From my own exploration of Google Deep Dream, largely with Dreamify for IOS, and also from Google Image results on the topic, a few of the images I have produced/seen have led me to 3 conclusions about the networks understanding of images, that seem too common to be coincidences.By understanding I mean, being taken into account, and therefore being part of the calculations.These are by far not all the images, but Deep Dreams, even after minimal effort, can be surprisingly coherent.I would like to know if these are recognised as consequences of the approach or at least to some degree are imagined in my own mind while trying to understand the complicated images the Deep Dream algorithm often produces?There is a 3 dimensional understanding of real and dreamt objects, including rotation, occlusion (close things covering distant things), reflection etc...There is an understanding of how objects group and are arranged, to form believable landscapes, settlements, narrative and physical interactions, including between people.Objects, including people, can be intricately thematically/stylistically designed to fit in a scene.For example:http://s11.postimg.org/mpllxnb77/image.jpghttp://oi57.tinypic.com/ne9s42.jpg(note the interaction of shadows and estimated view behind some of the photographed teapot)http://s12.postimg.org/azv0l0625/image.jpg(most things are matched for light and in at least physically plausible places, following a coherent narrative about the use of the space)http://s12.postimg.org/x06rnvzcd/image.jpghttp://s21.postimg.org/4yve7je93/image.jpghttp://s12.postimg.org/4r9orf8h9/image.jpghttp://s12.postimg.org/jxfqicyi5/image.jpghttp://s12.postimg.org/5n1kt4srx/image.jpghttp://s12.postimg.org/dl0l8ivfx/image.jpg(views into entirely invented worlds)http://s12.postimg.org/bqnqqs8fh/image.jpg(If these buildings were architecturally from elsewhere in the world, and the space in the middle was a car park, this is indeed how it might look. Many objects in the space have been removed entirely.)I don't have a better example for buildings, but they can become photo realistic/surrealistic, and so nuanced that it's hard to comprehend a lack of a design process.
Google Deep Dream has these understandings?
terminology;machine learning;neural networks
Understanding is a human concept ie a term used for human psychology. It may be used with machine learning systems informally. However, being flexible in interpretation of your question & not strictly literal, there is of course an open scientific question/ research program of how these systems actually work. In ML, one trains systems and the systems exhibit the desired behavior but some of this relates to an old psychology theory of behaviorism where only the observed behavior is seen to be relevant and attributing particular mental states is seen to be something of a problematic/nonobjective (anthropomorphic) projection by the experimenter.With that caveat, the current scientific understanding of (deep) neural networks, with lots of related research and active/ongoing, is roughly that they build/ use feature detection. This overlaps with neurobiology theory and knowledge of the visual cortex in mammals. The exact features that are evolved (via emergence) in the network are somewhat unique to each network, but general trends have been observed also, namely orientation columns (eg esp in lower levels). These types of features are also known to arise with sparse coding techniques/ mathematics.There is a hierarchy of features. Higher level features are built out of lower level features inside the network hierarchy.So the answer is roughly yes, the network develops spatial/ visual concepts in the form of  features. The networks recognize structural patterns in common across many images of real-world objects. These types of patterns include different/ various orientations, placements, relative spatial relationships, and sometimes more abstract styles of images found eg in paintings/even architecture etc.