PaperlayerView exact revision on arXiv

Source-linked AI summary

Probabilistic Model-Agnostic Meta-Learning

Chelsea Finn, Kelvin Xu, Sergey Levine

arXiv:1806.02817v2cs.LGcs.AIstat.ML

TL;DR

Few-shot task data can be ambiguous, making a single accurate model uncertain even with a learned prior. The paper extends MAML with variationally trained parameter distributions and noise-injected gradient adaptation, showing that it can sample plausible models for ambiguous tasks and support active learning.

  • Problem

    Few-shot examples may be too ambiguous to determine a single accurate task model, while scalable uncertainty modeling is difficult for expressive neural networks.

  • Method

    PLATIPUS extends MAML by training a parameter distribution with a variational lower bound so noise-injected gradient descent produces approximate posterior samples at meta-test time.

  • Results

    Experiments show plausible sampled regressors and classifiers for ambiguous few-shot problems, with better log-likelihood and comparable accuracy to standard MAML.

  • Takeaways & Limitations

    Sampling multiple task models enables uncertainty representation that can inform few-shot active learning and capture different modes of ambiguous tasks.

  • Takeaways & Limitations

    The current posterior-variance estimator is relatively impoverished and may be less effective when tasks differ in their degrees of ambiguity.

Abstract

from arXiv · show

Meta-learning for few-shot learning entails acquiring a prior over previous tasks and experiences, such that new tasks be learned from small amounts of data. However, a critical challenge in few-shot learning is task ambiguity: even when a powerful prior can be meta-learned from a large number of prior tasks, a small dataset for a new task can simply be too ambiguous to acquire a single model (e.g., a classifier) for that task that is accurate. In this paper, we propose a probabilistic meta-learning algorithm that can sample models for a new task from a model distribution. Our approach extends model-agnostic meta-learning, which adapts to new tasks via gradient descent, to incorporate a parameter distribution that is trained via a variational lower bound. At meta-test time, our algorithm adapts via a simple procedure that injects noise into gradient descent, and at meta-training time, the model is trained such that this stochastic adaptation procedure produces samples from the approximate model posterior. Our experimental results show that our method can sample plausible classifiers and regressors in ambiguous few-shot learning problems. We also show how reasoning about ambiguity can also be used for downstream active learning problems.

1 Introduction

Few-shot meta-learning can exploit shared structure across prior tasks, but ambiguous new-task data may support multiple plausible solutions. The paper seeks a scalable method that preserves uncertainty awareness while using expressive neural networks.

  • Motivation: Meta-learning discovers shared task structure so new tasks can be learned efficiently from few examples.The shared structure may include recurring visual features or semantic cues.
  • Motivation: Task ambiguity arises when few examples cannot resolve a new task with high certainty, motivating methods that propose multiple potential solutions.Such samples can support uncertainty evaluation, active learning, or direct human supervision.
  • Challenge: Modeling ambiguity is difficult for high-dimensional data, large function approximators, and multimodal task structure.Explicit distributions over millions of neural-network parameters can be intractable.
  • Motivation: Recent scalable few-shot methods often learn deterministic algorithms that disregard ambiguity over the underlying function.The paper asks whether scalability and uncertainty awareness can be combined.
  • Approach: The approach extends MAML, which uses gradient descent to adapt to new tasks and meta-trains parameters for rapid adaptation.MAML effectively learns a neural-network initialization suited to few-shot learning.
  • Contribution: The paper reframes MAML as graphical-model inference and uses variational inference to model uncertainty.Experiments target sampled regressors, sampled classifiers, and few-shot active learning.

2 Related Work

Prior few-shot methods provide either uncertainty modeling or scalable meta-learning, but the paper combines probabilistic inference with model-agnostic gradient-based adaptation. Its graphical model introduces dependencies that compensate for approximating task parameters with MAP inference.

