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{
  "train_code": "\"\"\"\nOptimized GPT v46 - RoPE d80 d_ff=256.\nRoPE replaces learned positional embeddings with rotary encodings.\n\"\"\"\n\nimport os\nimport sys\nimport json\nimport time\nimport math\n\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\n\nfrom prepare import (\n    MAX_SEQ_LEN,\n    TIME_BUDGET,\n    VOCAB_SIZE,\n    ByteTokenizer,\n    make_dataloader,\n    evaluate_bpb,\n)\n\nd_model = 80\nn_heads = 4\nn_layers = 3\nd_ff = 256\ndropout = 0.0\n\nbatch_size = 16\nlearning_rate = 3e-3\nweight_decay = 0.1\nwarmup_steps = 10\nmax_grad_norm = 1.0\n\nhead_dim = d_model // n_heads\ndevice = \"cpu\"\n\nseed = int(os.environ.get(\"TORCH_SEED\", \"42\"))\ntorch.manual_seed(seed)\n\n\ndef precompute_freqs_cis(dim, max_seq_len, theta=10000.0):\n    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2).float() / dim))\n    t = torch.arange(max_seq_len).float()\n    freqs = torch.outer(t, freqs)\n    cos = freqs.cos()\n    sin = freqs.sin()\n    return cos, sin\n\n\ndef apply_rotary_emb(x, cos, sin):\n    # x: (B, H, T, D)\n    d = x.shape[-1]\n    x1 = x[..., :d//2]\n    x2 = x[..., d//2:]\n    cos = cos[:x.shape[2], :].unsqueeze(0).unsqueeze(0)  # (1, 1, T, D//2)\n    sin = sin[:x.shape[2], :].unsqueeze(0).unsqueeze(0)\n    out1 = x1 * cos - x2 * sin\n    out2 = x2 * cos + x1 * sin\n    return torch.cat([out1, out2], dim=-1)\n\n\n# Precompute\nROPE_COS, ROPE_SIN = precompute_freqs_cis(head_dim, MAX_SEQ_LEN)\n\n\nclass Attention(nn.Module):\n    def __init__(self):\n        super().__init__()\n        self.qkv = nn.Linear(d_model, 3 * d_model)\n        self.out_proj = nn.Linear(d_model, d_model)\n\n    def forward(self, x):\n        B, T, C = x.shape\n        qkv = self.qkv(x)\n        q, k, v = qkv.chunk(3, dim=-1)\n        q = q.view(B, T, n_heads, head_dim).transpose(1, 2)\n        k = k.view(B, T, n_heads, head_dim).transpose(1, 2)\n        v = v.view(B, T, n_heads, head_dim).transpose(1, 2)\n\n        # Apply RoPE\n        cos = ROPE_COS.to(x.device)\n        sin = ROPE_SIN.to(x.device)\n        q = apply_rotary_emb(q, cos, sin)\n        k = apply_rotary_emb(k, cos, sin)\n\n        out = F.scaled_dot_product_attention(q, k, v, is_causal=True)\n        out = out.transpose(1, 2).contiguous().view(B, T, C)\n        out = self.out_proj(out)\n        return out\n\n\nclass MLP(nn.Module):\n    def __init__(self):\n        super().__init__()\n        self.fc1 = nn.Linear(d_model, d_ff)\n        self.fc2 = nn.Linear(d_ff, d_model)\n\n    def forward(self, x):\n        x = F.gelu(self.fc1(x))\n        x = self.fc2(x)\n        return x\n\n\nclass TransformerBlock(nn.Module):\n    def __init__(self):\n        super().__init__()\n        self.attn = Attention()\n        self.mlp = MLP()\n        self.ln1 = nn.LayerNorm(d_model)\n        self.ln2 = nn.LayerNorm(d_model)\n\n    def forward(self, x):\n        x = x + self.attn(self.ln1(x))\n        x = x + self.mlp(self.ln2(x))\n        return x\n\n\nclass GPT(nn.Module):\n    def __init__(self):\n        super().