1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
|
import torch, numpy as np
from scipy.optimize import linear_sum_assignment
np.set_printoptions(precision=3, suppress=True, linewidth=200)
rng=np.random.default_rng(0)
def standardise(M):
M=np.asarray(M,dtype=np.float64); mask=~np.eye(len(M),dtype=bool); v=M[mask]
out=(M-v.mean())/v.std(); np.fill_diagonal(out,0.0); return out
d=torch.load('artifacts/synth_v1/omit_size.pt',map_location='cpu')
V=standardise(d['visual_field']); T=standardise(d['text_field']); N=len(V)
wV,UV=np.linalg.eigh(V); wV=wV[::-1]; UV=UV[:,::-1]
wT,UT=np.linalg.eigh(T); wT=wT[::-1]; UT=UT[:,::-1]
truth=np.arange(N)
def acc(p): return 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
print("### 1. ORACLE orthogonal mixing O between top-r spectral embeddings")
for r in (6,8,10,12,16,20,24,32,42):
for scale in ('none','sqrt','lam'):
f=lambda w: np.ones_like(w) if scale=='none' else (np.sqrt(np.abs(w)) if scale=='sqrt' else np.abs(w))
XV=UV[:,:r]*f(wV[:r]); XT=UT[:,:r]*f(wT[:r])
# oracle Procrustes using truth
M=XT.T@XV; u,s,vt=np.linalg.svd(M); O=u@vt
p=hung(XV,XT@O)
# also cosine-normalised rows
nV=XV/np.linalg.norm(XV,axis=1,keepdims=True); nT=(XT@O); nT=nT/np.linalg.norm(nT,axis=1,keepdims=True)
p2=hung(nV,nT)
print(f" r={r:3d} scale={scale:5s} oracle-O acc={acc(p):.3f} rownorm acc={acc(p2):.3f}")
|
