Neural networks in pulsed dipolar spectroscopy: A practical guide.

This is a methodological guide to the use of deep neural networks in the processing of pulsed dipolar spectroscopy (PDS) data encountered in structural biology, organic photovoltaics, photosynthesis research, and other domains featuring long-lived radical pairs and paramagnetic metal ions. PDS uses distance dependence of magnetic dipolar interactions; measuring a single well-defined distance is straightforward, but extracting distance distributions is a hard and mathematically ill-posed problem requiring careful regularisation and background fitting. Neural networks do this exceptionally well, but their "robust black box" reputation hides the complexity of their design and training - particularly when the training dataset is effectively infinite. The objective of this paper is to give insight into training against simulated databases, to discuss network architecture choices, to describe options for handling DEER (double electron-electron resonance) and RIDME (relaxation-induced dipolar modulation enhancement) experiments, and to provide a practical data processing flowchart.

Neural network interpretation using descrambler groups.

The lack of interpretability and trust is a much-criticized feature of deep neural networks. In fully connected nets, the signaling between inner layers is scrambled because backpropagation training does not require perceptrons to be arranged in any particular order. The result is a black box; this problem is particularly severe in scientific computing and digital signal processing (DSP), where neural nets perform abstract mathematical transformations that do not reduce to features or concepts. We present here a group-theoretical procedure that attempts to bring inner-layer signaling into a human-readable form, the assumption being that this form exists and has identifiable and quantifiable features-for example, smoothness or locality. We applied the proposed method to DEERNet (a DSP network used in electron spin resonance) and managed to descramble it. We found considerable internal sophistication: the network spontaneously invents a bandpass filter, a notch filter, a frequency axis rescaling transformation, frequency-division multiplexing, group embedding, spectral filtering regularization, and a map from harmonic functions into Chebyshev polynomials-in 10 min of unattended training from a random initial guess.