# Barcelona Analysis Conference

Here’s the link to the conference website.

Some cool papers related to Bruna’s talk:

Global convergence of neuron birth-death dynamics

Neural Networks as Interacting Particle Systems: Asymptotic Convexity of the Loss Landscape and Universal Scaling of the Approximation Error

Idea: The parameter’s in a single layer neural network can be modeled by a charged particle system $\{ y_i, c_i \}$, where the evolution is given by a coupled ODE in terms of the positions $y_i$ and charges $c_i$. This deviates from standard kinetic theory since the charges are changing. The potential is given by a particular type of error measuring function of the particles. The particle evolution as $n \rightarrow \infty$ and as $t \rightarrow \infty$ approaches (assuming a convex landscape) the minimizer of our potential.

Perhaps one can proceed as in the Boltzmann, QMBD system limiting theory; Derive a PDE (Boltzmann, Schrodinger) and prove results here, then pull back this theory to the many body system case.

Has anyone studied the PDE formally derived from this type of particle system?