Pruning MoE experts independently is a first-order approximation, and fixing it adds 6.1% on agentic coding.

HOPE points out existing expert-pruning methods decide each expert in isolation and assume contributions are purely additive, when MoE expert usage is cooperative. It derives a second-order objective that provably minimizes an upper bound on pruning error, and shows the state-of-the-art first-order method REAP is the special case where interaction terms are dropped. Across three frontier MoE models up to 122B, two calibration sets, and math, instruction-following, coding and agentic benchmarks, HOPE averages rank 1.58 of 5 methods at 50% pruning against REAP's 2.42, with the widest margins at high pruning rates.