| """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() |
|
|
