# Interpretable epistemic uncertainty decomposition in sequential generative models via polynomial chaos surrogates

arXiv: https://arxiv.org/abs/2510.21523 · HTML: https://mlsanity.com/paper/2510.21523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [GFlowVLM: Enhancing Multi-step Reasoning in Vision-Language Models with Generative Flow Networks](https://mlsanity.com/paper/2503.06514/) (2025)
- [GFlowNet Fine-tuning for Diverse Correct Solutions in Mathematical Reasoning Tasks](https://mlsanity.com/paper/2410.20147/) (2024)
- [PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty](https://mlsanity.com/paper/2202.05063/) (2022)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory](https://mlsanity.com/paper/2306.14753/) (2023)

## Abstract (arXiv)

Sequential generative models conditioned on uncertain rewards are central to AI-driven scientific discovery, yet the epistemic uncertainty they inherit from imperfect reward estimates remains unquantified. We propagate this uncertainty through generative flow networks (GFlowNets) by fitting polynomial chaos expansions (PCEs) to small ensembles of trained models. The PCE coefficients yield analytical Sobol sensitivity indices, providing the first interpretable decomposition of which reward components drive which generative decisions, a capability unavailable from deep ensembles, Bayesian neural networks, or Monte Carlo dropout. Convergence guarantees are established theoretically and four of five are formally verified in the Lean 4 proof assistant. Across three real-world tasks the framework reveals actionable structure invisible to ensembles alone. On the Doyle-Dreher Buchwald-Hartwig dataset catalyst selection is robust (Dcatalyst≈ 71) while additive selection is fragile (Dadditive≈ 179, 2.5× higher). In fragment-based molecular design the linker position is the most sensitive (Dlinker≈ 28) while decoration positions are the most robust (D≈ 14-18), reversing the conventional scaffold-robust / decoration-fragile assumption. On the Sachs protein signalling network, MAPK-cascade edges and PKA/PKC hub edges separate into distinct sensitivity regimes, providing a targeted map for perturbation experiments. Calibration coverage at the 95% level reaches 0.97-1.00 across the dominant steps, and the surrogate evaluates 10,000 policy samples in milliseconds - 103-104× faster than exhaustive retraining.