Machine learning identification of impurities in the STM images

The structure of the NN. The voltage arrow indicates a sequence of images taken at different voltages. Each image ${X}_{i}^{l}$ is mapped to tensors of the query ${Q}_{i}^{l}$, the key ${K}_{i}^{l}$, and the value ${V}_{i}^{l}$. By the attention mechanism, it leads to normalized value ${\tilde{V}}_{i}^{l}$ computed by Eq. (1). Then, we sum over all ${\tilde{V}}_{i}^{l}$ and reach the output following a linear projection and a Softmax.

Computation graph for the loss function. The NN is trained on the theoretical data via the regression loss ${ {\mathcal L} }_{0}$, and regularized by the experimental data via the prediction confidence regularization ${ {\mathcal L} }_{{\rm{reg}}}$.

Comparison between the prediction of the NN and a reference answer from another experiment. Red squares are the prediction of NN, determined by local maxima of the ${\mathscr{S}}$ layer generated by the NN. Black dots are the reference answer from another experiment, determined by the local maxima of the DoS of bound states shown as the color plot. Here, for training the NN, we use loss function ${ {\mathcal L} }_{0}+\alpha { {\mathcal L} }_{{\rm{reg}}}$ with α = 0.03 and training data with η = 0.8 Gaussian noise.

Compare the performance of different approaches on the experimental data. The curves are the ratio of the reference points perfectly agreed with prediction to the total reference points. The blue line and the purple line are given by NN trained by loss function ${ {\mathcal L} }_{0}$, and the training data have no noise for the blue line and include noise for the purple line. The yellow line is given by NN trained by loss function ${ {\mathcal L} }_{0}+\alpha { {\mathcal L} }_{{\rm{reg}}}$ including confidence regularization and data without noise. Finally, the green line is given by NN trained by loss function ${ {\mathcal L} }_{0}+\alpha { {\mathcal L} }_{{\rm{reg}}}$ and data with noise. Here we take α = 0.03. The ratios are plotted as a function of the training epoch, and the results are averaged over ten independent training processes.

Experimental data on Au(111) surface. (a) Typical dI/dV spectra measured on defect (red curve) and on defect-free area (black curve). The abrupt increase of spectra above −520 mV shows the itinerant surface states on Au(111). Additional spectra on black curve indicates the bound state of defect below the surface band. (b) Differential conductance maps. Top panel, two representative dI/dV maps (at −20 mV and −175 mV) taken at 5 K with tunneling junction R = 5 GΩ, showing spatial oscillation from the quantum interference of surface states. Bottom, the conductance map at −520 mV, revealing the spatial distribution of the defect states.