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- Not necessarily! See our conjecture with Valentin: given a neural nonlinearity (p-times diff’able), you can get a spectrum with slope (alpha) close to 1 from low-dim “pre-activations” (inputs of dimension d)
- Ah, but doesn't this mean that the activity of the neurons is still high-D (even if the pre-activations are low-D)?Dec 15, 2025 16:02
- Yes, exactly. I agree with you that most claims of low-D neural activity are probably high-D by our definition. But, the underlying dynamics can still be low-D.
