Embedding Geometry Shapes LLM Routing: Tracing Failure Modes and Improving Generalization

Large language model (LLM) routing aims to select the most suitable model for each incoming query. Most existing routers learn this decision directly from query embeddings, model representations, preference data, or clusters of similar examples. Such approaches can be effective, yet the representation used for routing rarely states what a query actually requires. We introduce SeLMRoute, a routing framework that separates the extraction of candidate-independent semantic evidence from the learning of candidate performance and the application of deployment objectives. A decision model first evaluates a set of interpretable questions about the query, such as its reasoning requirements and use of external knowledge, with each judgment retained as a probability distribution. The resulting probabilistic semantic state is used by a lightweight supervised router to estimate candidate model performance. Routing objectives are applied after performance estimation, which allows the same semantic state to support performance-oriented and cost-aware decisions. On the LLMRouterBench (15 datasets, 20 candidate models, 11,481 queries), SeLMRoute achieves an average accuracy of $72.08\% \pm 0.45$, while grouped five-fold out-of-fold evaluation reaches $72.64\%$, compared with $69.23\%$ for the strongest fixed candidate. The representation achieves the highest mean performance among the evaluated semantic, dense, lexical, and domain-level representations. In a separate 13-model performance-cost setting, SeLMRoute improves performance in all five grouped splits, with a mean PerfGain of $2.66\%$. Our code is available at https://github.com/Indigma-Innovations/SeLMRoute.

An LLM router picks which model should answer each query. The appeal is that models fail on different questions. Whatever single model is best overall still gets some wrong, and another model in the pool gets many of those right. Getting that choice right every time is the ceiling, and a router is an attempt to approach it. However, recent work reports that routers do not get close. Across 21 routing methods on five benchmarks, sharply different designs land within a fraction of a point of each other, and all of them stay far below that ceiling. Learned routers often fail to beat simply always calling the strongest model. We ask what those missed questions have in common. We set fourteen models to answer all 294 questions, with 7 task types across 3 languages: Korean, English and Hindi. We ran the whole matrix twice, changing nothing, but 5.37% of the 4,116 model-question pairs came out scored differently anyway. Run-to-run movement like that is normal, and we argue that a small win does not show that routing did anything, ours or anyone else's. Counting an answer correct only when the model got it right in both runs, 29 questions on this matrix can be improved with routing. Every correct-answer count here is on that rule. Task type accounts for most of them: assigning each task type one model in advance, chosen once and never updated, improves 21 of the 29. Splitting each task type by language improves 2 more and leaves 6 of 294 unoptimized. That handful is what a learned router would have been built for, and it is smaller than the run-to-run movement above, which is a share of pairs rather than of questions. The static table we adopted answers 262 of 294 questions at $3.33 per run, against the best single model's 245 at $7.69. All of this is fitted and scored on the same 294 questions with no holdout.

Large Language Model (LLM) routers commonly rely on neural query embeddings, with larger encoders expected to better capture query intent and difficulty. Yet scaling Qwen2.5 encoders from 0.5B to 72B parameters brings little improvement in routing accuracy (Figure 1b), suggesting that small encoders may already capture the query properties needed for routing. We therefore investigate which properties matter and whether they can be extracted directly from text without a neural encoder. We introduce REGEXROUTE, a pipeline that uses sparse autoencoders (SAEs) to discover interpretable regular-expression (regex) features. Using unlabeled text, an LLM turns descriptions of grouped SAE latents into regex extractors and refines them to match latent activation patterns. These extractors supply numerical features to a lightweight routing head, eliminating neural encoding at inference (Figure 1a). Across four benchmarks, one fixed set of 128 features achieves 76.43% average routing accuracy, comparable to 76.41% for the strongest neural text encoder baseline, with much smaller latency and strong robustness. These findings establish explicit, interpretable text features as a practical basis for designing and understanding LLM routers.