Regina Ruane

Marios Papamichalis, Regina Ruane

Contact-rich robot dynamics are hybrid: a single observation can match several latent states and contact regimes (free, impact, stick--slip). A standard amortized filter that places no probability on a feasible contact transition will permanently lose the branch the robot actually follows. We introduce VHYDRO, a variational hybrid dynamics learner that prevents this branch loss. At each step, VHYDRO mixes the learned proposal with a feasible transition law before sampling and importance weighting, ensuring that every transition retained by the model-feasible carrier remains covered. VHYDRO jointly infers a continuous latent state and a discrete contact mode, and fits a sparse port-Hamiltonian law to each recovered regime. On top of this, three guarantees connect: support coverage stabilizes filtering, the stabilized filter concentrates the discrete contact posterior on coherent regimes, and mode-pure segments admit sparse port-Hamiltonian recovery. The recovery error separates cleanly into filtering, derivative, mode-impurity, and physics-residual parts. Three empirical findings track the same mechanism. Under heavy occlusion the support-safe filter stays usable while a non-defensive proposal collapses. On ManiSkill demonstrations and on four Sawyer/BridgeData task families the discrete state forms temporally coherent contact-regime segments that the discrete state yields a stronger joint profile across ARI, change-point F1, and segment purity than post-hoc and mode-free baselines. On hybrid systems with known equations the mode-conditioned sparse fit recovers the active physical terms; purely predictive baselines do not.

Alan F. Karr, Regina Ruane

We describe extensive numerical experiments assessing and quantifying how classifier performance depends on the quality of the training data, a frequently neglected component of the analysis of classifiers. More specifically, in the scientific context of metagenomic assembly of short DNA reads into "contigs," we examine the effects of degrading the quality of the training data by multiple mechanisms, and for four classifiers -- Bayes classifiers, neural nets, partition models and random forests. We investigate both individual behavior and congruence among the classifiers. We find breakdown-like behavior that holds for all four classifiers, as degradation increases and they move from being mostly correct to only coincidentally correct, because they are wrong in the same way. In the process, a picture of spatial heterogeneity emerges: as the training data move farther from analysis data, classifier decisions degenerate, the boundary becomes less dense, and congruence increases.

Alan F. Karr, Zac Bowen, Adam A. Porter et al.

Classifiers assign complex input data points to one of a small number of output categories. For a Bayes classifier whose input space is a graph, we study the structure of the \emph{boundary}, which comprises those points for which at least one neighbor is classified differently. The scientific setting is assignment of DNA reads produced by \NGSs\ to candidate source genomes. The boundary is both large and complicated in structure. We introduce a new measure of uncertainty, Neighbor Similarity, that compares the result for an input point to the distribution of results for its neighbors. This measure not only tracks two inherent uncertainty measures for the Bayes classifier, but also can be implemented for classifiers without inherent measures of uncertainty.

Marios Papamichals, Regina Ruane

Generative models on curved spaces rely on charts to map Euclidean spaces to manifolds. Exponential maps preserve geodesics but have stiff, radius-dependent Jacobians, while volume-preserving charts maintain densities but distort geodesic distances. Both approaches entangle curvature with model parameters, inflating gradient variance. In high-dimensional latent normalizing flows, the wrapped exponential prior can stretch radii far beyond the curvature scale, leading to poor test likelihoods and stiff solvers. We introduce Radial Compensation (RC), an information-geometric method that selects the base density in the tangent space so that the likelihood depends only on geodesic distance from a pole, decoupling parameter semantics from curvature. RC lets radial parameters retain their usual meaning in geodesic units, while the chart can be tuned as a numerical preconditioner. We extend RC to manifolds with known geodesic polar volume and show that RC is the only construction for geodesic-radial likelihoods with curvature-invariant Fisher information. We derive the Balanced-Exponential (bExp) chart family, balancing volume distortion and geodesic error. Under RC, all bExp settings preserve the same manifold density and Fisher information, with smaller dial values reducing gradient variance and flow cost. Empirically, RC yields stable generative models across densities, VAEs, flows on images and graphs, and protein models. RC improves likelihoods, restores clean geodesic radii, and prevents radius blow-ups in high-dimensional flows, making RC-bExp a robust default for likelihood-trained generative models on manifolds.