We present software based on novel techniques, aiming at track finding in silicon trackers with a small number of layers. The core algorithm is a cellular automaton, followed by a Kalman filter and a Hopfield neural network. The first of two test cases is the forward tracking detector (FTD) of the International Large Detector (ILD) at a future linear collider, which covers the forward and backward regions between beam tube and a TPC. It consists of seven disk-shaped silicon detectors (pixels and strips) on either side. Results presented on simulated events without and with background show that our method performs better than a previous one in terms of efficiency, ghost rate and processing speed. The second test case is the silicon vertex detector (SVD) of the Belle II experiment at the B factory at KEK, which is a new device located between a vertex pixel detector and a central drift chamber. It consists of only four cylindrical layers of silicon strip sensors. The focus of this study is on the reconstruction of tracks with very low momentum that miss the surrounding drift chamber. We present results from simulated data, including ghost hits and hits from the machine background.