> One key term to look for is "feature manifolds" or "multi-diemsnional features"
I should probably read the updates more. Not enough time in the day. But yea the way you're describing feature manifolds and multidimensional features, especially the importance of linearity-in-properties and not necessarily linearity-in-dimensions, makes a lot of sense and is basically how I default think about these things.
> but doesn't quite capture the technical nuance. So it's hard to know the full scope of what you intend.
Fair, I'm only passingly familiar with compressed sensing so I'm not sure I could offer a more technical definition without, like, a much longer conversation! But it's good to know in the future that in a technical sense linear representations and superposition are dependent.
> all features are linear, rather than just most or some
Potentially a tangent, but compared to what? I suppose the natural answer is "non linear features" but has there been anything to suggest that neural networks represent concepts in this way? I'd be rather surprised if they did within a single layer. (Across layers, sure, but that actually starts to pull me more towards circuits)
I should probably read the updates more. Not enough time in the day. But yea the way you're describing feature manifolds and multidimensional features, especially the importance of linearity-in-properties and not necessarily linearity-in-dimensions, makes a lot of sense and is basically how I default think about these things.
> but doesn't quite capture the technical nuance. So it's hard to know the full scope of what you intend.
Fair, I'm only passingly familiar with compressed sensing so I'm not sure I could offer a more technical definition without, like, a much longer conversation! But it's good to know in the future that in a technical sense linear representations and superposition are dependent.
> all features are linear, rather than just most or some
Potentially a tangent, but compared to what? I suppose the natural answer is "non linear features" but has there been anything to suggest that neural networks represent concepts in this way? I'd be rather surprised if they did within a single layer. (Across layers, sure, but that actually starts to pull me more towards circuits)