1import numpy as np
 2
 3class SpectralEdgeController:
 4    """Multiplicative edge controller for h'=tanh(g W h + input)."""
 5    def __init__(self, target=0.9, alpha=0.25, g_min=1e-3, g_max=3.0):
 6        self.target = float(target)
 7        self.alpha = float(alpha)
 8        self.g_min, self.g_max = float(g_min), float(g_max)
 9        self.g = 1.0
10
11    @staticmethod
12    def edge_estimate(W, derivative, iterations=5, rng=None):
13        # Singular edge of D W is robust when the nonlinear local Jacobian is nonsymmetric.
14        rng = np.random.default_rng() if rng is None else rng
15        v = rng.normal(size=W.shape[0]); v /= np.linalg.norm(v)
16        for _ in range(iterations):
17            u = derivative * (W @ v)
18            nu = np.linalg.norm(u)
19            if nu == 0: return 0.0
20            u /= nu
21            v = W.T @ (derivative * u)
22            nv = np.linalg.norm(v)
23            if nv == 0: return 0.0
24            v /= nv
25        return float(np.linalg.norm(derivative * (W @ v)))
26
27    def update(self, edge):
28        self.g *= np.exp(self.alpha * (self.target - self.g * edge))
29        self.g = float(np.clip(self.g, self.g_min, self.g_max))
30        return self.g