Generative Modeling on Metric Graphs via Neural Optimal Transport

We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target measures on a metric graph, our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization, and projects generated samples back onto the original graph. We study two embedded geometries: an extrinsic Euclidean realization and the intrinsic tropical Abel--Jacobi embedding into the Jacobian torus. In both cases, the resulting generator is graph-supported by construction. We prove that, in the joint limit of increasing neural expressivity, the learned generator converges weakly to a valid transport coupling between the original graph measures. Empirically, across a range of geometrically distinct graphs, our method matches or improves upon heuristic transport baselines based on discrete graph OT, while scaling more favorably. Finally, we demonstrate scalability on real-world urban mobility data by training our model on one million Uber pickup locations in Manhattan, New York City.

Bayesian Selective Latent Inference for Wastewater-First Influenza Monitoring

Wastewater influenza surveillance can reveal community circulation before clinical reporting, but wastewater alone is not a fully identifiable proxy for human burden. Existing wastewater models assume a fixed evidence set, while generic evidence-acquisition methods treat official surveillance streams as interchangeable costly features. We cast wastewater-first influenza monitoring as a selective decision problem: starting from mandatory wastewater evidence, the system must decide whether wastewater is sufficient, which delayed official stream to query next, and when abstention is the only scientifically defensible action under source ambiguity. We propose Bayesian Selective Latent Inference (BSLI), a principled Bayesian method that maintains a posterior over latent burden and identifiability, certifies answerability through explicit scientific gates, and optimizes query-stop decisions with an exact cost-calibrated Bellman policy. We prove the key variational, answerability, Bellman-optimality, and one-dimensional cost-calibration properties. On a fixed public-data benchmark with 5,933 forecasting episodes and 3,102 source-ambiguity episodes, BSLI improves the matched-budget cost-performance frontier while preserving conservative abstention under source ambiguity.

iLoRA: Bayesian Low-Rank Adaptation with Latent Interaction Graphs for Microbiome Diagnosis

Parameter-efficient adaptation has made LLMs practical for domain prediction, but standard LoRA still relies on a static low-rank update and does not expose the latent interactions that often drive scientific labels. We introduce iLoRA. To our knowledge, it is the first Bayesian graph-conditioned LoRA framework. It infers a latent interaction graph from the input and uses it to generate input-conditioned LoRA updates. As a result, iLoRA learns prediction and latent interaction structure jointly, rather than training a predictor and applying interaction analysis only post hoc. We instantiate this idea for microbiome diagnosis, where disease state can depend on both species-level abundance and microbe-microbe cross-talk, and evaluate it in two complementary settings: interactive QA with human-annotated graphs, which tests latent structure recovery, and multi-cohort IBD diagnosis, which tests biomedical utility. Across both settings, iLoRA improves over strong LoRA and Bayesian adaptation baselines, recovers graphs aligned with human annotations and cohort-level microbiome associations, and provides calibrated uncertainty with moderate graph-branch overhead.

PlayClass: Automated Play Behaviour Classification in Poultry

Automated monitoring of animal welfare has largely targeted negative indicators, leaving positive welfare behaviours such as play underexplored. To address this gap, we present PlayClass, a pipeline for play-behaviour classification in poultry from top-down pen video. The pipeline leverages long-duration tracking with SAM 3 via YOLO-guided chunk boundaries to minimise identity errors in point-based prompting, and frozen embeddings from image and video foundation models for play action classification. Although handcrafted motion features from tracked masks alone achieved competitive accuracy, V-JEPA 2.1 consistently outperformed all other backbones across model scales, reaching 77.0 macro-averaged F$_1$ when combined with handcrafted features. Despite this result, the dataset remains challenging due to play sub-types sharing similar kinematic profiles with non-play and inter-bird occlusion. Overall, our work provides encouraging evidence towards automated frameworks for play behaviour classification in poultry.

Interdomain Attention: Beyond Token-Level Key-Value Memory

Transformers and deep state space models (SSMs) sit at opposite ends of a basic design choice: attention routes each query through a growing key-value (KV) cache by content-based matching at quadratic cost, while deep SSMs compress context into a fixed-size recurrent state that is not directly addressed by query-key matching. We propose Interdomain Attention, which integrates an SSM into an attention module through kernel methods: an attention kernel is approximated by a finite feature map, the resulting key features and values are projected onto a shared set of basis functions maintained by a single SSM recurrence, and each query attends to the compressed coefficients through its own feature map, recovering query-conditioned attention over a fixed-size state. The scalable layer is a learned relaxation of this derivation, and we validate its components through ablations. In a 125M to 1.3B autoregressive language-modeling study on FineWeb-Edu at matched recurrent-state budget, Interdomain Attention improves on an SSM token mixer at every scale, surpasses a same-recipe softmax baseline at 1.3B on validation perplexity and on the eight-task commonsense suite, and inherits the length-flat behavior of its fixed-state core out to 3.5x the training context. Ablations indicate that the query-conditioned projection is the main source of the gain.

