The KV-cache system is fully implemented and working. Here's a summary:

## Implementation Summary

### 1. Data Structures (`kv_cache.py`)

| Class | Purpose |
|-------|---------|
| `CacheConfig` | Configuration for cache dimensions and memory format |
| `KVCacheBlock` | Single block for paged attention (fixed-size memory unit) |
| `PagedKVCache` | Block-wise KV storage with on-demand allocation |
| `FlatKVCache` | Pre-allocated flat storage for max throughput |
| `MultiHeadAttention` | Attention with integrated cache read/write |
| `TransformerBlock` | Single layer with pre-norm and FFN |
| `BatchedInferenceEngine` | Manages variable-length batch sequences |

### 2. Memory Layout

```
[layers, batch, seq, 2, heads, dim]   # Flat format
[block_size, heads, dim] × N blocks    # Paged format
```

### 3. Key Algorithms

- **Incremental decoding**: Only computes Q for new token, reuses cached K,V
- **Causal masking**: Prevents attending to future tokens
- **Attention**: `softmax(Q × K^T / √d) × V`

### 4. Memory Analysis Results

| Sequence Length | Prefill Cost | Cached Decode | Speedup |
|----------------|--------------|--------------|---------|
| 4096 | 16,777,216 | 4,096 | **4,096x** |

### 5. Optimizations Proposed

1. **Paged Attention**: Block-based allocation (16 tokens/block) reduces memory waste from pre-allocation

2. **Quantization**: FP16→INT8 = 2x compression, INT4 = 4x

3. **Chunked Attention** (Flash Attention style): 256x memory reduction for attention scores

### 6. GPU Execution Mapping

- HBM → Shared Memory → Registers hierarchy
- KV-cache loaded from HBM per decode step
- Tensor cores for GEMM operations
- Critical bottlenecks: memory bandwidth, O(S²) attention

Run with:
```bash
python kv_cache.py
```