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:
We conduct a mathematical analysis on the Batch normalization (BN) effect on gradient backpropagation in residual network training in this work, which is believed to play a critical role in addressing the gradient vanishing/explosion problem. Specifically, by analyzing the mean and variance behavior of the input and the gradient in the forward and backward passes through the BN and residual branches, respectively, we show that they work together to confine the gradient variance to a certain range across residual blocks in backpropagation. As a result, the gradient vanishing/explosion problem is avoided. Furthermore, we use the same analysis to discuss the tradeoff between depth and width of a residual network and demonstrate that shallower yet wider resnets have stronger learning performance than deeper yet thinner resnets.

Ex Output:
Batch normalisation maintains gradient variance throughout training, thus stabilizing optimization.

Ex Input:
Goal recognition is the problem of inferring the correct goal towards which an agent executes a plan, given a set of goal hypotheses, a domain model, and a (possibly noisy) sample of the plan being executed.
This is a key problem in both cooperative and competitive agent interactions and recent approaches have produced fast and accurate goal recognition algorithms.
In this paper, we leverage advances in operator-counting heuristics computed using linear programs over constraints derived from classical planning problems to solve goal recognition problems.
Our approach uses additional operator-counting constraints derived from the observations to efficiently infer the correct goal, and serves as basis for a number of further methods with additional constraints.

Ex Output:
A goal recognition approach based on operator counting heuristics used to account for noise in the dataset.

Ex Input:
Intrinsically motivated goal exploration algorithms enable machines to discover repertoires of policies that produce a diversity of effects in complex environments. These exploration algorithms have been shown to allow real world robots to acquire skills such as tool use in high-dimensional continuous state and action spaces. However, they have so far assumed that self-generated goals are sampled in a specifically engineered feature space, limiting their autonomy. In this work, we propose an approach using deep representation learning algorithms to learn an adequate goal space. This is a developmental 2-stage approach: first, in a perceptual learning stage, deep learning algorithms use passive raw sensor observations of world changes to learn a corresponding latent space; then goal exploration happens in a second stage by sampling goals in this latent space. We present experiments with a simulated robot arm interacting with an object, and we show that exploration algorithms using such learned representations can closely match, and even sometimes improve, the performance obtained using engineered representations.

Ex Output:
We propose a novel Intrinsically Motivated Goal Exploration architecture with unsupervised learning of goal space representations, and evaluate how various implementations enable the discovery of a diversity of policies.