Meta-Learning without Memorization

ICLR, 2020.

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Other Links: dblp.uni-trier.de|arxiv.org
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We show that meta-regularization in model-agnostic meta-learning can be rigorously motivated by a PAC-Bayes bound on generalization

Abstract:

The ability to learn new concepts with small amounts of data is a critical aspect of intelligence that has proven challenging for deep learning methods. Meta-learning has emerged as a promising technique for leveraging data from previous tasks to enable efficient learning of new tasks. However, most meta-learning algorithms implicitly req...More
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Introduction
  • The ability to learn new concepts and skills with small amounts of data is a critical aspect of intelligence that many machine learning systems lack.
  • The meta-learner is trained such that, after being presented with a small task training set, it can accurately make predictions on test datapoints for that meta-training task.
  • The model will collapse to one that makes zero-shot decisions
  • This presents an opportunity for overfitting where the meta-learner generalizes on meta-training tasks, but fails to adapt when presented with training data from novel tasks.
  • The authors call this form of overfitting the memorization problem in meta-learning because the meta-learner memorizes a function that solves all of the meta-training tasks, rather than learning to adapt
Highlights
  • The ability to learn new concepts and skills with small amounts of data is a critical aspect of intelligence that many machine learning systems lack
  • We show that meta-regularization in model-agnostic meta-learning can be rigorously motivated by a PAC-Bayes bound on generalization
  • We find that model-agnostic meta-learning and conditional neural processes frequently converge to this memorization solution (Table 2)
  • We consider model-agnostic meta-learning (MAML) and conditional neural processes (CNP) as representative meta-learning algorithms. We study both variants of our method in combination with model-agnostic meta-learning and conditional neural processes
  • Once we add the additional amplitude input which indicates the task identity, we find that both model-agnostic meta-learning and conditional neural processes converge to the complete memorization solution and fail to generalize well to test data (Table 1 and Appendix Figures 7 and 8)
  • We evaluate model-agnostic meta-learning, TAML (Jamal & Qi, 2019), MR-model-agnostic meta-learning, fine-tuning, and a nearest neighbor baseline on non-mutually-exclusive classification tasks (Table 4)
Methods
  • MAML

    MR-MAML (A) MR-MAML (W) CNP

    MR-CNP (A) MR-CNP (W)

    5 shot 0.46 (0.04) 10 shot 0.13 (0.01)

    6.2 POSE PREDICTION

    To illustrate the memorization problem on a more realistic task, the authors create a multi-task regression dataset based on the Pascal 3D data (Xiang et al, 2014) (See Appendix A.5.1 for a complete description).
  • Because the number of objects in the meta-training dataset is small, it is straightforward for a single network to memorize the canonical pose for each training object and to infer the orientation from the input image, achieving a low meta-training error without using D.
  • The high pre-update meta-training accuracy and low meta-test accuracy are evidence of the memorization problem for MAML and TAML, indicating that it is learning a model that ignores the task data.
  • MR-MAML successfully controls the pre-update accuracy to be near chance and encourages the learner to use the task training data to achieve low meta-training error, resulting in good performance at meta-test time
Conclusion
  • CONCLUSION AND DISCUSSION

    Meta-learning has achieved remarkable success in few-shot learning problems.
  • The key idea is that by placing a soft restriction on the information flow from meta-parameters in prediction of test set labels, the authors can encourage the meta-learner to use task training data during meta-training.
  • The authors achieve this by successfully controlling the complexity of model prior to the task adaptation
Summary
  • Introduction:

    The ability to learn new concepts and skills with small amounts of data is a critical aspect of intelligence that many machine learning systems lack.
  • The meta-learner is trained such that, after being presented with a small task training set, it can accurately make predictions on test datapoints for that meta-training task.
  • The model will collapse to one that makes zero-shot decisions
  • This presents an opportunity for overfitting where the meta-learner generalizes on meta-training tasks, but fails to adapt when presented with training data from novel tasks.
  • The authors call this form of overfitting the memorization problem in meta-learning because the meta-learner memorizes a function that solves all of the meta-training tasks, rather than learning to adapt
  • Methods:

    MAML

    MR-MAML (A) MR-MAML (W) CNP

    MR-CNP (A) MR-CNP (W)

    5 shot 0.46 (0.04) 10 shot 0.13 (0.01)

    6.2 POSE PREDICTION

    To illustrate the memorization problem on a more realistic task, the authors create a multi-task regression dataset based on the Pascal 3D data (Xiang et al, 2014) (See Appendix A.5.1 for a complete description).
  • Because the number of objects in the meta-training dataset is small, it is straightforward for a single network to memorize the canonical pose for each training object and to infer the orientation from the input image, achieving a low meta-training error without using D.
  • The high pre-update meta-training accuracy and low meta-test accuracy are evidence of the memorization problem for MAML and TAML, indicating that it is learning a model that ignores the task data.
  • MR-MAML successfully controls the pre-update accuracy to be near chance and encourages the learner to use the task training data to achieve low meta-training error, resulting in good performance at meta-test time
  • Conclusion:

    CONCLUSION AND DISCUSSION

    Meta-learning has achieved remarkable success in few-shot learning problems.
  • The key idea is that by placing a soft restriction on the information flow from meta-parameters in prediction of test set labels, the authors can encourage the meta-learner to use task training data during meta-training.
  • The authors achieve this by successfully controlling the complexity of model prior to the task adaptation
Tables
  • Table1: Test MSE for the non-mutually-exclusive sinusoid regression problem. We compare MAML and CNP against meta-regularized MAML (MR-MAML) and meta-regularized CNP (MR-CNP) where regularization is either on the activations (A) or the weights (W). We report the mean over 5 trials and the standard deviation in parentheses
  • Table2: Meta-test MSE for the pose prediction problem. We compare MR-MAML (ours) with conventional MAML and fine-tuning (FT). We report the average over 5 trials and standard deviation in parentheses
  • Table3: Meta-testing MSE for the pose prediction problem. We compare MR-CNP (ours) with conventional CNP, CNP with weight decay, and CNP with Bayes-by-Backprop (BbB) regularization on all the weights. We report the average over 5 trials and standard deviation in parentheses
  • Table4: Meta-test accuracy on non-mutually-exclusive (NME) classification. The fine-tuning and nearestneighbor baseline results for MiniImagenet are from (<a class="ref-link" id="cRavi_2016_a" href="#rRavi_2016_a">Ravi & Larochelle, 2016</a>)
  • Table5: Meta-training pre-update accuracy on non-mutually-exclusive classification. MR-MAML controls the meta-training pre-update accuracy close to random guess and achieves low training error after adaptation
Download tables as Excel
Related work
  • Previous works have developed approaches for mitigating various forms of overfitting in metalearning. These approaches aim to improve generalization in several ways: by reducing the number of parameters that are adapted in MAML (Zintgraf et al, 2019), by compressing the task embedding (Lee et al, 2019), through data augmentation from a GAN (Zhang et al, 2018), by using an auxiliary objective on task gradients (Guiroy et al, 2019), and via an entropy regularization objective (Jamal & Qi, 2019). These methods all focus on the setting with mutually-exclusive task distributions. We instead recognize and formalize the memorization problem, a particular form of overfitting that manifests itself with non-mutually-exclusive tasks, and offer a general and principled solution. Unlike prior methods, our approach is applicable to both contextual and gradientbased meta-learning methods. We additionally validate that prior regularization approaches, namely TAML (Jamal & Qi, 2019), are not effective for addressing this problem setting.
Funding
  • Zhou acknowledge the support of the U.S National Science Foundation under Grant IIS-1812699
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