Three Types of Symmetry

Past 6 months brought a lot of travel, relocation to a new city & country, new job…  now let’s try to get back into good habits like writing.

From 101 Things I Learned in Architecture School I finally understood the appeal of asymmetrical architecture and why is it so beloved by modern architects. This appreciation resonated with a 900 year old echo when we visited Angkor Wat.

1. Static symmetry

The most basic type of symmetry is the one we all imagine when one mentions “symmetry”. Invariance of shapes (or systems) under certain transformations (rotation, reflection, scaling) is deeply appealing to us. Like the layout of the Angkor Wat complex.


2. Symmetry, broken

The breaking of symmetry is however a quintessential physical mechanism that gives rise, among others, to replicating complex patterns balancing on the edge of chaos (aka “life”).

The breaking of symmetry between past and future gives rise to the arrow of time. And where is time there are stories – such as the The Battle of Kurukshetra. Static symmetry of the army formations is ultimately broken to be able to tell the story of the big battle.


3. Dynamic balance – the symmetry of asymetry

Finally, we arrive at the least obvious form of symmetry – the dynamical balance.

From 101 Things I Learned in Architecture School:

Balance is inherent in a symmetrical composition, but asymmetrical com-
positions can be either balanced or unbalanced. Consequently, asymmetry tends to
require a more complex and sophisticated understanding of wholeness.

An example – a dancer is in dynamic balance, yet the posture is not symmetrical in the static sense.


A spinning dancer is in dynamical balance. To keep with the Angkor Wat theme I could have showed a picture of dancing Apsaras. I found this optical illusion however extra interesting, because in addition to dynamical balance it demonstrates a dynamical clockwise/anti-clockwise symmetry in rotation.

This concept too hasn’t been unknown to the builders of Angkor Wat in the 11th century. My favourite bas relief is The Churning of Ocean of Milk.


It shows 92 gods and 88 demons fighting for the elixir of immortality and a snake caught up in the middle. The gods hold the tail, the demons hold the head, while the snake coils itself around Mt. Mandala. Each time the gods and demons pull from their sides, the mountain turns and the ocean churns.

There is a lot of static (translational) symmetry in the repeating figures. The symmetry is also broken (the head and tail of the world-snake, gods and demons, 92 vs. 88). But ultimately there is a dynamical balance, at least for the moment.

And to close the circle (another symmetry), my new “home” town is famous for its own version of a building in a dynamic equilibrium, that is inspired by dancers: The Dancing House.





We have stumbled into the era of machine psychology

Emergent science in an emergent world

When describing complex emergent systems, science has to switch from lower to higher level descriptions. Here is a typical example of such transitions:

  1. We go from physics to chemistry when we encounter complex arrangements of large number of atoms/molecules.
  2. Complex chemistry in living systems is then described in terms of biology.
  3. Complex (neuro-) biology in human brains finally gives raise to the field of psychology.

Of course, the world is not discrete and the transitions between the fields are fuzzy (think about the chemistry-biology shoreline of bio-macromolecules and cytology). And yes, the (mostly infertile) philosophical wars on the ontology of emergence are still being waged. Yet, nobody would deny the epistemic usefulness of higher level descriptions. Every transition to higher order description brings its own ‘language’ describing the object as well as a suite of research methods.

In this game, it is however very easy to miss the forest (high-level) for the trees (low-level). One interesting example I’ve noticed recently is in the field of machine learning. When studying deep neural networks (DNNs), we have already unknowingly stumbled into such a transition. Historically, most of the research has been done on the “biology” of the DNNs – the architecture of the networks, activation functions, training algorithms etc. (and yes, saying “biology” is bio-chauvinistic on my part. We should find a better word!)

Recently however, we are more and more tapping into the “psychology” of the neural networks.

Machine psychology

The deep architectures that are now in use aren’t reaching anywhere near the complexity of human brains, yet. However, with connections in the billions (here is an early example), they are too complex, too opaque, for a low-level description to be sufficient for their understanding. This lead to a steady influx of research strategies, that shift the approach from the bottom-up understanding of “machine biology” to a more top-down, “input-output”, strategy typical for psychology.

Of course, neural networks are commonly, though not quite deservedly, described as “black boxes”. And historically, parts of psychology had its flirtations with cybernetics. But it is only recently that the we see a curious methodological convergence between these two fields as machine learning is starting to adopt methods of psychology.

The interesting distinction between machine and human psychology is that we have a direct access to “brain” states of the network (inputs and activation of each neuron). With machine psychology, we are now shifting attention to their “mental” states, something that is accessible only with higher order, indirect methods.

Psychology of machine perception

A first example of the convergence comes from the psychology of perception.

Deep neural networks have revolutionized the field of computer vision by crushing competing approaches in all benchmarks (see e.g. last year’s ImageNet competition). Yet a deeper intuition for how the DNNs are actually solving image classification requires techniques similar to those used in psychology of perception

As an example: recently, an “input-output” strategy yielded an attack on neural network image classification developed by Szegedy et al. 2013. In this work, they took correctly classified images. modified them imperceptibly, so that the trained network got completely confused (see Fig 1a. below). While on the surface level such a confusion seems alarming, one should just remind oneself of the many quirks of the human visual cortex (Fig 1b.)


