arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
arXiv:2602. 03282v2 Announce Type: replace-cross Abstract: A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations.
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:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
arXiv:2609.05575v1 Announce Type: new Abstract: Understanding how concepts are encoded in the internal representations of machine learning models is a central problem in mechanistic interpretability,...
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.
arXiv:2607. 06497v1 Announce Type: new Abstract: We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths.
arXiv:2607. 03671v1 Announce Type: cross Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes.
The paper introduces an unsupervised framework that merges manifold learning with rank‑based interpretable graph embeddings to address the Geometric and Interpretability Gaps in visual representation learning. By first analyzing contextual information on the dataset manifold and then producing sparse, self‑explainable embeddings, the method achieves dimensionality reduction while preserving or improving performance in image retrieval and semi‑supervised Graph Convolutional Network classification. Experiments across varied datasets confirm that these context‑aware representations maintain high downstream effectiveness.
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
arXiv:2605. 25811v2 Announce Type: replace-cross Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure.