We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.

We generalize the continuous time framework for score-based generative models from an underlying Brownian motion (BM) to an approximation of fractional Brownian motion (FBM). We derive a continuous reparameterization trick and the reverse time model by representing FBM as a stochastic integral over a family of Ornstein-Uhlenbeck processes to define generative fractional diffusion models (GFDM) with driving noise converging to a non-Markovian process of infinite quadratic variation. The Hurst index $H\in(0,1)$ of FBM enables control of the roughness of the distribution transforming path. To the best of our knowledge, this is the first attempt to build a generative model upon a stochastic process with infinite quadratic variation.

We present DiffInfinite, a hierarchical diffusion model that generates arbitrarily large histological images while preserving long-range correlation structural information. Our approach first generates synthetic segmentation masks, subsequently used as conditions for the high-fidelity generative diffusion process. The proposed sampling method can be scaled up to any desired image size while only requiring small patches for fast training. Moreover, it can be parallelized more efficiently than previous large-content generation methods while avoiding tiling artifacts. The training leverages classifier-free guidance to augment a small, sparsely annotated dataset with unlabelled data. Our method alleviates unique challenges in histopathological imaging practice: large-scale information, costly manual annotation, and protective data handling. The biological plausibility of DiffInfinite data is evaluated in a survey by ten experienced pathologists as well as a downstream classification and segmentation task. Samples from the model score strongly on anti-copying metrics which is relevant for the protection of patient data.

Camera images are ubiquitous in machine learning research. They also play a central role in the delivery of important services spanning medicine and environmental surveying. However, the application of machine learning models in these domains has been limited because of robustness concerns. A primary failure mode are performance drops due to differences between the training and deployment data. While there are methods to prospectively validate the robustness of machine learning models to such dataset drifts, existing approaches do not account for explicit models of the primary object of interest: the data. This limits our ability to study and understand the relationship between data generation and downstream machine learning model performance in a physically accurate manner. In this study, we demonstrate how to overcome this limitation by pairing traditional machine learning with physical optics to obtain explicit and differentiable data models. We demonstrate how such data models can be constructed for image data and used to control downstream machine learning model performance related to dataset drift. The findings are distilled into three applications. First, drift synthesis enables the controlled generation of physically faithful drift test cases to power model selection and targeted generalization. Second, the gradient connection between machine learning task model and data model allows advanced, precise tolerancing of task model sensitivity to changes in the data generation. These drift forensics can be used to precisely specify the acceptable data environments in which a task model may be run. Third, drift optimization opens up the possibility to create drifts that can help the task model learn better faster, effectively optimizing the data generating process itself. A guide to access the open code and datasets is available at https://github.com/aiaudit-org/raw2logit.