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Flexible Routing via Uncertainty Decomposition

NeurIPS 2026 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Priors and functional variational uncertainty · 0 citations (OpenAlex)

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Proposes an uncertainty-aware model router that decomposes loss into irreducible and reducible parts using higher-order calibration, enabling predict/route/abstain decisions that adapt to new losses and costs without retraining.

Problem

Model routing between a cheap weak model and an expensive oracle (or abstention) wastes oracle calls on inherently ambiguous inputs with high irreducible (aleatoric) uncertainty, and supervised routers must be retrained when losses or costs change.

Approach

Use higher-order calibrated predictors (mixtures over label distributions estimated from multi-annotator snapshots) to estimate irreducible and reducible loss per bin, then choose predict, route, or abstain by minimizing estimated cost; the saved bin statistics are independent of the routing configuration, so new losses and penalties are handled by cheap post-hoc decisions.

Key results

• On synthetic data, the higher-order router substantially outperforms routing by total uncertainty when reducible and irreducible uncertainty are decorrelated.
• On real datasets (CIFAR-10H, SNLI, ChaosNLI), total and irreducible loss are highly correlated, so decomposition gives little gain over total-uncertainty routing once models are calibrated.
• A three-way predict/route/abstain router traces the lower envelope of two-way predict/route and predict/abstain curves on SNLI.

Surprising findings

• Benefits of the method on real datasets largely vanish after calibrating the weak model, suggesting earlier gains came from miscalibration rather than decomposition.
• Total and irreducible loss remain highly correlated across level sets on real datasets, limiting the value of uncertainty decomposition in practice.

Limitations

• Relies on multiple independent annotations per input (k-snapshot calibration set), which may be expensive to collect.
• Assumes the oracle is strictly stronger than the weak model and that higher-order predictor shares level sets with the weak model.
• Real-data benefits over total-uncertainty routing are small once models are calibrated.

Experimental setup

Datasets: CIFAR-10H SNLI ChaosNLI synthetic binary classification

Benchmarks: CIFAR-10H SNLI ChaosNLI synthetic binary classification

Metrics: total routing loss vs percentage routed cost-penalized loss

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