The advent of multiple readers in magnetic recording opens the possibility of replacing the current industry's single-track detection with the more promising multitrack detection architectures. We have proposed a first solution, a generalized partial-response maximum-likelihood (GPRML) architecture, that extends the conventional PRML paradigm to jointly detect multiple asynchronous tracks. In this paper, we propose to replace the conventional communication-theoretic multiple-input multiple-output equalizer in the GPRML architecture with a neural network equalizer for better adaption to the nonlinearity of the underlying channel. We evaluate the proposed equalization strategy on a realistic two-dimensional magnetic-recording channel, and find that the proposed equalizer outperforms the conventional linear equalizer, by a 35% reduction in the bit-error rate.