An LLM wrote the weights of small scoring networks: 0.37× SCIP's default on independent set, but bus-crew gains came from a rule SCIP already ships
Synopsis
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.
Interpretation
A large language model can write the weights of a small multilayer perceptron with no gradient step and place it in an exact solver's scoring step, leaving the solution unchanged while affecting only running time and tree size. Earlier attempts to bring learning into branching and column generation needed training data and a training pipeline, such as learning to branch by ranking, regressing on strong-branching scores, or imitating strong branching with graph neural networks. On synthetic independent-set instances the written rule was faster on all 18 paired instances, with a geometric-mean time ratio of 0.37 and 1426 versus 2786 nodes on the medium set; optimal values were identical on every instance both rules solved.
The written network is a multilayer perceptron stored as JSON, mostly one linear layer or one ReLU layer of width 6, which scores each fractional candidate from quantities already available at the node and branches on the largest output. The model edited the weights after reading per-feature agreement with strong branching and where its earlier version disagreed with strong-branching picks, for example cutting the pseudocost weight from 0.7 to 0.2, with a written note explaining each term. Practice and test instances were generated with different seeds, and weights were written on practice only and frozen before the test; all rules ran paired on the same instances, with time compared only within a batch.
On a crew-scheduling set-partitioning model built from the Atlanta transit agency's public GTFS feed, the written rules took 0.63 the time of SCIP's default on 32 held-out garages and solved as many or more instances. The model was solved through a native C plugin with SCIP's factory settings, and the C port reproduced the Python node counts. The decisive control is SCIP's own plain pseudocost rule, which uses no strong branching at all and was as fast as the written rules at a 0.99 time ratio; the network written specifically for this family was no better than the generic version, at a ratio of 1.00.
Perspective
The conclusions cover column generation on XTW instances up to 256 customers plus the 10 largest, four synthetic MILP classes, 39 readable MIPLIB 2017 instances, and a driver-scheduling model built from MARTA's real GTFS data, whose labour rules and garage grouping are synthetic.
The authors list several qualifications: runs were concurrent, so absolute times vary across batches; the synthetic studies compute features in Python; two SCIP versions were used and conclusions are drawn within one build; instance sets are small, 8 to 40 per comparison; practice instances were chosen as non-trivial for the default; and the trained baseline is small. The same model wrote the weights, ran the analysis and wrote the paper, so every number is regenerated by a script from released logs.