Add train_gpt_kernel.py directly + simplify app

app.py

@@ -1,11 +1,9 @@
 import gradio as gr
 import subprocess
-import os
 import sys
-from pathlib import Path
 
 def train_model():
-    """Train the μ⁸ Kernel model for Parameter Golf - streaming version"""
+    """Train the μ⁸ Kernel model - simplified version"""
     log = []
     
     def log_step(msg):
@@ -13,85 +11,31 @@ def train_model():
         return "\n".join(log)
     
     try:
-        # Clone if needed
-        if not Path("parameter-golf").exists():
-            yield log_step("🔄 Cloning repository...")
-            result = subprocess.run(
-                ["git", "clone", "https://github.com/beanapologist/parameter-golf"],
-                capture_output=True, text=True, timeout=120
-            )
-            if result.returncode != 0:
-                yield log_step(f"❌ Clone failed:\n{result.stderr[:500]}")
-                return
-            yield log_step("✅ Repository cloned")
-        else:
-            yield log_step("✅ Repository exists")
-        
-        os.chdir("parameter-golf")
-        
-        # Fetch and checkout the kernel PR branch
-        yield log_step("🔄 Checking out kernel branch...")
-        
-        # Track and checkout the remote branch
-        subprocess.run(["git", "fetch", "origin"], capture_output=True)
-        result = subprocess.run(
-            ["git", "checkout", "-b", "kernel", "origin/copilot/integrate-critical-eigenvalue-functionality"],
-            capture_output=True, text=True
-        )
-        
-        if result.returncode == 0:
-            yield log_step("✅ Kernel branch active")
-        else:
-            # Maybe branch already exists locally, try switching
-            result2 = subprocess.run(
-                ["git", "checkout", "origin/copilot/integrate-critical-eigenvalue-functionality"],
-                capture_output=True, text=True
-            )
-            if result2.returncode == 0:
-                yield log_step("✅ Kernel branch active (detached HEAD)")
-            else:
-                yield log_step(f"⚠️  Branch checkout failed: {result.stderr[:200]}")
-                yield log_step("⚠️  Trying direct file download...")
-                # Fallback: download the file directly
-                import urllib.request
-                url = "https://raw.githubusercontent.com/beanapologist/parameter-golf/copilot/integrate-critical-eigenvalue-functionality/train_gpt_kernel.py"
-                urllib.request.urlretrieve(url, "train_gpt_kernel.py")
-                yield log_step("✅ Downloaded train_gpt_kernel.py directly")
-        
-        # Check for kernel training script
-        if not Path("train_gpt_kernel.py").exists():
-            yield log_step("❌ train_gpt_kernel.py not found")
-            yield log_step("Available: " + ", ".join([f.name for f in Path(".").glob("train_*.py")]))
-            return
-        
-        yield log_step("✅ Found train_gpt_kernel.py")
-        
-        # Install deps
-        yield log_step("🔄 Installing torch...")
+        yield log_step("🔄 Installing dependencies...")
         subprocess.run([sys.executable, "-m", "pip", "install", "-q", "torch", "numpy", "tiktoken"], timeout=180)
         yield log_step("✅ Dependencies ready")
         
         # GPU check
         gpu_result = subprocess.run(
-            [sys.executable, "-c", "import torch; print(f'GPU available: {torch.cuda.is_available()}')"],
+            [sys.executable, "-c", "import torch; print(f'GPU: {torch.cuda.is_available()}')"],
             capture_output=True, text=True
         )
         yield log_step(gpu_result.stdout.strip())
         
-        # Run minimal training test (avoid data download OOM)
         yield log_step("=" * 60)
-        yield log_step("🚀 Starting coherence-based training (test run: 100 steps)")
+        yield log_step("🚀 Starting μ⁸ Kernel training")
+        yield log_step("Coherence activation C(r)=2r/(1+r²) | Silver ratio δ_S=1+√2 | 8-head attention")
         yield log_step("=" * 60)
         
-        # Small model config to avoid OOM
+        # Run training (small config for Zero GPU)
+        import os
         env = os.environ.copy()
         env.update({
             "NUM_LAYERS": "4",
-            "MODEL_DIM": "192", 
+            "MODEL_DIM": "192",
             "MAX_STEPS": "100",
         })
         
-        # Stream training output
         process = subprocess.Popen(
             [sys.executable, "train_gpt_kernel.py"],
             stdout=subprocess.PIPE,
@@ -109,30 +53,25 @@ def train_model():
         
         yield log_step("=" * 60)
         if process.returncode == 0:
-            yield log_step("✅ Training completed successfully!")
+            yield log_step("✅ Training complete!")
         else:
-            yield log_step(f"⚠️  Exited with code {process.returncode}")
+            yield log_step(f"⚠️ Exit code {process.returncode}")
             
-    except subprocess.TimeoutExpired:
-        yield log_step("⏱️  Timeout exceeded")
     except Exception as e:
         yield log_step(f"❌ Error: {str(e)}")
 
-# Gradio UI
 with gr.Blocks(title="μ⁸ Kernel") as demo:
     gr.Markdown("""
     # μ⁸ Kernel Training - Parameter Golf
     
-    Formally verified LM architecture:
-    - **C(r) = 2r/(1+r²)** coherence activation
-    - **δ_S = 1+√2** silver MLP expansion
-    - **μ⁸ = 1** eight-head attention
-    
-    464 Lean 4 proofs, 0 sorry.
+    Formally verified LM architecture (464 Lean 4 proofs):
+    - **C(r) = 2r/(1+r²)** coherence activation  
+    - **δ_S = 1+√2 ≈ 2.414** silver MLP expansion  
+    - **μ⁸ = 1** eight-cycle attention
     """)
     
     btn = gr.Button("🚀 Start Training", variant="primary", size="lg")
-    out = gr.Textbox(label="Log", lines=25, max_lines=40, autoscroll=True)
+    out = gr.Textbox(label="Training Log", lines=25, max_lines=40, autoscroll=True)
     
     btn.click(fn=train_model, outputs=out)
 

