# Revisiting Logistic-softmax Likelihood in Bayesian Meta-Learning for Few-Shot Classification

arXiv: https://arxiv.org/abs/2310.10379 · HTML: https://mlsanity.com/paper/2310.10379/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Free Lunch for Few-shot Learning: Distribution Calibration](https://mlsanity.com/paper/2101.06395/) (2021)
- [General Multi-label Image Classification with Transformers](https://mlsanity.com/paper/2011.14027/) (2020)
- [Use All The Labels: A Hierarchical Multi-Label Contrastive Learning Framework](https://mlsanity.com/paper/2204.13207/) (2022)
- [A Variational Analysis of Stochastic Gradient Algorithms](https://mlsanity.com/paper/1602.02666/) (2016)
- [Bayesian Few-Shot Classification with One-vs-Each P'olya-Gamma Augmented Gaussian Processes](https://mlsanity.com/paper/2007.10417/) (2020)
- [A Contrastive Divergence for Combining Variational Inference and MCMC](https://mlsanity.com/paper/1905.04062/) (2019)
- [Multi-Class Gaussian Process Classification Made Conjugate: Efficient Inference via Data Augmentation](https://mlsanity.com/paper/1905.09670/) (2019)
- [A Concise Review of Recent Few-shot Meta-learning Methods](https://mlsanity.com/paper/2005.10953/) (2020)
- [Efficient Gaussian Process Model on Class-Imbalanced Datasets for Generalized Zero-Shot Learning](https://mlsanity.com/paper/2210.06120/) (2022)

## Built on by (most cited first, 6 of 6)

- [Bayesian Exploration of Pre-trained Models for Low-shot Image Classification](https://mlsanity.com/paper/2404.00312/) (2024)
- [MetaCoCo: A New Few-Shot Classification Benchmark with Spurious Correlation](https://mlsanity.com/paper/2404.19644/) (2024)
- [Cross-Modal Few-Shot Learning: a Generative Transfer Learning Framework](https://mlsanity.com/paper/2410.10663/) (2024)
- [Accelerating Convergence in Bayesian Few-Shot Classification](https://mlsanity.com/paper/2405.01507/) (2024)
- [RAMSeS: Robust and Adaptive Model Selection for Time-Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2602.21766/) (2026)
- [AUCH-Net: Action Unit-Based Consistency-Aware Hypergraph Network for Cross-Domain Few-Shot Facial Expression Recognition](https://mlsanity.com/paper/2607.21004/) (2026)

## Abstract (arXiv)

Meta-learning has demonstrated promising results in few-shot classification (FSC) by learning to solve new problems using prior knowledge. Bayesian methods are effective at characterizing uncertainty in FSC, which is crucial in high-risk fields. In this context, the logistic-softmax likelihood is often employed as an alternative to the softmax likelihood in multi-class Gaussian process classification due to its conditional conjugacy property. However, the theoretical property of logistic-softmax is not clear and previous research indicated that the inherent uncertainty of logistic-softmax leads to suboptimal performance. To mitigate these issues, we revisit and redesign the logistic-softmax likelihood, which enables control of the textita priori confidence level through a temperature parameter. Furthermore, we theoretically and empirically show that softmax can be viewed as a special case of logistic-softmax and logistic-softmax induces a larger family of data distribution than softmax. Utilizing modified logistic-softmax, we integrate the data augmentation technique into the deep kernel based Gaussian process meta-learning framework, and derive an analytical mean-field approximation for task-specific updates. Our approach yields well-calibrated uncertainty estimates and achieves comparable or superior results on standard benchmark datasets. Code is publicly available at urlhttps://github.com/keanson/revisit-logistic-softmax.