Source
Cammarata et al. (2021), Curve Circuits, LIT-1629, read in full in NOTE-1207: the introduction, The Curve Detector Algorithm, The Components of Curve Detectors and An Artificial Artificial Neural Network.
What is asserted
“Although curve detection involves more than 50,000 parameters, those parameters actually implement a simple algorithm that can be read off the weights and described in just a few English sentences.” The sentences: “Gabor filters turn into proto-lines which build lines and early curves. Finally, lines and early curves are composed into curves. In each case, each shape family … has positive weight across the tangent of the shape family it builds”, and each “implements the rotational equivariance motif”. After the reimplementation: “we think this is strong evidence these patterns accurately reflect the underlying circuits that construct curve detectors.”
What the record holds toward it
- The echo edit, the reimplementation and the substitution (THEORY-1038): one tested weight-level prediction, a qualitative match on synthetic curves and strong dataset examples, and 26 of 46 lost classifications recovered on 2,000 images.
- The structure, read from the strongest weights and the highest-magnitude position per layer, by decomposed feature visualization and weight matrices.
- Against it, the authors’ own caveats: a “long tail of neurons with low magnitude that collectively make up a large fraction of the total weight”; mixed3a’s line-to-curve matrix is “indecipherable” until one goes back a layer; the hand-written units lack colour and texture, and the authors expect “many false-negatives”.
Why it stays Proposed
“Simple” and “accurately reflect” are claims about the whole circuit, and the evidence is about its strongest parts, compared by figure. The weak firings that THEORY-1022 finds unexplained are not compared.
What would confirm or reject it
The promote_when above.