train_gpt_kernel.py

@@ -0,0 +1,1094 @@
+"""
+train_gpt_kernel.py — Parameter-Golf training pipeline informed by the
+formal Lean 4 theorems in formal-lean/CriticalEigenvalue.lean.
+
+Three mathematical objects from the Kernel formalization are wired
+directly into the model architecture:
+
+  1. Coherence activation  C(r) = 2r / (1 + r²)
+     Defined in §5 of CriticalEigenvalue.lean and proved to satisfy:
+       • C(r) ≤ 1  for r ≥ 0             (AM–GM bound)
+       • C(1) = 1  (unique maximum)
+       • C(−r) = −C(r)                   (odd symmetry)
+       • C(r)² + ((r²−1)/(1+r²))² = 1   (Pythagorean identity §18)
+       • C(exp λ) = sech λ               (Lyapunov duality §10)
+     Used here as the nonlinearity inside every MLP block, replacing the
+     standard relu² activation from the baseline.
+
+  2. Silver ratio  δS = 1 + √2 ≈ 2.414
+     Defined in §7 (Proposition 4) and proved to satisfy:
+       • δS = 2 + 1/δS                   (self-similarity §20)
+       • δS is the positive root of x²−2x−1 = 0
+     Used here as the MLP hidden-dimension multiplier, so the MLP
+     expands from d_model to ⌊δS · d_model⌋ neurons.
+
+  3. Z/8Z rotational memory  (μ^8 = 1, §2 and §15)
+     The critical eigenvalue μ = exp(3πi/4) generates an exact 8-cycle.
+     The default number of attention heads is set to 8, so that each head
+     occupies one slot of the cyclic group, providing uniform coverage of
+     the 8 distinct phase positions proven distinct in §3.
+
+Hard stop: to stay readable for newcomers, keep this file under 1500 lines.
+"""
+
+from __future__ import annotations
+
+import copy
+import glob
+import io
+import math
+import os
+import random
+import subprocess
+import sys
+import time
+import uuid
+import zlib
+from pathlib import Path
+
+import numpy as np
+import sentencepiece as spm
+import torch
+import torch.distributed as dist
+import torch.nn.functional as F
+from torch import Tensor, nn
+from torch.nn.parallel import DistributedDataParallel as DDP
+
+# ─────────────────────────────────────────────────────────────────────────────
+# KERNEL CONSTANTS  (from formal-lean/CriticalEigenvalue.lean)
+# ─────────────────────────────────────────────────────────────────────────────
+
+# Silver ratio δS = 1 + √2  (CriticalEigenvalue.lean §7, Proposition 4).
+# Self-similar: δS = 2 + 1/δS.  Positive root of x² − 2x − 1 = 0.
+SILVER_RATIO: float = 1.0 + math.sqrt(2)  # ≈ 2.4142135…
+
+# Critical eigenvalue angle θ = 3π/4, so μ = exp(I·θ).
+# μ^8 = 1 (CriticalEigenvalue.lean §2) and gcd(3,8)=1 (§3).
+MU_ANGLE: float = 3.0 * math.pi / 4.0  # 135°
+
+# Number of distinct μ-orbit slots: Z/8Z (§15).
+MU_ORBIT_SIZE: int = 8
+
+# ─────────────────────────────────────────────────────────────────────────────
+# HYPERPARAMETERS
+# ─────────────────────────────────────────────────────────────────────────────
+
+class Hyperparameters:
+    # Data paths are shard globs produced by the existing preprocessing pipeline.
+    data_path = os.environ.get("DATA_PATH", "./data/datasets/fineweb10B_sp1024")
+    train_files = os.path.join(data_path, "fineweb_train_*.bin")
+    val_files = os.path.join(data_path, "fineweb_val_*.bin")
+    tokenizer_path = os.environ.get("TOKENIZER_PATH", "./data/tokenizers/fineweb_1024_bpe.model")
+    run_id = os.environ.get("RUN_ID", str(uuid.uuid4()))
+    seed = int(os.environ.get("SEED", 1337))
+
+    # Validation cadence and batch size.
+    val_batch_size = int(os.environ.get("VAL_BATCH_SIZE", 524_288))
+    val_loss_every = int(os.environ.get("VAL_LOSS_EVERY", 1000))
+    train_log_every = int(os.environ.get("TRAIN_LOG_EVERY", 200))
+
+    # Training length.
+    iterations = int(os.environ.get("ITERATIONS", 20000))
+    warmdown_iters = int(os.environ.get("WARMDOWN_ITERS", 1200))
+    warmup_steps = int(os.environ.get("WARMUP_STEPS", 20))
+    train_batch_tokens = int(os.environ.get("TRAIN_BATCH_TOKENS", 524_288))
+    train_seq_len = int(os.environ.get("TRAIN_SEQ_LEN", 1024))
+    max_wallclock_seconds = float(os.environ.get("MAX_WALLCLOCK_SECONDS", 600.0))
+    qk_gain_init = float(os.environ.get("QK_GAIN_INIT", 1.5))
+
+    # Model shape.
+    # num_heads=8: one head per slot of the Z/8Z orbit (CriticalEigenvalue.lean §15).
+    vocab_size = int(os.environ.get("VOCAB_SIZE", 1024))
+    num_layers = int(os.environ.get("NUM_LAYERS", 9))
+    num_kv_heads = int(os.environ.get("NUM_KV_HEADS", 4))
+    model_dim = int(os.environ.get("MODEL_DIM", 512))
+    num_heads = int(os.environ.get("NUM_HEADS", MU_ORBIT_SIZE))  # 8 → Z/8Z
+    tie_embeddings = bool(int(os.environ.get("TIE_EMBEDDINGS", "1")))
+    rope_base = float(os.environ.get("ROPE_BASE", 10000.0))
+    logit_softcap = float(os.environ.get("LOGIT_SOFTCAP", 30.0))
+
+    # MLP hidden width is ⌊δS · model_dim⌋ unless overridden.
+    # δS ≈ 2.414 (CriticalEigenvalue.lean §7).
+    # Re-read MODEL_DIM from env so that overrides are honoured even when MLP_HIDDEN is unset.
+    mlp_hidden = int(os.environ.get("MLP_HIDDEN", round(SILVER_RATIO * int(os.environ.get("MODEL_DIM", 512)))))
+
+    # Optimizer hyperparameters.
+    embed_lr = float(os.environ.get("EMBED_LR", 0.6))
+    head_lr = float(os.environ.get("HEAD_LR", 0.008))
+    tied_embed_lr = float(os.environ.get("TIED_EMBED_LR", 0.05))
+    tied_embed_init_std = float(os.environ.get("TIED_EMBED_INIT_STD", 0.005))
+    matrix_lr = float(os.environ.get("MATRIX_LR", 0.04))
+    scalar_lr = float(os.environ.get("SCALAR_LR", 0.04))
+    muon_momentum = float(os.environ.get("MUON_MOMENTUM", 0.95))
+    muon_backend_steps = int(os.environ.get("MUON_BACKEND_STEPS", 5))
+    muon_momentum_warmup_start = float(os.environ.get("MUON_MOMENTUM_WARMUP_START", 0.85))
+    muon_momentum_warmup_steps = int(os.environ.get("MUON_MOMENTUM_WARMUP_STEPS", 500))
+    beta1 = float(os.environ.get("BETA1", 0.9))
+    beta2 = float(os.environ.get("BETA2", 0.95))
+    adam_eps = float(os.environ.get("ADAM_EPS", 1e-8))
+    grad_clip_norm = float(os.environ.get("GRAD_CLIP_NORM", 0.0))
+
+# ─────────────────────────────────────────────────────────────────────────────
+# MUON OPTIMIZER  (unchanged from baseline train_gpt.py)
+# ─────────────────────────────────────────────────────────────────────────────
+
+def zeropower_via_newtonschulz5(G: Tensor, steps: int = 10, eps: float = 1e-7) -> Tensor:
+    a, b, c = (3.4445, -4.7750, 2.0315)
+    X = G.bfloat16()
+    X /= X.norm() + eps
+    transposed = G.size(0) > G.size(1)
+    if transposed:
+        X = X.T
+    for _ in range(steps):
+        A = X @ X.T
+        B = b * A + c * A @ A
+        X = a * X + B @ X
+    return X.T if transposed else X
+
+
+class Muon(torch.optim.Optimizer):
+    def __init__(self, params, lr: float, momentum: float, backend_steps: int, nesterov: bool = True):
+        super().__init__(
+            params,
+            dict(lr=lr, momentum=momentum, backend_steps=backend_steps, nesterov=nesterov),
+        )
+
+    @torch.no_grad()
+    def step(self, closure=None):
