{"ID":22918836,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17940","arxiv_id":"2609.17940","title":"Beyond the Previous Layer: Residual Predictive Structure in Sparse MoE Routing","abstract":"Sparse mixture-of-experts models route each token through a sequence of expert selections. We ask whether the immediately preceding selection adequately summarizes this trajectory for predicting the next router. Using frozen OLMoE and JetMoE models, we measure the held-out predictive gain from earlier expert selections while retaining the most recent selection as a common baseline. In OLMoE, extending the history from one to eleven layers raises router-logit $R^2$ from 0.59879 to 0.66544. A preregistered JetMoE replication yields four-layer gains of 0.14275 and 0.20528 at two target depths, with paired bootstrap intervals above zero. These gains survive nonlinear decoding: adding history to a small multilayer perceptron improves $R^2$ by 0.17137 and 0.21861, whereas nonlinear decoding of the recent state alone adds 0.00139 and 0.00936 over a linear probe. Parameter-matched controls preserve the advantage, and cross-fitted history residuals predict target residuals with $R^2$ of 0.20549 and 0.23556. These findings identify residual predictive structure in expert-selection trajectories beyond adjacent-layer persistence.","short_abstract":"Sparse mixture-of-experts models route each token through a sequence of expert selections. We ask whether the immediately preceding selection adequately summarizes this trajectory for predicting the next router. Using frozen OLMoE and JetMoE models, we measure the held-out predictive gain from earlier expert selections...","url_abs":"https://arxiv.org/abs/2609.17940","url_pdf":"https://arxiv.org/pdf/2609.17940v1","authors":"[\"Hao Li\",\"Yasuyuki Tahara\",\"Yuichi Sei\"]","published":"2026-09-15T23:57:34Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}