File size: 3,559 Bytes
1f48ccf | 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 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | """Smoke test + timing benchmark for sim.py."""
import math
import sys
import time
import torch
sys.path.insert(0, __file__.rsplit("/", 1)[0])
import sim
dev = "cuda" if torch.cuda.is_available() else "cpu"
print("device:", dev, torch.cuda.get_device_name(0) if dev == "cuda" else "")
# --- activation sanity ------------------------------------------------------
z = torch.linspace(-6, 6, 13, device=dev, dtype=torch.float64)
for act in ("quad", "trunc", "smooth"):
s = sim.sigma(z, act, 8.0)
print(f"{act:7s} sigma:", [round(float(v), 3) for v in s])
# numeric derivative check
eps = 1e-6
for act in ("quad", "trunc", "smooth"):
zz = torch.tensor([0.5, 1.5, 2.5, 3.5], device=dev, dtype=torch.float64)
num = (sim.sigma(zz + eps, act, 8.0) - sim.sigma(zz - eps, act, 8.0)) / (2 * eps)
ana = sim.sigma_prime(zz, act, 8.0)
print(f"{act:7s} d/dz max err:", float((num - ana).abs().max()))
# --- E[2 y x x^T] spectrum sanity (population lambda1=6, lambda2=2 for quad) --
for act in ("quad", "trunc", "smooth"):
d, n = 64, 64 * 400
data = sim.make_data(d, n, 0, act, 8.0, dev, torch.float64)
A = sim.a_star(data)
l1, l2, v1 = sim.top2_eig(A)
ov = float((v1 @ data.theta_star) ** 2)
print(f"{act:7s} n/d=400: lam1={l1:.3f} lam2={l2:.3f} ov^2={ov:.4f}")
# --- flow smoke -------------------------------------------------------------
for act in ("quad", "trunc"):
d, n = 256, 256 * 8
data = sim.make_data(d, n, 1, act, 8.0, dev, torch.float32)
th0 = sim.rand_sphere(d, 1234, dev, torch.float32)
t0 = time.time()
th, steps, _ = sim.spherical_flow(data, th0, act, 8.0, eta=0.1, T=20000)
ov = float((th @ data.theta_star) ** 2)
l1, l2, v1 = sim.top2_eig(sim.a_star(data))
print(
f"{act:7s} flow d={d} delta=8: ov^2={ov:.4f} steps={steps} "
f"({time.time()-t0:.1f}s) v1(A*) ov^2={float((v1@data.theta_star)**2):.4f}"
)
# --- squared-loss GD smoke --------------------------------------------------
d, n = 256, 2560
data = sim.make_data(d, n, 2, "trunc", 8.0, dev, torch.float64)
th0 = sim.rand_sphere(d, 7, dev, torch.float64) * d ** -2.0
t0 = time.time()
rec = sim.squared_gd(data, th0, "trunc", 8.0, eta=0.1 / 64, T=4000, record_every=20)
print(
f"squared GD d={d} delta=10: final ov^2={rec['sq_overlap'][-1]:.5f} "
f"norm={rec['norm'][-1]:.4f} dist2={rec['dist2'][-1]:.3e} ({time.time()-t0:.1f}s)"
)
# --- timing benchmark -------------------------------------------------------
for d in (1024, 4096):
n = 11 * d
t0 = time.time()
data = sim.make_data(d, n, 3, "trunc", 8.0, dev, torch.float32)
torch.cuda.synchronize() if dev == "cuda" else None
t_gen = time.time() - t0
th0 = sim.rand_sphere(d, 5, dev, torch.float32)
t0 = time.time()
sim.spherical_flow(data, th0, "trunc", 8.0, T=200, check_every=10 ** 9)
torch.cuda.synchronize() if dev == "cuda" else None
t_flow = time.time() - t0
t0 = time.time()
A = sim.a_star(data)
torch.cuda.synchronize() if dev == "cuda" else None
t_A = time.time() - t0
t0 = time.time()
sim.spherical_flow(data, th0, "quad", 8.0, T=2000, check_every=10 ** 9)
torch.cuda.synchronize() if dev == "cuda" else None
t_mat = time.time() - t0
print(
f"d={d} n={n}: gen={t_gen:.2f}s trunc-flow 200 steps={t_flow:.2f}s "
f"form A*={t_A:.2f}s matrix-flow 2000 steps={t_mat:.2f}s"
)
del data
torch.cuda.empty_cache() if dev == "cuda" else None
print("T=1000 log^2 d:", {d: sim.log2_steps(d) for d in (64, 1024, 4096, 8192)})
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