+        loss = None
+        if closure is not None:
+            with torch.enable_grad():
+                loss = closure()
+
+        distributed = dist.is_available() and dist.is_initialized()
+        world_size = dist.get_world_size() if distributed else 1
+        rank = dist.get_rank() if distributed else 0
+
+        for group in self.param_groups:
+            params = group["params"]
+            if not params:
+                continue
+            lr = group["lr"]
+            momentum = group["momentum"]
+            backend_steps = group["backend_steps"]
+            nesterov = group["nesterov"]
+
+            total_params = sum(int(p.numel()) for p in params)
+            updates_flat = torch.zeros(total_params, device=params[0].device, dtype=torch.bfloat16)
+
+            curr = 0
+            for i, p in enumerate(params):
+                if i % world_size == rank and p.grad is not None:
+                    g = p.grad
+                    state = self.state[p]
+                    if "momentum_buffer" not in state:
+                        state["momentum_buffer"] = torch.zeros_like(g)
+                    buf = state["momentum_buffer"]
+                    buf.mul_(momentum).add_(g)
+                    if nesterov:
+                        g = g.add(buf, alpha=momentum)
+                    g = zeropower_via_newtonschulz5(g, steps=backend_steps)
+                    g *= max(1, g.size(0) / g.size(1)) ** 0.5
+                    updates_flat[curr : curr + p.numel()] = g.reshape(-1)
+                curr += p.numel()
+
+            if distributed:
+                dist.all_reduce(updates_flat, op=dist.ReduceOp.SUM)
+
+            curr = 0
+            for p in params:
+                g = updates_flat[curr : curr + p.numel()].view_as(p).to(dtype=p.dtype)
+                p.add_(g, alpha=-lr)
+                curr += p.numel()
+
+        return loss
+
+# ─────────────────────────────────────────────────────────────────────────────
+# TOKENIZER-AGNOSTIC EVALUATION  (unchanged from baseline)
+# ─────────────��───────────────────────────────────────────────────────────────
+
+def build_sentencepiece_luts(
+    sp: spm.SentencePieceProcessor, vocab_size: int, device: torch.device
+) -> tuple[Tensor, Tensor, Tensor]:
+    sp_vocab_size = int(sp.vocab_size())
+    table_size = max(sp_vocab_size, vocab_size)
+    base_bytes_np = np.zeros((table_size,), dtype=np.int16)
+    has_leading_space_np = np.zeros((table_size,), dtype=np.bool_)
+    is_boundary_token_np = np.ones((table_size,), dtype=np.bool_)
+    for token_id in range(sp_vocab_size):
+        if sp.is_control(token_id) or sp.is_unknown(token_id) or sp.is_unused(token_id):
+            continue
+        is_boundary_token_np[token_id] = False
+        if sp.is_byte(token_id):
+            base_bytes_np[token_id] = 1
+            continue
+        piece = sp.id_to_piece(token_id)
+        if piece.startswith("▁"):
+            has_leading_space_np[token_id] = True
+            piece = piece[1:]
+        base_bytes_np[token_id] = len(piece.encode("utf-8"))
+    return (
+        torch.tensor(base_bytes_np, dtype=torch.int16, device=device),
+        torch.tensor(has_leading_space_np, dtype=torch.bool, device=device),
+        torch.tensor(is_boundary_token_np, dtype=torch.bool, device=device),
+    )
+
+
+def load_validation_tokens(pattern: str, seq_len: int) -> Tensor:
+    files = [Path(p) for p in sorted(glob.glob(pattern))]
+    if not files:
+        raise FileNotFoundError(f"No files found for pattern: {pattern}")
+    tokens = torch.cat([load_data_shard(file) for file in files]).contiguous()
+    usable = ((tokens.numel() - 1) // seq_len) * seq_len
+    if usable <= 0:
+        raise ValueError(f"Validation split is too short for TRAIN_SEQ_LEN={seq_len}")
+    return tokens[: usable + 1]
+
+
+def eval_val(
+    args: Hyperparameters,
+    model: nn.Module,
+    rank: int,
+    world_size: int,
+    device: torch.device,
+    grad_accum_steps: int,
+    val_tokens: Tensor,
+    base_bytes_lut: Tensor,
+    has_leading_space_lut: Tensor,
+    is_boundary_token_lut: Tensor,
+) -> tuple[float, float]:
+    local_batch_tokens = args.val_batch_size // (world_size * grad_accum_steps)
+    if local_batch_tokens < args.train_seq_len:
+        raise ValueError(
+            "VAL_BATCH_SIZE must provide at least one sequence per rank; "
+            f"got VAL_BATCH_SIZE={args.val_batch_size}, WORLD_SIZE={world_size}, "
+            f"GRAD_ACCUM_STEPS={grad_accum_steps}, TRAIN_SEQ_LEN={args.train_seq_len}"
+        )
+    local_batch_seqs = local_batch_tokens // args.train_seq_len
+    total_seqs = (val_tokens.numel() - 1) // args.train_seq_len
+    seq_start = (total_seqs * rank) // world_size
+    seq_end = (total_seqs * (rank + 1)) // world_size
+    val_loss_sum = torch.zeros((), device=device, dtype=torch.float64)
+    val_token_count = torch.zeros((), device=device, dtype=torch.float64)
+    val_byte_count = torch.zeros((), device=device, dtype=torch.float64)
+
+    model.eval()
+    with torch.inference_mode():
+        for batch_seq_start in range(seq_start, seq_end, local_batch_seqs):
+            batch_seq_end = min(batch_seq_start + local_batch_seqs, seq_end)
+            raw_start = batch_seq_start * args.train_seq_len
+            raw_end = batch_seq_end * args.train_seq_len + 1
+            local = val_tokens[raw_start:raw_end].to(device=device, dtype=torch.int64, non_blocking=True)
+            x = local[:-1].reshape(-1, args.train_seq_len)
+            y = local[1:].reshape(-1, args.train_seq_len)
+            with torch.autocast(device_type="cuda", dtype=torch.bfloat16, enabled=True):
+                batch_loss = model(x, y).detach()
+            batch_token_count = float(y.numel())
+            val_loss_sum += batch_loss.to(torch.float64) * batch_token_count
+            val_token_count += batch_token_count
+            prev_ids = x.reshape(-1)
+            tgt_ids = y.reshape(-1)
+            token_bytes = base_bytes_lut[tgt_ids].to(dtype=torch.int16)
+            token_bytes += (has_leading_space_lut[tgt_ids] & ~is_boundary_token_lut[prev_ids]).to(dtype=torch.int16)
+            val_byte_count += token_bytes.to(torch.float64).sum()
+
+    if dist.is_available() and dist.is_initialized():
+        dist.all_reduce(val_loss_sum, op=dist.ReduceOp.SUM)
+        dist.all_reduce(val_token_count, op=dist.ReduceOp.SUM)
+        dist.all_reduce(val_byte_count, op=dist.ReduceOp.SUM)
+
+    val_loss = val_loss_sum / val_token_count
+    bits_per_token = val_loss.item() / math.log(2.0)
+    tokens_per_byte = val_token_count.item() / val_byte_count.item()
+    model.train()
+    return float(val_loss.item()), float(bits_per_token * tokens_per_byte)
+
+# ─────────────────────────────────────────────────────────────────────────────
+# POST-TRAINING QUANTIZATION  (unchanged from baseline)
+# ───��─────────────────────────────────────────────────────────────────────────
+
+CONTROL_TENSOR_NAME_PATTERNS = tuple(
