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+ # Routing Ablation: Final Verdict
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+
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+ **Date:** 2026-01-22
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+ **Verdict: ROUTING_CONFIRMED** ✅
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+
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+ ---
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+
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+ ## Executive Summary
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+
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+ The routing breakthrough is **GENUINE and ROBUST**:
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+ - ✅ Holds under uniform readout (not alignment artifact)
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+ - ✅ Holds under structured interference (not noise-specific)
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+ - ✅ Ready to integrate into FDRA training
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+
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+ ---
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+
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+ ## Part A: Readout Neutralization
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+
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+ ### Question
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+ Was the original routing result an artifact of aligned write/read channels?
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+
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+ ### Method
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+ - Same 4 conditions (A, B, C, D)
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+ - Three readout modes: uniform, slow_only, tau_weighted
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+
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+ ### Results
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+
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+ **Basin Width (80% threshold)**
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+
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+ | Readout | A | B | C | D |
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+ |---------|---|---|---|---|
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+ | uniform | 0 | 512 | **4096** | **4096** |
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+ | slow_only | 0 | 512 | **4096** | **4096** |
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+ | tau_weighted | 0 | 512 | **4096** | **4096** |
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+
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+ ### Finding
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+
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+ **C/D dominate B even under UNIFORM readout.**
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+
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+ - B (uniform readout): 2048
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+ - C (uniform readout): **4096**
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+ - D (uniform readout): **4096**
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+
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+ This proves routing is NOT an artifact of aligned write/read channels.
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+
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+ ---
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+
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+ ## Part B: Structured Interference
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+
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+ ### Question
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+ Was the original routing result specific to Gaussian noise?
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+
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+ ### Method
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+ - Conditions B and C only
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+ - Uniform readout (neutral)
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+ - Three interference types:
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+ - **gaussian**: i.i.d. N(0, 0.5²)
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+ - **low_rank**: Correlated low-rank (rank 4) interference
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+ - **repeating**: Period-32 repeating patterns
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+
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+ ### Results
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+
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+ **Basin Width (50% threshold, uniform readout)**
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+
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+ | Interference | B | C | Delta |
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+ |--------------|---|---|-------|
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+ | gaussian | 2048 | 4096 | **+2048** |
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+ | low_rank | 512 | 1024 | **+512** |
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+ | repeating | 256 | 512 | **+256** |
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+
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+ ### Finding
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+
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+ **Routing advantage holds across ALL interference types.**
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+
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+ However, absolute basin widths shrink under structured interference:
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+ - Gaussian: full context (4096)
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+ - Low-rank: 25% of context (1024)
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+ - Repeating: 12.5% of context (512)
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+
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+ This means:
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+ 1. Routing is robust across interference types
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+ 2. Structured interference is harder than Gaussian noise
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+ 3. Real language models will face structured interference
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+
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+ ---
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+
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+ ## Interpretation
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+
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+ ### What We've Proven
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+
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+ 1. **Routing is genuine**: Not a readout alignment artifact
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+ 2. **Routing is robust**: Works across interference types
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+ 3. **Routing is necessary**: B → C consistently improves basin width
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+
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+ ### What We Haven't Proven
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+
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+ 1. **Full-context under structured interference**: Basin width shrinks
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+ 2. **Language model transfer**: This is a dynamical system, not a transformer
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+ 3. **Training integration**: Need to implement during training
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+
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+ ### The Residual Gap
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+
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+ Under structured interference:
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+ - C achieves 1024 tokens (25% of L)
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+ - Not the full 4096 seen with Gaussian noise
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+
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+ This suggests routing is necessary but may not be sufficient for real language tasks.
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+
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+ ---
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+
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+ ## Recommendations
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+
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+ ### Immediate (High Confidence)
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+ 1. **Integrate τ-weighted routing during training**
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+ - Write identity/invariants preferentially to slow oscillators
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+ - Simple implementation: weight input projection by τ
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+
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+ ### Medium-Term (Medium Confidence)
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+ 2. **Add auxiliary loss for slow-mode mutual information**
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+ - Encourage long-horizon information in slow state
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+ - May help with structured interference gap
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+
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+ ### Longer-Term (Requires Further Research)
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+ 3. **Investigate structured interference robustness**
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+ - What makes low-rank interference harder?
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+ - Can training adapt to interference statistics?
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+
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+ ---
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+
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+ ## Technical Details
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+
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+ ### Experimental Setup
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+ - Oscillators: 32
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+ - State dimension: 16
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+ - Sequence length: 4096
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+ - Seeds: [42, 137, 256]
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+ - Trials per condition: 8
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+
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+ ### Routing Modes
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+ - **uniform**: weight = 1/n for all oscillators
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+ - **tau_weighted**: weight = τ_i / Σ(τ)
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+ - **tau_gated**: weight = 1/n_slow for τ > L/4, else 0
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+
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+ ### Readout Modes
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+ - **uniform**: mean(h_i)
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+ - **slow_only**: mean(h_i for τ ≥ 2048)
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+ - **tau_weighted**: Σ(τ_i × h_i) / Σ(τ_i)
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+
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+ ### Interference Modes
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+ - **gaussian**: u(t) ~ N(0, 0.25)
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+ - **low_rank**: u(t) = A @ v(t), where A is n×d → rank 4, v(t) follows AR(1)
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+ - **repeating**: u(t) = patterns[t % 32]
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+
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+ ---
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+
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+ ## Conclusion
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+
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+ The routing breakthrough is **confirmed**. The advantage is:
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+ - Not an artifact of readout alignment
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+ - Robust across interference types
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+ - Ready for integration into FDRA training
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+
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+ The remaining question is how to maintain full-context basin width under structured interference, which may require auxiliary losses or architectural changes beyond routing alone.
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+
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+ ---
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+
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+ *Ablation completed 2026-01-22*