Non-record: Training data ordering by model perplexity (-0.0033 BPB)

Case study: reordering training shards by model difficulty (hardest
first) gives -0.0033 BPB improvement over sequential ordering. Zero
architecture changes, zero compute cost, ten lines of code.

Key finding: token-level statistics (KL divergence) find 0.0009 range
across shards. Model perplexity finds 0.0475 range -- 100x more
variation. The two metrics are uncorrelated (r = -0.056).

3-seed validated on PR #549 (merged #1):
  Seed 1337: 1.1217 -> 1.1183 (-0.0034)
  Seed 42:   1.1222 -> 1.1181 (-0.0041)
  Seed 2025: 1.1221 -> 1.1198 (-0.0023)
  Mean:      1.1220 -> 1.1187 (-0.0033)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: abaybektursun

records/track_non_record_16mb/2026-03-24_ShardOrdering_CaseStudy/README.md

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+# You're Training on 57% of Your Data. Does It Matter Which 57%?
+
+**Non-record submission: a case study on training data ordering.**
+
+Everyone in this competition trains sequentially through the shards. Nobody questions the order. We did — and found a free **-0.0033 BPB** improvement by reordering shards based on model perplexity. Zero architecture changes, zero hyperparameter tuning, ten lines of code.
+
+## The Setup
+
+At 83ms/step we get ~7,200 steps in 600s. That's 5.66B tokens out of 10B — **57% of the dataset**. Shards 0 through ~45 get seen. Shards 46-79 never do.
+
+## Token Statistics Say It Doesn't Matter
+
+We computed KL(val || shard) for all 80 training shards. Every shard has essentially the same token distribution. Range: 0.0009. Translates to ~0.00005 BPB. Dead end.
+
+![Token frequencies vs model perplexity](figures/fig1_kl_vs_perplexity.png)
+
+Left panel. All shards look identical by token frequency.
+
+## The Model Disagrees
+
+Trained a model 500 steps on one shard, then scored all 80 shards by cross-entropy loss. Right panel above. Range: **0.0475** — 100× larger than the KL signal. The shards are NOT all the same. Token statistics just can't see the difference.
+
+As expected — KL counts tokens, the model scores sequences. But the magnitude of the gap is what matters: the model finds **100× more variation** than token statistics do.
+
+![KL rank vs perplexity rank](figures/fig4_the_insight.png)
+
+**r = -0.056.** The two metrics are uncorrelated. The shard most similar to val by token frequency is middling by model difficulty.
+
+## Where the Hard Shards Are
+
+The difficulty is about content, not position. Hard and easy shards are scattered randomly across the dataset.
+
+![Shard difficulty heatmap](figures/fig2_shard_heatmap.png)
+
+Shard 44 (hardest, rank #1) sits next to shard 43 (rank #48). Sequential ordering — the default in every training framework — isn't optimized for anything except simplicity.
+
+![Sequential vs optimal ordering](figures/fig3_sequential_vs_optimal.png)
+
+## Results: 3-Seed Validated