+    pattern
+    for pattern in os.environ.get(
+        "CONTROL_TENSOR_NAME_PATTERNS",
+        "attn_scale,attn_scales,mlp_scale,mlp_scales,resid_mix,resid_mixes,q_gain,skip_weight,skip_weights",
+    ).split(",")
+    if pattern
+)
+INT8_KEEP_FLOAT_FP32_NAME_PATTERNS = tuple(
+    pattern
+    for pattern in os.environ.get(
+        "INT8_KEEP_FLOAT_FP32_NAME_PATTERNS",
+        ",".join(CONTROL_TENSOR_NAME_PATTERNS),
+    ).split(",")
+    if pattern
+)
+INT8_KEEP_FLOAT_MAX_NUMEL = 65_536
+INT8_KEEP_FLOAT_STORE_DTYPE = torch.float16
+INT8_PER_ROW_SCALE_DTYPE = torch.float16
+INT8_CLIP_PERCENTILE = 99.99984
+INT8_CLIP_Q = INT8_CLIP_PERCENTILE / 100.0
+
+
+def tensor_nbytes(t: Tensor) -> int:
+    return int(t.numel()) * int(t.element_size())
+
+
+def keep_float_tensor(name: str, t: Tensor, passthrough_orig_dtypes: dict[str, str]) -> Tensor:
+    if any(pattern in name for pattern in INT8_KEEP_FLOAT_FP32_NAME_PATTERNS):
+        return t.float().contiguous()
+    if t.dtype in {torch.float32, torch.bfloat16}:
+        passthrough_orig_dtypes[name] = str(t.dtype).removeprefix("torch.")
+        return t.to(dtype=INT8_KEEP_FLOAT_STORE_DTYPE).contiguous()
+    return t
+
+
+def quantize_float_tensor(t: Tensor) -> tuple[Tensor, Tensor]:
+    t32 = t.float()
+    if t32.ndim == 2:
+        clip_abs = (
+            torch.quantile(t32.abs(), INT8_CLIP_Q, dim=1)
+            if t32.numel()
+            else torch.empty((t32.shape[0],), dtype=torch.float32)
+        )
+        clipped = torch.maximum(torch.minimum(t32, clip_abs[:, None]), -clip_abs[:, None])
+        scale = (clip_abs / 127.0).clamp_min(1.0 / 127.0)
+        q = torch.clamp(torch.round(clipped / scale[:, None]), -127, 127).to(torch.int8).contiguous()
+        return q, scale.to(dtype=INT8_PER_ROW_SCALE_DTYPE).contiguous()
+    clip_abs = float(torch.quantile(t32.abs().flatten(), INT8_CLIP_Q).item()) if t32.numel() else 0.0
+    scale = torch.tensor(clip_abs / 127.0 if clip_abs > 0 else 1.0, dtype=torch.float32)
+    q = torch.clamp(torch.round(torch.clamp(t32, -clip_abs, clip_abs) / scale), -127, 127).to(torch.int8).contiguous()
+    return q, scale
+
+
+def quantize_state_dict_int8(state_dict: dict[str, Tensor]):
+    quantized: dict[str, Tensor] = {}
+    scales: dict[str, Tensor] = {}
+    dtypes: dict[str, str] = {}
+    passthrough: dict[str, Tensor] = {}
+    passthrough_orig_dtypes: dict[str, str] = {}
+    qmeta: dict[str, dict[str, object]] = {}
+    stats = dict.fromkeys(
+        ("param_count", "num_tensors", "num_float_tensors", "num_nonfloat_tensors", "baseline_tensor_bytes", "int8_payload_bytes"),
+        0,
+    )
+
+    for name, tensor in state_dict.items():
+        t = tensor.detach().to("cpu").contiguous()
+        stats["param_count"] += int(t.numel())
+        stats["num_tensors"] += 1
+        stats["baseline_tensor_bytes"] += tensor_nbytes(t)
+
+        if not t.is_floating_point():
+            stats["num_nonfloat_tensors"] += 1
+            passthrough[name] = t
+            stats["int8_payload_bytes"] += tensor_nbytes(t)
+            continue
+
+        if t.numel() <= INT8_KEEP_FLOAT_MAX_NUMEL:
+            kept = keep_float_tensor(name, t, passthrough_orig_dtypes)
+            passthrough[name] = kept
+            stats["int8_payload_bytes"] += tensor_nbytes(kept)
+            continue
+
+        stats["num_float_tensors"] += 1
+        q, s = quantize_float_tensor(t)
+        if s.ndim > 0:
+            qmeta[name] = {"scheme": "per_row", "axis": 0}
+        quantized[name] = q
+        scales[name] = s
+        dtypes[name] = str(t.dtype).removeprefix("torch.")
+        stats["int8_payload_bytes"] += tensor_nbytes(q) + tensor_nbytes(s)
+
+    obj: dict[str, object] = {
+        "__quant_format__": "int8_clean_per_row_v1",
+        "quantized": quantized,
+        "scales": scales,
+        "dtypes": dtypes,
+        "passthrough": passthrough,
+    }
+    if qmeta:
+        obj["qmeta"] = qmeta
+    if passthrough_orig_dtypes:
+        obj["passthrough_orig_dtypes"] = passthrough_orig_dtypes
+    return obj, stats
+
+
+def dequantize_state_dict_int8(obj: dict[str, object]) -> dict[str, Tensor]:
+    out: dict[str, Tensor] = {}
+    qmeta = obj.get("qmeta", {})
+    passthrough_orig_dtypes = obj.get("passthrough_orig_dtypes", {})
+    for name, q in obj["quantized"].items():
+        dtype = getattr(torch, obj["dtypes"][name])
+        s = obj["scales"][name]
+        if qmeta.get(name, {}).get("scheme") == "per_row" or s.ndim > 0:
+            s = s.to(dtype=torch.float32)
+            out[name] = (q.float() * s.view(q.shape[0], *([1] * (q.ndim - 1)))).to(dtype=dtype).contiguous()
+        else:
+            scale = float(s.item())
+            out[name] = (q.float() * scale).to(dtype=dtype).contiguous()
+    for name, t in obj["passthrough"].items():
+        out_t = t.detach().to("cpu").contiguous()
+        orig_dtype = passthrough_orig_dtypes.get(name)
+        if isinstance(orig_dtype, str):
+            out_t = out_t.to(dtype=getattr(torch, orig_dtype)).contiguous()
+        out[name] = out_t
+    return out
+
+# ─────────────────────────────────────────────────────────────────────────────
+# DATA LOADING  (unchanged from baseline)
+# ─────────────────────────────────────────────────────────────────────────────
+
+def load_data_shard(file: Path) -> Tensor:
+    header_bytes = 256 * np.dtype("<i4").itemsize
+    token_bytes = np.dtype("<u2").itemsize
+    header = np.fromfile(file, dtype="<i4", count=256)
+    if header.size != 256 or int(header[0]) != 20240520 or int(header[1]) != 1:
+        raise ValueError(f"Unexpected shard header for {file}")
+    num_tokens = int(header[2])
+    expected_size = header_bytes + num_tokens * token_bytes
+    if file.stat().st_size != expected_size:
+        raise ValueError(f"Shard size mismatch for {file}: expected {expected_size} bytes")
+    tokens_np = np.fromfile(file, dtype="<u2", count=num_tokens, offset=header_bytes)
+    if tokens_np.size != num_tokens:
+        raise ValueError(f"Short read for {file}")
+    return torch.from_numpy(tokens_np.astype(np.uint16, copy=False))
+
+
+class TokenStream:
+    def __init__(self, pattern: str):
+        self.files = [Path(p) for p in sorted(glob.glob(pattern))]
+        if not self.files:
+            raise FileNotFoundError(f"No files found for pattern: {pattern}")
+        self.file_idx = 0
+        self.tokens = load_data_shard(self.files[0])
+        self.pos = 0
+
+    def _advance_file(self) -> None:
+        self.file_idx = (self.file_idx + 1) % len(self.files)
+        self.tokens = load_data_shard(self.files[self.file_idx])
+        self.pos = 0
+
+    def take(self, n: int) -> Tensor:
+        chunks: list[Tensor] = []
+        remaining = n
+        while remaining > 0:
+            avail = self.tokens.numel() - self.pos
+            if avail <= 0:
+                self._advance_file()
+                continue
+            k = min(remaining, avail)
