# Multidimensional Belief Quantification for Label-Efficient Meta-Learning

arXiv: https://arxiv.org/abs/2203.12768 · HTML: https://mlsanity.com/paper/2203.12768/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 23 Mar 2022.

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

- [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)
- [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)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Few-Shot Learning with Graph Neural Networks](https://mlsanity.com/paper/1711.04043/) (2017)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Meta-Transfer Learning for Few-Shot Learning](https://mlsanity.com/paper/1812.02391/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [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)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Edge-labeling Graph Neural Network for Few-shot Learning](https://mlsanity.com/paper/1905.01436/) (2019)
- [Meta-Learning Probabilistic Inference For Prediction](https://mlsanity.com/paper/1805.09921/) (2018)
- [Multimodal Model-Agnostic Meta-Learning via Task-Aware Modulation](https://mlsanity.com/paper/1910.13616/) (2019)
- [Meta-Learning with Adaptive Hyperparameters](https://mlsanity.com/paper/2011.00209/) (2020)
- [Hierarchically Structured Meta-learning](https://mlsanity.com/paper/1905.05301/) (2019)
- [Learning to Balance: Bayesian Meta-Learning for Imbalanced and Out-of-distribution Tasks](https://mlsanity.com/paper/1905.12917/) (2019)
- [Adaptive Task Sampling for Meta-Learning](https://mlsanity.com/paper/2007.08735/) (2020)
- [Uncertainty in Model-Agnostic Meta-Learning using Variational Inference](https://mlsanity.com/paper/1907.11864/) (2019)
- [Probabilistic Active Meta-Learning](https://mlsanity.com/paper/2007.08949/) (2020)
- [Information-theoretic Task Selection for Meta-Reinforcement Learning](https://mlsanity.com/paper/2011.01054/) (2020)

## Built on by (most cited first, 9 of 9)

- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluation](https://mlsanity.com/paper/2512.23753/) (2025)
- [Bi-level Meta-Policy Control for Dynamic Uncertainty Calibration in Evidential Deep Learning](https://mlsanity.com/paper/2510.08938/) (2025)
- [Evidential learning driven Breast Tumor Segmentation with Stage-divided Vision-Language Interaction](https://mlsanity.com/paper/2603.11206/) (2026)
- [ELDiff: When Evidential Learning Meets Text-to-Image Diffusion](https://mlsanity.com/paper/2606.20924/) (2026)

## Abstract (arXiv)

Optimization-based meta-learning offers a promising direction for few-shot learning that is essential for many real-world computer vision applications. However, learning from few samples introduces uncertainty, and quantifying model confidence for few-shot predictions is essential for many critical domains. Furthermore, few-shot tasks used in meta training are usually sampled randomly from a task distribution for an iterative model update, leading to high labeling costs and computational overhead in meta-training. We propose a novel uncertainty-aware task selection model for label efficient meta-learning. The proposed model formulates a multidimensional belief measure, which can quantify the known uncertainty and lower bound the unknown uncertainty of any given task. Our theoretical result establishes an important relationship between the conflicting belief and the incorrect belief. The theoretical result allows us to estimate the total uncertainty of a task, which provides a principled criterion for task selection. A novel multi-query task formulation is further developed to improve both the computational and labeling efficiency of meta-learning. Experiments conducted over multiple real-world few-shot image classification tasks demonstrate the effectiveness of the proposed model.