We introduce a new type of neural network activation function based on recent physiological rate models for complex cells in visual area V1. A single-hidden-layer neural network of this kind of model achieves 1.5% error on MNIST. We also introduce an existing criterion for learning slow, decorrelated features as a pretraining strategy for image models. This pretraining strategy results in orientation-selective features, similar to the receptive fields of complex cells. With this pretraining, the same single-hidden-layer model achieves better generalization error, even though the pretraining sample distribution is very different from the fine-tuning distribution. To implement this pretraining strategy, we derive a fast algorithm for online learning of decorrelated features such that each iteration of the algorithm runs in linear time with respect to the number of features.

We present a mixture model whose components are Restricted Boltzmann Machines (RBMs). This possibility has not been considered before because computing the partition function of an RBM is intractable, which appears to make learning a mixture of RBMs intractable as well. Surprisingly, when formulated as a third-order Boltzmann machine, such a mixture model can be learned tractably using contrastive divergence. The energy function of the model captures three-way interactions among visible units, hidden units, and a single hidden multinomial unit that represents the cluster labels. The distinguishing feature of this model is that, unlike other mixture models, the mixing proportions are not explicitly parameterized. Instead, they are defined implicitly via the energy function and depend on all the parameters in the model. We present results for the MNIST and NORB datasets showing that the implicit mixture of RBMs learns clusters that reflect the class structure in the data.

For many pattern recognition tasks, the ideal input feature would be invariant to multiple confounding properties (such as illumination and viewing angle, in computer visionapplications). Recently, deep architectures trained in an unsupervised manner have been proposed as an automatic method for extracting useful features. However, it is difficult to evaluate the learned features by any means other than using them in a classifier. In this paper, we propose a number of empirical tests that directly measure the degree to which these learned features are invariant to different input transformations. We find that stacked autoencoders learn modestly increasingly invariant features with depth when trained on natural images. We find that convolutional deep belief networks learn substantially more invariant features in each layer. These results further justify the use of "deep" vs. "shallower" representations, butsuggest that mechanisms beyond merely stacking one autoencoder on top of another may be important for achieving invariance. Our evaluation metrics canalso be used to evaluate future work in deep learning, and thus help the development of future algorithms.

We introduce a new type of Deep Belief Net and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database(normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5% error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2% error, making it the current best result for NORB.

We present a simple new Monte Carlo algorithm for evaluating probabilities of observations in complex latent variable models, such as Deep Belief Networks. While the method is based on Markov chains, estimates based on short runs are formally unbiased. In expectation, the log probability of a test set will be underestimated, and this could form the basis of a probabilistic bound. The method is much cheaper than gold-standard annealing-based methods and only slightly more expensive than the cheapest Monte Carlo methods. We give examples of the new method substantially improving simple variational bounds at modest extra cost.

In this paper we focus on training deep neural networks for visual recognition tasks. One challenge is the lack of an informative regularization on the network parameters, to imply a meaningful control on the computed function. We propose a training strategy that takes advantage of kernel methods, where an existing kernel function represents useful prior knowledge about the learning task of interest. We derive an efficient algorithm using stochastic gradient descent, and demonstrate very positive results in a wide range of visual recognition tasks.

Offline handwriting recognition---the transcription of images of handwritten text---is an interesting task, in that it combines computer vision with sequence learning. In most systems the two elements are handled separately, with sophisticated preprocessing techniques used to extract the image features and sequential models such as HMMs used to provide the transcriptions. By combining two recent innovations in neural networks---multidimensional recurrent neural networks and connectionist temporal classification---this paper introduces a globally trained offline handwriting recogniser that takes raw pixel data as input. Unlike competing systems, it does not require any alphabet specific preprocessing, and can therefore be used unchanged for any language. Evidence of its generality and power is provided by data from a recent international Arabic recognition competition, where it outperformed all entries (91.4% accuracy compared to 87.2% for the competition winner) despite the fact that neither author understands a word of Arabic.

The Temporal Restricted Boltzmann Machine (TRBM) is a probabilistic model for sequences that is able to successfully model (i.e., generate nice-looking samples of) several very high dimensional sequences, such as motion capture data and the pixels of low resolution videos of balls bouncing in a box. The major disadvantage of the TRBM is that exact inference is extremely hard, since even computing a Gibbs update for a single variable of the posterior is exponentially expensive. This difficulty has necessitated the use of a heuristic inference procedure, that nonetheless was accurate enough for successful learning. In this paper we introduce the Recurrent TRBM, which is a very slight modification of the TRBM for which exact inference is very easy and exact gradient learning is almost tractable. We demonstrate that the RTRBM is better than an analogous TRBM at generating motion capture and videos of bouncing balls.

Artificial Intelligence (AI) has recently become a real formal science: the new millennium brought the first mathematically sound, asymptotically optimal, universal problem solvers, providing a new, rigorous foundation for the previously largely heuristic field of General AI and embedded agents. At the same time there has been rapid progress in practical methods for learning true sequence-processing programs, as opposed to traditional methods limited to stationary pattern association. Here we will briefly review some of the new results, and speculate about future developments, pointing out that the time intervals between the most notable events in over 40,000 years or 2^9 lifetimes of human history have sped up exponentially, apparently converging to zero within the next few decades. Or is this impression just a by-product of the way humans allocate memory space to past events?

The topic of deep learning systems has received significant attention during the past few years, particularly as a biologically-inspired approach to processing highdimensional signals. The latter often involve spatiotemporal information that may span large scales, rendering its representation in the general case highly challenging. Deep learning networks attempt to overcome this challenge by means of a hierarchical architecture that is comprised of common circuits with similar (and often cortically influenced) functionality. The goal of such systems is to represent sensory observations in a manner that will later facilitate robust pattern classification, mimicking a key attribute of the mammal brain. This stands in contrast with the mainstream approach of pre-processing the data so as to reduce its dimensionality — a paradigm that often results in sub-optimal performance. This paper presents a Deep SpatioTemporal Inference Network (DeSTIN) — a scalable deep learning architecture that relies on a combination of unsupervised learning and Bayesian inference. Dynamic pattern learning forms an inherent way of capturing complex spatiotemporal dependencies. Simulation results demonstrate the core capabilities of the proposed framework, particularly in the context of high-dimensional signal classification.