nucleation

LIT-363: Understanding image representations by measuring their equivariance and equivalence

2 min read

Properties7
StatusActive — read in full 2026-09-29 (NOTE-309); worth reading as the origin of two standard probes of trained networks, fitted linear equivariance maps and model stitching, and as the closest prior art for "measuring symmetry in a trained network's representation"; read it knowing that every transformation tested is named in advance and applied to the input, that each is fitted separately with no group structure, and that its deep-layer "equivariance" is judged by recovered task accuracy through a high-capacity learned layer.
Version2
Tagsrepresentation-learning, anthology-candidate
Extended byLIT-850 — Revisiting Model Stitching to Compare Neural Representations
SupportsCLAIM-126 — Model stitching tests whether a transport preserves decision-relevant information only in its reconstruction form: a map fitted to reproduce the target representation certifies one direction of Blackwell sufficiency, while task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency, CLAIM-268 — Model stitching certifies an order of information only in its reconstruction form: a map fitted to reproduce the target layers shows the source representation is at least as informative for every decision on the label, task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency
Cited as “paper” byNOTE-309 — Understanding image representations by measuring their equivariance and equivalence
Cited as “source” byTHEORY-176 — A task-loss stitching penalty compares representations in one decision problem, through a fixed top network and a restricted map class, so it is not Blackwell's order: representations that are functions of each other can stitch differently, and a negative penalty shows the fitted map did not reproduce the layers it replaced

Graph View

Lenc & Vedaldi (2014), 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 991–999, doi 10.1109/CVPR.2015.7298701 (verified on Crossref; the arXiv v2 PDF carries no venue line); arXiv v1 21 Nov 2014, v2 20 Jun 2015 (the version read); extended version in International Journal of Computer Vision, pp. 456–476, published online 18 May 2018, doi 10.1007/s11263-018-1098-y (from Crossref; volume not checked; not read) — arXiv:1411.5908

Standing in the record

Filed on 2026-09-29 as a supplemental reading. The close readings of the owner’s prior-art novelty map’s references found the map’s citation for this point wrong, or its source unreachable, and this work is the candidate replacement. published: is the first appearance (ADR-002).

It was filed Deferred, unread. NOTE-309 is the close reading of 2026-09-29, and it placed the work: Active — worth reading as the origin of two standard probes of trained networks, fitted linear equivariance maps and model stitching, and as the closest prior art for “measuring symmetry in a trained network’s representation”; read it knowing that every transformation tested is named in advance and applied to the input, that each is fitted separately with no group structure, and that its deep-layer “equivariance” is judged by recovered task accuracy through a high-capacity learned layer.

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