mlsanityData to 7 Oct 2026

Uncertainty Quantification via Stable Distribution Propagation

arXiv 2402.08324 ↗First posted 13 Feb 2024cs.LG cs.AIcited by 10

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Abstract (arXiv)

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 35 of its 52 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

35 of 52 references.

References · 35

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23 more
  1. 2019On Evaluating Adversarial Robustnesscited by 442
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 5; 2026: 3.

10 papers.

  1. 2025Consensus Entropy: Harnessing Multi-VLM Agreement for Self-Verifying and Self-Improving OCRcited by 12
  2. 2025Enhancing Uncertainty Modeling with Semantic Graph for Hallucination Detectioncited by 8
  3. 2024Streamlining Prediction in Bayesian Deep Learningcited by 5
  4. 2024Generalizing Stochastic Smoothing for Differentiation and Gradient Estimationcited by 4
  5. 2025Low-Order Flow Reconstruction and Uncertainty Quantification in Disturbed Aerodynamics Using Sparse Pressure Measurementscited by 4
  6. 2025Assumed Density Filtering and Smoothing with Neural Network Surrogate Modelscited by 1
  7. 2025A Start To End Machine Learning Approach To Maximize Scientific Throughput From The LCLS-II-HEcited by 0
  8. 2026Calibrated Sampling-Free Uncertainty Estimation in Bayesian Deep Learningcited by 0
  9. 2026Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fieldscited by 0
  10. 2026Uncertainty propagation in auto-regressive random neural network modelscited by 0