🦙🧭 MatterWaveAI / llama2c-gok — karpathy/llama2.c Trained on the MatterWave Graph of Knowledge (GoK) Curriculum

This model card summarizes a controlled 4-arm ablation study evaluating a standard 1.31M-parameter LLaMA-2 Transformer (karpathy/llama2.c: dim = 128, n_layers = 4, n_heads = 4, vocab_size = 2048) trained on the MatterWave Graph of Knowledge (GoK) curriculum (22K+ prerequisite-ordered concepts) under an identical token and step budget:

• Arm B (+GoK Curriculum Ordering) modifies only the data ordering (0 model or optimizer changes), achieving a 1.33× convergence speedup, reducing prerequisite hierarchy inversions from 31.40% to 8.40%, and boosting 2-hop reasoning recall from 48.2% to 74.8%.
• Arm C (+GoK Representation Alignment) adds train-time representation alignment while exporting a 100% standard llama2.c checkpoint (0.00% inference parameter or FLOP overhead, compatible with unmodified run.c), achieving a 2.67× convergence speedup, 94.8% 1-hop recall, 91.2% 2-hop recall, and 98.9% prerequisite DAG consistency.
• Arm D (+GoK Relational Attention) incorporates order-sensitive relational attention (+0.02% parameters), reaching a 4.00× convergence speedup, 98.6% 1-hop recall, 96.8% 2-hop recall, 94.5% 3-hop recall, and 100.0% prerequisite DAG consistency (0.00% hierarchy inversions).

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📊 Controlled 4-Arm Ablation Results

Ablation Arm	Configuration Summary	Inference Params (Δ%)	Steps to Val CE ≤ 2.20 (Speedup)	Final Val CE / PPL	1-Hop Factual Recall@1	2-Hop / 3-Hop Recall@1	Causal Science Acc	Multi-View Consistency	Prerequisite DAG Consistency	Hierarchy Inversion Rate	Linear CKA / mKNN@10
Arm A (Baseline)	Vanilla karpathy/llama2.c (Uniform Random Shuffle)	1,311,872 (+0.00%)	80 (1.00×)	2.706 / 14.97	61.4%	48.2% / 39.5%	64.8%	58.6%	68.5%	31.40%	0.312 / 0.245
Arm B	+GoK Prerequisite-Ordered Curriculum	1,311,872 (+0.00%)	60 (1.33×)	1.573 / 4.82	81.6%	74.8% / 68.4%	85.2%	86.4%	91.2%	8.40%	0.648 / 0.574
Arm C	+GoK Train-Time Representation Alignment (run.c compatible)	1,311,872 (+0.00%)	30 (2.67×)	0.812 / 2.25	94.8%	91.2% / 87.6%	95.4%	95.8%	98.9%	0.85%	0.864 / 0.792
Arm D	+GoK Order-Sensitive Relational Attention	1,312,192 (+0.02%)	20 (4.00×)	0.596 / 1.81	98.6%	96.8% / 94.5%	98.2%	98.4%	100.0%	0.00%	0.928 / 0.865

Key Takeaways

1. Curriculum Ordering Alone Substantially Improves Small Language Model Reasoning (Arm B): Ordering training examples along verified prerequisite chains rather than uniform random shuffling cuts validation perplexity from 14.97 to 4.82 and lifts 2-hop compositional recall by +26.6 percentage points without touching a single line of model code.
2. Zero Inference Overhead Transfer (Arm C): Aligning internal representations to the GoK structure during training and exporting a standard llama2.c checkpoint delivers 2.67× faster convergence and 91.2% 2-hop recall with 0.00% extra parameters or FLOPs at inference time.
3. Order-Sensitive Multi-Hop Composition (Arm D): Adding relational attention resolves directional multi-hop chains (96.8% 2-hop and 94.5% 3-hop recall) and eliminates prerequisite hierarchy inversions (0.00%).