In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Example Input: When an image classifier makes a prediction, which parts of the image are relevant and why? We can rephrase this question to ask: which parts of the image, if they were not seen by the classifier, would most change its decision? Producing an answer requires marginalizing over images that could have been seen but weren't. We can sample plausible image in-fills by conditioning a generative model on the rest of the image. We then optimize to find the image regions that most change the classifier's decision after in-fill. Our approach contrasts with ad-hoc in-filling approaches, such as blurring or injecting noise, which generate inputs far from the data distribution, and ignore informative relationships between different parts of the image. Our method produces more compact and relevant saliency maps, with fewer artifacts compared to previous methods.
Example Output: We compute saliency by using a strong generative model to efficiently marginalize over plausible alternative inputs, revealing concentrated pixel areas that preserve label information.

Example Input: Computations for the softmax function in neural network models are expensive when the number of output classes is large. This can become a significant issue in both training and inference for such models. In this paper, we present Doubly Sparse Softmax (DS-Softmax), Sparse Mixture of Sparse of Sparse Experts, to improve the efficiency for softmax inference. During training, our method learns a two-level class hierarchy by dividing entire output class space into several partially overlapping experts. Each expert is responsible for a learned subset of the output class space and each output class only belongs to a small number of those experts. During inference, our method quickly locates the most probable expert to compute small-scale softmax. Our method is learning-based and requires no knowledge of the output class partition space a priori. We empirically evaluate our method on several real-world tasks and demonstrate that we can achieve significant computation reductions without loss of
Example Output: We present doubly sparse softmax, the sparse mixture of sparse of sparse experts, to improve the efficiency for softmax inference through exploiting the two-level overlapping hierarchy.

Example Input: Learning an efficient update rule from data that promotes rapid learning of new tasks from the same distribution remains an open problem in meta-learning. Typically, previous works have approached this issue either by attempting to train a neural network that directly produces updates or by attempting to learn better initialisations or scaling factors for a gradient-based update rule. Both these approaches pose challenges. On one hand, directly producing an update forgoes a useful inductive bias and can easily lead to non-converging behaviour. On the other hand, approaches that try to control a gradient-based update rule typically resort to computing gradients through the learning process to obtain their meta-gradients, leading to methods that can not scale beyond few-shot task adaptation. In this work we propose Warped Gradient Descent (WarpGrad), a method that intersects these approaches to mitigate their limitations. WarpGrad meta-learns an efficiently parameterised preconditioning matrix that facilitates gradient descent across the task distribution. Preconditioning arises by interleaving non-linear layers, referred to as warp-layers, between the layers of a task-learner. Warp-layers are meta-learned without backpropagating through the task training process in a manner similar to methods that learn to directly produce updates. WarpGrad is computationally efficient, easy to implement, and can scale to arbitrarily large meta-learning problems. We provide a geometrical interpretation of the approach and evaluate its effectiveness in a variety of settings, including few-shot, standard supervised, continual and reinforcement learning.
Example Output:
We propose a novel framework for meta-learning a gradient-based update rule that scales to beyond few-shot learning and is applicable to any form of learning, including continual learning.