# Tilt and Average : Geometric Adjustment of the Last Layer for Recalibration

arXiv: https://arxiv.org/abs/2406.10017 · HTML: https://mlsanity.com/paper/2406.10017/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Local Temperature Scaling for Probability Calibration](https://mlsanity.com/paper/2008.05105/) (2020)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [Meta-Cal: Well-controlled Post-hoc Calibration by Ranking](https://mlsanity.com/paper/2105.04290/) (2021)
- [Angular Visual Hardness](https://mlsanity.com/paper/1912.02279/) (2019)
- [Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning](https://mlsanity.com/paper/2006.13092/) (2020)
- [Beyond Confidence: Reliable Models Should Also Consider Atypicality](https://mlsanity.com/paper/2305.18262/) (2023)
- [Efficient Multi-Domain Network Learning by Covariance Normalization](https://mlsanity.com/paper/1906.10267/) (2019)
- [Deep Feature Space: A Geometrical Perspective](https://mlsanity.com/paper/2007.00062/) (2020)
- [Angular Gap: Reducing the Uncertainty of Image Difficulty through Model Calibration](https://mlsanity.com/paper/2207.08525/) (2022)

## Built on by (most cited first, 1 of 1)

- [Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax](https://mlsanity.com/paper/2506.10572/) (2025)

## Abstract (arXiv)

After the revelation that neural networks tend to produce overconfident predictions, the problem of calibration, which aims to align confidence with accuracy to enhance the reliability of predictions, has gained significant importance. Several solutions based on calibration maps have been proposed to address the problem of recalibrating a trained classifier using additional datasets. In this paper, we offer an algorithm that transforms the weights of the last layer of the classifier, distinct from the calibration-map-based approach. We concentrate on the geometry of the final linear layer, specifically its angular aspect, and adjust the weights of the corresponding layer. We name the method Tilt and Average(textscTna), and validate the calibration effect empirically and theoretically. Through this, we demonstrate that our approach, in addition to the existing calibration-map-based techniques, can yield improved calibration performance. Code available : https://github.com/GYYYYYUUUUU/TNAAngularScaling.