“A conceptor by any other name” by Keenan Pepper

I just had one of those delightful moments where I have a very specific idea, and then I search for it (Claude Research in this case), and it turns out that people have already been using that exact concept but just calling it by a name I'd never heard of.

That name is conceptor, but the basic construction is not new and has gone by many other names.

What a conceptor is

I'll quote from "Conceptors for Semantic Steering" (Triantafyllopoulos et al.) since I couldn't say it any better myself:

Given a collection of neural activation vectors associated with a particular concept, the conceptor matrix is defined as the solution to the regularized reconstruction problem:

where denotes the Frobenius norm and is the aperture parameter controlling the trade-off between faithfully preserving the activation patterns and regularization. Defining the sample correlation matrix , where has activation vectors as rows, the optimization admits the closed-form solution:

This reveals the conceptor as a soft projection operator: rather than fully retaining or discarding each direction, continuously attenuates directions according to the signal energy in .

That's it, that's the whole thing. But in case you're like me and your eyes glaze over just [...]

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Outline:

(00:29) What a conceptor is

(01:31) Persona transplantation example

(02:52) Methods of transplanting a concept

(04:54) Other names for this linear algebra structure

(08:42) History and properties of conceptors

(11:14) Operations on conceptors

(13:25) From deep roots to modern LLM steering

The original text contained 7 footnotes which were omitted from this narration.

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First published:
July 7th, 2026

Source:
https://www.lesswrong.com/posts/9aZYJinAyxequjQbn/a-conceptor-by-any-other-name

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Narrated by TYPE III AUDIO.