Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that trajectories of transient activity can be particularly informative about stimulus identity and may form the basis of computations through dynamics. Yet an understanding of the dynamical mechanisms needed to generate a population code based on transient trajectories is still missing . Here we show that a broad class of high-dimensional linear networks of recurrently connected units exhibits the properties needed for transient coding. We first identify a general criterion that distinguishes two classes of networks depending on properties of the connectivity matrix : networks in which all inputs lead to weak, decaying transients, and networks in which specific inputs elicit strongly amplified transient responses and are mapped onto orthogonal output states during the dynamics.  For the second class of networks,  we provide a procedure to identify transiently amplified inputs and the corresponding readouts for arbitrary connectivity matrices. We then exploit our approach to build the minimalconnectivity which robustly implements trajectories that map a specific input onto a specific output state , and we demonstrate that the capacity of the obtained networks increases proportionally with their size.
Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that trajectories of transient activity can be particularly informative about stimulus identity and may form the basis of computations through dynamics. Yet the dynamical mechanisms needed to generate a population code based on transient trajectories have not been fully elucidated . Here we examine transient coding in a broad class of high-dimensional linear networks of recurrently connected units . We start by reviewing a well-known result that leads to a distinction between two classes of networks : networks in which all inputs lead to weak, decaying transients, and networks in which specific inputs elicit strongly amplified transient responses and are mapped onto orthogonal output states during the dynamics. Theses two classes are simply distinguished based on the spectrum of the symmetric part of the connectivity matrix. For the second class of networks, which is a sub-class of non-normal networks, we provide a procedure to identify transiently amplified inputs and the corresponding readouts . We first apply these results to standard randomly-connected and two-population networks. We then build minimal, low-rank networks that robustly implement trajectories mapping a specific input onto a specific output state . Finally, we demonstrate that the capacity of the obtained networks increases proportionally with their size.
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