# Laplacian Regularized Few-Shot Learning

arXiv: https://arxiv.org/abs/2006.15486 · HTML: https://mlsanity.com/paper/2006.15486/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 30 of 92)

- [Parameter-free Online Test-time Adaptation](https://mlsanity.com/paper/2201.05718/) (2022)
- [A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunities](https://mlsanity.com/paper/2205.06743/) (2022)
- [Learning from Few Examples: A Summary of Approaches to Few-Shot Learning](https://mlsanity.com/paper/2203.04291/) (2022)
- [Relational Embedding for Few-Shot Classification](https://mlsanity.com/paper/2108.09666/) (2021)
- [Joint Distribution Matters: Deep Brownian Distance Covariance for Few-Shot Classification](https://mlsanity.com/paper/2204.04567/) (2022)
- [Boosting Vision-Language Models with Transduction](https://mlsanity.com/paper/2406.01837/) (2024)
- [Transductive Zero-Shot and Few-Shot CLIP](https://mlsanity.com/paper/2405.18437/) (2024)
- [Meta Discovery: Learning to Discover Novel Classes given Very Limited Data](https://mlsanity.com/paper/2102.04002/) (2021)
- [Transductive Few-shot Learning with Prototype-based Label Propagation by Iterative Graph Refinement](https://mlsanity.com/paper/2304.11598/) (2023)
- [Realistic Evaluation of Transductive Few-Shot Learning](https://mlsanity.com/paper/2204.11181/) (2022)
- [Transductive Few-Shot Classification on the Oblique Manifold](https://mlsanity.com/paper/2108.04009/) (2021)
- [Inductive and Transductive Few-Shot Video Classification via Appearance and Temporal Alignments](https://mlsanity.com/paper/2207.10785/) (2022)
- [A Strong Baseline for Generalized Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2211.14126/) (2022)
- [Bilevel Fast Scene Adaptation for Low-Light Image Enhancement](https://mlsanity.com/paper/2306.01343/) (2023)
- [FHIST: A Benchmark for Few-shot Classification of Histological Images](https://mlsanity.com/paper/2206.00092/) (2022)
- [Reinforced Attention for Few-Shot Learning and Beyond](https://mlsanity.com/paper/2104.04192/) (2021)
- [EASY: Ensemble Augmented-Shot Y-shaped Learning: State-Of-The-Art Few-Shot Classification with Simple Ingredients](https://mlsanity.com/paper/2201.09699/) (2022)
- [POODLE: Improving Few-shot Learning via Penalizing Out-of-Distribution Samples](https://mlsanity.com/paper/2206.04679/) (2022)
- [Squeezing Backbone Feature Distributions to the Max for Efficient Few-Shot Learning](https://mlsanity.com/paper/2110.09446/) (2021)
- [Realistic Test-Time Adaptation of Vision-Language Models](https://mlsanity.com/paper/2501.03729/) (2025)
- [Few-Shot Learning with Uncertainty-based Quadruplet Selection for Interference Classification in GNSS Data](https://mlsanity.com/paper/2402.09466/) (2024)
- [MetaNODE: Prototype Optimization as a Neural ODE for Few-Shot Learning](https://mlsanity.com/paper/2103.14341/) (2021)
- [Hubs and Hyperspheres: Reducing Hubness and Improving Transductive Few-shot Learning with Hyperspherical Embeddings](https://mlsanity.com/paper/2303.09352/) (2023)
- [MetaDelta: A Meta-Learning System for Few-shot Image Classification](https://mlsanity.com/paper/2102.10744/) (2021)
- [Adaptive Dimension Reduction and Variational Inference for Transductive Few-Shot Classification](https://mlsanity.com/paper/2209.08527/) (2022)
- [Open-Set Likelihood Maximization for Few-Shot Learning](https://mlsanity.com/paper/2301.08390/) (2023)
- [Towards Practical Few-Shot Query Sets: Transductive Minimum Description Length Inference](https://mlsanity.com/paper/2210.14545/) (2022)
- [Nearest Neighbour Few-Shot Learning for Cross-lingual Classification](https://mlsanity.com/paper/2109.02221/) (2021)
- [Prototypes-oriented Transductive Few-shot Learning with Conditional Transport](https://mlsanity.com/paper/2308.03047/) (2023)
- [Enhancing Remote Sensing Vision-Language Models for Zero-Shot Scene Classification](https://mlsanity.com/paper/2409.00698/) (2024)

## Abstract (arXiv)

We propose a transductive Laplacian-regularized inference for few-shot tasks. Given any feature embedding learned from the base classes, we minimize a quadratic binary-assignment function containing two terms: (1) a unary term assigning query samples to the nearest class prototype, and (2) a pairwise Laplacian term encouraging nearby query samples to have consistent label assignments. Our transductive inference does not re-train the base model, and can be viewed as a graph clustering of the query set, subject to supervision constraints from the support set. We derive a computationally efficient bound optimizer of a relaxation of our function, which computes independent (parallel) updates for each query sample, while guaranteeing convergence. Following a simple cross-entropy training on the base classes, and without complex meta-learning strategies, we conducted comprehensive experiments over five few-shot learning benchmarks. Our LaplacianShot consistently outperforms state-of-the-art methods by significant margins across different models, settings, and data sets. Furthermore, our transductive inference is very fast, with computational times that are close to inductive inference, and can be used for large-scale few-shot tasks.