path: root/scripts/early_kernel_predictors.py

#!/usr/bin/env python3
"""Early kernel-drift predictors for finite-time FA/BP gaps."""

from __future__ import annotations

import argparse
import csv
import json
import sys
from dataclasses import asdict, dataclass
from pathlib import Path

import numpy as np
import torch

SCRIPT_DIR = Path(__file__).resolve().parent
if str(SCRIPT_DIR) not in sys.path:
    sys.path.insert(0, str(SCRIPT_DIR))

import downstream_capacity_sweep as dcs  # noqa: E402
from fa_tangent_kernel_capacity import pseudo_jacobian  # noqa: E402


@dataclass(frozen=True)
class PredictorRow:
    init_seed: int
    feedback_seed: int
    target_steps: int
    early_steps: int
    empirical_bp_loss: float
    empirical_fa_loss: float
    empirical_gap: float
    fixed_bp_loss: float
    fixed_fa_loss: float
    fixed_gap: float
    directional_bp_loss: float
    directional_fa_loss: float
    directional_gap: float
    kfa_fro_drift: float
    kbp_fro_drift: float
    fa_bp_overlap_0: float
    fa_bp_overlap_s: float
    fa_bp_overlap_slope: float
    fa_directional_gain_s: float
    bp_directional_gain_s: float
    fa_directional_drift_s: float
    bp_directional_drift_s: float


def parse_args() -> argparse.Namespace:
    parser = argparse.ArgumentParser(description="Compute early kernel predictors.")
    parser.add_argument("--input-dim", type=int, default=16)
    parser.add_argument("--output-dim", type=int, default=4)
    parser.add_argument("--width", type=int, default=64)
    parser.add_argument("--train-samples", type=int, default=128)
    parser.add_argument("--test-samples", type=int, default=512)
    parser.add_argument("--target-steps", type=int, default=50)
    parser.add_argument("--early-steps", type=int, nargs="+", default=[1, 2, 5])
    parser.add_argument("--lr", type=float, default=1e-3)
    parser.add_argument("--init-seeds", type=int, default=4)
    parser.add_argument("--feedback-seeds", type=int, default=8)
    parser.add_argument("--data-seed", type=int, default=123)
    parser.add_argument(
        "--feedback-scale",
        choices=["relu", "fan-in", "unit"],
        default="relu",
    )
    parser.add_argument("--device", choices=["cpu", "cuda"], default="cpu")
    parser.add_argument("--torch-threads", type=int, default=8)
    parser.add_argument(
        "--outdir",
        type=Path,
        default=Path("outputs/early_kernel_predictors"),
    )
    return parser.parse_args()


def make_config(args: argparse.Namespace) -> dcs.RunConfig:
    return dcs.RunConfig(
        task="random",
        input_dim=args.input_dim,
        output_dim=args.output_dim,
        teacher_rank=4,
        teacher_width=64,
        teacher_hidden_layers=2,
        normalize_targets=False,
        widths=[args.width],
        train_samples=args.train_samples,
        test_samples=args.test_samples,
        probe_samples=8,
        steps=args.target_steps,
        lr=args.lr,
        optimizer="sgd",
        init_seeds=args.init_seeds,
        feedback_seeds=args.feedback_seeds,
        init_seed_offset=0,
        feedback_seed_offset=0,
        data_seed=args.data_seed,
        noise_std=0.0,
        feedback_scale=args.feedback_scale,
        capacity_q=0.01,
        jacobian_lambda_rel=1e-3,
        skip_jacobian=True,
        device=args.device,
        torch_threads=args.torch_threads,
        outdir=str(args.outdir),
        plot=False,
    )


def sgd_step(
    weights: list[torch.Tensor],
    x: torch.Tensor,
    y: torch.Tensor,
    lr: float,
    feedback: list[torch.Tensor] | None,
) -> list[torch.Tensor]:
    grads = dcs.gradients(weights, x, y, feedback)
    return [weight - lr * grad for weight, grad in zip(weights, grads)]


