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Omri Barak Collaborators: Larry Abbott David Sussillo Misha Tsodyks Sloan-Swartz July 12, 2011 Messy nice stuff & Nice messy stuff

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Neural representation Representation of task parameters by neural population. We know that large populations of neurons are involved. Yet we look for and are inspired by impressive single neurons. Case study: Delayed vibrotactile discrimination (from Ranulfo Romo’s lab)

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f 1 f 2 time (sec) Romo & Salinas, Nat Neurosci Rev, 2003

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f1f2 f1>f2? YN time (sec) Romo & Salinas, Nat Neurosci Rev, 2003

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Romo task Encoding of analog variable Memory of analog variable Arithmetic operation “f1-f2”

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Romo, Brody, Hernandez, Lemus. Nature 1999 Machens, Romo, Brody. Science 2005

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Striking tuning properties Lead to “simple / low dimensional” models “Typical” neurons are used to define model populations.

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Existing models Machens et al Miller et al Barak et al Miller et al Not shown: Verguts Deco Singh and Eliasmith 2006

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But… Are all cells that good? Barak et al Brody et al Jun et al prestim Time (sec) 10 Hz 22 Hz 34 Hz

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Echo state network Jaeger 2001 Maass et al 2002 Buonomano and Merzenich 1995

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Echo state network x r x + Noise N = 1000 / 2000 K = 100 (sparseness) g = 1.5

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Implementing the Romo task f1f1 f2f2 f r Sussillo and Abbott 2009 Jaeger and Haas 2004

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Input (f 1,f 2 ) Output

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Input (f 1,f 2 ) Output Unit activity

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It works, but… How does it work? –After the training, we have a network that is almost a black box. Relation to experimental data.

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Hypothesis Consider the state of the network in D as the trial evolves

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f1f1 f2f2 time (sec)

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Hypothesis Focus only at the end of the 2 nd stimulus. For each (f1,f2) pair, there is a point in 1000-D space.

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Hypothesis Focus only at the end of the 2 nd stimulus. For each (f1,f2) pair, there is a point in 1000-D space. So there is a 2D manifold in the 1000-D space. Can the dynamics (after learning) draw a line through this manifold?

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Dynamics or just fancy readout? Distance in state space The two responses are different in network activity, not just through the particular readout we chose.

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Saddle point

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Searching for a saddle in 1000D Vector function: Scalar function:

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Searching for a saddle in 1000D

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1 Number of unstable eigenvalues Distance along trajectory Number of unstable eigenvalues Norm of fixed point

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Saddle point

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Slightly more realistic Positive firing rates Avoid fixed point between trials. Introduce reset signal. Chaotic activity in delay period = 0

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It works

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Nice persistent neurons Time Activity

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a 1 -a 2 plane Romo and Salinas 2003 f 1 tuning f 2 tuning

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Problems / predictions Reset signal Generalization

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Reset There is a reset (Barak et al 2010, Churchland et al) There is no reset, and performance shows it (Buonomano et al 2007) Time (sec) Correlation Correlation between trials with different frequencies

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Generalization Interpolation vs. Extrapolation f1f1 f2f2

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Generalization Interpolation vs. Extrapolation f1f1 f2f2

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Generalization Interpolation vs. Extrapolation f1f1 f2f2

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Extrapolation Delosh et al 1997

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Conclusions Response properties of individual neurons can be misleading. An echo state network can solve decision making tasks. Dynamical systems analysis can reveal function of echo state networks. Need to find a middle ground.

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