Abstract:
We discuss a possibility that the entire universe on its most fundamental level is a
neural network. We identify two different types of dynamical degrees of freedom: “trainable”
variables (e.g. bias vector or weight matrix) and “hidden” variables (e.g. state vector of
neurons). We first consider stochastic evolution of the trainable variables to argue that
near equilibrium their dynamics is well approximated by Madelung equations (with free
energy representing the phase) and further away from the equilibrium by Hamilton-Jacobi
equations (with free energy representing the Hamilton’s principal function). This shows that
the trainable variables can indeed exhibit classical and quantum behaviors with the state
vector of neurons representing the hidden variables. We then study stochastic evolution of
the hidden variables by considering D non-interacting subsystems with average state vectors,
x¯
1
, ..., x¯
D and an overall average state vector x¯
0
. In the limit when the weight matrix is
a permutation matrix, the dynamics of x¯
µ
can be described in terms of relativistic strings
in an emergent D + 1 dimensional Minkowski space-time. If the subsystems are minimally
interacting, with interactions described by a metric tensor, then the emergent space-time
becomes curved. We argue that the entropy production in such a system is a local function
of the metric tensor which should be determined by the symmetries of the Onsager tensor.
It turns out that a very simple and highly symmetric Onsager tensor leads to the entropy
production described by the Einstein-Hilbert term. This shows that the learning dynamics
of a neural network can indeed exhibit approximate behaviors described by both quantum
mechanics and general relativity. We also discuss a possibility that the two descriptions are
holographic duals of each other.
To this end, Vanchurin concludes:
In this paper we discussed a possibility that the entire universe on its most fundamental level is a neural network. This is a very bold claim. We are not just saying that the artificial neural networks can be useful for analyzing physical systems or for discovering physical laws, we are saying that this is how the world around us actually works. With this respect it could be considered as a proposal for the theory of everything, and as such it should be easy to prove it wrong. All that is needed is to find a physical phenomenon which cannot be described by neural networks. Unfortunately (or fortunately) it is easier said than done.
Full paper available here.
