Nemenman & Mehta on Random-with-Constraints

Nemenman & Mehta (2025) argue for random-with-constraints as a minimal modeling strategy for high-dimensional biology. At the heart of this approach was the realization that when systems become sufficiently complex, many properties of these systems become “typical” and hence can be modeled using random interactions with constraints. (e.g. species classes, interaction types, and symmetries; connectivity statistics, such as sparsity, bipartite, etc.; conservation laws; evolutionary constraints; or biophysical limits.)

This approach can be used to discover structure on top of the random base.

The core idea is to have minimal models that can explain high complexity systems, which was a success in nuclear physics.

1. Random networks may approximate the statistics of the world, which also could be random.
2. This may also reflect the random nature of evolution, such as how synapses are connected to each other.
3. Random interactions could be an effective theory of the recurrent network in the weak, non-specific interaction limit.

Since this is a review paper, it gives many useful papers I should read.