  • Bayesian few-shot learning: Hierarchical Bayesian models naturally represent uncertainty over functions but had not scaled to the paper’s more complex few-shot problems.Earlier demonstrations focused on simple few-shot image-classification datasets.
  • Probabilistic meta-learning: The method is model agnostic and directly samples task-specific model weights for any network architecture.The paper contrasts this with approaches using an explicit task variable or architecture-specific uncertainty modeling.
  • Probabilistic meta-learning: The approach improves on MAML, which itself outperforms the model of Edwards and Storkey.This comparison is reported in the related-work discussion.
  • Probabilistic meta-learning: Unlike LLAMA’s local Laplace approximation, the method approximately infers pre-update parameters using a gradient-operation-parameterized approximate posterior.This avoids approximating a high-dimensional covariance matrix.
  • Bayesian neural networks: The approach explicitly trains a hierarchical Bayesian model over weights with a task-specific posterior conditioned on a learned weight prior and few-shot data.This distinguishes it from generic Bayesian neural-network approximations.
  • Graphical model: Figure 1 shows the graphical model changing after inference over φi and adding prior dependencies on training data.The added dependencies compensate for using a MAP estimate to approximate p(φi).

3 Preliminaries

Meta-learning trains models to adapt rapidly to new tasks drawn from a shared task distribution. MAML uses few-shot training data for gradient updates and held-out test data to optimize few-shot generalization.

  • Meta-learning setting: Meta-learning assumes training and testing tasks are sampled from a distribution whose tasks share exploitable structure.The objective is to discover that structure for faster learning of new tasks.
  • Meta-learning setting: Each task’s sampled data is split into few-shot training data Dtr and test data Dtest for measuring adaptation effectiveness.Dtest drives meta-training of the learning procedure.
  • MAML: MAML optimizes initial parameters θ so one or a few gradient-descent steps on Dtr achieve good performance on Dtest.This turns few-shot generalization into an optimization over adaptation-friendly initializations.
  • MAML: The adapted parameters φi are evaluated using a loss corresponding to the negative log likelihood of the data.For supervised classification, the loss is defined under classifier fθ.

4 Method

The method formulates few-shot learning as hierarchical probabilistic inference, extending MAML with distributions over global and task-specific parameters. Variational inference and gradient-based adaptation provide a scalable way to model uncertainty while retaining a simple test-time procedure.

  • Probabilistic formulation: The graphical model represents uncertainty over a prior parameter distribution θ and task-specific parameters φ_i for each few-shot task.Predictions depend on φ_i, which is influenced by the learned prior and observed training data.
  • Connection to MAML: MAML is interpreted as approximate posterior inference, with gradient descent on the training likelihood starting from the prior parameters; the equivalence is exact for Gaussian likelihoods and locally approximate otherwise.This implicit prior can better reflect nonlinear neural-network parameter structure than a simple explicit Gaussian prior.
  • Variational inference: Structured variational inference uses q_i(θ, φ_i)=q_i(θ)q_i(φ_i|θ) so uncertainty can propagate from θ to φ_i.Amortization uses a shared inference network conditioned on each task’s training inputs rather than storing a separate distribution for every task.
  • Gradient-based inference: The inference distribution reuses the learned prior mean and shifts it by a learned, coordinate-wise gradient step with diagonal covariance.The learned vector γ_q scales the gradient, while v_q supplies stochastic variation.
  • Hybrid inference: The simplified procedure samples global parameters from a learned distribution, then performs additional gradient-based MAP adaptation to obtain task-specific parameters.At meta-training, the variational objective uses likelihood terms evaluated with sampled parameters and a learned Gaussian prior; the algorithm requires no inference network at meta-test time.
  • Additional dependencies: Conditioning the learned prior on training data compensates for dependencies omitted by the crude approximation and yields a modified model trained with the corresponding likelihood term.The resulting approach uses stochastic adaptation to represent multiple plausible solutions.

5 Experiments

The experiments evaluate whether PLATIPUS can represent ambiguity by sampling plausible functions and improve few-shot learning and active learning relative to deterministic MAML. Across regression and classification settings, PLATIPUS represents uncertainty and uses it to select informative data.

  • Experimental setup: The evaluation compares PLATIPUS with MAML on ambiguous regression, classification, active learning, and image-classification tasks using matched architectures and inner-step counts.The experiments test sampling potential functions, improvement over MAML under ambiguity, and scaling to deep convolutional networks.
  • Regression: In 5-shot regression, PLATIPUS samples multiple sinusoidal and linear functions, whereas deterministic MAML learns a single function.PLATIPUS also reduces uncertainty as additional datapoints become available, despite training only on five-shot tasks.
  • Active learning: PLATIPUS uses uncertainty to select additional regression datapoints from regions with high variance across sampled functions.The active-learning setup starts with five datapoints in a constrained input region and permits up to five sequentially selected labels.
  • Active learning: After up to five selected datapoints, PLATIPUS decreases regression error more quickly than random selection and MAML.The comparison evaluates active-learning performance as additional datapoints are selected.
  • Classification: In 1-shot 2D classification, PLATIPUS samples circular decision boundaries with varying centers and sizes, while MAML produces one deterministic classifier.The task is highly ambiguous because only a single positive example is provided.
  • Ambiguous image classification: For ambiguous image classification, PLATIPUS achieves better log-likelihood and comparable accuracy to MAML while capturing closer to two of three possible task modes on average.Different sampled classifiers attend to different attributes, whereas deterministic MAML captures only one mode.