+
+Reran our merged #1 submission (PR #549) with shards reordered hardest-first. Same code, same hyperparameters, same compute budget.
+
+| Seed | Sequential (PR #549) | Hardest-first | Delta |
+|------|---------------------|--------------|-------|
+| 1337 | 1.1217 | **1.1183** | **-0.0034** |
+| 42 | 1.1222 | **1.1181** | **-0.0041** |
+| 2025 | 1.1221 | **1.1198** | **-0.0023** |
+| **Mean** | **1.1220** | **1.1187** | **-0.0033** |
+
+Every seed improves. Mean improvement: **-0.0033 BPB.**
+
+![Three-seed comparison](figures/fig5_three_seed_comparison.png)
+
+![Improvement consistency and cost](figures/fig6_delta_consistency.png)
+
+For context: our last three PRs each took days of architecture and quantization work to gain 0.001-0.003 BPB. This took ten lines of code.
+
+## The Change
+
+```python
+class TokenStream:
+    def __init__(self, pattern: str):
+        self.files = [Path(p) for p in sorted(glob.glob(pattern))]
+        # NEW: reorder shards by model difficulty (hardest first)
+        shard_order = os.environ.get("SHARD_ORDER", "")
+        if shard_order:
+            order = [int(x) for x in shard_order.split(",")]
+            reordered = [self.files[i] for i in order if i < len(self.files)]
+            remaining = [f for i, f in enumerate(self.files) if i not in set(order)]
+            self.files = reordered + remaining
+```
+
+```bash
+SHARD_ORDER=44,63,65,42,18,67,30,69,61,3,13,19,50,49,56,45,73,79,57,32,\
+28,68,66,34,46,38,17,77,0,14,26,74,59,62,41,9,58,22,78,4,48,8,12,27,75,\
+36,16,43,52,15,33,47,25,55,54,23,37,51,31,21,60,1,20,72,24,53,39,35,71,\
+76,40,5,10,2,7,6,70,11,64,29
+```
+
+## Method: How We Ranked Shards
+
+1. Train a 6-layer, 512d model for 500 steps on shard 0 (single GPU, ~40 seconds)
+2. Score all 80 shards by cross-entropy loss with this partially-trained model
+3. Sort shards by loss descending (hardest first)
+4. Pass the ordering via `SHARD_ORDER` environment variable
+
+The ranking model is deliberately small and undertrained — it captures which shards have patterns the model hasn't learned yet. A fully-trained model would rank differently (everything is "easy" by then).
+
+## Open Questions
+
+- **Adaptive curriculum**: Re-rank shards every 1,000 steps as the model learns. The optimal ordering probably changes during training.
+- **Anti-curriculum**: We haven't tested easiest-first. It might help build foundations before tackling hard patterns. *(Experiment running.)*
+- **Transfer across architectures**: Our ranking was done with a 6-layer model. Does it transfer to 11-layer? To different hyperparameters?
+- **Interaction with SWA/EMA**: Does the ordering effect survive weight averaging?
+
+## Credits
+
+- Original idea (train on similar data): Lucas Fievet
+- Base model: [PR #549](https://github.com/openai/parameter-golf/pull/549) by @abaybektursun (merged #1)
+- Analysis and implementation: @abaybektursun

