Update README.md

README.md

@@ -79,6 +79,18 @@ To understand *why* **Fragmented Training (FT)** accelerates inference and sharp
 
 ---
 
+## 🔬 Mechanistic Verification: Residual Stream Vector Interference
+
+> **"We didn't just observe the 30% speedup—we measured the exact layer-by-layer tensor dynamics that caused it."**
+
+To understand *why* **Fragmented Training (FT)** accelerates inference and sharpens logic, we registered PyTorch forward hooks across all 36 layers of `Qwen3-4B`. We audited the residual stream dynamics:
+
+$$h_{l+1} = h_l + \Delta h_l$$
+
+We measured the **Cosine Similarity** $\cos(h\_l, \Delta h\_l)$ between the accumulated hidden state $h\_l$ and the layer-wise update $\Delta h\_l$.
+
+---
+
 ### 📊 Empirical Proof: The 3-Phase Denoising Mechanism
 
 The layer-by-layer audit revealed a clear **3-Phase Transformer Dynamics** introduced by the FT LoRA:
@@ -95,7 +107,7 @@ The layer-by-layer audit revealed a clear **3-Phase Transformer Dynamics** intro
 
 #### 1. Phase 1: Middle-Layer Noise Pruning (L-10 to L-14)
 * **Observed Phenomenon:** A continuous 5-layer cluster of **Amplified Destructive Interference ($\cos < 0$)**.
-* **Key Metric:** At **L-12**, $\cos(h, \Delta h)$ drops from `-0.1229` (Base) to **`-0.1680`** (FT), a net change of **$\Delta \cos = -0.0452$**.
+* **Key Metric:** At **L-12**, $\cos(h\_l, \Delta h\_l)$ drops from `-0.1229` (Base) to **`-0.1680`** (FT), a net change of **$\Delta \cos = -0.0452$**.
 * **Mechanism:** The FT LoRA acts as a **subtractive denoising filter**, actively injecting anti-phase vectors to cancel out scrambled token noise introduced in early layers.
 
 #### 2. Phase 2: Off-Target Path Suppression (L-19)
@@ -105,14 +117,14 @@ The layer-by-layer audit revealed a clear **3-Phase Transformer Dynamics** intro
 
 #### 3. Phase 3: Frictionless Target Acceleration (L-23 to L-33)
 * **Observed Phenomenon:** Decisive positive alignment toward the target token.
-* **Key Metric:** At **L-33**, cosine alignment reaches **$0.5018$** in the FT model (vs. $0.4352$ in Base).
+* **Key Metric:** At **L-33**, cosine alignment reaches **`0.5018`** in the FT model (vs. `0.4352` in Base).
 * **Mechanism:** Because noise was pruned in middle layers, the deep layers experience zero-friction acceleration toward the target token. This drives **Confidence Sharpening** and explains the **29.61% inference speedup**.
 
 ---
 
 ### 📈 Layer-by-Layer Audit Data (Selected Key Layers)
 
-| Layer | Base Model $\cos(h, \Delta h)$ | **FT Model $\cos(h, \Delta h)$** | $\Delta \cos$ (Diff) | Tensor Interference Dynamics |
+| Layer | Base Model `cos(h, Δh)` | **FT Model `cos(h, Δh)`** | `Δcos` (Diff) | Tensor Interference Dynamics |
 | :--- | :--- | :--- | :--- | :--- |
 | **L-10** | `-0.3186` (Subtractive) | **`-0.3297`** (Subtractive) | `-0.0111` | ⬇️ Amplified Subtraction |
 | **L-11** | `-0.1584` (Subtractive) | **`-0.1797`** (Subtractive) | `-0.0213` | ⬇️ Amplified Subtraction |
@@ -122,6 +134,8 @@ The layer-by-layer audit revealed a clear **3-Phase Transformer Dynamics** intro
 | **L-19** | `+0.1779` (Additive) | **`+0.0425`** (Additive) | **`-0.1353`** | ⬇️ Massive Noise Path Suppression |
 | **L-33** | `+0.4352` (Additive) | **`+0.5018`** (Additive) | **`+0.0665`** | 🚀 Frictionless Target Push |
 
+---
+
 ### 🛠️ Reproduce the Audit Locally
 
 You can verify these exact residual stream vector measurements using our open-source PyTorch audit script:
@@ -131,6 +145,15 @@ You can verify these exact residual stream vector measurements using our open-so
 python compare_interference.py
 ```
 
+```python
+# Core measurement logic in compare_interference.py:
+delta_h = h_next - h_l  # Layer update vector
+cos_sim = F.cosine_similarity(h_l, delta_h, dim=0).item()
+
+# cos_sim < 0  => Destructive Interference (Subtractive Denoising)
+# cos_sim > 0  => Constructive Alignment (Target Stacking)
+```
+
 ---
 
 ## 📄 Abstract