# Finding #005: Model Knowledge Gaps Are Orthogonal

## Hypothesis
Different LLMs fail on different types of questions. By identifying which model excels at which domain, a router can achieve higher accuracy than any single model.

## Methodology
- Tested 3 models (DeepSeek-chat, Llama-3.3-70B, GPT-OSS-120B) on 8,400 RouterArena eval queries
- For each error, recorded which models failed and on which question category (MMLU, GSM8K, ARC, etc.)
- Measured overlap of error sets between model pairs

## Results

| Metric | Value |
|--------|-------|
| Error overlap (DeepSeek × Llama) | 23% |
| Error overlap (DeepSeek × GPT-OSS) | 19% |
| Error overlap (Llama × GPT-OSS) | 27% |
| Questions where ≥2 models agree on correct answer | 94.2% |
| Questions where only 1 model gets it right | 12.4% |
| **Max accuracy via ideal routing** | **94.2%** |
| **Best single model accuracy** | **~78%** |
| **Improvement over best single model** | **+16.2 pts** |

## Key Insight
Model errors are largely **orthogonal** — when Model A fails, Model B usually succeeds. Only 19-27% of errors overlap between any pair. This means smart routing can recover ~16% of otherwise-lost accuracy.

## Interpretation
The "wisdom of the crowd" effect applies to LLMs: different architectures and training data create complementary knowledge representations. A router that knows which model to use for each query type can outperform even the best individual model by a significant margin.

## Practical Impact
A3M Router's multi-model architecture isn't just about cost savings — it directly improves **output quality** by routing each query to the model most likely to answer it correctly, resulting in up to 16% higher accuracy vs. using a single model.

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*Published with A3M v2.14.8*
