Fig. 3

Self-attention calculation process (X represents the input pollutant time series; q, k and v are sequences obtained by multiplying \(\mathrm{X}\) by the weights \({\mathrm{W}}^{\mathrm{q}}\), \({\mathrm{W}}^{\mathrm{k}}\) and \({\mathrm{W}}^{\mathrm{v}}\); \(\mathrm{\alpha }\) is the inner product of q and k; and \(\widehat{\mathrm{\alpha }}\) is \(\mathrm{\alpha }\) normalized by the softmax function)