def kernel_pair(
    weights: list[torch.Tensor],
    x: torch.Tensor,
    feedback: list[torch.Tensor],
) -> tuple[np.ndarray, np.ndarray]:
    j_bp = pseudo_jacobian(weights, x, feedback=None).cpu().numpy()
    j_fa = pseudo_jacobian(weights, x, feedback=feedback).cpu().numpy()
    return j_bp @ j_bp.T, j_bp @ j_fa.T


def fixed_prediction(
    k_bp0: np.ndarray,
    k_fa0: np.ndarray,
    residual: np.ndarray,
    lr: float,
    steps: int,
    samples: int,
) -> tuple[float, float]:
    scale = lr / samples
    rb = residual.copy()
    rf = residual.copy()
    for _ in range(steps):
        rb = rb - scale * (k_bp0 @ rb)
        rf = rf - scale * (k_fa0 @ rf)
    return 0.5 * float(rb @ rb) / samples, 0.5 * float(rf @ rf) / samples


def loss_from_residual(residual: np.ndarray, samples: int) -> float:
    return 0.5 * float(residual @ residual) / samples


def overlap(a: np.ndarray, b: np.ndarray) -> float:
    denom = np.linalg.norm(a, "fro") * np.linalg.norm(b, "fro")
    if denom == 0:
        return 0.0
    return float(np.sum(a * b) / denom)


def directional_gain(kernel: np.ndarray, residual: np.ndarray) -> float:
    denom = float(residual @ residual)
    if denom == 0:
        return 0.0
    return float(residual @ (kernel @ residual) / denom)


def directional_loss_prediction(
    residual: np.ndarray,
    lambda_0: float,
    lambda_s: float,
    early_step: int,
    lr: float,
    target_steps: int,
    samples: int,
) -> float:
    slope = (lambda_s - lambda_0) / early_step
    cumulative = target_steps * lambda_0 + 0.5 * target_steps * (target_steps - 1) * slope
    # Keep the early linear extrapolation from producing an unstable negative
    # integrated rate; this is a stability projection, not a fitted coefficient.
    cumulative = max(cumulative, 0.0)
    initial_loss = loss_from_residual(residual, samples)
    return initial_loss * float(np.exp(-(2.0 * lr / samples) * cumulative))


def train_to_steps(
    weights: list[torch.Tensor],
    x: torch.Tensor,
    y: torch.Tensor,
    lr: float,
    steps: int,
    feedback: list[torch.Tensor] | None,
) -> list[torch.Tensor]:
    current = dcs.clone_weights(weights)
    for _ in range(steps):
        current = sgd_step(current, x, y, lr, feedback)
    return current


def run_one(
    config: dcs.RunConfig,
    x: torch.Tensor,
    y: torch.Tensor,
    init_seed: int,
    feedback_seed: int,
    early_step: int,
) -> PredictorRow:
    initial = dcs.initialize_weights(config, config.widths[0], init_seed)
    feedback = dcs.init_feedback(config, config.widths[0], feedback_seed)
    with torch.no_grad():
        r0 = (dcs.predict(initial, x) - y).reshape(-1).cpu().numpy()

    kbp0, kfa0 = kernel_pair(initial, x, feedback)
    fixed_bp, fixed_fa = fixed_prediction(
        kbp0, kfa0, r0, config.lr, config.steps, config.train_samples
    )

    bp_target = train_to_steps(initial, x, y, config.lr, config.steps, feedback=None)
    fa_target = train_to_steps(initial, x, y, config.lr, config.steps, feedback=feedback)
    empirical_bp = dcs.mse(bp_target, x, y)
    empirical_fa = dcs.mse(fa_target, x, y)

    bp_early = train_to_steps(initial, x, y, config.lr, early_step, feedback=None)
    fa_early = train_to_steps(initial, x, y, config.lr, early_step, feedback=feedback)
    kbp_s, _kfa_unused = kernel_pair(bp_early, x, feedback)
    _kbp_unused, kfa_s = kernel_pair(fa_early, x, feedback)

    with torch.no_grad():
        rb_s = (dcs.predict(bp_early, x) - y).reshape(-1).cpu().numpy()
        rf_s = (dcs.predict(fa_early, x) - y).reshape(-1).cpu().numpy()

