In the power spectra of oscillating red giants, there are visually distinct features defining stars ascending the red giant branch from those that have commenced helium core burning. We train a one-dimensional convolutional neural network by supervised learning to automatically learn these visual features from images of folded oscillation spectra. By training and testing on \textit{Kepler} red giants, we achieve an accuracy of up to 99\% in separating helium-burning red giants from those ascending the red giant branch. The convolutional neural network additionally shows capability in accurately predicting the evolutionary states of 5379 previously unclassified \textit{Kepler} red giants, by which we now have greatly increased the number of classified stars.