A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. In this paper, two novel learning techniques are introduced which use BL for improving robustness to white noise static and adversarial examples. The first method is bidirectional propagation of errors, which the error propagation occurs in backward and forward directions. Motivated by the fact that its generative model receives as input a constant vector per class, we introduce as a second method the hybrid adversarial networks (HAN). Its generative model receives a random vector as input and its training is based on generative adversarial networks (GAN). To assess the performance of BL, we perform experiments using several architectures with fully and convolutional layers, with and without bias. Experimental results show that both methods improve robustness to white noise static and adversarial examples, but have different behaviour depending on the architecture and task, being more beneficial to use the one or the other. Nevertheless, HAN using a convolutional architecture with batch normalization presents outstanding robustness, reaching state-of-the-art accuracy on adversarial examples of hand-written digits.
High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such “autoencoder” networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data. This paper describes a machine learning approach for visual object detection which is capable of processing images extremely rapidly and achieving high detection rates. This work is distinguished by three key contributions. The first is the introduction of a new image representation called the "integral image" which allows the features used by our detector to be computed very quickly. The second is a learning algorithm, based on AdaBoost, which selects a small number of critical visual features from a larger set and yields extremely efficient classifiers. The third contribution is a method for combining increasingly more complex classifiers in a "cascade" which allows background regions of the image to be quickly discarded while spending more computation on promising object-like regions. The cascade can be viewed as an object specific focus-of-attention mechanism which unlike previous approaches provides statistical guarantees that discarded regions are unlikely to contain the object of interest. In the domain of face detection the system yields detection rates comparable to the best previous systems. Used in real-time applications, the detector runs at 15 frames per second without resorting to image differencing or skin color detection. We show how to use "complementary priors" to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.  A major shortcoming of discriminative recognition and detection methods is their noise sensitivity, both during training and recognition. This may lead to very sensitive and brittle recognition systems focusing on irrelevant information. This paper proposes a method that selects generative and discriminative features. In particular, we boost classical Haar-like features and use the same features to approximate a generative model (i.e., eigenimages). A modified error function for boosting ensures that only features are selected that show a good discrimination and reconstruction. This allows a robust feature selection using boosting. Thus, we can handle problems where discriminant classifiers fail while still retaining the discriminative power. Our experiments show that we can significantly improve the recognition performance when learning from noisy data. Moreover, the feature type used allows efficient recognition and reconstruction. We proposed a new self-organizing net based on the principle of Least Mean Square Error Reconstruction (LMSER) of an input pattern. With this principle, a local learning rule called LMSER is naturally obtained for training nets consisting of either one or several layers. We proved that for one layer with n"1 linear units, the LMSER rule lets their weights converge to rotations of the data's first n"1 principal components. These converged points are stable and corresponding to the global minimum in the Mean Square Error (MSE) landscape, which has many saddles but no local minimum. The results indirectly provided a picture about LMSER's global convergence, which is also suitable for Oja rule since we proved that the evolution direction of the Oja rule has a positive projection on that of LMSER. We have also revealed an interesting fact that slight modifications of the LMSER rule (also the Oja rule) can perform the true Principal Component Analysis (PCA) without externally designing for building asymmetrical circuits required by previous studies. 