We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is the Gaussian process neuron, a probabilistic unit that can be used as the basic building block for probabilistic graphical models that resemble the structure of neural networks. The proposed model can intrinsically handle uncertainties in its inputs and self-estimate the confidence of its predictions. Using variational Bayesian inference and the central limit theorem, a fully deterministic loss function is derived, allowing it to be trained as efficiently as a conventional neural network using mini-batch gradient descent. The posterior distribution of activation functions is inferred from the training data alongside the weights of the network. The proposed model favorably compares to deep Gaussian processes, both in model complexity and efficiency of inference. It can be directly applied to recurrent or convolutional network structures, allowing its use in audio and image processing tasks. As an preliminary empirical evaluation we present experiments on regression and classification tasks, in which our model achieves performance comparable to or better than a Dropout regularized neural network with a fixed activation function. Experiments are ongoing and results will be added as they become available.
This achievement led to a wave of follow-up research in activation functions specifically tailored to deep networks. While the ReLU solved the problem of vanishing gradients for positive values, it completely cut off the gradient for negative ones; thus once a neuron enters the negative regime (either through initialization or during training) for most samples, no training signal can pass through it. To mitigate this problem maas2013rectifier introduced the leaky ReLU, which is also linear for negative values but with a very small, although non-zero, slope; for positive values it behaves like the ReLU. Soon after he2015delving demonstrated that it is advantageous to make the slope of the negative part of the leaky ReLU an additional parameter of each neuron. This parameter was trained alongside the weights and biases of the neural network using gradient descent. A CNN using these so-called parametric ReLUs was the first to surpass human-level performance on the ImageNet classification task @cite_9 .
@cite_9
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In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evaluate these activation function on standard image classification task. Our experiments suggest that incorporating a non-zero slope for negative part in rectified activation units could consistently improve the results. Thus our findings are negative on the common belief that sparsity is the key of good performance in ReLU. Moreover, on small scale dataset, using deterministic negative slope or learning it are both prone to overfitting. They are not as effective as using their randomized counterpart. By using RReLU, we achieved 75.68 accuracy on CIFAR-100 test set without multiple test or ensemble. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. Learning Convolutional Neural Networks (CNN) is commonly carried out by plain supervised gradient descent. With sufficient training data, this leads to very competitive results for visual recognition tasks when starting from a random initialization. When the amount of labeled data is limited, CNNs reveal their strong dependence on large amounts of training data. However, recent results have shown that a well chosen optimization starting point can be beneficial for convergence to a good generalizing minimum. This starting point was mostly found using unsupervised feature learning techniques such as sparse coding or transfer learning from related recognition tasks. In this work, we compare these two approaches against a simple patch based initialization scheme and a random initialization of the weights. We show that pre-training helps to train CNNs from few samples and that the correct choice of the initialization scheme can push the network's performance by up to 41 compared to random initialization. In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is @math in a basin of attraction near the global optima for most popular activation functions, like ReLU, Leaky ReLU, Squared ReLU, Sigmoid and Tanh. The required sample complexity is proportional to the dimension of the input and polynomial in the number of kernels and a condition number of the parameters. We also show that tensor methods are able to initialize the parameters to the local strong convex region. Hence, for most smooth activations, gradient descent following tensor initialization is guaranteed to converge to the global optimal with time that is linear in input dimension, logarithmic in precision and polynomial in other factors. To the best of our knowledge, this is the first work that provides recovery guarantees for CNNs with multiple kernels under polynomial sample and computational complexities.