Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques. Deep neural networks (DNNs) are a potentially promising and under-explored solution to solve these problems due to their powerful function approximation abilities, and their fast feed-forward computation. In this paper, we outline a method for converting an orienteering problem into a classification problem, and design a customised multi-layer deep learning network to approximate traditional optimisation solutions to this problem. We test the performance of the network on a real-world parking violation dataset, and conduct a generic study that empirically shows the critical architectural components that affect network performance for this problem.
Additionally, there numerous recent works in effectively combining optimisation with deep learning. Fischetti and Jo modelled deep neural networks as a 0-1 mixed integer linear program @cite_2 . used a deep neural net to learn the structure of a combinatorial problem, and mentioned that such research is still at an early stage @cite_3 . Our work makes a small contribution to this area.
@cite_3 @cite_2
2214429195 2763421725 1645800954 2248723555
Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to applications like question answering that may involve complex arithmetic and logic reasoning. A major limitation of these models is in their inability to learn even simple arithmetic and logic operations. For example, it has been shown that neural networks fail to learn to add two binary numbers reliably. In this work, we propose Neural Programmer, an end-to-end differentiable neural network augmented with a small set of basic arithmetic and logic operations. Neural Programmer can call these augmented operations over several steps, thereby inducing compositional programs that are more complex than the built-in operations. The model learns from a weak supervision signal which is the result of execution of the correct program, hence it does not require expensive annotation of the correct program itself. The decisions of what operations to call, and what data segments to apply to are inferred by Neural Programmer. Such decisions, during training, are done in a differentiable fashion so that the entire network can be trained jointly by gradient descent. We find that training the model is difficult, but it can be greatly improved by adding random noise to the gradient. On a fairly complex synthetic table-comprehension dataset, traditional recurrent networks and attentional models perform poorly while Neural Programmer typically obtains nearly perfect accuracy. Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models also increases. We introduce a technique to train deep neural networks using half precision floating point numbers. In our technique, weights, activations and gradients are stored in IEEE half-precision format. Half-precision floating numbers have limited numerical range compared to single-precision numbers. We propose two techniques to handle this loss of information. Firstly, we recommend maintaining a single-precision copy of the weights that accumulates the gradients after each optimizer step. This single-precision copy is rounded to half-precision format during training. Secondly, we propose scaling the loss appropriately to handle the loss of information with half-precision gradients. We demonstrate that this approach works for a wide variety of models including convolution neural networks, recurrent neural networks and generative adversarial networks. This technique works for large scale models with more than 100 million parameters trained on large datasets. Using this approach, we can reduce the memory consumption of deep learning models by nearly 2x. In future processors, we can also expect a significant computation speedup using half-precision hardware units. Deep neural networks such as Convolutional Networks (ConvNets) and Deep Belief Networks (DBNs) represent the state-of-the-art for many machine learning and computer vision classification problems. To overcome the large computational cost of deep networks, spiking deep networks have recently been proposed, given the specialized hardware now available for spiking neural networks (SNNs). However, this has come at the cost of performance losses due to the conversion from analog neural networks (ANNs) without a notion of time, to sparsely firing, event-driven SNNs. Here we analyze the effects of converting deep ANNs into SNNs with respect to the choice of parameters for spiking neurons such as firing rates and thresholds. We present a set of optimization techniques to minimize performance loss in the conversion process for ConvNets and fully connected deep networks. These techniques yield networks that outperform all previous SNNs on the MNIST database to date, and many networks here are close to maximum performance after only 20 ms of simulated time. The techniques include using rectified linear units (ReLUs) with zero bias during training, and using a new weight normalization method to help regulate firing rates. Our method for converting an ANN into an SNN enables low-latency classification with high accuracies already after the first output spike, and compared with previous SNN approaches it yields improved performance without increased training time. The presented analysis and optimization techniques boost the value of spiking deep networks as an attractive framework for neuromorphic computing platforms aimed at fast and efficient pattern recognition. Deep learning methods such as convolutional neural networks (CNNs) can deliver highly accurate classification results when provided with large enough data sets and respective labels. However, using CNNs along with limited labeled data can be problematic, as this leads to extensive overfitting. In this letter, we propose a novel method by considering a pretrained CNN designed for tackling an entirely different classification problem, namely, the ImageNet challenge, and exploit it to extract an initial set of representations. The derived representations are then transferred into a supervised CNN classifier, along with their class labels, effectively training the system. Through this two-stage framework, we successfully deal with the limited-data problem in an end-to-end processing scheme. Comparative results over the UC Merced Land Use benchmark prove that our method significantly outperforms the previously best stated results, improving the overall accuracy from 83.1 up to 92.4 . Apart from statistical improvements, our method introduces a novel feature fusion algorithm that effectively tackles the large data dimensionality by using a simple and computationally efficient approach.