arXiv:2607. 13046v1 Announce Type: new Abstract: We develop a framework for the information discarded by machine learning models whose inputs carry a Lie group action.
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:2606. 20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it.
arXiv:2609.07031v1 Announce Type: new Abstract: Learning with group invariances is central to many scientific and geometric learning problems, yet its computational foundations remain poorly understo...
arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.
arXiv:2608.24700v1 Announce Type: new Abstract: When a network has learned a function with a known symmetry, can that symmetry be moved through the parametrisation---is there a motion in parameter sp...
arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
arXiv:2607. 06723v2 Announce Type: replace-cross Abstract: Adaptive optimizers carry hidden states that change how visible gradients become parameter motion.
The paper investigates observability in neural state‑space models, particularly the Mamba architecture, using tools from ordinary differential equations and control theory. It introduces several strategies—based on eigenvalues, roots of unity, permutations, Fourier transforms, and Vandermonde matrices—to enforce observability in high‑dimensional, learnable hidden states while maintaining computational efficiency. The authors also present a shared‑parameter construction for Mamba and a training algorithm that satisfies a Robbins‑Monro condition, contrasting it with classical procedures that fail to meet contraction requirements.
arXiv:2609.37344v1 Announce Type: cross Abstract: Data reconstruction attacks have empirically been successful in recovering training samples from learned models, raising privacy concerns and motivat...
arXiv:2409. 01062v4 Announce Type: replace Abstract: Model Inversion (MI) attacks pose a significant privacy threat by reconstructing private training data from machine learning models.
arXiv:2605. 24042v3 Announce Type: replace-cross Abstract: Of $1{,}536$ Gaussian release covariances we tested for single-layer hidden-state privacy, zero achieve both moderate utility and moderate privacy against an adaptive retrieval attacker.
arXiv:2609.25987v1 Announce Type: new Abstract: Equivariant convolutional neural networks are usually built from a group acting globally on the space of signals. This hypothesis is inappropriate for...