File size: 2,861 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 | """One-pass (online) spherical SGD baseline on the correlation loss.
Ben Arous et al. (2021), Thm 1.4: for information exponent 2 activations, one-pass
SGD with the largest stable step size eta ~ 1/d needs n >~ d log d samples for weak
recovery. This is the baseline that Claims 2/5 of arXiv:2602.02431 separate from.
Each replica sees every sample exactly once, so a single run of length n_max also
gives the overlap for every smaller n -> the whole delta-curve comes from one pass.
"""
from __future__ import annotations
import argparse
import csv
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="64,128,256,512,1024,2048,4096,8192")
p.add_argument("--seeds", type=int, default=32)
p.add_argument("--M", type=float, default=8.0)
p.add_argument("--eta-cs", default="0.025,0.05,0.1,0.2",
help="grid of step sizes eta = c/d (the c values)")
p.add_argument("--delta-max-mult", type=float, default=6.0,
help="delta_max = mult * log(d)")
p.add_argument("--n-checkpoints", type=int, default=60)
p.add_argument("--out", required=True)
args = p.parse_args()
dev = "cuda" if torch.cuda.is_available() else "cpu"
dims = [int(v) for v in args.dims.split(",")]
rows = []
t_start = time.time()
for d in dims:
dmax = args.delta_max_mult * math.log(d)
deltas = [round(dmax * (i + 1) / args.n_checkpoints, 4) for i in range(args.n_checkpoints)]
cps = sorted({max(1, int(round(dl * d))) for dl in deltas})
n_max = cps[-1]
chunk = max(128, min(2048, (1 << 23) // (d * args.seeds)))
for c in [float(v) for v in args.eta_cs.split(",")]:
eta = c / d
t0 = time.time()
out = sim.online_sgd(
d, n_max, args.seeds, args.act, args.M, eta, 4242 + d, dev,
torch.float32, cps, chunk=chunk,
)
for n_used, ov in out.items():
rows.append(dict(act=args.act, d=d, n=n_used, delta=round(n_used / d, 4),
eta_c=c, eta=eta, seeds=args.seeds,
sq_overlap=round(ov, 6)))
print(f"[{time.time()-t_start:7.1f}s] d={d:5d} n_max={n_max} eta={eta:.3g} "
f"(c={c}) final ov2={out[cps[-1]]:.4f} ({time.time()-t0:.1f}s)", flush=True)
with open(args.out, "w", newline="") as f:
w = csv.DictWriter(f, fieldnames=list(rows[0].keys()))
w.writeheader()
w.writerows(rows)
print(f"wrote {args.out} ({len(rows)} rows, {time.time()-t_start:.1f}s)")
if __name__ == "__main__":
main()
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