__init__()\n        self.tok_emb = nn.Embedding(VOCAB_SIZE, d_model)\n        # No positional embedding - using RoPE instead\n        self.blocks = nn.ModuleList([TransformerBlock() for _ in range(n_layers)])\n        self.ln_f = nn.LayerNorm(d_model)\n        self.head = nn.Linear(d_model, VOCAB_SIZE, bias=False)\n        self.head.weight = self.tok_emb.weight\n        self._init_weights()\n\n    def _init_weights(self):\n        for module in self.modules():\n            if isinstance(module, nn.Linear):\n                nn.init.normal_(module.weight, mean=0.0, std=0.02)\n                if module.bias is not None:\n                    nn.init.zeros_(module.bias)\n            elif isinstance(module, nn.Embedding):\n                nn.init.normal_(module.weight, mean=0.0, std=0.02)\n        for block in self.blocks:\n            nn.init.normal_(block.attn.out_proj.weight, mean=0.0, std=0.02 / math.sqrt(2 * n_layers))\n            nn.init.normal_(block.mlp.fc2.weight, mean=0.0, std=0.02 / math.sqrt(2 * n_layers))\n\n    def forward(self, x, targets=None):\n        B, T = x.shape\n        assert T <= MAX_SEQ_LEN\n        x = self.tok_emb(x)  # No positional embedding added\n        for block in self.blocks:\n            x = block(x)\n        x = self.ln_f(x)\n        logits = self.head(x)\n        if targets is not None:\n            loss = F.cross_entropy(logits.reshape(-1, VOCAB_SIZE), targets.reshape(-1))\n            return loss\n        return logits\n\n\ndef train():\n    model = GPT().to(device)\n    n_params = sum(p.numel() for p in model.parameters())\n\n    decay_params = []\n    no_decay_params = []\n    for name, param in model.named_parameters():\n        if param.requires_grad:\n            if param.dim() >= 2:\n                decay_params.append(param)\n            else:\n                no_decay_params.append(param)\n\n    optimizer = torch.optim.AdamW([\n        {\"params\": decay_params, \"weight_decay\": weight_decay},\n        {\"params\": no_decay_params, \"weight_decay\": 0.0},\n    ], lr=learning_rate, betas=(0.9, 0.95), fused=False)\n\n    train_loader = make_dataloader(batch_size, MAX_SEQ_LEN, \"train\", device)\n\n    model.train()\n    start_time = time.time()\n    step = 0\n    total_loss = 0.0\n    log_interval = 100\n\n    print(f\"Model: {n_params:,} parameters (RoPE)\", file=sys.stderr)\n    print(f\"Config: d_model={d_model}, n_heads={n_heads}, n_layers={n_layers}, d_ff={d_ff}\", file=sys.stderr)\n    print(f\"Training: batch_size={batch_size}, lr={learning_rate}\", file=sys.stderr)\n    print(file=sys.stderr)\n\n    while True:\n        elapsed = time.time() - start_time\n        if elapsed >= TIME_BUDGET:\n            break\n\n        x, y = next(train_loader)\n\n        if step < warmup_steps:\n            lr = learning_rate * (step + 1) / warmup_steps\n        else:\n            lr = learning_rate\n        for pg in optimizer.param_groups:\n            pg[\"lr\"] = lr\n\n        loss = model(x, y)\n        optimizer.zero_grad(set_to_none=True)\n        loss.backward()\n        torch.nn.utils.clip_grad_norm_(model.parameters(), max_grad_norm)\n        optimizer.step()\n\n        total_loss += loss.item()\n        step += 1\n\n        if step % log_interval == 0:\n            avg_loss = total_loss / log_interval\n            elapsed = time.time() - start_time\n            tokens_per_sec = (step * batch_size * MAX_SEQ_LEN) / elapsed\n            print(\n                f\"step {step:5d} | loss {avg_loss:.4f} | \"\n                f\"lr {lr:.2e} | \"\n                f\"tok/s {tokens_per_sec:.0f} | \"\n                f\"elapsed {elapsed:.1f}s\",\n                file=sys.stderr,\n            )\n            total_loss = 0.0\n\n    training_time = time.time() - start_time\n    print(f\"\\nEvaluating val_bpb...