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Spectral Representation of Thermal OTO Correlators

We study the spectral representation of finite temperature, out of time ordered (OTO) correlators on the multi-time-fold generalised Schwinger-Keldysh contour. We write the contour-ordered correlators as a sum over time-order permutations acting on a funda- mental array of Wightman correlators. We decompose this Wightman array in a basis of column vectors, which provide a natural generalisation of the familiar retarded-advanced basis in the finite temperature Schwinger-Keldysh formalism. The coefficients of this de- composition take the form of generalised spectral functions, which are Fourier transforms of nested and double commutators. Our construction extends a variety of classical results on spectral functions in the SK formalism at finite temperature to the OTO case.Comment: 19 pages+appendices, references adde

A multi-stage recurrent neural network better describes decision-related activity in dorsal premotor cortex

We studied how a network of recurrently connected artificial units solve a visual perceptual decision-making task. The goal of this task is to discriminate the dominant color of a central static checkerboard and report the decision with an arm movement. This task has been used to study neural activity in the dorsal premotor (PMd) cortex. When a single recurrent neural network (RNN) was trained to perform the task, the activity of artificial units in the RNN differed from neural recordings in PMd, suggesting that inputs to PMd differed from inputs to the RNN. We expanded our architecture and examined how a multi-stage RNN performed the task. In the multi-stage RNN, the last stage exhibited similarities with PMd by representing direction information but not color information. We then investigated how the representation of color and direction information evolve across RNN stages. Together, our results are a demonstration of the importance of incorporating architectural constraints into RNN models. These constraints can improve the ability of RNNs to model neural activity in association areas.https://doi.org/10.32470/CCN.2019.1123-0Accepted manuscrip