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Laplacian Regularized Few-Shot Learning
Imtiaz Masud Ziko, Jose Dolz, Eric Granger, Ismail Ben Ayed
TL;DR
Few-shot learning seeks to classify novel classes from only a few labeled examples despite the limited generalization of models trained on base classes. The paper introduces transductive Laplacian-regularized inference that combines prototype assignments with query-graph consistency without retraining the base model, and reports consistent gains across five benchmarks without complex meta-learning. Its efficient parallel optimizer supports fast transductive inference, while the relaxation is approximate for soft assignments.
Problem
Models trained on large labeled base datasets struggle to generalize to novel classes when only a few labeled examples are available.
Method
LaplacianShot combines nearest-prototype unary assignments with a pairwise Laplacian regularizer over query features, using parallel updates without retraining the base model.
Results
LaplacianShot consistently outperforms state-of-the-art methods across five few-shot benchmarks, models, settings, and datasets without complex meta-learning.
Takeaways & Limitations
The transductive method provides state-of-the-art results and can be used with any base-class training model while remaining suitable for fast, large-scale few-shot inference.
Takeaways & Limitations
The equivalence used in the optimization is exact for binary simplex-vertex assignments but only approximate for soft assignments.
Abstract
from arXiv · showhide
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.
1. Introduction
Few-shot learning addresses the difficulty of adapting models trained on large labeled base datasets to novel classes with only a few labeled examples. Prior transductive methods improve joint query prediction but can incur substantial inference costs, motivating LaplacianShot's efficient graph-based alternative.
- Deep models rely on extensive labeled datasets yet struggle to generalize to unseen classes from only a few examples.
- Few-shot learning trains on base classes, then evaluates novel-class tasks using limited support labels and unlabeled query samples.
- Much prior few-shot work uses complex meta-learning and episodic training to simulate test-time generalization during base training.
- Transductive inference predicts all unlabeled query samples jointly, with prior approaches using label propagation, attention, or inference-time fine-tuning.
- Prior transductive methods can be computationally heavy because they retrain networks or require matrix inversion cubic in the number of query samples.
- LaplacianShot proposes efficient transductive inference that avoids base-model retraining and updates query assignments independently in parallel with guaranteed convergence.
2. Laplacian Regularized Few-Shot Learning
LaplacianShot formulates transductive few-shot inference as a prototype-based assignment problem regularized by query-sample affinities. A relaxed bound-optimization solver provides convergent, parallel updates without retraining the base model.
- Problem: The task classifies unlabeled query samples from C novel classes using limited labeled support examples.The setting is |X_c^s|-shot C-way few-shot learning.
- Proposed formulation: LaplacianShot uses a base embedding trained with standard cross-entropy, then optimizes binary assignment variables subject to simplex constraints during transductive inference.The method does not require complex episodic or meta-learning training.
- Proposed formulation: The objective combines unary nearest-prototype assignments with a Laplacian term that encourages nearby query features to share labels.The pairwise term is equivalently written as tr(Y^tLY), with affinities determined by feature similarity.
- Optimization: Bound optimization guarantees that the original objective does not increase, while independent point-wise updates support parallel computation.The algorithm typically converges in fewer than 15 iterations in the reported experiments.
- Optimization: Relaxing integer constraints yields a concave Laplacian component when the symmetric affinity matrix is positive semidefinite, enabling efficient optimization.The relaxed expression approximates the original Laplacian term inside the simplex and is exact at simplex vertices.
- Optimization: A negative-entropy barrier avoids expensive projection and inner dual iterations while preserving simplex-feasible soft assignments.The barrier also produces closed-form updates for the equality constraints.
3. Experiments
Experiments span five few-shot benchmarks, multiple backbone models, standard and challenging data settings, and studies of regularization, convergence, and inference time. LaplacianShot consistently improves accuracy while retaining fast, convergent transductive inference.
- Experimental setup: Experiments cover generic, fine-grained, cross-domain, and imbalanced few-shot classification across miniImageNet, tieredImageNet, CUB, cross-domain CUB, and iNat.The evaluation uses multiple network models and standard few-shot task protocols.
- Generic image classification: Nearly 22%, 17%, and 9% improvements are reported over MAML, ProtoNet, and MetaoptNet, respectively, under the same evaluation conditions.These gains occur in challenging 1-shot settings with low-capacity models.
- Fine-grained image classification: 7% margin over the best-performing method is reported for fine-grained CUB few-shot classification with ResNet-18.The comparison is reported for the CUB setting in Table 2.
- Imbalanced class distribution: Laplacian regularization yields significant improvements on class-imbalanced iNat across network models and feature normalizations.Unlike SimpleShot, LaplacianShot performs best with unnormalized features and does not use rectified prototypes on iNat.
- Regularization parameter: Validation-selected λ values generally correspond to good test accuracy, with λ = 0.7 best for 1-shot tasks and λ = 0.1 mostly best for 5-shot test tasks.The study evaluates λ values from 0.1 to 1.5 on miniImageNet.
- Ablation and convergence: The Laplacian term improves 1-shot performance by at least 3%, while the iterative bound optimizer typically converges in fewer than 15 iterations.The ablation uses ResNet-18, and the convergence study examines different network features with λ = 1.0.
4. Conclusion
The conclusion reports strong performance without meta-learning and presents LaplacianShot as a simple, broadly compatible transductive graph-clustering method.
- Without meta-learning, LaplacianShot achieves state-of-the-art results across all evaluated benchmarks.The method consistently improves performance with different base-class training models and benchmark datasets.