Graph Diffusion Residuals for Control-Function Instrumental Variables

Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a deterministic graph-diffusion residual extractor for flexible control functions. A-IHF treats treatment as a signal on a graph of first-stage features, uses pilot diffusion to detect large treatment jumps, attenuates conductance across those jumps, and computes the generated control with a sparse graph resolvent. Its observational selection rule uses only $(Z,X)$, combining graph generalized cross-validation, roughness, residualized-treatment relevance, and graph-admissibility filtering. The analysis decomposes error into structural leakage, residual attenuation, and residualized treatment variation, yielding finite-sample bounds, graph-admissibility rates under latent piecewise-smooth geometry, and finite-path selection calibration. Across 54 synthetic benchmark cells with tuned graph, kernel, tree, boosting, series, and neural control-function baselines, guarded observational A-IHF has the lowest average structural-response MSE; the A-IHF family beats the best non-A-IHF baseline in 32 cells. Performance is strongest when the graph captures piecewise-smooth first-stage structure.

Hysteresis-Aware Neural Network Modeling and Whole-Body Reinforcement Learning Control of Soft Robots

Soft robots exhibit inherent compliance and safety, which makes them particularly suitable for applications requiring direct physical interaction with humans, such as surgical procedures. However, their nonlinear and hysteretic behavior, resulting from the properties of soft materials, presents substantial challenges for accurate modeling and control. In this study, we present a soft robotic system designed for surgical applications and propose a hysteresis-aware whole-body neural network model that accurately captures and predicts the soft robot's whole-body motion, including its hysteretic behavior. Building upon the high-precision dynamic model, we construct a highly parallel simulation environment for soft robot control and apply an on-policy reinforcement learning algorithm to efficiently train whole-body motion control strategies. Based on the trained control policy, we developed a soft robotic system for surgical applications and validated it through phantom-based laser ablation experiments in a physical environment. The results demonstrate that the hysteresis-aware modeling reduces the Mean Squared Error (MSE) by 84.95 percent compared to traditional modeling methods. The deployed control algorithm achieved a trajectory tracking error ranging from 0.126 to 0.250 mm on the real soft robot, highlighting its precision in real-world conditions. The proposed method showed strong performance in phantom-based surgical experiments and demonstrates its potential for complex scenarios, including future real-world clinical applications.