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.

Ex Input:
Noise injection is a fundamental tool for data augmentation, and yet there is no widely accepted procedure to incorporate it with learning frameworks. This study analyzes the effects of adding or applying different noise models of varying magnitudes to Convolutional Neural Network (CNN) architectures. Noise models that are distributed with different density functions are given common magnitude levels via Structural Similarity (SSIM) metric in order to create an appropriate ground for comparison. The basic results are conforming with the most of the common notions in machine learning, and also introduces some novel heuristics and recommendations on noise injection. The new approaches will provide better understanding on optimal learning procedures for image classification.

Ex Output:
Ideal methodology to inject noise to input data during CNN training

Ex Input:
We consider a simple and overarching representation for permutation-invariant functions of sequences (or set functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.

Ex Output:
We propose Janossy pooling, a method for learning deep permutation invariant functions designed to exploit relationships within the input sequence and tractable inference strategies such as a stochastic optimization procedure we call piSGD

Ex Input:
Character-level language modeling is an essential but challenging task in Natural Language Processing.
Prior works have focused on identifying long-term dependencies between characters and have built deeper and wider networks for better performance. However, their models require substantial computational resources, which hinders the usability of character-level language models in applications with limited resources. In this paper, we propose a lightweight model, called Group-Transformer, that reduces the resource requirements for a Transformer, a promising method for modeling sequence with long-term dependencies. Specifically, the proposed method partitions linear operations to reduce the number of parameters and computational cost. As a result, Group-Transformer only uses 18.2\% of parameters compared to the best performing LSTM-based model, while providing better performance on two benchmark tasks, enwik8 and text8. When compared to Transformers with a comparable number of parameters and time complexity, the proposed model shows better performance. The implementation code will be available.

Ex Output:
This paper proposes a novel lightweight Transformer for character-level language modeling, utilizing group-wise operations.