Cornell and Harvard University Researchers Develops Correlation Convolutional Neural Networks (CCNN): To Determine Which Correlations Are Most Important


A team of researchers from Cornell and Harvard University introduces a novel approach to parse quantum matter and make crucial data distinctions. This proposed technique will enable researchers to decipher the most perplexing phenomena in the subatomic realm.

In their paper, “Correlator Convolutional Neural Networks as an Interpretable Architecture for Image-like Quantum Matter Data,” the team discusses ways to extract new information about quantum systems from snapshots of image-like data. They are now thus developing ML tools to identify relationships between microscopic properties in data that would otherwise be impossible to determine at that scale.

Convolutional neural networks (CNN) are used to analyze image data by scanning it with a filter to find characteristic features in the data regardless of where they occur—a process known as “convolution.” The convolution is then passed through nonlinear functions, causing convolutional neural networks to learn all kinds of correlations between the features.

However, because nonlinear functions are difficult to track, the versatility provided by nonlinearity makes it challenging to determine how the neural network used a specific filter to make its decision.

To address this issue, the team proposes an improved approach called Correlation Convolutional Neural Networks (CCNN), which is based on the development of an “interpretable architecture.” The researchers can use CCNN to determine which correlations are most important.

To put CCNN to the test, the Harvard team used quantum gas microscopy to simulate a fermionic Hubbard model, which is frequently used to demonstrate how quantum particles interact in a lattice.

The team created synthetic data for two difficult-to-distinguish states: geometric string theory and pi-flux theory. In geometric string theory, the system approaches antiferromagnetic order, with electron spins forming an anti-alignment (i.e., up, down, up, down, up, down) that is disrupted when an electron-hole begins to move on a different timescale. While according to pi-flux theory, the spins form pairs called singlets (when a hole is introduced) begin to flip and flop around, resulting in a scrambled state. 

The results demonstrated the CCNN approach’s ability to differentiate between the two simulations by identifying correlations in the data to the fourth-order.

By repeating this exercise, the neural network is forced to pick one or two features that will help it make the best decision. This way, the CCNN essentially learns which events in the image were necessary for neural networks to make a decision. And by doing so, one can determine what the critical aspects, the essence of what defines a state or phase, are.

The method is applicable to other scanning probe microscopies that produce image-type data on quantum materials and programmable quantum simulators. 

The team plans to incorporate a type of unsupervised machine learning to provide a broader objective perspective that will be less affected by the decisions of researchers handpicking which samples to compare.