Neural responses are typically characterized by computing the mean firing rate, but response variability can exist across trials. Many studies have examined the effect of a stimulus on the mean response, but few have examined the effect on response variability. We measured neural variability in 13 extracellularly recorded datasets and one intracellularly recorded dataset from seven areas spanning the four cortical lobes in monkeys and cats. In every case, stimulus onset caused a decline in neural variability. This occurred even when the stimulus produced little change in mean firing rate. The variability decline was observed in membrane potential recordings, in the spiking of individual neurons and in correlated spiking variability measured with implanted 96-electrode arrays. The variability decline was observed for all stimuli tested, regardless of whether the animal was awake, behaving or anaesthetized. This widespread variability decline suggests a rather general property of cortex, that its state is stabilized by an input.

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This work was supported by a Helen Hay Whitney postdoctoral fellowship (M.M.C.), Burroughs Welcome Fund Career Awards in the Biomedical Sciences (M.M.C. and K.V.S.), Gatsby Charitable Foundation (M.S. and B.M.Y.), US National Institutes of Health (NIH), National Institute of Neurological Disorders and Stroke Collaborative Research in Computational Neuroscience grant R01-NS054283 (K.V.S. and M.S.), the Michael Flynn Stanford Graduate Fellowship (J.P.C.), the Howard Hughes Medical Institute and NIH grant EY05603 (W.T.N., L.P.S., M.R.C. and G.S.C.), a Howard Hughes Medical Institute predoctoral fellowship (M.R.C.), NIH grant EY014924 (T.M. and K.M.A.), Sloan Foundation (T.M. and K.V.S.), Pew Charitable Trust (T.M.), NIH EY015958 and EY018894 (M.A.S.), NIH EY02017 and EY04440 (J.A.M.), NIH EY016774 (A.K.), NIH 1 EY13138-01 (D.C.B., A.M.C., P.H. and B.B.S.), NIH EY019288 (N.J.P.), the Pew Charitable Trust (N.J.P.), EY04726 (D.F.), US National Defense Science and Engineering Graduate Fellowships (B.M.Y. and G.S.), National Science Foundation Graduate Research Fellowships (B.M.Y. and G.S.), the Christopher and Dana Reeve Foundation (K.V.S. and S.I.R.), and the awards from Stanford Center for Integrated Systems, National Science Foundation Center for Neuromorphic Systems Engineering at Caltech, Office of Naval Research, NIH Director's Pioneer Award 1DP1OD006409 and Whitaker Foundation (K.V.S.).

Author information

Author notes

    • Mark M Churchland
    •  & Byron M Yu

    These authors contributed equally to this work.


  1. Department of Electrical Engineering, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Mark M Churchland
    • , Byron M Yu
    • , John P Cunningham
    • , Stephen I Ryu
    • , Gopal Santhanam
    •  & Krishna V Shenoy
  2. Neurosciences Program, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Mark M Churchland
    • , Byron M Yu
    • , Leo P Sugrue
    • , Marlene R Cohen
    • , Greg S Corrado
    • , William T Newsome
    • , Katherine M Armstrong
    • , Tirin Moore
    •  & Krishna V Shenoy
  3. Gatsby Computational Neuroscience Unit, University College London, London, UK.

    • Byron M Yu
    •  & Maneesh Sahani
  4. Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Leo P Sugrue
    • , Marlene R Cohen
    • , Greg S Corrado
    •  & William T Newsome
  5. Department of Neurobiology, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • William T Newsome
    • , Katherine M Armstrong
    •  & Tirin Moore
  6. Department of Psychology and Committee on Computational Neuroscience, University of Chicago, Chicago, Illinois, USA.

    • Andrew M Clark
    • , Paymon Hosseini
    • , Benjamin B Scott
    •  & David C Bradley
  7. Department of Neuroscience and Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.

    • Matthew A Smith
  8. Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York, USA.

    • Adam Kohn
  9. Center for Neural Science, New York University, New York, New York, USA.

