# Multi-layer Radial Basis Function Networks for Out-of-distribution Detection

arXiv: https://arxiv.org/abs/2501.02616 · HTML: https://mlsanity.com/paper/2501.02616/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 5 Jan 2025.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [Are All Losses Created Equal: A Neural Collapse Perspective](https://mlsanity.com/paper/2210.02192/) (2022)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Neural Collapse in the Intermediate Hidden Layers of Classification Neural Networks](https://mlsanity.com/paper/2308.02760/) (2023)
- [Deep-RBF Networks Revisited: Robust Classification with Rejection](https://mlsanity.com/paper/1812.03190/) (2018)
- [Deep RBFNet: Point Cloud Feature Learning using Radial Basis Functions](https://mlsanity.com/paper/1812.04302/) (2018)
- [Feature Collapse](https://mlsanity.com/paper/2305.16162/) (2023)

## Abstract (arXiv)

Existing methods for out-of-distribution (OOD) detection use various techniques to produce a score, separate from classification, that determines how ``OOD'' an input is. Our insight is that OOD detection can be simplified by using a neural network architecture which can effectively merge classification and OOD detection into a single step. Radial basis function networks (RBFNs) inherently link classification confidence and OOD detection; however, these networks have lost popularity due to the difficult of training them in a multi-layer fashion. In this work, we develop a multi-layer radial basis function network (MLRBFN) which can be easily trained. To ensure that these networks are also effective for OOD detection, we develop a novel depression mechanism. We apply MLRBFNs as standalone classifiers and as heads on top of pretrained feature extractors, and find that they are competitive with commonly used methods for OOD detection. Our MLRBFN architecture demonstrates a promising new direction for OOD detection methods.