+            chunks.append(self.tokens[self.pos : self.pos + k])
+            self.pos += k
+            remaining -= k
+        return chunks[0] if len(chunks) == 1 else torch.cat(chunks)
+
+
+class DistributedTokenLoader:
+    def __init__(self, pattern: str, rank: int, world_size: int, device: torch.device):
+        self.rank = rank
+        self.world_size = world_size
+        self.device = device
+        self.stream = TokenStream(pattern)
+
+    def next_batch(self, global_tokens: int, seq_len: int, grad_accum_steps: int) -> tuple[Tensor, Tensor]:
+        local_tokens = global_tokens // (self.world_size * grad_accum_steps)
+        per_rank_span = local_tokens + 1
+        chunk = self.stream.take(per_rank_span * self.world_size)
+        start = self.rank * per_rank_span
+        local = chunk[start : start + per_rank_span].to(dtype=torch.int64)
+        x = local[:-1].reshape(-1, seq_len)
+        y = local[1:].reshape(-1, seq_len)
+        return x.to(self.device, non_blocking=True), y.to(self.device, non_blocking=True)
+
+# ─────────────────────────────────────────────────────────────────────────────
+# TRANSFORMER MODULES — KERNEL EDITION
+# ─────────────────────────────────────────────────────────────────────────────
+
+class RMSNorm(nn.Module):
+    def __init__(self, eps: float | None = None):
+        super().__init__()
+        self.eps = eps
+
+    def forward(self, x: Tensor) -> Tensor:
+        return F.rms_norm(x, (x.size(-1),), eps=self.eps)
+
+
+class CastedLinear(nn.Linear):
+    def forward(self, x: Tensor) -> Tensor:
+        bias = self.bias.to(x.dtype) if self.bias is not None else None
+        return F.linear(x, self.weight.to(x.dtype), bias)
+
+
+def restore_low_dim_params_to_fp32(module: nn.Module) -> None:
+    with torch.no_grad():
+        for name, param in module.named_parameters():
+            if (param.ndim < 2 or any(pattern in name for pattern in CONTROL_TENSOR_NAME_PATTERNS)) and param.dtype != torch.float32:
+                param.data = param.data.float()
+
+
+class Rotary(nn.Module):
+    def __init__(self, dim: int, base: float = 10000.0):
+        super().__init__()
+        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32) / dim))
+        self.register_buffer("inv_freq", inv_freq, persistent=False)
+        self._seq_len_cached = 0
+        self._cos_cached: Tensor | None = None
+        self._sin_cached: Tensor | None = None
+
+    def forward(self, seq_len: int, device: torch.device, dtype: torch.dtype) -> tuple[Tensor, Tensor]:
+        if (
+            self._cos_cached is None
+            or self._sin_cached is None
+            or self._seq_len_cached != seq_len
+            or self._cos_cached.device != device
+        ):
+            t = torch.arange(seq_len, device=device, dtype=self.inv_freq.dtype)
+            freqs = torch.outer(t, self.inv_freq.to(device))
+            self._cos_cached = freqs.cos()[None, None, :, :]
+            self._sin_cached = freqs.sin()[None, None, :, :]
+            self._seq_len_cached = seq_len
+        return self._cos_cached.to(dtype=dtype), self._sin_cached.to(dtype=dtype)
+
+
+def apply_rotary_emb(x: Tensor, cos: Tensor, sin: Tensor) -> Tensor:
+    half = x.size(-1) // 2
+    x1, x2 = x[..., :half], x[..., half:]
+    return torch.cat((x1 * cos + x2 * sin, x1 * (-sin) + x2 * cos), dim=-1)
+
+
+class CausalSelfAttention(nn.Module):
+    def __init__(self, dim: int, num_heads: int, num_kv_heads: int, rope_base: float, qk_gain_init: float):
+        super().__init__()
+        if dim % num_heads != 0:
+            raise ValueError("model_dim must be divisible by num_heads")
+        if num_heads % num_kv_heads != 0:
+            raise ValueError("num_heads must be divisible by num_kv_heads")
+        self.num_heads = num_heads
+        self.num_kv_heads = num_kv_heads
+        self.head_dim = dim // num_heads
+        if self.head_dim % 2 != 0:
+            raise ValueError("head_dim must be even for RoPE")
+        kv_dim = self.num_kv_heads * self.head_dim
+        self.c_q = CastedLinear(dim, dim, bias=False)
+        self.c_k = CastedLinear(dim, kv_dim, bias=False)
+        self.c_v = CastedLinear(dim, kv_dim, bias=False)
+        self.proj = CastedLinear(dim, dim, bias=False)
+        self.proj._zero_init = True
+        self.q_gain = nn.Parameter(torch.full((num_heads,), qk_gain_init, dtype=torch.float32))
+        self.rotary = Rotary(self.head_dim, base=rope_base)
+
+    def forward(self, x: Tensor) -> Tensor:
+        bsz, seqlen, dim = x.shape
+        q = self.c_q(x).reshape(bsz, seqlen, self.num_heads, self.head_dim).transpose(1, 2)
+        k = self.c_k(x).reshape(bsz, seqlen, self.num_kv_heads, self.head_dim).transpose(1, 2)
+        v = self.c_v(x).reshape(bsz, seqlen, self.num_kv_heads, self.head_dim).transpose(1, 2)
+        q = F.rms_norm(q, (q.size(-1),))
+        k = F.rms_norm(k, (k.size(-1),))
+        cos, sin = self.rotary(seqlen, x.device, q.dtype)
+        q = apply_rotary_emb(q, cos, sin)
+        k = apply_rotary_emb(k, cos, sin)
+        q = q * self.q_gain.to(dtype=q.dtype)[None, :, None, None]
+        y = F.scaled_dot_product_attention(
+            q, k, v,
+            attn_mask=None,
+            is_causal=True,
+            enable_gqa=(self.num_kv_heads != self.num_heads),
+        )
+        y = y.transpose(1, 2).contiguous().reshape(bsz, seqlen, dim)
+        return self.proj(y)
+
+
+def coherence(x: Tensor) -> Tensor:
+    """Coherence activation  C(r) = 2r / (1 + r²).
+
+    Defined in CriticalEigenvalue.lean §5.  Machine-checked properties:
+      • C(r) ≤ 1 for r ≥ 0  (AM–GM: 1 + r² ≥ 2r)
+      • C(1) = 1             (unique maximum on ℝ⁺)
+      • C(−r) = −C(r)        (odd / anti-symmetric)
+      • Pythagorean: C(r)² + ((r²−1)/(1+r²))² = 1  (§18)
+      • Lyapunov:   C(exp λ) = sech λ               (§10)
+
+    As a neural activation this is a smooth, bounded nonlinearity with
+    range (−1, 1), zero at the origin, unit gradient at zero, and graceful
+    saturation for large |r| — resembling a normalised sinc or tanh but
+    with a closed-form Pythagorean partner.
+    """
+    return 2.0 * x / (1.0 + x.square())
+
+
+class CoherenceMLP(nn.Module):
+    """MLP block whose hidden width is ⌊δS·dim⌋ and activation is C(r).
+
+    Both choices come directly from formal-lean/CriticalEigenvalue.lean:
+      • δS = 1+√2 (silver ratio, §7 Proposition 4) determines hidden width.
+      • C(r) = 2r/(1+r²) (coherence function, §5) is the nonlinearity.
+
+    The silver ratio satisfies δS = 2 + 1/δS (self-similarity §20), so the
+    expansion is slightly larger than 2× but smaller than 3×, giving a
+    natural intermediate width that is mathematically well-motivated.
+    """
+
+    def __init__(self, dim: int, hidden: int):
+        super().__init__()
+        self.fc = CastedLinear(dim, hidden, bias=False)
+        self.proj = CastedLinear(hidden, dim, bias=False)
+        self.proj._zero_init = True
+
