably outperforms state-of-the-art methods on the public benchmark datasets of two different research domains. Furthermore, offline and online A/B test on multi-task recommendation are conducted too. EMTL improves multi-task recommendation significantly, demonstrating the superiority and practicability of our method in industrial landscape.