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: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers.   After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.
Example Output: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning.

Example Input: Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers often with little or no drop in classification accuracy. However most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. In this paper we propose a cheap pruning algorithm based on difference of convex (DC) optimisation. We also provide theoretical analysis for the growth in the Generalisation Error (GE) of the new pruned network. Our method can be used with any convex regulariser and allows for a controlled degradation in classification accuracy while being orders of magnitude faster than competing approaches. Experiments on common feedforward neural networks show that for sparsity levels above 90% our method achieves 10% higher classification accuracy compared to Hard Thresholding.
Example Output: A fast pruning algorithm for fully connected DNN layers with theoretical analysis of degradation in Generalisation Error.

Example Input: We study model recovery for data classification, where the training labels are generated from a one-hidden-layer fully -connected neural network with sigmoid activations, and the goal is to recover the weight vectors of the neural network. We prove that under Gaussian inputs, the empirical risk function using cross entropy exhibits strong convexity and smoothness uniformly in a local neighborhood of the ground truth, as soon as the sample complexity is sufficiently large. This implies that if initialized in this neighborhood, which can be achieved via the tensor method, gradient descent converges linearly to a critical point that is provably close to the ground truth without requiring a fresh set of samples at each iteration. To the best of our knowledge, this is the first global convergence guarantee established for the empirical risk minimization using cross entropy via gradient descent for learning one-hidden-layer neural networks, at the near-optimal sample and computational complexity with respect to the network input dimension.
Example Output:
We provide the first theoretical analysis of guaranteed recovery of one-hidden-layer neural networks under cross entropy loss for classification problems.