6 Discussion and Future Work

PLATIPUS enables sampling diverse task-specific models through noisy gradient adaptation and variational training, supporting ambiguous regression and classification as well as uncertainty-guided active learning. Its posterior-variance estimator remains limited when tasks differ in ambiguity.

  • Method: PLATIPUS adapts through gradient descent with injected noise to produce approximate samples from the model posterior.Meta-training optimizes a variational lower bound so this stochastic adaptation procedure can sample models conditioned on few-shot data.
  • Capabilities: The method samples diverse regressors and classifiers for ambiguous few-shot tasks, including task families with multimodal distributions.Figure 6 illustrates sampled classifiers capturing different explanations of an ambiguous training set.
  • Method: PLATIPUS introduces only a variance parameter for each model weight in addition to the initial weights, so added parameters scale linearly with model size.
  • Applications: Uncertainty from the sampled models can guide data acquisition and lead to better few-shot active learning.
  • Limitations: The posterior-variance estimator may be too impoverished when different tasks have different degrees of ambiguity.The paper suggests conditioning the variance estimator on the few-shot training set as future work.

A Ambiguous CelebA Details

The ambiguous CelebA benchmark partitions attributes across meta-training, validation, and testing, then constructs Boolean classification tasks from attribute combinations. Testing tasks use three attributes to create ambiguity across corresponding two-attribute pairs.

  • Dataset: CelebA uses canonical image splits of 162770/19867/19962 images for meta-training, validation, and testing.
  • Dataset: The 40 attributes are randomly partitioned into 25/5/10 attributes for meta-training, validation, and testing.
  • Task construction: Training tasks randomly sample two attributes as Boolean variables, assigning one class their shared setting and the other class the converse.For example, a task can classify not Smiling, Pale Skin versus Smiling, not Pale Skin.
  • Task construction: At test time, three attributes form the training task and their three corresponding two-tuples form the test task, yielding 583/19/53 meta-training, validation, and test tasks.
  • Preprocessing: Images are center-cropped to approximately 168 × 168 and downsampled to 84 × 84 to retain regions needed for non-facial attribute classification.

B Experimental Details

Experiments use matched neural architectures and specified inner-loop optimization settings, while meta-test evaluation samples models from the prior and averages results across test tasks.

  • Architecture: Illustrative experiments use a fully connected network with three ReLU layers of size 100 and a 20-dimensional bias transformation variable.
  • Optimization: Both methods use five inner gradient steps on Dtr, with step size α = 0.001 for regression and α = 0.01 for classification.
  • Optimization: PLATIPUS uses one gradient step for both its inference network and prior, while its objective weights the KL term differently by task setting.The stated KL weight is 1.5 for 1D regression and 0.01 for classification.
  • CelebA settings: For CelebA, the approximate posterior and prior match the dimensionality of the underlying model, with hyperparameters tuned over learning rate, KL weights, and variance initialization.
  • Evaluation: Meta-test evaluation takes 15 prior samples for assignment, averages results over 100 test tasks, and uses 100 prior samples for marginal log-likelihood.

C MiniImagenet Comparison

On the 5-way, 1-shot MiniImagenet benchmark, the method is compared using a standard 4-block convolutional architecture to separate algorithmic effects from architecture choice. It gives a small boost over MAML and remains comparable to other methods.

  • Experimental design: The benchmark is used for algorithm comparison rather than state-of-the-art performance because it contains limited ambiguity.
  • Results: On 5-way, 1-shot MiniImagenet, PLATIPUS gives a small accuracy boost over MAML and comparable performance to other prior approaches.
  • Experimental design: The comparison uses the standard 4-block convolutional architecture to decouple meta-learning algorithms from architecture effects.The authors note that tuning the architecture could improve performance.
Loading 1806.02817v2…