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bd894ac | 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 | from __future__ import annotations
import json
import math
from pathlib import Path
import pandas as pd
import torch
import trackio
from model import MatchedMLP, SplineKAN, parameter_count
from safetensors.torch import save_file
from torch.nn import functional as F
PROJECT_DIR = Path(__file__).resolve().parent
ARTIFACT_DIR = PROJECT_DIR / "artifacts" / "spline-kan-pocket"
DATA_DIR = PROJECT_DIR / "data"
SEED = 2161
def target_function(inputs: torch.Tensor) -> torch.Tensor:
x = inputs[:, :1]
y = inputs[:, 1:]
return (
torch.sin(math.pi * x * y)
+ 0.35 * (x.pow(3) - y.square())
+ 0.2 * torch.cos(2 * math.pi * x)
)
@torch.inference_mode()
def evaluate(model: torch.nn.Module, *, extrapolation: bool) -> dict:
generator = torch.Generator().manual_seed(SEED + int(extrapolation) + 10_000)
if extrapolation:
values = []
while sum(len(batch) for batch in values) < 20_000:
candidate = -1.5 + 3 * torch.rand(25_000, 2, generator=generator)
values.append(candidate[(candidate.abs() > 1).any(dim=1)])
inputs = torch.cat(values)[:20_000]
else:
inputs = -1 + 2 * torch.rand(20_000, 2, generator=generator)
target = target_function(inputs)
prediction = model(inputs)
error = prediction - target
return {
"rmse": float(error.square().mean().sqrt()),
"mae": float(error.abs().mean()),
"maximum_absolute_error": float(error.abs().max()),
"examples": len(inputs),
"domain": "outside training square" if extrapolation else "training square",
}
def train_variant(name: str, model: torch.nn.Module) -> tuple[torch.nn.Module, int]:
optimizer = torch.optim.AdamW(model.parameters(), lr=2e-3, weight_decay=1e-6)
best = float("inf")
best_state = None
best_step = 0
validation_generator = torch.Generator().manual_seed(SEED + 5_000)
validation_inputs = -1 + 2 * torch.rand(
5_000, 2, generator=validation_generator
)
validation_target = target_function(validation_inputs)
for step in range(1, 4_001):
generator = torch.Generator().manual_seed(SEED + step)
inputs = -1 + 2 * torch.rand(512, 2, generator=generator)
prediction = model(inputs)
loss = F.mse_loss(prediction, target_function(inputs))
if name == "spline_kan":
spline_l1 = model.first.coefficients.abs().mean()
spline_l1 = spline_l1 + model.second.coefficients.abs().mean()
loss = loss + 1e-6 * spline_l1
optimizer.zero_grad(set_to_none=True)
loss.backward()
optimizer.step()
if step % 200 == 0:
with torch.inference_mode():
validation_rmse = float(
(model(validation_inputs) - validation_target)
.square()
.mean()
.sqrt()
)
trackio.log(
{
"variant": name,
"training_step": step,
"training_mse": float(loss.detach()),
"validation_rmse": validation_rmse,
}
)
if validation_rmse < best:
best = validation_rmse
best_step = step
best_state = {
key: value.detach().cpu().clone()
for key, value in model.state_dict().items()
}
assert best_state is not None
model.load_state_dict(best_state)
return model, best_step
def main() -> None:
torch.manual_seed(SEED)
torch.set_num_threads(1)
models = {"spline_kan": SplineKAN(), "matched_mlp": MatchedMLP()}
assert parameter_count(models["spline_kan"]) == parameter_count(
models["matched_mlp"]
)
trackio.init(
project="spline-kan-pocket",
name="edge-splines-versus-mlp-v1",
config={
"parameters_per_model": parameter_count(models["spline_kan"]),
"training_steps": 4_000,
"training_domain": "[-1, 1]^2",
},
)
results = {}
ARTIFACT_DIR.mkdir(parents=True, exist_ok=True)
DATA_DIR.mkdir(parents=True, exist_ok=True)
for name, model in models.items():
model, best_step = train_variant(name, model)
results[name] = {
"parameters": parameter_count(model),
"best_step": best_step,
"interpolation": evaluate(model, extrapolation=False),
"extrapolation": evaluate(model, extrapolation=True),
}
save_file(model.state_dict(), ARTIFACT_DIR / f"{name}.safetensors")
generator = torch.Generator().manual_seed(SEED + 30_000)
inputs = -1.5 + 3 * torch.rand(10_000, 2, generator=generator)
with torch.inference_mode():
frame = {
"x": inputs[:, 0].numpy(),
"y": inputs[:, 1].numpy(),
"target": target_function(inputs)[:, 0].numpy(),
"spline_kan": models["spline_kan"](inputs)[:, 0].numpy(),
"matched_mlp": models["matched_mlp"](inputs)[:, 0].numpy(),
}
report = {
"experiment": "Spline KAN versus exactly parameter-matched MLP",
"target": "sin(pi*x*y) + 0.35*(x^3-y^2) + 0.2*cos(2*pi*x)",
"results": results,
}
(ARTIFACT_DIR / "evaluation.json").write_text(
json.dumps(report, indent=2), encoding="utf-8"
)
pd.DataFrame(frame).to_parquet(DATA_DIR / "surface_predictions.parquet", index=False)
trackio.log(
{
"kan_interpolation_rmse": results["spline_kan"]["interpolation"]["rmse"],
"mlp_interpolation_rmse": results["matched_mlp"]["interpolation"]["rmse"],
"kan_extrapolation_rmse": results["spline_kan"]["extrapolation"]["rmse"],
"mlp_extrapolation_rmse": results["matched_mlp"]["extrapolation"]["rmse"],
}
)
trackio.finish()
print(json.dumps(report, indent=2))
if __name__ == "__main__":
main()
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