+    def forward(self, x: Tensor) -> Tensor:
+        return self.proj(coherence(self.fc(x)))
+
+
+class KernelBlock(nn.Module):
+    """Transformer block using CoherenceMLP in place of the baseline relu² MLP."""
+
+    def __init__(self, dim: int, num_heads: int, num_kv_heads: int, mlp_hidden: int, rope_base: float, qk_gain_init: float):
+        super().__init__()
+        self.attn_norm = RMSNorm()
+        self.mlp_norm = RMSNorm()
+        self.attn = CausalSelfAttention(dim, num_heads, num_kv_heads, rope_base, qk_gain_init)
+        self.mlp = CoherenceMLP(dim, mlp_hidden)
+        self.attn_scale = nn.Parameter(torch.ones(dim, dtype=torch.float32))
+        self.mlp_scale = nn.Parameter(torch.ones(dim, dtype=torch.float32))
+        self.resid_mix = nn.Parameter(torch.stack((torch.ones(dim), torch.zeros(dim))).float())
+
+    def forward(self, x: Tensor, x0: Tensor) -> Tensor:
+        mix = self.resid_mix.to(dtype=x.dtype)
+        x = mix[0][None, None, :] * x + mix[1][None, None, :] * x0
+        attn_out = self.attn(self.attn_norm(x))
+        x = x + self.attn_scale.to(dtype=x.dtype)[None, None, :] * attn_out
+        x = x + self.mlp_scale.to(dtype=x.dtype)[None, None, :] * self.mlp(self.mlp_norm(x))
+        return x
+
+
+class KernelGPT(nn.Module):
+    """GPT variant implementing the Kernel eigenvalue formalization.
+
+    Architectural choices derived from CriticalEigenvalue.lean:
+      • num_heads = 8  (one slot per Z/8Z orbit element, §15)
+      • MLP hidden  = ⌊δS · model_dim⌋  (silver ratio expansion, §7)
+      • MLP activation = C(r) = 2r/(1+r²)  (coherence function, §5)
+    """
+
+    def __init__(
+        self,
+        vocab_size: int,
+        num_layers: int,
+        model_dim: int,
+        num_heads: int,
+        num_kv_heads: int,
+        mlp_hidden: int,
+        tie_embeddings: bool,
+        tied_embed_init_std: float,
+        logit_softcap: float,
+        rope_base: float,
+        qk_gain_init: float,
+    ):
+        super().__init__()
+        if logit_softcap <= 0.0:
+            raise ValueError(f"logit_softcap must be positive, got {logit_softcap}")
+        self.tie_embeddings = tie_embeddings
+        self.tied_embed_init_std = tied_embed_init_std
+        self.logit_softcap = logit_softcap
+        self.tok_emb = nn.Embedding(vocab_size, model_dim)
+        self.num_encoder_layers = num_layers // 2
+        self.num_decoder_layers = num_layers - self.num_encoder_layers
+        self.num_skip_weights = min(self.num_encoder_layers, self.num_decoder_layers)
+        self.skip_weights = nn.Parameter(torch.ones(self.num_skip_weights, model_dim, dtype=torch.float32))
+        self.blocks = nn.ModuleList(
+            [
+                KernelBlock(model_dim, num_heads, num_kv_heads, mlp_hidden, rope_base, qk_gain_init)
+                for _ in range(num_layers)
+            ]
+        )
+        self.final_norm = RMSNorm()
+        self.lm_head = None if tie_embeddings else CastedLinear(model_dim, vocab_size, bias=False)
+        if self.lm_head is not None:
+            self.lm_head._zero_init = True
+        self._init_weights()
+
+    def _init_weights(self) -> None:
+        if self.tie_embeddings:
+            nn.init.normal_(self.tok_emb.weight, mean=0.0, std=self.tied_embed_init_std)
+        for module in self.modules():
+            if isinstance(module, nn.Linear) and getattr(module, "_zero_init", False):
+                nn.init.zeros_(module.weight)
+
+    def forward(self, input_ids: Tensor, target_ids: Tensor) -> Tensor:
+        x = self.tok_emb(input_ids)
+        x = F.rms_norm(x, (x.size(-1),))
+        x0 = x
+        skips: list[Tensor] = []
+
+        for i in range(self.num_encoder_layers):
+            x = self.blocks[i](x, x0)
+            skips.append(x)
+        for i in range(self.num_decoder_layers):
+            if skips:
+                x = x + self.skip_weights[i].to(dtype=x.dtype)[None, None, :] * skips.pop()
+            x = self.blocks[self.num_encoder_layers + i](x, x0)
+
+        x = self.final_norm(x).reshape(-1, x.size(-1))
+        targets = target_ids.reshape(-1)
+        if self.tie_embeddings:
+            logits_proj = F.linear(x, self.tok_emb.weight)
+        else:
+            if self.lm_head is None:
+                raise RuntimeError("lm_head is required when tie_embeddings=False")
+            logits_proj = self.lm_head(x)
+        logits = self.logit_softcap * torch.tanh(logits_proj / self.logit_softcap)
+        return F.cross_entropy(logits.float(), targets, reduction="mean")
+
+# ─────────────────────────────────────────────────────────────────────────────
+# TRAINING
+# ─────────────────────────────────────────────────────────────────────────────
+
+def main() -> None:
+    global zeropower_via_newtonschulz5
+
+    code = Path(__file__).read_text(encoding="utf-8")
+    args = Hyperparameters()
+    zeropower_via_newtonschulz5 = torch.compile(zeropower_via_newtonschulz5)
+
+    # ── Distributed + CUDA setup ──────────────────────────────────────────────
+
+    distributed = "RANK" in os.environ and "WORLD_SIZE" in os.environ
+    rank = int(os.environ.get("RANK", "0"))
+    world_size = int(os.environ.get("WORLD_SIZE", "1"))
+    local_rank = int(os.environ.get("LOCAL_RANK", "0"))
+    if world_size <= 0:
+        raise ValueError(f"WORLD_SIZE must be positive, got {world_size}")
+    if 8 % world_size != 0:
+        raise ValueError(f"WORLD_SIZE={world_size} must divide 8 so grad_accum_steps stays integral")
+    grad_accum_steps = 8 // world_size
+    grad_scale = 1.0 / grad_accum_steps
+    if not torch.cuda.is_available():
+        raise RuntimeError("CUDA is required")
+    device = torch.device("cuda", local_rank)
+    torch.cuda.set_device(device)
+    if distributed:
+        dist.init_process_group(backend="nccl", device_id=device)
+        dist.barrier()
+    master_process = rank == 0
+
+    torch.backends.cuda.matmul.allow_tf32 = True
+    torch.backends.cudnn.allow_tf32 = True
+    from torch.backends.cuda import enable_cudnn_sdp, enable_flash_sdp, enable_math_sdp, enable_mem_efficient_sdp
+    enable_cudnn_sdp(False)
+    enable_flash_sdp(True)
+    enable_mem_efficient_sdp(False)
+    enable_math_sdp(False)
+
+    logfile = None
+    if master_process:
+        os.makedirs("logs", exist_ok=True)
+        logfile = f"logs/{args.run_id}.txt"
+        print(logfile)
+
+    def log0(msg: str, console: bool = True) -> None:
+        if not master_process:
+            return
+        if console:
+            print(msg)
+        if logfile is not None:
+            with open(logfile, "a", encoding="utf-8") as f:
+                print(msg, file=f)
+
+    log0(code, console=False)
+    log0("=" * 100, console=False)
+    log0(f"Running Python {sys.version}", console=False)
+    log0(f"Running PyTorch {torch.__version__}", console=False)
+    log0(
+        subprocess.run(["nvidia-smi"], stdout=subprocess.PIPE, stderr=subprocess.PIPE, text=True, check=False).stdout,
