To assign charge states prior to training, we used a brute force assignment strategy, as described in the Supplemental Methods (SM2). After charge states had been assigned, 90% of the clusters were kept as training data, and 10% were randomly separated into testing data. The result was a large set of narrow, centroided isotopic clusters surrounding charge states of known charge. The charge distribution was heavily skewed toward lower charge states, especially 1, as shown in Figure . In the final data collection, we had over 6.1 million assigned isotope clusters in the training data and over 680,000 clusters in the test data. spacing. For peaks that have a uniform spacing, they should have the same mass defect relative to a repeating unit of 1.0033/z. Here, 1.0033 is used rather than 1 because it is the average isotope spacing, corresponding to roughly the mass difference between C and 12 C. Another way to describe this effect is that the phase of each cluster is consistent with respect to a wave of frequency 1.0033/z (Figure and). To capture this spacing, we summed the intensity from peaks with similar mass defect/phase values. Notice that there are hotspots in the encoded matrix corresponding to +7, but also +14, +21, and subsequent harmonic multiples of 7.