  Convex optimisation has provided a mechanism to determine arbitrage trades on
automated market markets (AMMs) since almost their inception. Here we outline
generic closed-form solutions for $N$-token geometric mean market maker pool
arbitrage, that in simulation (with synthetic and historic data) provide better
arbitrage opportunities than convex optimisers and is able to capitalise on
those opportunities sooner. Furthermore, the intrinsic parallelism of the
proposed approach (unlike convex optimisation) offers the ability to scale on
GPUs, opening up a new approach to AMM modelling by offering an alternative to
numerical-solver-based methods. The lower computational cost of running this
new mechanism can also enable on-chain arbitrage bots for multi-asset pools.
