We study finite-horizon continuous-time policy evaluation from discrete closed-loop trajectories under time-inhomogeneous dynamics. The target value surface solves a backward parabolic equation, but the Bellman baseline obtained from one-step recursion is only first-order in the grid width. We estimate the time-dependent generator from multi-step transitions using moment-matching coefficients that cancel lower-order truncation terms, and combine the resulting surrogate with backward regression. The main theory gives an end-to-end decomposition into generator misspecification, projection error, pooling bias, finite-sample error, and start-up error, together with a decision-frequency regime map explaining when higher-order gains should be visible. Across calibration studies, four-scale benchmarks, feature and start-up ablations, and gain-mismatch stress tests, the second-order estimator consistently improves on the Bellman baseline and remains stable in the regime where the theory predicts visible gains. These results position high-order generator regression as an interpretable continuous-time policy-evaluation method with a clear operating region.

In this section, we present the training algorithm for Self-Tuning Networks. The full algorithm is showninAlg.2.

An automatic approach to adapting these hyperparameters would improve performance and simplifytheengineering process.

Aggregating intracranial recordings across subjects is challenging since electrode count, placement, and covered regions vary widely. Spatial normalization methods like MNI coordinates offer a shared anatomical reference, but often fail to capture true functional similarity, particularly when localization is imprecise; even at matched anatomical coordinates, the targeted brain region and underlying neural dynamics can differ substantially between individuals. We propose a scalable representation-learning framework that (i) learns a subject-agnostic functional identity for each electrode from multi-region local field potentials using a Siamese encoder with contrastive objectives, inducing an embedding geometry that is locality-sensitive to region-specific neural signatures, and (ii) tokenizes these embeddings for a transformer that models inter-regional relationships with a variable number of channels. We evaluate this framework on a 20-subject dataset spanning basal ganglia-thalamic regions collected during flexible rest/movement recording sessions with heterogeneous electrode layouts. The learned functional space supports accurate within-subject discrimination and forms clear, region-consistent clusters; it transfers zero-shot to unseen channels. The transformer, operating on functional tokens without subject-specific heads or supervision, captures cross-region dependencies and enables reconstruction of masked channels, providing a subject-agnostic backbone for downstream decoding. Together, these results indicate a path toward large-scale, cross-subject aggregation and pretrain-ing for intracranial neural data where strict task structure and uniform sensor placement are unavailable. Building models that generalize across subjects in neuroscience requires representations that remain stable despite variability in data acquisition. Intracranial neural recordings lack this stability: electrode locations, counts, sampling, and coverage differ across individuals, reflecting clinical needs rather than standardized layouts. Without a shared representational system, cross-subject aggregation is unreliable, limiting scalable modeling and clinical translation. Such recordings are uniquely valuable for studying inter-regional communication, yet their heterogeneity makes them especially challenging to align. In practice, two obstacles dominate: Anatomical variability and inconsistent electrode coverage.

Fine-grained visual classification (FGVC) remains highly sensitive to geometric variability, where objects appear under arbitrary orientations, scales, and perspective distortions. While equivariant architectures address this issue, they typically require substantial computational resources and restrict the hypothesis space. We revisit Spatial Transformer Networks (STNs) as a canonicalization tool for transformer-based vision pipelines, emphasizing their flexibility, backbone-agnostic nature, and lack of architectural constraints. We propose a probabilistic, component-wise extension that improves robustness. Specifically, we decompose affine transformations into rotation, scaling, and shearing, and regress each component under geometric constraints using a shared localization encoder. To capture uncertainty, we model each component with a Gaussian variational posterior and perform sampling-based canonicalization during inference.A novel component-wise alignment loss leverages augmentation parameters to guide spatial alignment. Experiments on challenging moth classification benchmarks demonstrate that our method consistently improves robustness compared to other STNs.

Cone-Beam Computed Tomography (CBCT) is widely used for intraoperative imaging due to its rapid acquisition and low radiation dose. However, CBCT images typically suffer from artifacts and lower visual quality compared to conventional Computed Tomography (CT). A promising solution is synthetic CT (sCT) generation, where CBCT volumes are translated into the CT domain. In this work, we enhance sCT generation through multimodal learning by jointly leveraging intraoperative CBCT and preoperative CT data. To overcome the inherent misalignment between modalities, we introduce an end-to-end learnable registration module within the sCT pipeline. This model is evaluated on a controlled synthetic dataset, allowing precise manipulation of data quality and alignment parameters. Further, we validate its robustness and generalizability on two real-world clinical datasets. Experimental results demonstrate that integrating registration in multimodal sCT generation improves sCT quality, outperforming baseline multimodal methods in 79 out of 90 evaluation settings. Notably, the improvement is most significant in cases where CBCT quality is low and the preoperative CT is moderately misaligned.

Accurate intraoperative localization of the subthalamic nucleus (STN) is essential for the efficacy of Deep Brain Stimulation (DBS) in patients with Parkinson's disease. While microelectrode recordings (MERs) provide rich electrophysiological information during DBS electrode implantation, current localization practices often rely on subjective interpretation of signal features. In this study, we propose a quantitative framework that leverages nonlinear dynamics and entropy-based metrics to classify neural activity recorded inside versus outside the STN. MER data from three patients were preprocessed using a robust artifact correction pipeline, segmented, and labelled based on surgical annotations. A comprehensive set of recurrence quantification analysis, nonlinear, and entropy features were extracted from each segment. Multiple supervised classifiers were trained on every combination of feature domains using stratified 10-fold cross-validation, followed by statistical comparison using paired Wilcoxon signed-rank tests with Holm-Bonferroni correction. The combination of entropy and nonlinear features yielded the highest discriminative power, and the Extra Trees classifier emerged as the best model with a cross-validated F1-score of 0.902+/-0.027 and ROC AUC of 0.887+/-0.055. Final evaluation on a 20% hold-out test set confirmed robust generalization (F1= 0.922, ROC AUC = 0.941). These results highlight the potential of nonlinear and entropy signal descriptors in supporting real-time, data-driven decision-making during DBS surgeries