Supercharge your model performance with inductive bias. How to work smarter, not harder: Encoding real-life symmetries in machine learning models can improve their accuracy by orders of magnitude!
From the beautifully regular shape of a snowflake, and the self-similar (fractal) structure of romanesco, to the hexagonal pattern of honeycombs.
Nature seems to seek out symmetry. In fact the very laws of our existence exhibit a plethora of them: Physicists speak of translation (“move through”) symmetry in both time and space. What they mean is that forces such as gravity work the same way they did millions of years ago and that they don’t vary between Sydney and New York.
Another one of their favorites, rotation symmetry, simply states that an object’s properties don’t change as you look at it from different angles.
The list of symmetries goes on and on, and some of them are easier to grasp than others (Lorentz symmetry, stating that the speed of light is the same for co-moving observers in inertial frames, might already escape less physically versed minds).
Even though some of these symmetries are obvious to humans, most machine learning models are surprisingly oblivious to their existence. Let me give an example from my own work:
Bin im Garten / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)
Roughly speaking, the goal of my research is to use ML to *predict properties of molecules from structural information *only. This means, that I am given a list of atoms together with their coordinates.
For a water molecule, it would look like this:
The atom’s coordinates are conveniently summarized in a matrix with rows corresponding to atoms and columns corresponding to the x,y and z positions respectively. I would like to predict how much energy is needed to break up the molecule into its constituent atoms (the atomization energy). I could do so by training a neural network F that uses the raw coordinates as features and outputs the energy:
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