IsoAct is a post‑hoc debiasing framework that respects the geometry of non‑Euclidean representations. It identifies nuisance‑predictive directions via Fisher discriminant analysis in tangent coordinates and corrects them using manifold‑native actions that keep the representation on its manifold. Experiments on hyperspherical, hyperbolic, and SE(3) spaces show that IsoAct reduces nuisance recoverability while preserving utility and manifold validity, notably improving kinase‑group recoverability and structural prediction on the KLIFS dataset.
Learning representations that are robust to nuisance factors is essential for reliable deployment, but remains challenging when the representations lie on non-Euclidean manifolds. Existing debiasing m...
Semantic-preserving transformations can induce substantial motion in learned representations, while small changes may strongly affect model predictions, raising a basic question: what local metric bes...
arXiv:2609.36458v1 Announce Type: new Abstract: Semantic-preserving transformations can induce substantial motion in learned representations, while small changes may strongly affect model predictions...
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
arXiv:2602.02611v2 Announce Type: replace Abstract: A prevailing paradigm in modern representation learning is the map-first approach, in which a representation map is learned from reconstruction, em...
arXiv:2610.29168v1 Announce Type: cross Abstract: World action models (WAMs) are shown to substantially diverge under generalization performance based on their generative backbones. We investigate th...
arXiv:2207. 03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data.
arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.
LocaLeJEPA extends Joint-Embedding Predictive Architectures (JEPA) by introducing a manifold-theoretic reformulation that aligns representation learning with non‑Euclidean geometric priors. It incorporates a locally Euclidean distribution‑matching regularizer, LocaLeReg, to stabilize training and scale to large models. Experiments on ImageNet‑1K show that LocaLeJEPA outperforms the original LeJEPA across both hyperbolic and Euclidean backbones, improving linear and k‑NN classification as well as downstream tasks.
arXiv:2610.19007v1 Announce Type: new Abstract: World models are a powerful means of reasoning and planning, but many of these action-conditioned predictive models are high dimensional and computatio...
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.