Entropic Riemannian Neural Optimal Transport

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting optimal transport (OT) problem. Existing manifold OT methods have pursued amortized out-of-sample maps, while entropic regularization has made discrete OT more scalable, but these advantages have remained largely disjoint. We propose Entropic Riemannian Neural Optimal Transport (Entropic RNOT), a unified framework that combines intrinsic entropic OT with amortized out-of-sample evaluation on Riemannian manifolds. Our method learns a single target-side Schrödinger potential through a neural pullback parameterization, recovers the induced Gibbs coupling, and uses the resulting conditional laws to construct intrinsic transport surrogates. These include barycentric projections on Cartan-Hadamard manifolds and heat-smoothed conditional surrogates on stochastically complete manifolds, the latter turning possibly atomic target laws into absolutely continuous ones. For fixed regularization $\varepsilon>0$, we prove that the proposed hypothesis class recovers the entropic optimal coupling in strong probabilistic metrics. As consequences, barycentric surrogates converge in $L^2$, while heat-smoothed surrogates are stable at fixed heat time and asymptotically unbiased as the heat time vanishes. The guarantees hold for compactly supported data on possibly noncompact manifolds. Empirically, our method matches or improves over Euclidean, tangent-space, and log-Euclidean baselines on benchmarks over $\mathbb{S}^2$, $\mathrm{SO}(3)$, $\mathrm{SPD}(3)$, $\mathrm{SE}(3)$, and $\mathbb{H}^2$, scales favorably relative to discrete manifold Sinkhorn, and in a protein-ligand docking application, refines poses on $\mathrm{SE}(3)$ without retraining or per-instance optimization.

Riemannian Neural Optimal Transport

Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after training, but existing approaches are tailored to Euclidean geometry. Extending neural OT to high-dimensional Riemannian manifolds remains an open challenge. In this paper, we prove that any method for OT on manifolds that produces discrete approximations of transport maps necessarily suffers from the curse of dimensionality: achieving a fixed accuracy requires a number of parameters that grows exponentially with the manifold dimension. Motivated by this limitation, we introduce Riemannian Neural OT (RNOT) maps, which are continuous neural-network parameterizations of OT maps on manifolds that avoid discretization and incorporate geometric structure by construction. Under mild regularity assumptions, we prove that RNOT maps approximate Riemannian OT maps with sub-exponential complexity in the dimension. Experiments on synthetic and real datasets demonstrate improved scalability and competitive performance relative to discretization-based baselines.

Interpretable Graph Learning Over Sets of Temporally-Sparse Data

Real-world medical data often includes measurements from multiple signals that are collected at irregular and asynchronous time intervals. For example, different types of blood tests can be measured at different times and frequencies, resulting in fragmented and unevenly scattered temporal data. Similar issues of irregular sampling of different attributes occur in other domains, such as monitoring of large systems using event log files or the spread of fake news on social networks. Effectively learning from such data requires models that can handle sets of temporally sparse and heterogeneous signals. In this paper, we propose Graph Mixing Additive Networks (GMAN), a novel and interpretable-by-design model for learning over irregular sets of temporal signals. Our method achieves state-of-the-art performance in real-world medical tasks, including a 4-point increase in the AUROC score of in-hospital mortality prediction, compared to existing methods. We further showcase GMAN's flexibility by applying it to a fake news detection task. We demonstrate how its interpretability capabilities, including node-level, graph-level, and subset-level importance, allow for transition phases detection and gaining medical insights with real-world high-stakes implications. Finally, we provide theoretical insights on GMAN expressive power.

NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification

We introduce NeuralSurv, the first deep survival model to incorporate Bayesian uncertainty quantification. Our non-parametric, architecture-agnostic framework flexibly captures time-varying covariate-risk relationships in continuous time via a novel two-stage data-augmentation scheme, for which we establish theoretical guarantees. For efficient posterior inference, we introduce a mean-field variational algorithm with coordinate-ascent updates that scale linearly in model size. By locally linearizing the Bayesian neural network, we obtain full conjugacy and derive all coordinate updates in closed form. In experiments, NeuralSurv delivers superior calibration compared to state-of-the-art deep survival models, while matching or exceeding their discriminative performance across both synthetic benchmarks and real-world datasets. Our results demonstrate the value of Bayesian principles in data-scarce regimes by enhancing model calibration and providing robust, well-calibrated uncertainty estimates for the survival function.

Diffusion Models for Inverse Problems in the Exponential Family

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due to the intractability of the likelihood score, which until now has only been approximated in the simpler case of Gaussian likelihoods. In this work, we extend diffusion models to handle inverse problems where the observations follow a distribution from the exponential family, such as a Poisson or a Binomial distribution. By leveraging the conjugacy properties of exponential family distributions, we introduce the evidence trick, a method that provides a tractable approximation to the likelihood score. In our experiments, we demonstrate that our methodology effectively performs Bayesian inference on spatially inhomogeneous Poisson processes with intensities as intricate as ImageNet images. Furthermore, we demonstrate the real-world impact of our methodology by showing that it performs competitively with the current state-of-the-art in predicting malaria prevalence estimates in Sub-Saharan Africa.