  To generate actions in the face of physiological delays, the brain must
predict the future. Here we explore how prediction may lie at the core of brain
function by considering a neuron predicting the future of a scalar time series
input. Assuming that the dynamics of the lag vector (a vector composed of
several consecutive elements of the time series) are locally linear, Normal
Mode Decomposition decomposes the dynamics into independently evolving
(eigen-)modes allowing for straightforward prediction. We propose that a neuron
learns the top mode and projects its input onto the associated subspace. Under
this interpretation, the temporal filter of a neuron corresponds to the left
eigenvector of a generalized eigenvalue problem. We mathematically analyze the
operation of such an algorithm on noisy observations of synthetic data
generated by a linear system. Interestingly, the shape of the temporal filter
varies with the signal-to-noise ratio (SNR): a noisy input yields a monophasic
filter and a growing SNR leads to multiphasic filters with progressively
greater number of phases. Such variation in the temporal filter with input SNR
resembles that observed experimentally in biological neurons.