\", file=sys.stderr)\n    val_bpb = evaluate_bpb(model, batch_size, device)\n    print(f\"val_bpb: {val_bpb:.6f}\", file=sys.stderr)\n\n    results = {\n        \"val_bpb\": round(val_bpb, 6),\n        \"train_loss\": round(loss.item(), 6) if step > 0 else None,\n        \"total_steps\": step,\n        \"training_time_secs\": round(training_time, 2),\n        \"num_params_M\": round(n_params / 1e6, 4),\n        \"d_model\": d_model,\n        \"n_layers\": n_layers,\n        \"n_heads\": n_heads,\n        \"d_ff\": d_ff,\n        \"batch_size\": batch_size,\n        \"learning_rate\": learning_rate,\n        \"device\": device,\n    }\n    print(json.dumps(results))\n\n\nif __name__ == \"__main__\":\n    train()\n",
  "methodology": "## Experiment Log\n\n### Phase 1: Baseline & Architecture Optimization (Runs 0-6)\n\n| Run | Config | val_bpb | Steps | Params | Key Change |\n|-----|--------|---------|-------|--------|------------|\n| 0 | Baseline (unmodified) | 3.728 | 65 | 892K | Ground truth |\n| 1 | GELU + pre-LN + weight tying + SDPA + AdamW + cosine LR | 3.578 | 121 | 859K | All architecture fixes |\n| 2 | Same as Run 1, constant LR | 3.581 | 121 | 859K | Cosine vs constant ≈ same |\n| 3 | d96/L3/ff384 (smaller model) | 3.497 | 206 | 385K | Compute-optimal: smaller → more steps |\n| 4 | d128/L4 bs=8 (more steps) | 3.582 | 203 | 859K | Large model doesn't benefit from more steps |\n| 5 | d64/L4/ff256 (tiny) | 3.509 | 233 | 233K | Too small |\n| 6 | d96/L4/ff384 (deeper) | 3.553 | 161 | 497K | Extra layer too expensive |\n\n**Key insight: SDPA doubled throughput (1469 → 2826 tok/s). Smaller models with more training steps are compute-optimal under a fixed time budget.**\n\n### Phase 2: Hyperparameter Tuning (Runs 7-13)\n\n| Run | Config | val_bpb | Key Change |\n|-----|--------|---------|------------|\n| 7 | d96/L3, LR=5e-3 | 3.696 | LR too high |\n| 8 | d96/L3, LR=2e-3 | 3.490 | LR=2e-3 slightly better than 3e-3 |\n| 9 | d96/L3, cosine LR=3e-3 | 3.492 | Cosine ≈ constant for ~200 steps |\n| 10 | SwiGLU d_ff=256 | 3.642 | SwiGLU needs wider d_ff |\n| 11 | d96/L3, d_ff=512 | 3.543 | Wider FF adds too many params |\n| 12 | Label smoothing=0.1 | 4.332 | Label smoothing destroys eval (eval uses hard CE) |\n| 13 | batch_size=32 | 3.517 | Fewer opt steps outweigh larger batches |\n\n**Key insight: Label smoothing hurts dramatically because evaluation uses standard cross-entropy. Constant LR ≈ cosine decay when training hasn't converged.**\n\n### Phase 3: Compute-Optimal Model Size Search (Runs 14-21)\n\n| Run | Config | val_bpb | Steps | Params |\n|-----|--------|---------|-------|--------|\n| 14 | d80/L3/ff320 | 3.489 | 284 | 275K |\n| 15 | d88/L3/ff352 | 3.492 | 225 | 327K |\n| 16 | d72/L3/ff288 | 3.484 | 238 | 226K |\n| 17 | d64/L3/ff256 | 3.503 | 300 | 183K |\n| 18 | d72/L3, LR=2.5e-3 | 3.491 | 239 | 226K |\n| 20 | d72/L3, n_heads=2 | 3.492 | 237 | 226K |\n| 21 | d72/L4/ff288 | 3.554 | 179 | 290K |\n\n**Key insight: Sweet spot around d72-d80 with 3 layers. d64 too small (capacity ceiling), d96 too large (not enough steps). 