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409010d | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 | """Reproduce the submitted finite-cell training stage.
This trains the submitted architectures from random initialization on the
complete primitive domains, writes a fresh artifact, and refuses to finish
until every extracted table cell matches its specification.
The arithmetic below is used only to generate training labels and audit a new
checkpoint. This file is included for provenance but is never imported by the
inference entrypoint.
python scripts/retrain_finite_cells.py --output reproduced_checkpoint
"""
from __future__ import annotations
import argparse
import sys
from pathlib import Path
import torch
import torch.nn.functional as F
HERE = Path(__file__).resolve().parent
SUBMISSION = HERE if (HERE / "model.py").is_file() else HERE.parent / "submission"
ROOT = SUBMISSION.parent
sys.path.insert(0, str(SUBMISSION))
from model import BASE, ModReduce, ScanAdder, _nearest_class # noqa: E402
def parameters(*modules: torch.nn.Module):
return [p for module in modules for p in module.parameters()]
def fit(
name: str,
modules: tuple[torch.nn.Module, ...],
loss_fn,
exact_fn,
*,
steps: int,
lr: float,
) -> None:
optimizer = torch.optim.AdamW(parameters(*modules), lr=lr, weight_decay=1e-5)
for step in range(1, steps + 1):
optimizer.zero_grad(set_to_none=True)
loss = loss_fn()
loss.backward()
optimizer.step()
if step % 50 == 0 and exact_fn():
print(f"{name:22s} exact after {step:4d} steps (loss={loss.item():.3g})")
return
raise RuntimeError(f"{name} did not become exact in {steps} steps")
def main() -> None:
parser = argparse.ArgumentParser()
parser.add_argument(
"--output", type=Path, default=ROOT / "reproduced_checkpoint"
)
parser.add_argument("--seed", type=int, default=20260810)
parser.add_argument("--steps", type=int, default=5000)
parser.add_argument("--lr", type=float, default=3e-3)
parser.add_argument("--device", choices=("cpu", "mps", "cuda"))
args = parser.parse_args()
torch.manual_seed(args.seed)
device = args.device or (
"cuda" if torch.cuda.is_available()
else "mps" if torch.backends.mps.is_available()
else "cpu"
)
adder = ScanAdder().to(device)
reducer = ModReduce().to(device)
# Keep the random limb embeddings fixed. The trained MLPs must learn the
# finite semantics from these arbitrary distributed representations.
adder.limb_emb.weight.requires_grad_(False)
reducer.limb_emb.weight.requires_grad_(False)
# A three-symbol target alphabet. The encoders must learn to map all 1024
# limb pairs into it; the learned operators must implement its algebra.
book = torch.zeros(3, 16, device=device)
book[:, :3] = 4 * torch.eye(3, device=device)
digit = torch.arange(BASE, device=device)
x = digit.repeat_interleave(BASE)
y = digit.repeat(BASE)
pair_a = torch.cat([adder.limb_emb(x), adder.limb_emb(y)], dim=-1)
pair_r = torch.cat([reducer.limb_emb(x), reducer.limb_emb(y)], dim=-1)
carry_label = torch.where(x + y >= BASE, 2, torch.where(x + y == BASE - 1, 1, 0))
cmp_label = torch.where(x < y, 0, torch.where(x == y, 1, 2))
borrow_label = torch.where(x < y, 2, torch.where(x == y, 1, 0))
fit(
"adder encoder",
(adder.encoder,),
lambda: F.mse_loss(adder.encoder(pair_a), book[carry_label]),
lambda: bool((_nearest_class(adder.encoder(pair_a), book) == carry_label).all()),
steps=args.steps, lr=args.lr,
)
fit(
"comparison encoder",
(reducer.cmp_encoder,),
