# Variational Metric Scaling for Metric-Based Meta-Learning

arXiv: https://arxiv.org/abs/1912.11809 · HTML: https://mlsanity.com/paper/1912.11809/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2019.

## Built on by (most cited first, 17 of 17)

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- [Task-Agnostic Learning to Accomplish New Tasks](https://mlsanity.com/paper/2209.04100/) (2022)
- [SENet: A Spectral Filtering Approach to Represent Exemplars for Few-shot Learning](https://mlsanity.com/paper/2305.18970/) (2023)
- [Spatio-Temporal Fuzzy-oriented Multi-Modal Meta-Learning for Fine-grained Emotion Recognition](https://mlsanity.com/paper/2412.13541/) (2024)
- [RW-Net: Enhancing Few-Shot Point Cloud Classification with a Wavelet Transform Projection-based Network](https://mlsanity.com/paper/2501.03221/) (2025)
- [Riemannian Geometric-based Meta Learning](https://mlsanity.com/paper/2503.10993/) (2025)
- [ProtoTopic: Prototypical Network for Few-Shot Medical Topic Modeling](https://mlsanity.com/paper/2510.13542/) (2025)

## Abstract (arXiv)

Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning algorithms. However, there still lacks a principled method for learning the metric scaling parameter automatically. In this paper, we recast metric-based meta-learning from a Bayesian perspective and develop a variational metric scaling framework for learning a proper metric scaling parameter. Firstly, we propose a stochastic variational method to learn a single global scaling parameter. To better fit the embedding space to a given data distribution, we extend our method to learn a dimensional scaling vector to transform the embedding space. Furthermore, to learn task-specific embeddings, we generate task-dependent dimensional scaling vectors with amortized variational inference. Our method is end-to-end without any pre-training and can be used as a simple plug-and-play module for existing metric-based meta-algorithms. Experiments on mini-ImageNet show that our methods can be used to consistently improve the performance of existing metric-based meta-algorithms including prototypical networks and TADAM. The source code can be downloaded from https://github.com/jiaxinchen666/variational-scaling.