Bayesian methods have recently been used to improve LoRA finetuning and, although they improve calibration, their effect on other metrics (such as accuracy) is marginal and can sometimes even be detrimental. Moreover, Bayesian methods also increase computational overheads and require additional tricks for them to work well. Here, we fix these issues by using a recently proposed variational algorithm called IVON. We show that IVON is easy to implement and has similar costs to AdamW, and yet it can also drastically improve many metrics by using a simple posterior pruning technique. We present extensive results on billion-scale LLMs (Llama and Qwen series) going way beyond the scale of existing applications of IVON. For example, we finetune a Llama-3.2-3B model on a set of commonsense reasoning tasks and improve accuracy over AdamW by 1.3% and reduce ECE by 5.4%, outperforming AdamW and other recent Bayesian methods like Laplace-LoRA and BLoB. Overall, our results show that variational learning with IVON can effectively improve LoRA finetuning.

Adaptation is the holy grail of intelligence, but even the best AI models (like GPT) lack the adaptivity of toddlers. So the question remains: how can machines adapt quickly? Despite a lot of progress on model adaptation to facilitate continual and federated learning, as well as model merging, editing, unlearning, etc., little is known about the mechanisms by which machines can naturally learn to adapt in a similar way as humans and animals. Here, we show that all such adaptation methods can be seen as different ways of `correcting' the approximate posteriors. More accurate posteriors lead to smaller corrections, which in turn imply quicker adaptation. The result is obtained by using a dual-perspective of the Bayesian Learning Rule of Khan and Rue (2023) where interference created during adaptation is characterized by the natural-gradient mismatch over the past data. We present many examples to demonstrate the use of posterior-correction as a natural mechanism for the machines to learn to adapt quickly.

Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variational Autoencoder Graph Convolutional Neural Network framework for generating synthetic Abdominal Aorta Aneurysms (AAA). Using a small real-world dataset, our approach extracts key anatomical features and captures complex statistical relationships within a compact disentangled latent space. To address data limitations, low-impact data augmentation based on Procrustes analysis was employed, preserving anatomical integrity. The generation strategies, both deterministic and stochastic, manage to enhance data diversity while ensuring realism. Compared to PCA-based approaches, our model performs more robustly on unseen data by capturing complex, nonlinear anatomical variations. This enables more comprehensive clinical and statistical analyses than the original dataset alone. The resulting synthetic AAA dataset preserves patient privacy while providing a scalable foundation for medical research, device testing, and computational modeling.

In-context learning (ICL) has emerged as a powerful paradigm for task adaptation in large language models (LLMs), where models infer underlying task structures from a few demonstrations. However, ICL remains susceptible to biases that arise from prior knowledge and contextual demonstrations, which can degrade the performance of LLMs. Existing bias calibration methods typically apply fixed class priors across all inputs, limiting their efficacy in dynamic ICL settings where the context for each query differs. To address these limitations, we adopt implicit sequential Bayesian inference as a framework for interpreting ICL, identify "surprise" as an informative signal for class prior shift, and introduce a novel method--Surprise Calibration (SC). SC leverages the notion of surprise to capture the temporal dynamics of class priors, providing a more adaptive and computationally efficient solution for in-context learning. We empirically demonstrate the superiority of SC over existing bias calibration techniques across a range of benchmark natural language processing tasks.

People regularly make inferences about objects in the world that they cannot see by flexibly integrating information from multiple sources: auditory and visual cues, language, and our prior beliefs and knowledge about the scene. How are we able to so flexibly integrate many sources of information to make sense of the world around us, even if we have no direct knowledge? In this work, we propose a neurosymbolic model that uses neural networks to parse open-ended multi-modal inputs and then applies a Bayesian model to integrate different sources of information to evaluate different hypotheses. We evaluate our model with a novel object guessing game called "What's in the Box?" where humans and models watch a video clip of an experimenter shaking boxes and then try to guess the objects inside the boxes. Through a human experiment, we show that our model correlates strongly with human judgments, whereas unimodal ablated models and large multi-modal neural model baselines showed poor correlation.

