Some Approximation Bounds for Deep Networks

In this paper we introduce new bounds on the approximation of functions in deep networks and in doing so introduce some new deep network architectures for function approximation. These results give some theoretical insight into the success of autoencoders and ResNets.Comment: 9 page

Deep Radial Kernel Networks: Approximating Radially Symmetric Functions with Deep Networks

We prove that a particular deep network architecture is more efficient at approximating radially symmetric functions than the best known 2 or 3 layer networks. We use this architecture to approximate Gaussian kernel SVMs, and subsequently improve upon them with further training. The architecture and initial weights of the Deep Radial Kernel Network are completely specified by the SVM and therefore sidesteps the problem of empirically choosing an appropriate deep network architecture

PProCRC: Probabilistic Collaboration of Image Patches

We present a conditional probabilistic framework for collaborative representation of image patches. It incorporates background compensation and outlier patch suppression into the main formulation itself, thus doing away with the need for pre-processing steps to handle the same. A closed form non-iterative solution of the cost function is derived. The proposed method (PProCRC) outperforms earlier CRC formulations: patch based (PCRC, GP-CRC) as well as the state-of-the-art probabilistic (ProCRC and EProCRC) on three fine-grained species recognition datasets (Oxford Flowers, Oxford-IIIT Pets and CUB Birds) using two CNN backbones (Vgg-19 and ResNet-50)

Pseudo-Rehearsal: Achieving Deep Reinforcement Learning without Catastrophic Forgetting

Neural networks can achieve excellent results in a wide variety of applications. However, when they attempt to sequentially learn, they tend to learn the new task while catastrophically forgetting previous ones. We propose a model that overcomes catastrophic forgetting in sequential reinforcement learning by combining ideas from continual learning in both the image classification domain and the reinforcement learning domain. This model features a dual memory system which separates continual learning from reinforcement learning and a pseudo-rehearsal system that "recalls" items representative of previous tasks via a deep generative network. Our model sequentially learns Atari 2600 games while continuing to perform above human level and equally well as independent models trained separately on each game. This result is achieved without: demanding additional storage requirements as the number of tasks increases, storing raw data or revisiting past tasks. In comparison, previous state-of-the-art solutions are substantially more vulnerable to forgetting on these complex deep reinforcement learning tasks

Effects of the optimisation of the margin distribution on generalisation in deep architectures

Despite being so vital to success of Support Vector Machines, the principle of separating margin maximisation is not used in deep learning. We show that minimisation of margin variance and not maximisation of the margin is more suitable for improving generalisation in deep architectures. We propose the Halfway loss function that minimises the Normalised Margin Variance (NMV) at the output of a deep learning models and evaluate its performance against the Softmax Cross-Entropy loss on the MNIST, smallNORB and CIFAR-10 datasets

VASE: Variational Assorted Surprise Exploration for Reinforcement Learning

Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variational Assorted Surprise Exploration (VASE). VASE uses a Bayesian neural network as a model of the environment dynamics and is trained using variational inference, alternately updating the accuracy of the agent's model and policy. Our experiments show that in continuous control sparse reward environments VASE outperforms other surprise-based exploration techniques

Switched linear projections for neural network interpretability

We introduce switched linear projections for expressing the activity of a neuron in a deep neural network in terms of a single linear projection in the input space. The method works by isolating the active subnetwork, a series of linear transformations, that determine the entire computation of the network for a given input instance. With these projections we can decompose activity in any hidden layer into patterns detected in a given input instance. We also propose that in ReLU networks it is instructive and meaningful to examine patterns that deactivate the neurons in a hidden layer, something that is implicitly ignored by the existing interpretability methods tracking solely the active aspect of the network's computation

RocNet: Recursive Octree Network for Efficient 3D Deep Representation

We introduce a deep recursive octree network for the compression of 3D voxel data. Our network compresses a voxel grid of any size down to a very small latent space in an autoencoder-like network. We show results for compressing 32, 64 and 128 grids down to just 80 floats in the latent space. We demonstrate the effectiveness and efficiency of our proposed method on several publicly available datasets with three experiments: 3D shape classification, 3D shape reconstruction, and shape generation. Experimental results show that our algorithm maintains accuracy while consuming less memory with shorter training times compared to existing methods, especially in 3D reconstruction tasks

Conceptual capacity and effective complexity of neural networks

We propose a complexity measure of a neural network mapping function based on the diversity of the set of tangent spaces from different inputs. Treating each tangent space as a linear PAC concept we use an entropy-based measure of the bundle of concepts in order to estimate the conceptual capacity of the network. The theoretical maximal capacity of a ReLU network is equivalent to the number of its neurons. In practice however, due to correlations between neuron activities within the network, the actual capacity can be remarkably small, even for very big networks. Empirical evaluations show that this new measure is correlated with the complexity of the mapping function and thus the generalisation capabilities of the corresponding network. It captures the effective, as oppose to the theoretical, complexity of the network function. We also showcase some uses of the proposed measure for analysis and comparison of trained neural network models

Pseudo-Recursal: Solving the Catastrophic Forgetting Problem in Deep Neural Networks

In general, neural networks are not currently capable of learning tasks in a sequential fashion. When a novel, unrelated task is learnt by a neural network, it substantially forgets how to solve previously learnt tasks. One of the original solutions to this problem is pseudo-rehearsal, which involves learning the new task while rehearsing generated items representative of the previous task/s. This is very effective for simple tasks. However, pseudo-rehearsal has not yet been successfully applied to very complex tasks because in these tasks it is difficult to generate representative items. We accomplish pseudo-rehearsal by using a Generative Adversarial Network to generate items so that our deep network can learn to sequentially classify the CIFAR-10, SVHN and MNIST datasets. After training on all tasks, our network loses only 1.67% absolute accuracy on CIFAR-10 and gains 0.24% absolute accuracy on SVHN. Our model's performance is a substantial improvement compared to the current state of the art solution