arXiv:2507. 03065v2 Announce Type: replace Abstract: Why do some macroscopic structures remain identifiable even though their microscopic constituents continually change?
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2606. 07303v4 Announce Type: replace Abstract: Representation learning is central to modern machine learning, yet most research focuses on optimizing representations after a framework has been selected.
The paper introduces persistent magnitude homology as a functorial invariant for quantitative equational theories, providing a barcode that captures the metric structure of the free algebra generated by a metric space of generators. It shows how this invariant combines graded magnitude homology with persistence, yielding stability estimates and a method to compare barcodes when theories are extended. Four concrete examples illustrate the theory in each homological degree.
The paper investigates how neural representations maintain the structure of input changes, linking representation analysis with internal interventions. It characterises when transformations can be applied through an encoder, providing linear settings where defects depend on discarded information and detailing failure modes for rectifiers and harmonic carriers. Using colour as a case study, the authors show that hue orbits in frozen visual features concentrate most energy in the first two harmonics, that this structure is inherited from input and architecture, and that a compact, fixed‑action interface can read hue zero‑shot with low error on unseen shapes.
arXiv:2506. 20699v2 Announce Type: replace Abstract: Learning in non-stationary and multi-context environments requires more than ordinary within-task generalization.
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
How neural representations preserve the structure of input changes connects representation analysis with internal intervention. We study operable representational content through compatible actions of...