Developing agents capable of exploring, planning and learning in complex open-ended environments is a grand challenge in artificial intelligence (AI). Hierarchical reinforcement learning (HRL) offers a promising solution to this challenge by discovering and exploiting the temporal structure within a stream of experience. The strong appeal of the HRL framework has led to a rich and diverse body of literature attempting to discover a useful structure. However, it is still not clear how one might define what constitutes good structure in the first place, or the kind of problems in which identifying it may be helpful. This work aims to identify the benefits of HRL from the perspective of the fundamental challenges in decision-making, as well as highlight its impact on the performance trade-offs of AI agents. Through these benefits, we then cover the families of methods that discover temporal structure in HRL, ranging from learning directly from online experience to offline datasets, to leveraging large language models (LLMs). Finally, we highlight the challenges of temporal structure discovery and the domains that are particularly well-suited for such endeavours.

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.

Graph neural networks (GNNs) excel in graph representation learning by integrating graph structure and node features. Existing GNNs, unfortunately, fail to account for the uncertainty of class probabilities that vary with the depth of the model, leading to unreliable and risky predictions in real-world scenarios. To bridge the gap, in this paper, we propose a novel Evidence Fusing Graph Neural Network (EFGNN for short) to achieve trustworthy prediction, enhance node classification accuracy, and make explicit the risk of wrong predictions. In particular, we integrate the evidence theory with multi-hop propagation-based GNN architecture to quantify the prediction uncertainty of each node with the consideration of multiple receptive fields. Moreover, a parameter-free cumulative belief fusion (CBF) mechanism is developed to leverage the changes in prediction uncertainty and fuse the evidence to improve the trustworthiness of the final prediction. To effectively optimize the EFGNN model, we carefully design a joint learning objective composed of evidence cross-entropy, dissonance coefficient, and false confident penalty. The experimental results on various datasets and theoretical analyses demonstrate the effectiveness of the proposed model in terms of accuracy and trustworthiness, as well as its robustness to potential attacks. The source code of EFGNN is available at https://github.com/Shiy-Li/EFGNN.

ADMM is a popular method for federated deep learning which originated in the 1970s and, even though many new variants of it have been proposed since then, its core algorithmic structure has remained unchanged. Here, we take a major departure from the old structure and present a fundamentally new way to derive and extend federated ADMM. We propose to use a structure called Bayesian Duality which exploits a duality of the posterior distributions obtained by solving a variational-Bayesian reformulation of the original problem. We show that this naturally recovers the original ADMM when isotropic Gaussian posteriors are used, and yields non-trivial extensions for other posterior forms. For instance, full-covariance Gaussians lead to Newton-like variants of ADMM, while diagonal covariances result in a cheap Adam-like variant. This is especially useful to handle heterogeneity in federated deep learning, giving up to 7% accuracy improvements over recent baselines. Our work opens a new Bayesian path to improve primal-dual methods.

Recent advances in diffusion models have revolutionized generative AI, but their sheer size makes on device personalization, and thus effective federated learning (FL), infeasible. We propose Shared Backbone Personal Identity Representation Embeddings (SPIRE), a framework that casts per client diffusion based generation as conditional generation in FL. SPIRE factorizes the network into (i) a high capacity global backbone that learns a population level score function and (ii) lightweight, learnable client embeddings that encode local data statistics. This separation enables parameter efficient finetuning that touches $\leq 0.01\%$ of weights. We provide the first theoretical bridge between conditional diffusion training and maximum likelihood estimation in Gaussian mixture models. For a two component mixture we prove that gradient descent on the DDPM with respect to mixing weights loss recovers the optimal mixing weights and enjoys dimension free error bounds. Our analysis also hints at how client embeddings act as biases that steer a shared score network toward personalized distributions. Empirically, SPIRE matches or surpasses strong baselines during collaborative pretraining, and vastly outperforms them when adapting to unseen clients, reducing Kernel Inception Distance while updating only hundreds of parameters. SPIRE further mitigates catastrophic forgetting and remains robust across finetuning learning rate and epoch choices.