arXiv:2603.13496v2 Announce Type: replace Abstract: Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems...
arXiv:2601. 09173v5 Announce Type: replace Abstract: Representational similarity analysis and related methods compare the internal geometries of neural networks, but they measure only alignment between spaces, leaving a blind spot -- whether a representation's structure is reliably recoverable, not merely similar.
The paper investigates whether placing class prototypes on a hyperbolic manifold (Poincaré ball) rather than a Euclidean space improves the satisfaction of a tree‑structured regularizer in hierarchical classification. Experiments on WikiArt show that hyperbolic prototypes better preserve nearest‑neighbor topology (higher sibling and cousin recall) across multiple tree definitions, while Euclidean prototypes perform similarly to logistic regression on raw features and only hyperbolic models improve local retrieval. The study provides empirical evidence that the choice of latent geometry can affect the fidelity of tree‑structured regularization in real data.
arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...
We study a tree-structured regularizer over class-prototype layouts in a hierarchical-classification model and ask whether the choice of latent manifold for the prototypes (Euclidean R^d vs. the Poinc...
arXiv:2608. 05132v1 Announce Type: cross Abstract: Predicting how a subcortical structure's shape will evolve from a few prior scans could support prognosis and clinical-trial enrichment.
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:2606. 05957v1 Announce Type: new Abstract: Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate.
arXiv:2606. 32022v1 Announce Type: new Abstract: Residual-stream analysis asks how language-model computation evolves across depth, but intermediate decoding requires comparable readout coordinates across layers.
arXiv:2607. 12166v1 Announce Type: new Abstract: Sparse autoencoders (SAEs) are the standard for decomposing superposed neural representations into interpretable features, and evaluation relies predominantly on correlational recovery metrics -- cosine similarity between ground-truth directions and decoder atoms.
arXiv:2606. 15553v1 Announce Type: cross Abstract: Representation Autoencoders (RAEs) have improved diffusion and flow models by semantically richer latent space owing to the strongly label-wise clustered DINO features in the pretrained encoders.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.