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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
Meta-Learning without Memorization
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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- 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
- 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)
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 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
- 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
- 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.
- Zhou acknowledge the support of the U.S National Science Foundation under Grant IIS-1812699
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- Similar to (Achille & Soatto, 2018), we use ξ to denote the unknown parameters of the true data generating distribution. This defines a joint distribution p(ξ, M, θ) = p(ξ)p(M|ξ)q(θ|M). Furthermore, we have a predictive distribution q(y∗|x∗, D, θ) = Eφ|θ,D [q(y∗|x∗, φ, θ)].
- The meta-training loss in Eq. 1 is an upper bound for the cross entropy Hp,q(y1∗:N |x∗1:N, D1:N, θ). Using an information decomposition of cross entropy (Achille & Soatto, 2018), we have
- where for exposition we assume K = |Di∗| is the same for all i. We would like to relate er(Q) and er(Q, D1, D1∗,..., Dn, Dn∗ ), but the challenge is that Q may depend on D1, D1∗,..., Dn, Dn∗ due to the learning algorithm. There are two sources of generalization error: (i) error due to the finite number of observed tasks and (ii) error due to the finite number of examples observed per task. Closely following the arguments in (Amit & Meir, 2018), we apply a standard PAC-Bayes bound to each of these and combine the results with a union bound.
- Q(θ)q(φ|θ, Di)dθ for any Q. While, π and ρ may be complicated distributions (especially, if they are defined implicitly), we know that with this choice of π and ρ, DKL(ρ||π) ≤ DKL(Q||P ) (Cover & Thomas, 2012), hence, we have
- We create a multi-task regression dataset based on the Pascal 3D data (Xiang et al., 2014). The dataset consists of 10 classes of 3D object such as “aeroplane”, “sofa”, “TV monitor”, etc. Each class has multiple different objects and there are 65 objects in total. We randomly select 50 objects for meta-training and the other 15 objects for meta-testing. For each object, we use MuJoCo (Todorov et al., 2012) to render 100 images with random orientations of the instance on a table, visualized in Figure 1. For the meta-learning algorithm, the observation (x) is the 128 × 128 gray-scale image and the label (y) is the orientation re-scaled to be within [0, 10]. For each task, we randomly sample