nucleation

LIT-1629: Curve Circuits

1 min read

Properties6
StatusActive — read 2026-10-27 (NOTE-1207) in full, from the Distill article; worth reading as the second part of Curve Detectors (LIT-1575) and the one that supplies the three arguments that article deferred: the circuit that builds the ten mixed3b curve units from earlier families, a downstream use in mixed4a, and a hand-written "artificial artificial neural network" whose curve units approximate the natural ones (THEORY-1038). Read it knowing that every comparison but one is qualitative (figures), that the one number, the accuracy recovered by substituting the hand-written units, is on 2,000 validation images and called preliminary by the authors, that the hand-written units are grayscale, and that the claim that the circuit is "a simple algorithm" is the authors' (THEORY-1047).
Version2
Tagsrepresentation-learning, anthology-candidate
ExtendsLIT-1575 — Curve Detectors
Cited as “paper” byNOTE-1207 — Cammarata et al. — Curve circuits
Cited as “source” byTHEORY-1038 — In InceptionV1, the ten curve units of mixed3b, which respond to curves of one orientation and not to the opposite one, regain the 180° echo of earlier curve units when their input is restricted to mixed3a early curves with the negative weights removed, and not when the negative weights are kept; a network one author wrote by hand from the described circuit, without looking at the original weights and tuned afterwards, has grayscale curve units that the authors show, by figures only, approximating the natural ones on synthetic curves across radii and orientations; and substituting them for the ten units recovered 26 of the 46 top-5 classifications lost by deleting the units, on 2,000 validation images, a result the authors call preliminary, THEORY-1047 — The curve units of InceptionV1's mixed3b implement a simple algorithm that can be read off their weights and written down in a few sentences: families of Gabors, lines and early curves, each a set of rotated copies of one unit, tiled along the curve's tangent, with negative weights against similar shapes of opposing orientation, rotational and scale equivariance reducing the circuit's more than 50,000 parameters about fifty-fold, so that a network written from this description reimplements them and the description accurately reflects the circuit, as Cammarata, Goh, Carter, Voss, Schubert and Olah claim

Graph View

Cammarata, N., Goh, G., Carter, S., Voss, C., Schubert, L. and Olah, C. (2021). Curve circuits. Distill, 30 January 2021. https://distill.pub/2020/circuits/curve-circuits/ (the page prints doi:10.23915/distill.00024.006, which did not resolve on 2026-10-27).

Read in full on 2026-10-27 (NOTE-1207). Two accounts were drawn from it: THEORY-1038 (Active) and THEORY-1047 (Proposed).

Why this is here

Registered and read at the owner’s request of 2026-10-27 (“file the next readings”), as one of the works the circuits readings named and did not register. Zoom In (LIT-1543) argues curve detectors seven ways; Curve Detectors (LIT-1575) supplied four of them and deferred the other three, the implementing circuit, the downstream use and the hand-written reimplementation, to this article. THEORY-1013 and THEORY-1022 both name it as the missing piece. The record’s circuits line held the vision case’s behaviour and none of its mechanism. Read against them, it supplies all three deferred arguments for one family, mostly as figures and once as a small number, and it gives no count over a layer.

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