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: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: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.
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:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv:2606. 07598v1 Announce Type: cross Abstract: We propose a topological framework for comparing trained Graph Neural Networks (GNNs) by mapping the Stochastic Block Models (SBMs) induced on the graphon-signal space of a Message Passing Neural Network (MPNN) onto the unit $n$-sphere $\sphere^{n-1}\subset\R^n$.
arXiv:2512. 20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning.
arXiv:2607. 03108v1 Announce Type: new Abstract: Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters.
arXiv:2608. 10172v1 Announce Type: new Abstract: Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it.