# LLM-Written Scoring Networks

An empirical study tests whether a large language model can write the weights of small scoring networks directly, without gradient training and guided only by forward-pass outputs, to speed up exact algorithms such as column generation and branch-and-bound. On synthetic independent-set instances the written branching rule took 0.37 the time of SCIP's default and matched or beat networks trained by imitation of strong branching on the same features; on a bus-driver scheduling model built from Atlanta transit data, the 0.63 time ratio was fully reproduced by SCIP's own plain pseudocost rule at 0.99.

An empirical study tests whether a large language model can write the weights of small scoring networks directly, without gradient training and guided only by forward-pass outputs, to speed up exact algorithms such as column generation and branch-and-bound. On synthetic independent-set instances the written branching rule took 0.37 the time of SCIP's default and matched or beat networks trained by imitation of strong branching on the same features; on a bus-driver scheduling model built from Atlanta transit data, the 0.63 time ratio was fully reproduced by SCIP's own plain pseudocost rule at 0.99.