records/track_non_record_16mb/2026-03-24_ShardOrdering_CaseStudy/figures/fig1_perplexity_ranking.png

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+"""
+Score each training shard by model perplexity using a simple approach.
+
+1. Score all shards with random model (inherent difficulty baseline)
+2. Train 500 steps on shard 0
+3. Score all shards again (what's still hard after partial training)
+4. Rank by remaining loss
+
+Usage (single GPU is fine):
+    python3 analysis/score_shards_simple.py --data-dir ./data/datasets/fineweb10B_sp1024
+"""
+
+import argparse
+import glob
+import math
+import time
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from pathlib import Path
+
+
+class MiniGPT(nn.Module):
+    """Minimal GPT for shard scoring. Same architecture shape as competition model."""
+    def __init__(self, vocab=1024, dim=512, layers=6, heads=8):
+        super().__init__()
+        self.tok_emb = nn.Embedding(vocab, dim)
+        self.blocks = nn.ModuleList([
+            nn.TransformerEncoderLayer(d_model=dim, nhead=heads, dim_feedforward=dim*3,
+                                       batch_first=True, norm_first=True, dropout=0.0)
+            for _ in range(layers)
+        ])
+        self.norm = nn.LayerNorm(dim)
+        self.head = nn.Linear(dim, vocab, bias=False)
+        self.head.weight = self.tok_emb.weight  # tie embeddings
+
+    def forward(self, x):
+        B, T = x.shape
+        h = self.tok_emb(x)
+        mask = nn.Transformer.generate_square_subsequent_mask(T, device=x.device)
+        for block in self.blocks:
+            h = block(h, src_mask=mask, is_causal=True)
+        return self.head(self.norm(h))
+
+
+def load_shard(path, vocab_size=1024):
+    tokens = np.fromfile(path, dtype=np.uint16).astype(np.int64)
+    tokens = np.clip(tokens, 0, vocab_size - 1)
+    return torch.from_numpy(tokens)
+
+
+def score_shard(model, tokens, device, seq_len=1024, max_batches=50, batch_size=16):
+    model.eval()
+    n_seqs = len(tokens) // (seq_len + 1)
+    if n_seqs == 0:
+        return float('inf')
+
+    step = max(1, n_seqs // (max_batches * batch_size))
+    total_loss = 0.0
+    total_tokens = 0
+
+    with torch.no_grad(), torch.autocast(device_type="cuda", dtype=torch.bfloat16):
+        for bi in range(0, min(n_seqs, max_batches * batch_size), batch_size):
+            batch_starts = [((bi + b) * step) * (seq_len + 1) for b in range(batch_size)
+                           if (bi + b) * step < n_seqs]
+            if not batch_starts:
+                break
+            x = torch.stack([tokens[s:s+seq_len].to(device) for s in batch_starts])
+            y = torch.stack([tokens[s+1:s+seq_len+1].to(device) for s in batch_starts])
+            logits = model(x)
+            loss = F.cross_entropy(logits.reshape(-1, logits.size(-1)).float(),
+                                   y.reshape(-1), reduction="sum")
+            total_loss += loss.item()
+            total_tokens += y.numel()
+
+    return total_loss / max(total_tokens, 1)
+
+
+def train_steps(model, tokens, device, steps=500, seq_len=1024, batch_size=16, lr=0.001):
+    model.train()
+    optimizer = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=0.01)
+    n_seqs = len(tokens) // (seq_len + 1)
+
+    for step in range(steps):
+        idx = (step * batch_size) % n_seqs
+        batch_starts = [(idx + b) * (seq_len + 1) for b in range(batch_size) if idx + b < n_seqs]
+        if not batch_starts:
+            continue
+        x = torch.stack([tokens[s:s+seq_len].to(device) for s in batch_starts])
+        y = torch.stack([tokens[s+1:s+seq_len+1].to(device) for s in batch_starts])
+
+        with torch.autocast(device_type="cuda", dtype=torch.bfloat16):
+            logits = model(x)
+            loss = F.cross_entropy(logits.reshape(-1, logits.size(-1)).float(), y.reshape(-1))
+
+        optimizer.zero_grad()
+        loss.backward()
+        optimizer.step()
+
+        if (step + 1) % 100 == 0:
+            print(f"  Train step {step+1}/{steps}, loss: {loss.item():.4f}")
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--data-dir", required=True)
+    parser.add_argument("--train-steps", type=int, default=500)
+    parser.add_argument("--device", default="cuda:0")
+    args = parser.parse_args()
+
