How should a router pick k distinct experts?

research/topk-routing

Top-k MoE routing as a capped Hedge market: price min(1, λ w_i) with exact KL projection, regret vs the best fixed k-set held under k ln(N/k)/η+ηTk/2 in every run (41–58% of it), plain normalisation prices experts above 1 (282/300 rounds, loss understated 3.2×), and systematic sampling gives exactly k distinct experts with 8–14× lower variance.

6 tests

What it found

Sparse mixture-of-experts routing as a capped Hedge market: expert prices are min(1, λ w_i) with a single shadow price λ and an exact KL projection. Regret against the best fixed k-set stayed within k ln(N/k)/η + ηTk/2 in every run (41–58% of it, not proved here); plain normalisation prices an expert above 1 in 282 of 300 rounds and understates loss 3.2×; systematic sampling realises exactly k distinct experts with 8–14× lower loss variance. Oblivious losses only.

A figure from its own output

Figure produced by research/topk-routing: topk_regret — topk-routing/experiments/topk_regret.svg, written by the project's own experiment code.

Paper, code and results

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All 13 Markets as routers projects →

Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.