Record the matching battery: fifteen solvers, one amplifier

Adds MATCHING_RESULTS.md. Entropic GW annealed and PATH both reach 0.961
on the reference field, above the 0.958 the project's own pipeline
reached after months, and neither had been run. GW reaches 0.881 on the
rank-8 field where GRAMPA reaches 0.076 -- which retires the morning's
rank-ladder conclusion, since that ladder was run entirely with GRAMPA
and GRAMPA degrades on clustered eigenvalues.

The hard instance yields to amplification rather than a better solver:
descent multiplies a partial answer by about four, so the job is to feed
it a start that is 10-20% correct rather than to replace it.

Co-Authored-By: Claude <noreply@anthropic.com>

1 files changed, 52 insertions, 0 deletions

diff --git a/artifacts/spectral_frontier_probe/diag11.py b/artifacts/spectral_frontier_probe/diag11.py
new file mode 100644
index 0000000..4977c3c
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/diag11.py
@@ -0,0 +1,52 @@
+import numpy as np, torch, warnings, time
+warnings.filterwarnings('ignore')
+from scipy.optimize import linear_sum_assignment
+from sklearn.decomposition import NMF
+np.set_printoptions(precision=3,suppress=True,linewidth=200)
+d=torch.load('/home/yurenh2/emm/artifacts/synth_v1/omit_size.pt',map_location='cpu')
+V0=d['visual_field'].double().numpy(); T0=d['text_field'].double().numpy(); N=len(V0)
+rng=np.random.default_rng(777); sigma=rng.permutation(N)
+T0s=T0[np.ix_(sigma,sigma)]; truth=np.argsort(sigma)
+acc=lambda p: float((p==truth).mean())
+def hung(A,B):
+    C=((A**2).sum(1)[:,None]+(B**2).sum(1)[None,:]-2*A@B.T); r,c=linear_sum_assignment(C); return c
+def sym_nmf(M,r,iters=3000,seed=0):
+    """symmetric NMF  M ~ W W^T  by multiplicative updates (Ding et al.)"""
+    M=np.clip(M,0,None).copy(); np.fill_diagonal(M,np.clip(np.diag(M),0,None))
+    rg=np.random.default_rng(seed); W=np.abs(rg.standard_normal((len(M),r)))*np.sqrt(M.mean()/r)
+    for _ in range(iters):
+        num=M@W; den=W@(W.T@W)+1e-12
+        W=W*(0.5+0.5*num/den)
+    return W
+for r in (24,42):
+    t0=time.time()
+    WV=sym_nmf(V0,r,seed=1); WT=sym_nmf(T0s,r,seed=1)
+    print(f"r={r} symNMF resid V {np.linalg.norm(V0-WV@WV.T)/np.linalg.norm(V0):.3f} T {np.linalg.norm(T0s-WT@WT.T)/np.linalg.norm(T0s):.3f} [{time.time()-t0:.0f}s]")
+    A=WV.copy(); B=WT.copy()
+    # ORACLE column match for reference
+    An=A/np.linalg.norm(A,axis=0,keepdims=True); Bn=B/np.linalg.norm(B,axis=0,keepdims=True)
+    rr,cc=linear_sum_assignment(-(An[np.arange(N)].T@Bn[truth]))
+    print("   oracle col cos:",np.sort((An.T@Bn[truth])[rr,cc])[::-1][:10])
+    # BLIND column match by permutation-invariant column signatures
+    def sig(X):
+        Xn=X/ (np.linalg.norm(X,axis=0,keepdims=True)+1e-12)
+        q=np.quantile(Xn,np.linspace(0.5,1.0,16),axis=0).T
+        return np.hstack([q,(Xn>0.02).mean(0)[:,None],np.linalg.norm(X,axis=0)[:,None]/np.linalg.norm(X)])
+    sA=sig(A); sB=sig(B); m=hung(sA,sB)
+    agree=float((m==cc[np.argsort(rr)]).mean())
+    def scene_match(colmap):
+        AV=A; BT=B[:,colmap]
+        AV=AV/np.linalg.norm(AV,axis=1,keepdims=True).clip(1e-9); BT=BT/np.linalg.norm(BT,axis=1,keepdims=True).clip(1e-9)
+        return hung(AV,BT)
+    p=scene_match(m); print(f"   BLIND stat col-match agrees w/ oracle {agree:.2f} -> scene acc {acc(p):.3f}")
+    # alternate: scene Hungarian <-> column Hungarian
+    colmap=m.copy()
+    for it in range(25):
+        p=scene_match(colmap)
+        Ar=A/np.linalg.norm(A,axis=1,keepdims=True).clip(1e-9)
+        Br=B/np.linalg.norm(B,axis=1,keepdims=True).clip(1e-9)
+        rr2,cc2=linear_sum_assignment(-(Ar.T@Br[p])); newmap=cc2[np.argsort(rr2)]
+        if (newmap==colmap).all(): break
+        colmap=newmap
+    p=scene_match(colmap)
+    print(f"   after co-alternation ({it+1} iters): col agree {float((colmap==cc[np.argsort(rr)]).mean()):.2f} -> scene acc {acc(p):.3f}")