+    device = torch.device(args.device)
+    train_files = sorted(glob.glob(str(Path(args.data_dir) / "fineweb_train_*.bin")))
+    val_files = sorted(glob.glob(str(Path(args.data_dir) / "fineweb_val_*.bin")))
+    print(f"Found {len(train_files)} train shards, {len(val_files)} val shards")
+
+    model = MiniGPT(vocab=1024, dim=512, layers=6, heads=8).to(device)
+    print(f"Model params: {sum(p.numel() for p in model.parameters()):,}")
+
+    # Phase 1: Score with random model
+    print(f"\n{'='*60}")
+    print("PHASE 1: Random model scoring")
+    print(f"{'='*60}")
+    random_scores = {}
+    for i, f in enumerate(train_files):
+        tokens = load_shard(f)
+        loss = score_shard(model, tokens, device)
+        random_scores[i] = loss
+        if (i + 1) % 10 == 0 or i == len(train_files) - 1:
+            print(f"  [{i+1}/{len(train_files)}] shard {i}: loss={loss:.4f}")
+
+    val_tokens = torch.cat([load_shard(f) for f in val_files])
+    val_random = score_shard(model, val_tokens, device)
+    print(f"  Val loss (random): {val_random:.4f}")
+
+    # Phase 2: Train on shard 0
+    print(f"\n{'='*60}")
+    print(f"PHASE 2: Training {args.train_steps} steps on shard 0")
+    print(f"{'='*60}")
+    train_tokens = load_shard(train_files[0])
+    train_steps(model, train_tokens, device, steps=args.train_steps)
+
+    # Phase 3: Score with trained model
+    print(f"\n{'='*60}")
+    print("PHASE 3: Trained model scoring")
+    print(f"{'='*60}")
+    trained_scores = {}
+    for i, f in enumerate(train_files):
+        tokens = load_shard(f)
+        loss = score_shard(model, tokens, device)
+        trained_scores[i] = loss
+        if (i + 1) % 10 == 0 or i == len(train_files) - 1:
+            print(f"  [{i+1}/{len(train_files)}] shard {i}: loss={loss:.4f}")
+
+    val_trained = score_shard(model, val_tokens, device)
+    print(f"  Val loss (trained): {val_trained:.4f}")
+
+    # Results
+    print(f"\n{'='*60}")
+    print("RESULTS: Shard ranking by remaining loss (highest = most to learn)")
+    print(f"{'='*60}")
+    print(f"{'Rank':>4} {'Shard':>6} {'Random':>10} {'Trained':>10} {'Remaining':>10} {'Learned':>10}")
+    print("-" * 60)
+
+    shards = [(i, random_scores[i], trained_scores[i],
+               trained_scores[i], random_scores[i] - trained_scores[i])
+              for i in range(len(train_files))]
+    shards.sort(key=lambda x: -x[3])  # sort by remaining loss descending
+
+    for rank, (idx, rand, trained, remaining, learned) in enumerate(shards):
+        print(f"{rank+1:>4} {idx:>6} {rand:>10.4f} {trained:>10.4f} {remaining:>10.4f} {learned:>10.4f}")
+
+    # Key metrics
+    losses = [s[3] for s in shards]
+    loss_range = max(losses) - min(losses)
+    loss_std = np.std(losses)
+
+    print(f"\n{'='*60}")
+    print("SUMMARY")
+    print(f"{'='*60}")
+    print(f"Remaining loss range: {min(losses):.4f} — {max(losses):.4f} (range: {loss_range:.4f})")
+    print(f"Remaining loss std:   {loss_std:.4f}")
+    print(f"Val loss:             {val_trained:.4f}")
+    print(f"")
+    if loss_range < 0.01:
+        print("VERDICT: Small range — shards are similar even at model-perplexity level.")
+        print("Shard reordering unlikely to help significantly.")
+    else:
+        print(f"VERDICT: Range of {loss_range:.4f} — meaningful variation!")
+        print("Shard reordering could improve BPB.")
+
+    recommended = [s[0] for s in shards]  # already sorted by remaining loss desc
+    print(f"\nRecommended order (hardest first): {recommended[:20]}...")
+    print(f"Skip (easiest):                    {recommended[-10:]}")
+
+
+if __name__ == "__main__":
+    main()

records/track_non_record_16mb/2026-03-24_ShardOrdering_CaseStudy/figures/fig2_shard_heatmap.png

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+{
+  "name": "Case Study: Training Data Ordering by Model Perplexity",
+  "val_bpb": 1.1187,
+  "bytes_total": 15921633,
+  "blurb": "Non-record case study: reordering training shards by model perplexity (hardest first) gives -0.0033 BPB for free. Token-level statistics (KL divergence) miss 100x of the variation that model-level scoring reveals. 3-seed validated. Ten lines of code, zero compute cost.",
+  "author": "abaybektursun",
+  "github_id": "abaybektursun",
+  "date": "2026-03-24"
+}