2,425 research outputs found
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
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