[feat] Track entropy and MI of routing distribution for topk MoE

[oleksost]

✨ Description

To better detect potential routing collapse and have a better understanding about the routing distribution, we can track the average entropy and mutual information of routing probabilities.

Collapse routing would have low entropy and low mutual information. A healthy and specialised router would have low entropy and high mutual information, meaning that routing is specialised and considerably different across tokens.

More specifically:
Mutual info. measures the difference between:

• The entropy of the average distribution across all tokens.
• The average of the individual token entropies.

🔍 Type of change

Select all that apply:

• 🐛 Bug fix (non-breaking change that addresses a specific issue)
• 🚀 New feature (non-breaking change that adds functionality)
• ⚠️ Breaking change (a change that could affect existing functionality)
• 📈 Performance improvement/optimization (improves speed, memory usage, or efficiency)
• 🛠️ Code refactor (non-functional changes that improve code readability, structure, etc.)
• 📦 Dependency bump (updates dependencies, including Dockerfile or package changes)
• 📝 Documentation change (updates documentation, including new content or typo fixes)
• 🔧 Infrastructure/Build change (affects build process, CI/CD, or dependencies)

📝 Changes

• added calculation of both metrics in the mixture_of_experts.py, they are calculated only for the topk routing type.

✅ Checklist

General

• 📜 I have read and followed the contributing guidelines.
• 🏷️ I am using a clear and descriptive PR title that summarizes the key change or feature introduced.
• 🎉 The functionality is complete, and I have tested the changes.
• ⚠️ The change does not introduce any new issues (e.g., runtime warnings, type checker errors, linting problems, unhandled edge cases).
• 🧩 I have commented my code, especially in hard-to-understand areas.

Testing

• 🧪 I have added or updated tests to cover my changes.
• ✔️ New and existing tests pass locally with my changes.
• 🚦 I have tested these changes on GPUs and verified training stability.
• 🏋️ I have tested the changes on realistic training workloads, if applicable.

Performance Impact

• 📊 I have run benchmarks where applicable to evaluate the performance impact.
• ✅ The benchmarks show no performance regression.
• 🚀 The benchmarks indicate a potential performance improvement.
• ⚠️ The benchmarks indicate a potential performance degradation.
• 📈 I have provided benchmark results and detailed any performance impact below, if applicable.

📊 Performance Impact Details

I am not 100% sure there is no performance impact, we are calculating the stats at each forward pass through the router.

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🗒️ Additional Notes

Include any additional context, information, or considerations here, such as known issues, follow-up tasks, or backward compatibility concerns.

[tscholak]

idea is good, thanks @oleksost.
bit weird that all these metrics are appearing as losses. that name should be reserved for things for which gradients are computed. just call this dict metrics?

[oleksost]

Yes @tscholak, addressed. Using metrics dict instead.