    kfa_fro_drift = float(np.linalg.norm(kfa_s - kfa0, "fro") / np.linalg.norm(kfa0, "fro"))
    kbp_fro_drift = float(np.linalg.norm(kbp_s - kbp0, "fro") / np.linalg.norm(kbp0, "fro"))
    fa_bp_overlap_0 = overlap(kfa0, kbp0)
    fa_bp_overlap_s = overlap(kfa_s, kbp_s)
    fa_directional_gain_0 = directional_gain(kfa0, r0)
    fa_directional_gain_s = directional_gain(kfa_s, rf_s)
    bp_directional_gain_0 = directional_gain(kbp0, r0)
    bp_directional_gain_s = directional_gain(kbp_s, rb_s)
    directional_bp = directional_loss_prediction(
        r0,
        bp_directional_gain_0,
        bp_directional_gain_s,
        early_step,
        config.lr,
        config.steps,
        config.train_samples,
    )
    directional_fa = directional_loss_prediction(
        r0,
        fa_directional_gain_0,
        fa_directional_gain_s,
        early_step,
        config.lr,
        config.steps,
        config.train_samples,
    )

    return PredictorRow(
        init_seed=init_seed,
        feedback_seed=feedback_seed,
        target_steps=config.steps,
        early_steps=early_step,
        empirical_bp_loss=empirical_bp,
        empirical_fa_loss=empirical_fa,
        empirical_gap=empirical_fa - empirical_bp,
        fixed_bp_loss=fixed_bp,
        fixed_fa_loss=fixed_fa,
        fixed_gap=fixed_fa - fixed_bp,
        directional_bp_loss=directional_bp,
        directional_fa_loss=directional_fa,
        directional_gap=directional_fa - directional_bp,
        kfa_fro_drift=kfa_fro_drift,
        kbp_fro_drift=kbp_fro_drift,
        fa_bp_overlap_0=fa_bp_overlap_0,
        fa_bp_overlap_s=fa_bp_overlap_s,
        fa_bp_overlap_slope=(fa_bp_overlap_s - fa_bp_overlap_0) / early_step,
        fa_directional_gain_s=fa_directional_gain_s,
        bp_directional_gain_s=bp_directional_gain_s,
        fa_directional_drift_s=(fa_directional_gain_s - fa_directional_gain_0) / max(
            abs(fa_directional_gain_0), 1e-12
        ),
        bp_directional_drift_s=(bp_directional_gain_s - bp_directional_gain_0) / max(
            abs(bp_directional_gain_0), 1e-12
        ),
    )


def write_rows(path: Path, rows: list[PredictorRow]) -> None:
    path.parent.mkdir(parents=True, exist_ok=True)
    with path.open("w", newline="") as handle:
        writer = csv.DictWriter(handle, fieldnames=list(PredictorRow.__annotations__.keys()))
        writer.writeheader()
        for row in rows:
            writer.writerow(asdict(row))


def main() -> None:
    args = parse_args()
    if args.torch_threads > 0:
        torch.set_num_threads(args.torch_threads)
    config = make_config(args)
    x_train, y_train, _x_test, _y_test, _x_probe, _teacher = dcs.make_data(config)

    rows: list[PredictorRow] = []
    total = args.init_seeds * args.feedback_seeds * len(args.early_steps)
    count = 0
    for init_index in range(args.init_seeds):
        init_seed = 10_000 + init_index
        for feedback_index in range(args.feedback_seeds):
            feedback_seed = 100_000 + init_index * 1000 + feedback_index
            for early_step in args.early_steps:
                count += 1
                print(
                    f"[{count}/{total}] init={init_seed} feedback={feedback_seed} "
                    f"early={early_step}",
                    flush=True,
                )
                rows.append(
                    run_one(config, x_train, y_train, init_seed, feedback_seed, early_step)
                )

    outdir = Path(args.outdir)
    outdir.mkdir(parents=True, exist_ok=True)
    write_rows(outdir / "early_kernel_predictors.csv", rows)
    payload = {
        "config": {
            key: str(value) if isinstance(value, Path) else value
            for key, value in vars(args).items()
        },
        "rows": [asdict(row) for row in rows],
    }
    (outdir / "summary.json").write_text(json.dumps(payload, indent=2) + "\n")
    print(f"rows: {outdir / 'early_kernel_predictors.csv'}")


if __name__ == "__main__":
    main()