Relative Entropy Estimation in Function Space: Theory and Applications to Trajectory Inference

The harder problem here isn't the KL divergence estimation itself but the function space framing: most divergence estimators work on finite-dimensional distributions, so extending this to distributions over continuous trajectories required genuinely different theoretical machinery, not just a scaling trick applied to an existing approach.

Recent Modelwire coverage has concentrated heavily on LLM inference efficiency and evaluation reliability, and this paper sits largely disconnected from that cluster. The closest thematic neighbor is the conformal prediction work from mid-April ('Diagnosing LLM Judge Reliability'), which also grapples with the gap between aggregate metrics and per-instance reliability. Both papers are fundamentally about making model evaluation more trustworthy, just in very different domains. The single-cell genomics application is the concrete anchor: when you cannot observe a cell's trajectory directly because measurement destroys the cell, you need principled ways to score competing reconstructions, and that is precisely what this method provides.

The real test is whether this estimator gets adopted in benchmark comparisons for established trajectory inference tools like Waddington-OT or Moscot within the next year. Adoption by even one major single-cell analysis pipeline would signal the method is computationally practical, not just theoretically sound.