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"""Wall-breaking probe. The EP ceiling I measured comes from: rich (thick) block is
non-contractive -> EP needs heavy damping c to converge the free phase -> damping suppresses
the very expressivity that made the block good. ESCAPE ROUTE: get convergence from a SOLVER
(Anderson accel, DEQ-style) instead of from damping. Decisive question: for the THICK block,
at LOW damping (expressivity intact), can Anderson converge where plain relaxation cannot?
If yes -> the wall is a solver problem, not fundamental. If no -> the rich block has no fixed
point to find and the ceiling is intrinsic to the EP/fixed-point requirement."""
import math, sys, torch
from lt_ep_train import EQBlock, get_batch
dev = 'cuda' if torch.cuda.is_available() else 'cpu'
torch.manual_seed(0)
B, T, C, H = 16, 64, 128, 4
eps = 0.05
def gmap(blk, z, xin): # relaxation map; fixed point = equilibrium
with torch.no_grad():
return z + eps * blk.force(z, xin).detach()
def plain(blk, z0, xin, steps=200):
z = z0.clone()
for _ in range(steps):
z = gmap(blk, z, xin)
return ((gmap(blk, z, xin) - z).norm() / (z.norm() + 1e-9)).item()
def anderson(blk, z0, xin, m=6, max_iter=150, tol=1e-6, lam=1e-4):
Bs, d = z0.shape[0], z0[0].numel()
X = torch.zeros(Bs, m, d, device=dev); Fb = torch.zeros(Bs, m, d, device=dev)
X[:, 0] = z0.reshape(Bs, d); Fb[:, 0] = gmap(blk, z0, xin).reshape(Bs, d)
X[:, 1] = Fb[:, 0]; Fb[:, 1] = gmap(blk, X[:, 1].view_as(z0), xin).reshape(Bs, d)
Hm = torch.zeros(Bs, m + 1, m + 1, device=dev); Hm[:, 0, 1:] = 1; Hm[:, 1:, 0] = 1
yv = torch.zeros(Bs, m + 1, 1, device=dev); yv[:, 0] = 1
r, k = 1.0, 2
for k in range(2, max_iter):
n = min(k, m)
Gm = Fb[:, :n] - X[:, :n]
Hm[:, 1:n + 1, 1:n + 1] = torch.bmm(Gm, Gm.transpose(1, 2)) + lam * torch.eye(n, device=dev)[None]
alpha = torch.linalg.solve(Hm[:, :n + 1, :n + 1], yv[:, :n + 1])[:, 1:n + 1, 0]
X[:, k % m] = torch.bmm(alpha[:, None], Fb[:, :n])[:, 0]
Fb[:, k % m] = gmap(blk, X[:, k % m].view_as(z0), xin).reshape(Bs, d)
r = ((Fb[:, k % m] - X[:, k % m]).norm() / (Fb[:, k % m].norm() + 1e-9)).item()
if r < tol or not math.isfinite(r):
break
return r, k + 1
for mode in ['real', 'thick']:
torch.manual_seed(0)
blk = EQBlock(C, H, 256, T, attn_mode=mode)
idx, y = get_batch('train', B, T)
xin = blk.embed(idx).detach()
print(f"\n=== attn_mode={mode} === free-phase convergence: plain relax(200) vs Anderson, eps={eps}")
print(f"{'damp c':>7} {'plain_res':>11} {'anderson_res':>13} {'and_iters':>10}")
for c in [0.0, 0.25, 0.5, 1.0, 2.0]:
blk.c = c
pr = plain(blk, xin.clone(), xin)
ar, ak = anderson(blk, xin.clone(), xin)
flag = ' <- solver converges where plain fails' if (ar < 1e-4 and pr > 1e-2) else ''
print(f"{c:>7.2f} {pr:>11.2e} {ar:>13.2e} {ak:>10d}{flag}")
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