The authors improve simulation-based inference (SBI) for models with expensive likelihoods by augmenting the standard training loss with exact score information—the gradient of the log-likelihood with respect to parameters. SBI trains a neural network to approximate the likelihood using simulated data, but this is expensive; the authors show that when you can compute the score (even if the full likelihood is intractable), adding it to the loss function drastically improves the quality of the surrogate without needing much more training data. In their experiments, the method matches the performance of a 10× data increase with only a 1.1× increase in training time.
Main takeaways:
- Standard SBI treats the data-generating process as a black box and trains a likelihood surrogate via binary classification (real vs. simulated).
- This paper relaxes the black-box assumption: if you can compute the score (gradient of log p(x | θ)), you can add it as an auxiliary loss term.
- The score-augmented loss is combined with adaptive weighting based on loss gradients to balance the two objectives.
- Experiments on network dynamics and spatial processes show much better surrogate quality and downstream inference at a fraction of the simulation cost.
- Practical upshot: you get the benefit of ~10× more training data for ~1.1× more compute.