text: Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the relative feature space relationship between two rotated images? What is decoded when we interpolate in feature space? Ideally, we want to disentangle confounding factors, such as pose, appearance, and illumination, from object identity. Disentangling these is difficult because they interact in very nonlinear ways. We propose a simple method to construct a deep feature space, with explicitly disentangled representations of several known transformations. A person or algorithm can then manipulate the disentangled representation, for example, to re-render an image with explicit control over parameterized degrees of freedom. The feature space is constructed using a transforming encoder-decoder network with a custom feature transform layer, acting on the hidden representations. We demonstrate the advantages of explicit disentangling on a variety of datasets and transformations, and as an aid for traditional tasks, such as classification.
  @cite_4: Recent physiological research has indicated that the visual system makes use of units responsive to Gabor signals in the analysis of visual stimuli. Such functions effect a tradeoff between pure spatial- and frequency-domain descriptions. The authors explain the use of such representations in vision, considered as a process in inference from the retinal signals to a symbolic description. The appropriate mathematical structure for the inference is that of the subspaces of the signal vector space, a feature which it shares with quantum mechanics. The theory is derived directly from the fundamental constraints on visual inference. It is then shown to be consistent with many of the known properties of the visual system. In particular, a major feature of the inference system-the occurrence of interference effects-has already been observed in visual system operation. >
summary: A function @math is @cite_4 under a set of transformations @math if for any transformation @math of the input, we can associate a transformation @math of the output such that for all @math . Transformations @math and @math represent the same underlying transformation but in different spaces, denoted @math .