File size: 4,136 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 89 90 91 92 93 94 95 96 97 98 | """Full-batch Euclidean GD on the squared loss from small initialisation.
Reproduces Figures 2a/2b/2c of arXiv:2602.02431 and audits Theorem 4.1 (Claim 3)
and the two-phase trajectory decomposition of Section 4 (Claim 4).
sigma(z) = min(z^2, M), M = 8, eta = 0.1 / M^2, delta = n/d = 10,
theta_0 ~ Unif(r0 * S^{d-1}), r0 in {d^-2 (paper figures), d^-15 (Theorem 4.1)}.
All runs are float64 so that r0 = d^-15 (down to ~1e-54) does not underflow.
"""
from __future__ import annotations
import argparse
import csv
import json
import math
import os
import sys
import time
import torch
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import sim
def main():
p = argparse.ArgumentParser()
p.add_argument("--act", default="trunc", choices=["quad", "trunc", "smooth"])
p.add_argument("--dims", default="64,128,256,512,1024,2048,4096")
p.add_argument("--seeds", default="8", help="int, or one value per dim")
p.add_argument("--M", type=float, default=8.0)
p.add_argument("--delta", type=float, default=10.0)
p.add_argument("--eta-c", type=float, default=0.1, help="eta = c / M^2")
p.add_argument("--r0-exp", type=float, default=2.0, help="r0 = d^-exp")
p.add_argument("--T", type=int, default=6000)
p.add_argument("--record-every", type=int, default=5)
p.add_argument("--stop-err", type=float, default=1e-13)
p.add_argument("--out-prefix", required=True)
args = p.parse_args()
dev = "cuda" if torch.cuda.is_available() else "cpu"
dims = [int(v) for v in args.dims.split(",")]
seed_list = [int(v) for v in args.seeds.split(",")]
if len(seed_list) == 1:
seed_list = seed_list * len(dims)
assert len(seed_list) == len(dims)
eta = args.eta_c / (args.M ** 2)
traj_rows, summ_rows = [], []
t_start = time.time()
for d, nseeds in zip(dims, seed_list):
n = int(round(args.delta * d))
r0 = float(d) ** (-args.r0_exp)
for s in range(nseeds):
seed = 90000 + 137 * d + s
t0 = time.time()
data = sim.make_data(d, n, seed, args.act, args.M, dev, torch.float64)
th0 = sim.rand_sphere(d, 800_000 + seed, dev, torch.float64) * r0
rec = sim.squared_gd(
data, th0, args.act, args.M, eta, args.T,
record_every=args.record_every, stop_err=args.stop_err,
)
for i in range(len(rec["step"])):
traj_rows.append(dict(
act=args.act, d=d, delta=args.delta, M=args.M, eta=eta,
r0_exp=args.r0_exp, seed=seed, step=rec["step"][i],
sq_overlap=rec["sq_overlap"][i], norm=rec["norm"][i],
dist2=rec["dist2"][i], loss=rec["loss"][i]))
summ_rows.append(dict(
act=args.act, d=d, n=n, delta=args.delta, M=args.M, eta=eta,
r0_exp=args.r0_exp, r0=r0, seed=seed,
steps_run=rec["step"][-1], final_sq_overlap=rec["sq_overlap"][-1],
final_norm=rec["norm"][-1], final_dist2=rec["dist2"][-1],
final_loss=rec["loss"][-1], secs=round(time.time() - t0, 2)))
del data
torch.cuda.empty_cache() if dev == "cuda" else None
fin = [r["final_dist2"] for r in summ_rows if r["d"] == d]
stp = [r["steps_run"] for r in summ_rows if r["d"] == d]
print(f"[{time.time()-t_start:7.1f}s] d={d:5d} n={n} r0={r0:.3e} "
f"median dist2={sorted(fin)[len(fin)//2]:.3e} median steps={sorted(stp)[len(stp)//2]}",
flush=True)
with open(args.out_prefix + "_traj.csv", "w", newline="") as f:
w = csv.DictWriter(f, fieldnames=list(traj_rows[0].keys()))
w.writeheader()
w.writerows(traj_rows)
with open(args.out_prefix + "_summary.csv", "w", newline="") as f:
w = csv.DictWriter(f, fieldnames=list(summ_rows[0].keys()))
w.writeheader()
w.writerows(summ_rows)
print(f"wrote {args.out_prefix}_{{traj,summary}}.csv "
f"({len(traj_rows)} traj rows, {time.time()-t_start:.1f}s)")
if __name__ == "__main__":
main()
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