+        console=False,
+    )
+    log0("=" * 100, console=False)
+
+    # ── Kernel constants log ──────────────────────────────────────────────────
+    log0(f"kernel:silver_ratio:{SILVER_RATIO:.6f} mu_angle_deg:{math.degrees(MU_ANGLE):.1f} orbit_size:{MU_ORBIT_SIZE}")
+    log0(f"kernel:mlp_hidden:{args.mlp_hidden} (={args.mlp_hidden / args.model_dim:.4f}x model_dim)")
+
+    # ── Seed + tokenizer ──────────────────────────────────────────────────────
+
+    random.seed(args.seed)
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    torch.cuda.manual_seed_all(args.seed)
+
+    if not args.tokenizer_path.endswith(".model"):
+        raise ValueError(f"Script only setup for SentencePiece .model file: {args.tokenizer_path}")
+    sp = spm.SentencePieceProcessor(model_file=args.tokenizer_path)
+    if int(sp.vocab_size()) != args.vocab_size:
+        raise ValueError(
+            f"VOCAB_SIZE={args.vocab_size} does not match tokenizer vocab_size={int(sp.vocab_size())}"
+        )
+    dataset_dir = Path(args.data_path).resolve()
+    actual_train_files = len(list(dataset_dir.glob("fineweb_train_*.bin")))
+    val_tokens = load_validation_tokens(args.val_files, args.train_seq_len)
+    base_bytes_lut, has_leading_space_lut, is_boundary_token_lut = build_sentencepiece_luts(
+        sp, args.vocab_size, device
+    )
+    log0(f"val_bpb:enabled tokenizer_kind=sentencepiece tokenizer_path={args.tokenizer_path}")
+    log0(f"train_loader:dataset:{dataset_dir.name} train_shards:{actual_train_files}")
+    log0(f"val_loader:shards pattern={args.val_files} tokens:{val_tokens.numel() - 1}")
+
+    # ── Model + optimizer setup ───────────────────────────────────────────────
+
+    base_model = KernelGPT(
+        vocab_size=args.vocab_size,
+        num_layers=args.num_layers,
+        model_dim=args.model_dim,
+        num_heads=args.num_heads,
+        num_kv_heads=args.num_kv_heads,
+        mlp_hidden=args.mlp_hidden,
+        tie_embeddings=args.tie_embeddings,
+        tied_embed_init_std=args.tied_embed_init_std,
+        logit_softcap=args.logit_softcap,
+        rope_base=args.rope_base,
+        qk_gain_init=args.qk_gain_init,
+    ).to(device).bfloat16()
+    for module in base_model.modules():
+        if isinstance(module, CastedLinear):
+            module.float()
+    restore_low_dim_params_to_fp32(base_model)
+    compiled_model = torch.compile(base_model, dynamic=False, fullgraph=True)
+    model: nn.Module = DDP(compiled_model, device_ids=[local_rank], broadcast_buffers=False) if distributed else compiled_model
+
+    block_named_params = list(base_model.blocks.named_parameters())
+    matrix_params = [
+        p
+        for name, p in block_named_params
+        if p.ndim == 2 and not any(pattern in name for pattern in CONTROL_TENSOR_NAME_PATTERNS)
+    ]
+    scalar_params = [
+        p
+        for name, p in block_named_params
+        if p.ndim < 2 or any(pattern in name for pattern in CONTROL_TENSOR_NAME_PATTERNS)
+    ]
+    if base_model.skip_weights.numel() > 0:
+        scalar_params.append(base_model.skip_weights)
+    token_lr = args.tied_embed_lr if args.tie_embeddings else args.embed_lr
+    optimizer_tok = torch.optim.Adam(
+        [{"params": [base_model.tok_emb.weight], "lr": token_lr, "base_lr": token_lr}],
+        betas=(args.beta1, args.beta2), eps=args.adam_eps, fused=True,
+    )
+    optimizer_muon = Muon(matrix_params, lr=args.matrix_lr, momentum=args.muon_momentum, backend_steps=args.muon_backend_steps)
+    for group in optimizer_muon.param_groups:
+        group["base_lr"] = args.matrix_lr
+    optimizer_scalar = torch.optim.Adam(
+        [{"params": scalar_params, "lr": args.scalar_lr, "base_lr": args.scalar_lr}],
+        betas=(args.beta1, args.beta2), eps=args.adam_eps, fused=True,
+    )
+    optimizers: list[torch.optim.Optimizer] = [optimizer_tok, optimizer_muon, optimizer_scalar]
+    if base_model.lm_head is not None:
+        optimizer_head = torch.optim.Adam(
+            [{"params": [base_model.lm_head.weight], "lr": args.head_lr, "base_lr": args.head_lr}],
+            betas=(args.beta1, args.beta2), eps=args.adam_eps, fused=True,
+        )
+        optimizers.insert(1, optimizer_head)
+
+    n_params = sum(p.numel() for p in base_model.parameters())
+    log0(f"model_params:{n_params}")
+    log0(f"world_size:{world_size} grad_accum_steps:{grad_accum_steps}")
+    log0("sdp_backends:cudnn=False flash=True mem_efficient=False math=False")
+    log0(f"attention_mode:gqa num_heads:{args.num_heads} num_kv_heads:{args.num_kv_heads}")
+    log0(
+        f"tie_embeddings:{args.tie_embeddings} embed_lr:{token_lr} "
+        f"head_lr:{args.head_lr if base_model.lm_head is not None else 0.0} "
+        f"matrix_lr:{args.matrix_lr} scalar_lr:{args.scalar_lr}"
+    )
+    log0(
+        f"train_batch_tokens:{args.train_batch_tokens} train_seq_len:{args.train_seq_len} "
+        f"iterations:{args.iterations} warmup_steps:{args.warmup_steps} "
+        f"max_wallclock_seconds:{args.max_wallclock_seconds:.3f}"
+    )
+    log0(f"seed:{args.seed}")
+
+    # ── Data loader & model warmup ─────────────────────────────────────────────
+
+    train_loader = DistributedTokenLoader(args.train_files, rank, world_size, device)
+
+    def zero_grad_all() -> None:
+        for opt in optimizers:
+            opt.zero_grad(set_to_none=True)
+
+    max_wallclock_ms = 1000.0 * args.max_wallclock_seconds if args.max_wallclock_seconds > 0 else None
+
+    def lr_mul(step: int, elapsed_ms: float) -> float:
+        if args.warmdown_iters <= 0:
+            return 1.0
+        if max_wallclock_ms is None:
+            warmdown_start = max(args.iterations - args.warmdown_iters, 0)
+            return max((args.iterations - step) / max(args.warmdown_iters, 1), 0.0) if warmdown_start <= step < args.iterations else 1.0
+        step_ms = elapsed_ms / max(step, 1)
+        warmdown_ms = args.warmdown_iters * step_ms
+        remaining_ms = max(max_wallclock_ms - elapsed_ms, 0.0)
+        return remaining_ms / max(warmdown_ms, 1e-9) if remaining_ms <= warmdown_ms else 1.0
+
+    if args.warmup_steps > 0:
+        initial_model_state = {name: tensor.detach().cpu().clone() for name, tensor in base_model.state_dict().items()}
+        initial_optimizer_states = [copy.deepcopy(opt.state_dict()) for opt in optimizers]
+        model.train()
+        for warmup_step in range(args.warmup_steps):
+            zero_grad_all()
+            for micro_step in range(grad_accum_steps):
+                if distributed:
+                    model.require_backward_grad_sync = micro_step == grad_accum_steps - 1
+                x, y = train_loader.next_batch(args.train_batch_tokens, args.train_seq_len, grad_accum_steps)
+                with torch.autocast(device_type="cuda", dtype=torch.bfloat16, enabled=True):
+                    warmup_loss = model(x, y)
+                (warmup_loss * grad_scale).backward()
+            for opt in optimizers:
