Inferring the relations between two images is an important class of tasks in computer vision. Examples of such tasks include computing optical flow and stereo disparity. We treat the relation inference tasks as a machine learning problem and tackle it with neural networks. A key to the problem is learning a representation of relations. We propose a new neural network module, contrast association unit (CAU), which explicitly models the relations between two sets of input variables. Due to the non-negativity of the weights in CAU, we adopt a multiplicative update algorithm for learning these weights. Experiments show that neural networks with CAUs are more effective in learning five fundamental image transformations than conventional neural networks.
People can understand complex structures if they relate to more isolated yet understandable concepts. Despite this fact, popular pattern recognition tools, such as decision tree or production rule learners, produce only flat models which do not build intermediate data representations. On the other hand, neural networks typically learn hierarchical but opaque models. We show how constraining neurons' weights to be nonnegative improves the interpretability of a network's operation. We analyze the proposed method on large data sets: the MNIST digit recognition data and the Reuters text categorization data. The patterns learned by traditional and constrained network are contrasted to those learned with principal component analysis and nonnegative matrix factorization. To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubically many parameters, which form a three-dimensional interaction tensor. We describe a low-rank approximation to this interaction tensor that uses a sum of factors, each of which is a three-way outer product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans. Neurophysiological data support two models for the disparity selectivity of binocular simple and complex cells in primary visual cortex. These involve binocular combinations of monocular receptive fields that are shifted in retinal position (the position-shift model) or in phase (the phase-shift model) between the two eyes. This article presents a formal description and analysis of a binocular energy model with these forms of disparity selectivity. We propose how one might measure the relative contributions of phase and position shifts in simple and complex cells. The analysis also reveals ambiguities in disparity encoding that are inherent in these model neurons, suggesting a need for a second stage of processing. We propose that linear pooling of the binocular responses across orientations and scales (spatial frequency) is capable of producing an unambiguous representation of disparity. Abstract An important property of visual systems is to be simultaneously both selective to specific patterns found in the sensory input and invariant to possible variations. Selectivity and invariance (tolerance) are opposing requirements. It has been suggested that they could be joined by iterating a sequence of elementary selectivity and tolerance computations. It is, however, unknown what should be selected or tolerated at each level of the hierarchy. We approach this issue by learning the computations from natural images. We propose and estimate a probabilistic model of natural images that consists of three processing layers. Two natural image data sets are considered: image patches, and complete visual scenes downsampled to the size of small patches. For both data sets, we find that in the first two layers, simple and complex cell-like computations are performed. In the third layer, we mainly find selectivity to longer contours; for patch data, we further find some selectivity to texture, while for the downsampled complete scenes, some selectivity to curvature is observed. Bilinear models provide rich representations compared with linear models. They have been applied in various visual tasks, such as object recognition, segmentation, and visual question-answering, to get state-of-the-art performances taking advantage of the expanded representations. However, bilinear representations tend to be high-dimensional, limiting the applicability to computationally complex tasks. We propose low-rank bilinear pooling using Hadamard product for an efficient attention mechanism of multimodal learning. We show that our model outperforms compact bilinear pooling in visual question-answering tasks with the state-of-the-art results on the VQA dataset, having a better parsimonious property. A motion sequence may be represented as a single pattern in x–y–t space; a velocity of motion corresponds to a three-dimensional orientation in this space. Motion sinformation can be extracted by a system that responds to the oriented spatiotemporal energy. We discuss a class of models for human motion mechanisms in which the first stage consists of linear filters that are oriented in space-time and tuned in spatial frequency. The outputs of quadrature pairs of such filters are squared and summed to give a measure of motion energy. These responses are then fed into an opponent stage. Energy models can be built from elements that are consistent with known physiology and psychophysics, and they permit a qualitative understanding of a variety of motion phenomena. A new self-organizing map (SOM) architecture called the ASSOM (adaptive-subspace SOM) is shown to create sets of translation-invariant filters when randomly displaced or moving input patterns are used as training data. No analytical functional forms for these filters are thereby postulated. Different kinds of filters are formed by the ASSOM when pictures are rotated during learning, or when they are zoomed. The ASSOM can thus act as a learning feature-extraction stage for pattern recognizers, being able to adapt to many sensory environments and to many different transformation groups of patterns. Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same principle of independence maximization can explain the emergence of phase- and shift-invariant features, similar to those found in complex cells. This new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces (instead of the independence of simple linear filter outputs). The norms of the projections on such “independent feature subspaces” then indicate the values of invariant features. We describe a generative model of the relationship between two images. The model is defined as a factored three-way Boltzmann machine, in which hidden variables collaborate to define the joint correlation matrix for image pairs. Modeling the joint distribution over pairs makes it possible to efficiently match images that are the same according to a learned measure of similarity. We apply the model to several face matching tasks, and show that it learns to represent the input images using task-specific basis functions. Matching performance is superior to previous similar generative models, including recent conditional models of transformations. We also show that the model can be used as a plug-in matching score to perform invariant classification. Relation learning is a fundamental operation in many computer vision tasks. Recently, high-order Boltzmann machine and its variants have exhibited the great power of modelling various data relation. However, most of them are unsupervised learning models which are not very discriminative and thus cannot server as a standalone solution to relation learning tasks. In this paper, we explore supervised learning algorithms and propose a new model named Conditional High-order Boltzmann Machine (CHBM), which can be directly used as a bilinear classifier to assign similarity scores for pairwise images. Then, to better deal with complex data relation, we propose a gated version of CHBM which untangles factors of variation by exploiting a set of latent variables to gate classification. We perform four-order tensor factorization for parameter reduction, and present two efficient supervised learning algorithms from the perspectives of being generative and discriminative, respectively. The experimental results of image transformation visualization, binary-way classification and face verification demonstrate that, by performing supervised learning, our models can greatly improve the performance. The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and products as internal nodes, and weighted edges. We show that if an SPN is complete and consistent it represents the partition function and all marginals of some graphical model, and give semantics to its nodes. Essentially all tractable graphical models can be cast as SPNs, but SPNs are also strictly more general. We then propose learning algorithms for SPNs, based on backpropagation and EM. Experiments show that inference and learning with SPNs can be both faster and more accurate than with standard deep networks. For example, SPNs perform image completion better than state-of-the-art deep networks for this task. SPNs also have intriguing potential connections to the architecture of the cortex.