The Conclave Process

What the math gives to ML

The paper studies a synchronous reinforced-competition process in which candidates receiving more support become increasingly likely to receive support in the next round. Its transferable asset is an explicit power-law reinforcement map with a sharp dynamical phase transition: superlinear reinforcement produces consensus in order \(\log\log n\) rounds, while sublinear reinforcement prevents concentration for exponentially longer times. This suggests an iterative mixture-of-experts or token-routing module whose assignments are repeatedly sharpened from the previous load vector, rather than being produced once by a static softmax. The phase diagram also provides a principled way to select the reinforcement exponent from a desired number of routing rounds, although the paper's asymptotic winner guarantees must be empirically revalidated for learned, non-identically distributed routing scores.