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Register a new userMetaFun: Meta-Learning with Iterative Functional Updates
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We develop a functional encoder-decoder approach to supervised meta-learning, where labeled data is encoded into an infinite-dimensional functional representation rather than a finite-dimensional one. Furthermore, rather than directly producing the representation, we learn a neural update rule resembling functional gradient descent which iteratively improves the representation. The final representation is used to condition the decoder to make predictions on unlabeled data. Our approach is the first to demonstrates the success of encoder-decoder style meta-learning methods like conditional neural processes on large-scale few-shot classification benchmarks such as miniImageNet and tieredImageNet, where it achieves state-of-the-art performance.
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We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set of dynamic functional weights that can be visualized during the optimization process. This visualization leads to greater interpretability of the relationship between the covariates and the response relative to conventional neural networks. The model is shown to perform well in a number of contexts including prediction of new data and recovery of the true underlying functional weights; these results were confirmed through real applications and simulation studies. A forthcoming R package is developed on top of a popular deep learning library (Keras) allowing for general use of the approach.
Meta learning approaches to few-shot classification are computationally efficient at test time requiring just a few optimization steps or single forward pass to learn a new task, but they remain highly memory-intensive to train. This limitation arises because a tasks entire support set, which can contain up to 1000 images, must be processed before an optimization step can be taken. Harnessing the performance gains offered by large images thus requires either parallelizing the meta-learner across multiple GPUs, which may not be available, or trade-offs between task and image size when memory constraints apply. We improve on both options by proposing LITE, a general and memory efficient episodic training scheme that enables meta-training on large tasks composed of large images on a single GPU. We achieve this by observing that the gradients for a task can be decomposed into a sum of gradients over the tasks training images. This enables us to perform a forward pass on a tasks entire training set but realize significant memory savings by back-propagating only a random subset of these images which we show is an unbiased approximation of the full gradient. We use LITE to train meta-learners and demonstrate new state-of-the-art accuracy on the real-world ORBIT benchmark and 3 of the 4 parts of the challenging VTAB+MD benchmark relative to leading meta-learners. LITE also enables meta-learners to be competitive with transfer learning approaches but at a fraction of the test-time computational cost, thus serving as a counterpoint to the recent narrative that transfer learning is all you need for few-shot classification.
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.
While neural networks are powerful function approximators, they suffer from catastrophic forgetting when the data distribution is not stationary. One particular formalism that studies learning under non-stationary distribution is provided by continual learning, where the non-stationarity is imposed by a sequence of distinct tasks. Most methods in this space assume, however, the knowledge of task boundaries, and focus on alleviating catastrophic forgetting. In this work, we depart from this view and move the focus towards faster remembering -- i.e measuring how quickly the network recovers performance rather than measuring the networks performance without any adaptation. We argue that in many settings this can be more effective and that it opens the door to combining meta-learning and continual learning techniques, leveraging their complementary advantages. We propose a framework specific for the scenario where no information about task boundaries or task identity is given. It relies on a separation of concerns into what task is being solved and how the task should be solved. This framework is implemented by differentiating task specific parameters from task agnostic parameters, where the latter are optimized in a continual meta learning fashion, without access to multiple tasks at the same time. We showcase this framework in a supervised learning scenario and discuss the implication of the proposed formalism.
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