## 3 Results
In the second case, the wavelengths within the drifting range are included in the training set by randomly acquiring speckle patterns at  
Figure 4: (**a**) Classification accuracy as a function of wavelength and number of fiber spatial modes for the wavelength range of the tunable laser source; Normalized confusion matrix for the datasets collected at the (**b**) 700 nm; and (**c**) 1000 nm wavelength. Figure 3: Decomposition of images in cases of different numbers of supported fiber modes. The size of the input images was approximately \(100\times 100\) pixels. different wavelengths during the measurement, as described in the Methods section. For comparison, the speckle intensity correlation was calculated for a range of 100 nm around the central wavelength (800 nm) to study the DNN results as a function of the speckle decorrelation. As seen from Figure 5a, the speckle patterns decorrelate at 50% within a range of approximately 30 nm. Studying the first case, we train the DNN with data recorded at 800 nm and we test its ability to recover the information from data measured at 803, 806, 812 and 850 nm (Figure 5b, red circles). The classification accuracy drops at 69% for the shortest drift of 803 nm, while the speckle correlation has only dropped to 90% at this wavelength distance. The results become completely random at 812 nm, reaching 10% classification. Hence, it is shown that generalization of the VGG network for wavelengths further than the one used in the training is only efficient for a very narrow range of wavelengths with respect to the one used for the training data measurements. The classification results also show a decrease in performance with an increase in the wavelength drifting bandwidth, but at a much lower rate in the second case for which we include the wavelength drift during the training. For 6 nm drift, meaning \(\pm 3\) nm around the central wavelength, the VGG DNN shows minimal change of classification performance. Specifically, we achieve classification accuracy of 88% in this case while the one obtained in absence of drift (\(\Delta\lambda=0\)) 90% (Figure 4a). This value is remarkably better compared to the 69% observed in the experiments of the first case discussed before for the same wavelength drift of 3 nm. Even for approximately 100 nm drift, the VGG DNN classifies correctly 70% of the inputs (Figure 5b, blue circles). These results indicate high robustness of the DNNs in the presence of severe perturbations in the system as long as the training dataset is collected in the presence of the wavelength disturbance under study. The ability of the DNN to successfully classify the speckle patterns within a wide range of wavelengths can be beneficial for multicolor image transmission through a fiber system [19]. In Figure 6, we show, for comparison, the normalized confusion matrices for the two approaches for a drift of 3 nm and \(\pm 3\) nm, respectively. It is evident that many labels are mixed up in the first case; for example, the digit 9, which is quite similar to at least two other digits, such as 7 and 5 s, is highly misclassified. Another aspect evaluated is the effect of including the wavelength drift noise in the training set when we attempt to recover information outside the training bandwidth. We train the VGG classifier with data measured under 12 nm drifting situation and we afterwards test the classification accuracy of the trained model for data outside the 12 nm range, starting from 807 nm to 850 nm. In spite of the high efficiency reported for recovering information about the inputs within the drift range (Figure 5b, blue circles), this is not the case for speckle patterns recorded at wavelengths outside this range (Figure 5c).