W currently carrying signal.
| Melody | Free | Surv | N | ρ | leak | in | conn | ridge | temp | reps | seed |
|---|---|---|---|---|---|---|---|---|---|---|---|
| no runs yet | |||||||||||
An echo state network is a big pool of randomly wired neurons whose recurrent weights are
never trained. The melody is fed in one grid step at a time; the pool's activations become a
high-dimensional, fading-memory encoding of everything heard recently. The only thing fitted is a
linear map from the state to the next note — solved in one shot by ridge regression
(W = (XXᵀ + λI)⁻¹ XYᵀ), no gradient descent.
Spectral radius ρ sets memory length. Below ~0.5 the reservoir forgets too fast to know where it
is in the tune; above ~1.4 it drifts toward chaos and the loop destabilizes. Melodies with repeated
sections need more memory to tell one repeat from the next.
Leak rate is the state's update speed. Low leak smooths over many steps — useful for slow
signals, but here it blurs adjacent notes and scores badly.
Nodes raise capacity: more neurons, more linearly separable states, but also more parameters to
regularize and slower solves.
Ridge λ trades memorization for stability. Too small and the readout amplifies noise once the
loop is closed; too large and it collapses to predicting the most common token.
Free-run match is the real score: the network is primed on real notes, then fed only its own
output for two full choruses. Teacher-forced accuracy is much easier and can look perfect while
free-running fails completely.