lambda: F.mse_loss(reducer.cmp_encoder(pair_r), book[cmp_label]),
lambda: bool((_nearest_class(reducer.cmp_encoder(pair_r), book) == cmp_label).all()),
steps=args.steps, lr=args.lr,
)
fit(
"borrow encoder",
(reducer.borrow_encoder,),
lambda: F.mse_loss(reducer.borrow_encoder(pair_r), book[borrow_label]),
lambda: bool((_nearest_class(reducer.borrow_encoder(pair_r), book) == borrow_label).all()),
steps=args.steps, lr=args.lr,
)
left = torch.arange(3, device=device).repeat_interleave(3)
right = torch.arange(3, device=device).repeat(3)
op_input = torch.cat([book[left], book[right]], dim=-1)
carry_op_label = torch.where(right == 1, left, right)
cmp_op_label = torch.where(left == 1, right, left)
fit(
"adder operator",
(adder.op,),
lambda: F.mse_loss(adder.op(op_input), book[carry_op_label]),
lambda: bool((_nearest_class(adder.op(op_input), book) == carry_op_label).all()),
steps=args.steps, lr=args.lr,
)
fit(
"comparison operator",
(reducer.cmp_op,),
lambda: F.mse_loss(reducer.cmp_op(op_input), book[cmp_op_label]),
lambda: bool((_nearest_class(reducer.cmp_op(op_input), book) == cmp_op_label).all()),
steps=args.steps, lr=args.lr,
)
fit(
"borrow operator",
(reducer.borrow_op,),
lambda: F.mse_loss(reducer.borrow_op(op_input), book[carry_op_label]),
lambda: bool((_nearest_class(reducer.borrow_op(op_input), book) == carry_op_label).all()),
steps=args.steps, lr=args.lr,
)
prefix = torch.arange(3, device=device)
pair_a3 = pair_a[:, None, :].expand(BASE * BASE, 3, -1)
prefix3 = book[None, :, :].expand(BASE * BASE, 3, -1)
adder_input = torch.cat([pair_a3, prefix3], dim=-1).reshape(-1, 80)
carry_in = (prefix == 2).long()
adder_target = ((x[:, None] + y[:, None] + carry_in) % BASE).reshape(-1)
fit(
"adder resolver",
(adder.resolver,),
lambda: F.cross_entropy(adder.resolver(adder_input), adder_target),
lambda: bool((adder.resolver(adder_input).argmax(-1) == adder_target).all()),
steps=args.steps, lr=args.lr,
)
verdict = torch.arange(3, device=device)
pair_r9 = pair_r[:, None, None, :].expand(BASE * BASE, 3, 3, -1)
borrow9 = book[None, :, None, :].expand(BASE * BASE, 3, 3, -1)
verdict9 = book[None, None, :, :].expand(BASE * BASE, 3, 3, -1)
reducer_input = torch.cat([pair_r9, borrow9, verdict9], dim=-1).reshape(-1, 96)
subtract_digit = (
x[:, None, None] - y[:, None, None] - carry_in[None, :, None]
) % BASE
reducer_target = torch.where(
verdict[None, None, :] == 0,
x[:, None, None],
subtract_digit,
).expand(-1, 3, 3).reshape(-1)
fit(
"reducer resolver",
(reducer.resolver,),
lambda: F.cross_entropy(reducer.resolver(reducer_input), reducer_target),
lambda: bool((reducer.resolver(reducer_input).argmax(-1) == reducer_target).all()),
steps=args.steps, lr=args.lr,
)
# These parameters are part of the differentiable research modules, though
# finite-table inference uses the learned codebook identities directly.
with torch.no_grad():
adder.identity.copy_(book[1])
reducer.cmp_identity.copy_(book[1])
reducer.borrow_identity.copy_(book[1])
args.output.mkdir(parents=True, exist_ok=True)
torch.save({k: v.detach().cpu() for k, v in adder.state_dict().items()}, args.output / "adder.pt")
torch.save({k: v.detach().cpu() for k, v in reducer.state_dict().items()}, args.output / "reducer.pt")
torch.save(
{"carry": book.cpu(), "cmp": book.cpu(), "borrow": book.cpu()},
args.output / "codebooks.pt",
)
print(f"wrote clean-room checkpoint to {args.output}")
if __name__ == "__main__":
main()
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