Re:The wall confronting large language models
by diffeomorphism on Thursday September 04, 2025 @01:58AM
(#45124025)
As far as I understand, the terminology says "linear" but means compositions of affine (with cutoffs etc). That gives you arbitrary polynomials and piecewise affine, which are dense in most classes of interest.
Of course, in practice you don't actually get arbitrary degree polynomials but some finite degree, so the approximation might still be quite bad or inefficient.
This is impossible. When driven by a sinusoid, a linear system will only ever output a sinusoid with exactly the same frequency but a different amplitude and phase regardless of how many states you give it. A non-linear system can change the frequency or output multiple frequencies.