# Semantic-Aware Gaussian Process Calibration with Structured Layerwise Kernels for Deep Neural Networks

arXiv: https://arxiv.org/abs/2507.15987 · HTML: https://mlsanity.com/paper/2507.15987/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 78 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [Quantifying Point-Prediction Uncertainty in Neural Networks via Residual Estimation with an I/O Kernel](https://mlsanity.com/paper/1906.00588/) (2019)
- [Improving Output Uncertainty Estimation and Generalization in Deep Learning via Neural Network Gaussian Processes](https://mlsanity.com/paper/1707.05922/) (2017)

## Abstract (arXiv)

Calibrating the confidence of neural network classifiers is essential for quantifying the reliability of their predictions during inference. However, conventional Gaussian Process (GP) calibration methods often fail to capture the internal hierarchical structure of deep neural networks, limiting both interpretability and effectiveness for assessing predictive reliability. We propose a Semantic-Aware Layer-wise Gaussian Process (SAL-GP) framework that mirrors the layered architecture of the target neural network. Instead of applying a single global GP correction, SAL-GP employs a multi-layer GP model, where each layer's feature representation is mapped to a local calibration correction. These layerwise GPs are coupled through a structured multi-layer kernel, enabling joint marginalization across all layers. This design allows SAL-GP to capture both local semantic dependencies and global calibration coherence, while consistently propagating predictive uncertainty through the network. The resulting framework enhances interpretability aligned with the network architecture and enables principled evaluation of confidence consistency and uncertainty quantification in deep models.