Even Heads Fix Odd Errors: Mechanistic Discovery and Surgical Repair in Transformer Attention

or

The Surgeon's Dilemma: A Mechanistic Case Study

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Abstract

We present a mechanistic case study of a format-dependent reasoning failure in
Llama-3.1-8B-Instruct, where the model incorrectly judges "9.11" as larger than "9.8"
in chat or Q\&A formats, but answers correctly in simple format.

Through systematic intervention, we discover transformers implement even/odd
attention head specialization: even indexed heads handle numerical comparison, 
while odd heads serve incompatible functions. The bug requires exactly 8 even 
heads at Layer 10 for perfect repair. Any combination of 8+ even heads succeeds, 
while 7 or fewer completely fails, revealing sharp computational thresholds 
with perfect redundancy among the 16 even heads. 

SAE analysis reveals the mechanism: format representations separate 
(10\% feature overlap at Layer 7), then re-entangle with different 
weightings (80\% feature overlap at Layer 10), with specific features 
showing 1.5× amplification in failing formats. We achieve perfect 
repair using only 25\% of attention heads and identify a 60\% pattern 
replacement threshold, demonstrating that apparent full-module requirements 
hide sophisticated substructure with implications for interpretability and 
efficiency. 

Key Findings

🔬 Core Discovery

• Even/odd attention head specialization: Transformers systematically organize computation by head index parity - even heads (0,2,4,...,30) handle numerical comparison while odd heads (1,3,5,...,31) serve incompatible functions

🎯 Surgical Repair

• Perfect bug fix achieved: 100% success rate (1000/1000 trials) repairing the "9.11 > 9.8" error by transplanting attention patterns at Layer 10
• Precise intervention requirements: Works ONLY at Layer 10, not layers 9 or 11, demonstrating extreme specificity

📊 Sharp Computational Thresholds

• Binary phase transition: Exactly 8 even heads required - 7 heads = 0% success, 8+ heads = 100% success
• 60% pattern replacement threshold: Another sharp transition with no gradual degradation
• Perfect redundancy: Any combination of 8 even heads works equally well (16 choose 8 = 12,870 combinations tested)

🧠 Mechanistic Understanding

• Format-dependent failure mode: Bug only occurs in Q&A/chat formats (100% error) but not simple format (0% error)
• Re-entanglement bottleneck: SAE analysis shows formats separate (10% overlap at Layer 7) then re-entangle (80% overlap at Layer 10)
• Shared components, not separate circuits: 40-60% feature overlap proves bugs arise from differential orchestration of same features

💡 Broader Implications

• 75% efficiency gain: Only 8 of 32 heads needed for numerical tasks
• "Goldilocks principle": Intervention granularity determines success - not individual heads (too narrow) or full layers (too coarse), but complete submodules
• Hidden sophisticated architecture: Transformers implement discrete computational modes, not continuous processing