examples/train_task.py

"""Train GNOMON on a bigram task.



Task: tokens generated from a sharp row-stochastic transition matrix.

With temperature=0.3, the transition has significant structure — Bayes

CE is well below uniform, so the model has room to show learning.



The coupling KL should fall from ~0.04 to <0.005 during training.

"""
import os
import sys
import time

sys.path.insert(0, os.path.join(os.path.dirname(__file__), ".."))

import jax
import jax.numpy as jnp
import numpy as np

from gnomon import init_gnomon, init_mode_state, make_forward_jit
from gnomon.train import train_step
from gnomon.params import adam_init


def make_transition(rng, V, temperature=0.3):
    """Sharper than the previous version: temperature scales the noise."""
    logits = rng.standard_normal((V, V)) * temperature
    logits += 1.5 * np.eye(V)
    p = np.exp(logits - logits.max(axis=1, keepdims=True))
    p /= p.sum(axis=1, keepdims=True)
    return p.astype(np.float32)


def row_entropy(p):
    """Average per-row entropy of the transition matrix."""
    return float(-(p * np.log(p + 1e-12)).sum(axis=1).mean())


def sample_batch(rng, B, S, V, transition):
    ids = np.zeros((B, S), dtype=np.int32)
    ids[:, 0] = rng.integers(0, V, B)
    for t in range(1, S):
        prev = ids[:, t - 1]
        probs = transition[prev]
        cum = probs.cumsum(axis=1)
        u = rng.random((B, 1))
        ids[:, t] = (u > cum).sum(axis=1)
    return jnp.asarray(ids)


def coupling_kl(params, ids, mode, mode_sig, key, n_heads):
    raw_fn = make_forward_jit(n_heads=n_heads, use_reconstructed_kv=False)
    rec_fn = make_forward_jit(n_heads=n_heads, use_reconstructed_kv=True)
    out_raw = raw_fn(params, ids, mode, mode_sig, key)
    out_rec = rec_fn(params, ids, mode, mode_sig, key)
    jax.block_until_ready(out_raw["logits"])
    p = jax.nn.softmax(out_raw["logits"], axis=-1)
    q = jax.nn.log_softmax(out_rec["logits"], axis=-1)
    return float(jnp.mean(jnp.sum(p * (jnp.log(p + 1e-9) - q), axis=-1)))


def main():
    V, D, L, H, IB_K, S, B = 32, 64, 2, 4, 16, 24, 32
    STEPS = 2000
    LR = 2e-3
    D_SIGNAL = 16

    rng = np.random.default_rng(0)
    transition = make_transition(rng, V, temperature=0.3)
    bayes_ce = row_entropy(transition)
    uniform_ce = float(np.log(V))

    key = jax.random.PRNGKey(0)
    key, sub = jax.random.split(key)
    params = init_gnomon(
        sub, vocab_size=V, d_model=D, n_layers=L, n_heads=H,
        ib_k=IB_K, seq_len=S, d_signal=D_SIGNAL,
    )
    opt = adam_init(params)
    mode = init_mode_state(d_mod=4)

    step_fn = jax.jit(
        lambda p, o, b, m, r: train_step(p, o, b, m, r, n_heads=H, lr=LR)
    )

    print(f"Task:  bigram Markov chain (V={V}, temperature=0.3)")
    print(f"Bayes CE (row entropy): {bayes_ce:.4f}")
    print(f"Uniform CE:             {uniform_ce:.4f}")
    print(f"Model: {L} layers, d={D}, heads={H}, IB k={IB_K}")
    print(f"Train: {STEPS} steps, batch {B}×{S}, Adam lr={LR}")
    print()
    print(f"{'step':>5}  {'loss':>8}  {'ce':>8}  {'ib':>8}  {'coupling KL':>12}")
    print("-" * 52)

    key, sub = jax.random.split(key)
    ids_probe = sample_batch(rng, 4, S, V, transition)
    mode_sig_probe = jnp.zeros((4, S, D_SIGNAL))
    kl_0 = coupling_kl(params, ids_probe, mode, mode_sig_probe, sub, H)
    print(f"{'init':>5}  {'—':>8}  {'—':>8}  {'—':>8}  {kl_0:>12.4f}")

    t0 = time.perf_counter()
    final_ce = None
    final_kl = kl_0
    for step in range(STEPS):
        key, sub = jax.random.split(key)
        ids = sample_batch(rng, B, S, V, transition)
        mode_sig = jnp.zeros((B, S, D_SIGNAL))
        batch = {"input_ids": ids, "labels": ids, "mode_signal": mode_sig}
        params, opt, loss, aux = step_fn(params, opt, batch, mode, sub)
        final_ce = float(aux["ce"])

        if step % 200 == 0 or step == STEPS - 1:
            key, sub = jax.random.split(key)
            final_kl = coupling_kl(params, ids_probe, mode, mode_sig_probe, sub, H)
            print(f"{step:>5}  {float(loss):>8.4f}  {float(aux['ce']):>8.4f}  "
                  f"{float(aux['ib']):>8.4f}  {final_kl:>12.4f}")

    total = time.perf_counter() - t0
    print("-" * 52)
    print(f"{STEPS} steps in {total:.1f}s ({STEPS / total:.1f} steps/s)")
    print()

    print(f"Uniform CE:             {uniform_ce:.4f}")
    print(f"Bayes CE:               {bayes_ce:.4f}")
    print(f"Final model CE:         {final_ce:.4f}")
    print(f"Signal recovered:       "
          f"{100 * (uniform_ce - final_ce) / (uniform_ce - bayes_ce):.1f}% "
          f"of the uniform→Bayes gap")
    print(f"Coupling KL:            {kl_0:.4f} → {final_kl:.4f} "
          f"({kl_0 / max(final_kl, 1e-6):.0f}x tighter)")
    print()
    if final_ce <= bayes_ce + 0.3:
        print("  → Model captured the transition structure.")
    elif final_ce <= uniform_ce - 0.3:
        print("  → Model learned partial structure.")
    else:
        print("  → No learning. Check hyperparameters.")


if __name__ == "__main__":
    main()