Polynomial chaos expansion (PCE) is a widely used surrogate modeling technique in uncertainty quantification and sensitivity analysis. By expressing the model response as a linear combination of basis polynomials [1] that are orthonormal with respect to the distribution of uncertain inputs, PCE enables tractable computation of key statistical quantities, including (conditional) means, covariances, and Sobol sensitivity indices [2]. These quantities are essential for understanding system behavior and identifying influential parameters. Despite substantial progress in higher-dimensional settings [3, 4, 5], classical PCE remains less scalable than modern neural networks. Conversely, standard neural networks typically do not allow exact and efficient computation of expectations and sensitivities, relying instead on costly, and often inaccurate, Monte Carlo approximations. We bridge this gap by combining PCE with ideas from tractable probabilistic circuits [6], yielding the deep polynomial chaos expansion (DeepPCE) [7]. DeepPCE is a hierarchical generalization of PCE that scales gracefully to very high-dimensional inputs while preserving exact and efficient computation of Sobol sensitivity indices. Crucially, this is achieved without assuming sparsity, low effective dimensionality, latent embeddings, repeated re-orthogonalization, or sampling-based approximations. We demonstrate the method on the Sobol–G function as well as steady-state diffusion and Darcy flow with 100, 1024, and up to 4096 input dimensions. REFERENCES [1] Ernst et al., On the convergence of generalized polynomial chaos expansions. ESAIM. Math. Model. Num. Anal. 46(2), pp. 317-339. 2012 [2] Sudret, B., Global sensitivity analysis using polynomial chaos expansions. Reliab. Eng. Syst. Saf. 93.7 pp. 964-979. 2008 [3] Cheng, K., & Lu, Z., Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression. Computers & Structures, 194, 86-96. 2018. [4] Ehre, M. et al. Global sensitivity analysis in high dimensions with PLS- PCE. Reliab. Eng. Syst. Saf., 198, 106861. 2020 [5] Kontolati, K. et al. Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models. Int. J. UQ., 12(4). 2022. [6] Vergari, A. et al., A compositional atlas of tractable circuit operations for probabilistic inference. In: NeurIPS 2021 [7] Exenberger, J., Ranftl, S., Peharz, R., Deep Polynomial Chaos Expansion. AISTATS 2026