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.
--------
Question: In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values. But it cannot provide useful gradients and therefore requires complex optimization techniques. The L1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant and causes the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between L1 and L2 norms) used in traditional compressed sensing problems, we present DeepHoyer, a set of sparsity-inducing regularizers that are both differentiable almost everywhere and scale-invariant. Our experiments show that enforcing DeepHoyer regularizers can produce even sparser neural network models than previous works, under the same accuracy level. We also show that DeepHoyer can be applied to both element-wise and structural pruning.

Answer: We propose almost everywhere differentiable and scale invariant regularizers for DNN pruning, which can lead to supremum sparsity through standard SGD training.

Question: We propose a solution for evaluation of mathematical expression. However, instead of designing a single end-to-end model we propose a Lego bricks style architecture. In this architecture instead of training a complex end-to-end neural network, many small networks can be trained independently each accomplishing one specific operation and acting a single lego brick. More difficult or complex task can then be solved using a combination of these smaller network. In this work we first identify 8 fundamental operations that are commonly used to solve arithmetic operations (such as 1 digit multiplication, addition, subtraction, sign calculator etc). These fundamental operations are then learned using simple feed forward neural networks. We then shows that different operations can be designed simply by reusing these smaller networks. As an example we reuse these smaller networks to develop larger and a more complex network to solve n-digit multiplication, n-digit division, and cross product. This bottom-up strategy not only introduces reusability, we also show that it allows to generalize for computations involving n-digits and we show results for up to 7 digit numbers. Unlike existing methods, our solution also generalizes for both positive as well as negative numbers.

Answer: We train many small networks each for a specific operation, these are then combined to perform complex operations

Question: Previous work on adversarially robust neural networks requires large training sets and computationally expensive training procedures. On the other hand, few-shot learning methods are highly vulnerable to adversarial examples. The goal of our work is to produce networks which both perform well at few-shot tasks and are simultaneously robust to adversarial examples. We adapt adversarial training for meta-learning, we adapt robust architectural features to small networks for meta-learning, we test pre-processing defenses as an alternative to adversarial training for meta-learning, and we investigate the advantages of robust meta-learning over robust transfer-learning for few-shot tasks. This work provides a thorough analysis of adversarially robust methods in the context of meta-learning, and we lay the foundation for future work on defenses for few-shot tasks.

Answer:
We develop meta-learning methods for adversarially robust few-shot learning.