Fig 1a: Example from Szegedy et al. 2013: Image on the left is correctly classified by a neural net as school bus. On the right side the imperceptably modified image is however classified as an ostrich. The middle panel shows the pixel difference of the two images magnified 10x.


Fig 1b: Your visual cortex classifies the colors of fields A and B as distinct. They are the same.

Nguyen et al. 2014, then turned this game around and used genetic algorithms to purposely evolve abstract images that well trained neural networks confound with real objects. Again examples for a DNN and human visual cortex below (Fig. 2a and 2b).

Image evolved so that a neural network miss-classifies it as a guitar.

Fig 2a: Image evolved so that a neural network miss-classifies it as a guitar.

A lamp miss-classified by your dirty mind.

Fig 2b: An image of a lamp miss-classified by your dirty, dirty mind.

Gestalt psychology for hierarchical feature extraction?

These confounding attacks on classifiers are very important, since deep neural nets are being increasingly employed in the real world. Better understanding of machine perception is required to make the algorithms more robust to avoid fraud (some examples here).

The reason why image classification works so well with deep architectures is the ability to automatically extract hierarchies of features from images. To make them more robust to attacks, requires an improvement in integration of these hierarchies into “global wholes”, well summarized by the mantra of gestalt psychology by Kurt Koffka, “The whole is other than the sum of the parts” (not “The whole is greater than the sum of its parts”).

Psychometrics of neural networks

The cross-fertilization of machine learning by psychology doesn’t end with perception theory.

Measurement of psychological traits are the bread-and-butter of psychometry and the crown jewel is of course intelligence testing. This is even more salient for the field of artificial intelligence. In an early example, Wang et al. 2015 made just recently headlines (e.g. here) by claiming to beat average Amazon Mechanical Turk performance on a verbal IQ test.

Oddly enough, I haven’t yet found a reference using deep nets on Raven’s progressive matrices. This seems like a very obvious application for deep networks as Raven’s matrices are small, high-contrast images and successful solution requires extraction of multi-level hierarchies of features. I expect that DNNs should very soon blow humans out of water in this test.

Raven’s matrices are the go to test for human intelligence with g-loading around 0.8 and virtually no cultural bias. Such an experiment would likely show, that the nets to achieve IQ 200+ in a very vivid illustration of the relationship between proxies for g and the actual “general intelligence” – the holy grail of artificial general intelligence (AGI) research.

Here is then a nice summer project: put together a DNN for solving Raven’s matrices. I even recall a paper on machine generation of test examples so enough training data will not be a problem!

Deep nets and Raven’s progressive matrices are made for each other.

Machine psychotherapy, creativity and aesthetics

On a joking note – if there is machine psychology, could there be also machine psychotherapy? How could a venerable Freudian help his DNN clients?

There are some very playful examples done with generative models (based on recurrent deep networks), e.g. text generation à la Shakespear/Graham/Wikipedia. A machine therapist will definitely be able to use their good old tools of word association games and automatic writing to diagnose whatever will be the digital equivalent of Oedipus complex of his machine patients.


Did you again dream about electric sheep Mr. Android?

Even the good old cliché of dream interpretation can be brought out of retirement.
Geoffrey Hinton spoke about machine dreams long time ago. And the psychologist are already picking up on this:

One of the areas that I’ve been looking at recently is machine dreaming, the question whether AI systems are already dreaming. There’s little question that they meet our criteria for what a dream is, they meet all our definitional criteria. There’s better evidence really that machines, AI systems, are dreaming, than there is that animals are dreaming that are not human.

— Associate Professor of Psychology, James Pagel on the “All in the Mind” podcast.

The excellent paper by Google researchers, Inceptionism: Going Deeper into Neural Networks,  shows beautiful demonstrations of DNN fantasies, dreams and pareidolia. The psychology of digital psychedelic experience is close too.

What deep neural nets dream about actually.

What deep neural nets dream about actually.

This section is of course tongue in cheek, but its aim is to illustrate, that already now, the state-of-the-art DNNs can achieve very rich “mental” states.

Sidenote: speaking of machine therapy, the other way around, i.e. machines being therapist to humans, is a promising researched field. Indeed they seem to come a long way since the command line therapist and the `M-x doctor` (for the Emacs fans out there).

Machine ethology. Machine sociology. Machine etiquette. Machine politics.

Machines are already talking to each other a great deal: think of the internet, communication networks, or the budding world of internet of things. For now, the conversation is only between agents of low sophistication using simple, rigid protocols. We could perhaps already talk about machine ethology, maybe even nascent sociology. TCP/IP is an example of simple machine etiquette.

But the real deal will come when the artificial agents get more sophisticated (i.e. DNNs) and their communication bandwidth increases.

The final step is achieved, when the agents start to create mental self-models and also models of the other agents they are communicating with. The gates of social psychology, sociology and politics will be then pried wide open for our machine comrades.

Future of hard science is soft science?

Will your AI team soon have to hire a machine psychologist? Maybe so.
It is fascinating, that the hardest of hard fields – mathematics/statistics/AI research/software engineering in the areas of AI converges on methods from soft science.

Soft-sciences, mind you, not humanities.