The Fermionic Neural Network (FermiNet) is one of the first deep learning demonstrations for computing atomic energy. Fermionic Neural Network is a new neural network architecture successfully applied in modeling the quantum state of large collections of electrons.

**Challenges faced in representing the state of quantum systems:**

In quantum systems, the position of particles like electrons is described by a probability cloud as they donâ€™t have exact locations. This uncertainty in locating particles makes the representation of the state of a quantum system challenging. The probabilities assigned to possible configurations of electron positions are encoded in the wavefunction, which sets a positive or negative number to every electronsâ€™ configuration. Squaring the wavefunction gives the probability of finding the system.

The most challenging task is representing the state of a quantum system. The space of all possible configurations is vast. So if we try to represent it as a grid having 100 points along each respective dimension, the number of possible electron configurations observed for the silicon atoms would be larger than the number of atoms in the universe.

**FermiNet **

To address the problem of efficient representation, the researchers at DeepMind have suggested that neural networks can be used to represent quantum wavefunctions as they have historically fit high-dimensional functions in AI problems. The neural networks are arranged in layers and contain neurons that are mathematical functions. These neurons transmit signals from input data and slowly adjust the synaptic strength of each connection. This way, they extract features and learn to make predictions.

The wavefunction has to be antisymmetric because electrons are a type of particle known as fermions. Just like the property of determinant of a matrix, if the position of two electrons is swapped, the wavefunction is multiplied by -1. This implies that having two electrons on top of each other will make the wavefunction and the probability of that configuration zero.

The researchers at DeepMind, therefore, developed a new type of neural network, FermiNet. This new neural network is antisymmetric concerning its inputs and has a separate stream of information for each electron. The FermiNet averages data from across streams and passes it to each stream at the next layer. Thus the streams have the right symmetry properties enabling them to create an antisymmetric function.

The FermiNet randomly selects the electron configurations, evaluates the energy locally at each electronsâ€™ arrangement, and later it adds up each arrangementâ€™s contributions. Since squaring the wavefunction gives the probability of finding a particleâ€™s arrangement in any location, the FermiNet can directly generate samples from the wavefunction. The neural network itself generates the inputs required to train the neural network.

DeepMind released the FermiNet code after demonstrating its work on a deep learning model that can predict glass moleculesâ€™ movement as they transition between liquid and solid states. Researchers at DeepMind said that both the techniques and trained models could predict other qualities of interest in glass. The researchers have stated that this neural network has generated useful insights in general substance and biological transitions, leading to advances in manufacturing and medicine.

**GitHub: **https://github.com/deepmind/ferminet

**Source:** https://deepmind.com/blog/article/FermiNet