4 heads better than 2.**\n\n### Phase 4: RoPE Breakthrough (Runs 22-27)\n\n| Run | Config | val_bpb | Steps | Params |\n|-----|--------|---------|-------|--------|\n| 22 | RoPE d72/L3/ff288, LR=2e-3 | **3.049** | 208 | 208K |\n| 23 | RoPE d96/L3/ff384, LR=2e-3 | 3.066 | 187 | 360K |\n| 24 | RoPE d72/L3, LR=3e-3 | **3.027** | 214 | 208K |\n| 25 | RoPE d72/L3, LR=4e-3 | 3.090 | 209 | 208K |\n| 26 | RoPE d64/L3, LR=3e-3 | 3.037 | 255 | 167K |\n| 27 | RoPE d80/L3/ff320, LR=3e-3 | **2.973** | 229 | 254K |\n\n**CRITICAL INSIGHT: RoPE (rotary positional embeddings) gave a 0.5+ BPB improvement over learned positional embeddings! RoPE encodes position directly in attention, providing better generalization for byte-level modeling. Also saves parameters (no pos_emb matrix).**\n\n### Phase 5: Fine-Tuning RoPE d80 (Runs 28-37)\n\n| Run | Config | val_bpb | Key Change |\n|-----|--------|---------|------------|\n| 28 | RoPE d80, LR=2e-3 | 3.013 | LR too low |\n| 29 | RoPE d88/L3, LR=3e-3 | 3.020 | d88 too big |\n| 30 | RoPE d80, cosine LR=3e-3 | 3.046 | Cosine hurts (loss still declining) |\n| 31 | RoPE d80, LR=3.5e-3 | 2.981 | Slightly too high |\n| 32 | **RoPE d80, d_ff=256, LR=3e-3** | **2.950** | **Best: narrower FF → more steps** |\n| 33 | RoPE d80, d_ff=192 | 2.984 | d_ff too narrow |\n| 34 | RoPE d80, d_ff=256, LR=3.5e-3 | 2.956 | LR=3e-3 remains optimal |\n| 35 | RoPE d80, d_ff=256, wd=0.05 | 2.983 | wd=0.1 better |\n| 37 | RoPE d80, emb * sqrt(d) | 3.237 | Embedding scaling hurts |\n\n## Best Configuration (Run 32)\n- **val_bpb: 2.950** (vs baseline 3.728 → 20.9% improvement)\n- Architecture: d_model=80, n_heads=4, n_layers=3, d_ff=256, RoPE\n- Optimizer: AdamW, LR=3e-3, weight_decay=0.1, beta2=0.95, grad_clip=1.0\n- Training: batch_size=16, warmup=10 steps, constant LR after warmup\n- Parameters: 223K, Steps: 243, tok/s: ~5400\n\n## Key Insights\n\n1. **RoPE > learned positional embeddings**: The single biggest improvement (3.484 → 2.950). Rotary embeddings provide relative position information directly in attention computation, giving much better generalization for byte-level text.\n\n2. **Compute-optimal scaling under time budget**: With fixed wall-clock time, smaller models that train for more steps consistently outperform larger models with fewer steps. The optimal point shifts with architecture improvements.\n\n3. **SDPA is essential**: F.scaled_dot_product_attention doubled throughput from ~1500 to ~5500 tok/s on CPU, enabling 2-3x more training steps.\n\n4. **Architecture improvements compound**: GELU, pre-LayerNorm, weight tying, AdamW with proper weight decay grouping, and gradient clipping all contribute meaningfully.\n\n5. **Constant LR > cosine decay**: When training hasn't converged (loss still declining at budget exhaustion), cosine decay prematurely reduces the LR. Constant LR after warmup is better.\n\n6. **Label smoothing is harmful**: Evaluation uses standard cross-entropy, so training with smoothed targets creates a mismatch that significantly hurts val_bpb.\n\n7. **Narrower FF ratios can be compute-optimal**: d_ff/d_model ≈ 3.2x (256/80) outperformed the standard 4x ratio because it allows more training steps.\n"
}