Datasets:
Formats:
csv
Languages:
English
Size:
< 1K
Tags:
mathematics
linear-algebra
convex-optimization
optimal-recovery
neural-representations
robustness
File size: 3,231 Bytes
352b647 | 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 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | """Recreate the seven publication figures from recorded results.
No selected plot colors or style package; Matplotlib's default cycle is used.
"""
from pathlib import Path
import json
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
ROOT = Path(__file__).resolve().parents[1]
OUT = ROOT / 'figures'
OUT.mkdir(exist_ok=True)
v = json.loads((ROOT/'data/mathematical_verification.json').read_text())
b = json.loads((ROOT/'data/neural_digits_results.json').read_text())
def save(fig, name):
fig.tight_layout()
fig.savefig(OUT/f'{name}.pdf', bbox_inches='tight')
fig.savefig(OUT/f'{name}.png', dpi=180, bbox_inches='tight')
plt.close(fig)
curve = v['frontier_curve']
fig, ax = plt.subplots(figsize=(7.2,4.5))
ax.plot([r['B'] for r in curve],[r['exact'] for r in curve],label='Exact optimal frontier')
ax.plot([r['B'] for r in curve],[r['uniform'] for r in curve],'--',label='Uniform contraction')
ax.axvline(np.log(2),linestyle=':',label='Regime boundary: B = log 2')
ax.set(xlabel='Total log-contraction budget B',ylabel='Worst-scenario information floor')
ax.legend(); ax.grid(alpha=.2); save(fig,'noncommuting_frontier')
fig,ax=plt.subplots(figsize=(7.2,4.5)); n=np.arange(1,21)
ax.plot(n,(7/5)**(n/2),marker='o')
ax.set(xlabel='Number of tensor factors',ylabel='Full-memory / compressed-memory information floor')
ax.set_xticks([1,5,10,15,20]);ax.grid(alpha=.2);save(fig,'memory_amplification')
for metric,ylabel,name in [
('mean_accuracy','Mean held-out accuracy','neural_accuracy'),
('mean_reconstruction_RMSE','Mean latent-state reconstruction RMSE','neural_reconstruction'),
('mean_certified_stability','Certified prediction-stability fraction','neural_certificates')]:
fig,ax=plt.subplots(figsize=(7.2,4.5))
for method in ['uniform','optimized']:
rows=[r for r in b['aggregates'] if r['method']==method]
ax.plot([r['noise_norm'] for r in rows],[r[metric] for r in rows],marker='o',label=method.capitalize())
ax.set(xlabel='Aggregate observation-noise norm',ylabel=ylabel)
ax.legend();ax.grid(alpha=.2);save(fig,name)
fig,ax=plt.subplots(figsize=(7.2,4.5)); h=np.linspace(0,1.2,301)
d,s,R=4,.6,1.;tail=(d+1)**(-2*s)
exact=np.where(h<R,np.sqrt(h*h+(R*R-h*h)*tail),R)
ax.plot(h,exact,label='New release: exact minimax radius')
ax.plot(h,np.sqrt(h*h+R*R*tail),'--',label='Inherited v2 upper bound')
ax.plot(h,np.maximum(np.minimum(R,h),R*np.sqrt(tail)),':',label='Inherited v2 lower bound')
ax.set(xlabel='Effective noise h = ε/q',ylabel='Worst-case recovery radius')
ax.legend();ax.grid(alpha=.2);save(fig,'exact_ellipsoid_recovery')
fig,ax=plt.subplots(figsize=(6.2,5.2)); a=np.linspace(0,2*np.pi,401)
circle=np.vstack([np.cos(a),np.sin(a)])
for matrix,label in [(np.array([[2.,2.],[2.,8.]]),'Scenario +'),
(np.array([[2.,-2.],[-2.,8.]]),'Scenario −'),
(np.diag([1.,4.]),'Common maximum-volume ellipse')]:
ev,u=np.linalg.eigh(matrix);ellipse=((u*np.sqrt(ev))@u.T)@circle
ax.plot(ellipse[0],ellipse[1],label=label)
ax.set(xlabel='First coordinate',ylabel='Second coordinate',aspect='equal')
ax.legend(fontsize=8);ax.grid(alpha=.2);save(fig,'common_ellipse')
print('Seven figures regenerated in PDF and PNG formats.')
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