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. Significance statementClassical theories of sensory coding consider the neural activity following a stimulus as constant in time. Recent works have however suggested that the temporal variations following the appearance and disappearance of a stimulus are strongly informative. Yet their dynamical origin remains little understood. Here we show that strong temporal variations in response to a stimulus can be generated by collective interactions within a network of neurons if the connectivity between neurons satisfies a simple mathematical criterion. We moreover determine the relationship between connectivity and the stimuli that are represented in the most informative manner by the variations of activity, and estimate the number of different stimuli a given network can encode using temporal variations of neural activity.

The spatiotemporal structure of activity in populations of neurons is critical for accurate perception and behavior. Experimental and theoretical studies have focused on "noise" correlations -trial-totrial covariations in neural activity for a given stimulus -as a key feature of population activity structure. Much work has shown that these correlations limit the stimulus information encoded by a population of neurons, leading to the widely-held prediction that correlations are detrimental for perceptual discrimination behaviors. However, this prediction relies on an untested assumption: that the neural mechanisms that read out sensory information to inform behavior depend only on a population's total stimulus information independently of how correlations constrain this information across neurons or time. Here we make the critical advance of simultaneously studying how correlations affect both the encoding and the readout of sensory information. We analyzed calcium imaging data from mouse posterior parietal cortex during two perceptual discrimination tasks. Correlations limited the ability to encode stimulus information, but (seemingly paradoxically) correlations were higher when mice made correct choices than when they made errors. On a singletrial basis, a mouse's behavioral choice depended not only on the stimulus information in the activity of the population as a whole, but unexpectedly also on the consistency of information across neurons and time. Because correlations increased information consistency, sensory information was more efficiently converted into a behavioral choice in the presence of correlations. Given this enhancedby-consistency readout, we estimated that correlations produced a behavioral benefit that compensated or overcame their detrimental information-limiting effects. These results call for a reevaluation of the role of correlated neural activity, and suggest that correlations in association cortex can benefit task performance even if they decrease sensory information.