    • Adam Kohn
    •  & J Anthony Movshon
  10. Department of Anatomy and Neurobiology, Washington University School of Medicine, St. Louis, Missouri, USA.

    • Steve W Chang
    •  & Lawrence H Snyder
  11. Howard Hughes Medical Institute, W.M. Keck Foundation Center for Integrative Neuroscience and Department of Physiology, University of California San Francisco, San Francisco, California, USA.

    • Stephen G Lisberger
  12. Section of Neurobiology, School of Biological Sciences, University of Texas at Austin, Austin, Texas, USA.

    • Nicholas J Priebe
  13. Department of Neurobiology and Physiology, Northwestern University, Evanston, Illinois, USA.

    • Ian M Finn
    •  & David Ferster
  14. Department of Neurosurgery, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Stephen I Ryu
  15. Department of Bioengineering, Stanford University, Stanford, California, USA.

    • Krishna V Shenoy


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M.M.C. wrote the manuscript, performed the Fano factor and factor analyses and created the figures. GPFA was developed by B.M.Y., J.P.C., M.S. and K.V.S. This application of factor analysis was devised by M.M.C. and B.M.Y. The mean-matched Fano factor was developed by M.M.C. and K.V.S. The conception for the study arose from conversations between M.M.C., K.V.S., B.M.Y., D.C.B., M.R.C., W.T.N. and J.A.M. V1 data (extracellular) were collected in the laboratory of J.A.M. by M.A.S. and A.K. and in the laboratory of A.K. V4 data were collected in the laboratory of T.M. by K.M.A. MT (plaid) data were collected in the laboratory of D.C.B. by A.M.C., P.H. and B.B.S. MT (dots) data were collected in the laboratory of W.T.N. by M.R.C. LIP and OFC data were collected in the laboratory of W.T.N. by L.P.S. using an experimental design developed by L.P.S. and G.S.C. PRR data were collected in the laboratory of L.H.S. by S.W.C. PMd data were collected in the laboratory of K.V.S. by B.M.Y., S.I.R., G.S. and M.M.C. MT (direction/area and speed) data were collected by N.J.P. and M.M.C. in the laboratory of S.G.L. Intracellularly recorded V1 data were collected by N.J.P. and I.M.F. in the laboratory of D.F. All authors contributed to manuscript revisions and editing, particularly J.A.M., W.T.N., L.P.S., D.F., J.P.C., B.M.Y. and K.V.S.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Mark M Churchland.

Supplementary information

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  1. 1.

    Supplementary Text and Figures

    Supplementary Figures 1–8 and Supplementary Notes 1–3


  1. 1.

    Supplementary Video 1

    A movie version of Figure 7a. Data are from PMd, and show the decline in across-trial variance after the onset of the stimulus (a reach target). The movie spans 750 ms, beginning 400 ms before stimulus onset and ending 350 ms after. The movie ends before the go cue is given. Each black dot shows the state of PMd on one trial. Fifteen randomly-chosen trials are shown. Dots turn blue for a brief moment at the time of stimulus onset. Note the subsequent drop in the variance of the dot locations (i.e., a drop in firing-rate variance). This feature of the response is at least as clear as the change in mean dot location (i.e., the change in mean firing rates). G20040123 dataset.

  2. 2.

    Supplementary Video 2

    As in Supplementary Video 1, but more time is shown and the trajectory of the RT-outlier trial is now included (red). The movie spans 1500 ms. This time-span differs slightly across trials, as they have different go-cue and movement-onset times. At the time of the go cue, each dot turns green and further progress is halted. Progress resumes once all trials have passed the time of their respective go cues. This re-aligns the data to the go cue, much as is commonly done in PSTH's. Traces end at movement onset.

  3. 3.

    Supplementary Video 3

    As in Supplementary Video 1, but for the G20040122 PMd dataset (that shown in Figure 7c).

  4. 4.

    Supplementary Video 4

    As in Supplementary Video 2, but for the G20040122 PMd dataset (that shown in Figure 7c).

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