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.

--Contact-based estimation of object pose is challenging due to discontinuities and ambiguous observations that can correspond to multiple possible system states. This multimodality makes it difficult to efficiently sample valid hypotheses while respecting contact constraints. Diffusion models can learn to generate samples from such multimodal probability distributions through denoising algorithms. We leverage these probabilistic modeling capabilities to learn an inverse observation model conditioned on tactile measurements acquired from a distributed artificial skin. We present simulated experiments demonstrating efficient sampling of contact hypotheses for object pose estimation through touch.

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.

We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax of fuzzy propositional logic, but its semantics distinguishes stable models from non-stable models. The generality of the language allows for highly configurable nonmonotonic reasoning for dynamic domains involving graded truth degrees. We show that several properties of Boolean stable models are naturally extended to this many-valued setting, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.

In this paper, we introduce the Radon-Nikodym Estimator (RNE), a flexible, plug-and-play framework for diffusion inference-time density estimation and control, based on the concept of the density ratio between path distributions. RNE connects and unifies a variety of existing density estimation and inference-time control methods under a single and intuitive perspective, stemming from basic variational inference and probabilistic principles therefore offering both theoretical clarity and practical versatility. Experiments demonstrate that RNE delivers strong results in diffusion density estimation, and offers broad applicability to inference-time control tasks -- such as annealing, diffusion model composition, and reward-tilting -- with promising inference-time scaling performance.

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.

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL) divergence. In this paper, we focus on the following parametric family: mixtures of isotropic Gaussians (i.e., with diagonal covariance matrices proportional to the identity) and uniform weights. We develop a variational framework and provide efficient algorithms suited for this family. In contrast with mixtures of Gaussian with generic covariance matrices, this choice presents a balance between accurate approximations of multimodal Bayesian posteriors, while being memory and computationally efficient. Our algorithms implement gradient descent on the location of the mixture components (the modes of the Gaussians), and either (an entropic) Mirror or Bures descent on their variance parameters. We illustrate the performance of our algorithms on numerical experiments.