## **1. Dynamic Key-Value Cache:**
- Maintain a persistent KV cache for autobiographical content that updates via:
    - Linear gating: $$ \mathrm{new\_cache} = \gamma \cdot \mathrm{old\_cache} + (1-\gamma) \cdot \mathrm{current\_bio} $$
    - Content-aware update rules learned through backpropagation

---

## **2. Positional Encoding Strategies**
**Hierarchical Positional Embeddings:**
- Implement dual positional encoding streams:
    - **Autobiographical Position:** Use learned positional embeddings with windowed attention
    - **Main Context Position:** Apply RoPE (Rotary Position Embedding) for better length extrapolation

| Component          | Encoding Type       | Dimensions | Interaction Mechanism         |
|--------------------|---------------------|------------|--------------------------------|
| Autobiography      | Learned + Windowed  | 64         | Content-aware gating     |
| Main Context       | RoPE                | 128        | Standard self-attention       |

**Position-Aware Layer Norm:**
- Modify layer normalization to separately process positional signals:

```python
class BioAwareLayerNorm(nn.Module):
    def __init__(self, hidden_size):
        super().__init__()
        self.main_norm = nn.LayerNorm(hidden_size)
        self.bio_norm = nn.LayerNorm(hidden_size//2)
        
    def forward(self, x):
        bio, main = x.split([x.size(-1)//2, x.size(-1)//2], dim=-1)
        return torch.cat([self.bio_norm(bio), self.main_norm(main)], dim=-1)
```