+                opt.step()
+            zero_grad_all()
+            if args.warmup_steps <= 20 or (warmup_step + 1) % 10 == 0 or warmup_step + 1 == args.warmup_steps:
+                log0(f"warmup_step:{warmup_step + 1}/{args.warmup_steps}")
+        base_model.load_state_dict(initial_model_state, strict=True)
+        for opt, state in zip(optimizers, initial_optimizer_states, strict=True):
+            opt.load_state_dict(state)
+        zero_grad_all()
+        if distributed:
+            model.require_backward_grad_sync = True
+        train_loader = DistributedTokenLoader(args.train_files, rank, world_size, device)
+
+    # ── Main training loop ────────────────────────────────────────────────────
+
+    training_time_ms = 0.0
+    stop_after_step: int | None = None
+    torch.cuda.synchronize()
+    t0 = time.perf_counter()
+
+    step = 0
+    while True:
+        last_step = step == args.iterations or (stop_after_step is not None and step >= stop_after_step)
+
+        should_validate = last_step or (args.val_loss_every > 0 and step % args.val_loss_every == 0)
+        if should_validate:
+            torch.cuda.synchronize()
+            training_time_ms += 1000.0 * (time.perf_counter() - t0)
+            val_loss, val_bpb = eval_val(
+                args, model, rank, world_size, device, grad_accum_steps,
+                val_tokens, base_bytes_lut, has_leading_space_lut, is_boundary_token_lut,
+            )
+            log0(
+                f"step:{step}/{args.iterations} val_loss:{val_loss:.4f} val_bpb:{val_bpb:.4f} "
+                f"train_time:{training_time_ms:.0f}ms step_avg:{training_time_ms / max(step, 1):.2f}ms"
+            )
+            torch.cuda.synchronize()
+            t0 = time.perf_counter()
+
+        if last_step:
+            if stop_after_step is not None and step < args.iterations:
+                log0(
+                    f"stopping_early: wallclock_cap train_time:{training_time_ms:.0f}ms "
+                    f"step:{step}/{args.iterations}"
+                )
+            break
+
+        elapsed_ms = training_time_ms + 1000.0 * (time.perf_counter() - t0)
+        scale = lr_mul(step, elapsed_ms)
+        zero_grad_all()
+        train_loss = torch.zeros((), device=device)
+        for micro_step in range(grad_accum_steps):
+            if distributed:
+                model.require_backward_grad_sync = micro_step == grad_accum_steps - 1
+            x, y = train_loader.next_batch(args.train_batch_tokens, args.train_seq_len, grad_accum_steps)
+            with torch.autocast(device_type="cuda", dtype=torch.bfloat16, enabled=True):
+                loss = model(x, y)
+            train_loss += loss.detach()
+            (loss * grad_scale).backward()
+        train_loss /= grad_accum_steps
+
+        frac = min(step / args.muon_momentum_warmup_steps, 1.0) if args.muon_momentum_warmup_steps > 0 else 1.0
+        muon_momentum = (1 - frac) * args.muon_momentum_warmup_start + frac * args.muon_momentum
+        for group in optimizer_muon.param_groups:
+            group["momentum"] = muon_momentum
+
+        for opt in optimizers:
+            for group in opt.param_groups:
+                group["lr"] = group["base_lr"] * scale
+
+        if args.grad_clip_norm > 0:
+            torch.nn.utils.clip_grad_norm_(base_model.parameters(), args.grad_clip_norm)
+        for opt in optimizers:
+            opt.step()
+        zero_grad_all()
+
+        step += 1
+        approx_training_time_ms = training_time_ms + 1000.0 * (time.perf_counter() - t0)
+        should_log_train = (
+            args.train_log_every > 0
+            and (step <= 10 or step % args.train_log_every == 0 or stop_after_step is not None)
+        )
+        if should_log_train:
+            log0(
+                f"step:{step}/{args.iterations} train_loss:{train_loss.item():.4f} "
+                f"train_time:{approx_training_time_ms:.0f}ms step_avg:{approx_training_time_ms / step:.2f}ms"
+            )
+
+        reached_cap = max_wallclock_ms is not None and approx_training_time_ms >= max_wallclock_ms
+        if distributed and max_wallclock_ms is not None:
+            reached_cap_tensor = torch.tensor(int(reached_cap), device=device)
+            dist.all_reduce(reached_cap_tensor, op=dist.ReduceOp.MAX)
+            reached_cap = bool(reached_cap_tensor.item())
+        if stop_after_step is None and reached_cap:
+            stop_after_step = step
+
+    log0(
+        f"peak memory allocated: {torch.cuda.max_memory_allocated() // 1024 // 1024} MiB "
+        f"reserved: {torch.cuda.max_memory_reserved() // 1024 // 1024} MiB"
+    )
+
+    # ── Serialization + round-trip validation ─────────────────────────────────
+
+    if master_process:
+        torch.save(base_model.state_dict(), "final_model.pt")
+        model_bytes = os.path.getsize("final_model.pt")
+        code_bytes = len(code.encode("utf-8"))
+        log0(f"Serialized model: {model_bytes} bytes")
+        log0(f"Code size: {code_bytes} bytes")
+        log0(f"Total submission size: {model_bytes + code_bytes} bytes")
+
+    quant_obj, quant_stats = quantize_state_dict_int8(base_model.state_dict())
+    quant_buf = io.BytesIO()
+    torch.save(quant_obj, quant_buf)
+    quant_raw = quant_buf.getvalue()
+    quant_blob = zlib.compress(quant_raw, level=9)
+    quant_raw_bytes = len(quant_raw)
+    if master_process:
+        with open("final_model.int8.ptz", "wb") as f:
+            f.write(quant_blob)
+        quant_file_bytes = os.path.getsize("final_model.int8.ptz")
+        code_bytes = len(code.encode("utf-8"))
+        ratio = quant_stats["baseline_tensor_bytes"] / max(quant_stats["int8_payload_bytes"], 1)
+        log0(
+            f"Serialized model int8+zlib: {quant_file_bytes} bytes "
+            f"(payload:{quant_stats['int8_payload_bytes']} raw_torch:{quant_raw_bytes} payload_ratio:{ratio:.2f}x)"
+        )
+        log0(f"Total submission size int8+zlib: {quant_file_bytes + code_bytes} bytes")
+
+    if distributed:
+        dist.barrier()
+    with open("final_model.int8.ptz", "rb") as f:
+        quant_blob_disk = f.read()
+    quant_state = torch.load(io.BytesIO(zlib.decompress(quant_blob_disk)), map_location="cpu")
+    base_model.load_state_dict(dequantize_state_dict_int8(quant_state), strict=True)
+    torch.cuda.synchronize()
+    t_qeval = time.perf_counter()
+    q_val_loss, q_val_bpb = eval_val(
+        args, model, rank, world_size, device, grad_accum_steps,
+        val_tokens, base_bytes_lut, has_leading_space_lut, is_boundary_token_lut,
+    )
+    torch.cuda.synchronize()
+    log0(
+        f"final_int8_zlib_roundtrip val_loss:{q_val_loss:.4f} val_bpb:{q_val_bpb:.4f} "
+        f"eval_time:{1000.0 * (time.perf_counter() - t_qeval):.0f}ms"
+    )
+    log0(f"final_int8_zlib_roundtrip_exact val_loss:{q_val_loss:.8f} val_bpb:{q_val_bpb:.8f}")
+
+    if distributed:
+        dist.destroy_process_group()
+
+
+if __name__ == "__main__":
+    main()