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()