Dana Ballard - University of RochesterDana Ballard - University of Rochester 11

Distributed Synchrony: a model for cortical communication

Madhur Ambastha

Jonathan Shaw

Zuohua Zhang

Dana H. Ballard

Department of Computer Science

University of Rochester

Rochester, NY

Summary

1. There is a computational hierarchy.1. There is a computational hierarchy.

2. At the bottom of the hierarchy is the need to 2. At the bottom of the hierarchy is the need to calibrate. calibrate.

3 . To communicate throughout cortex quickly, 3 . To communicate throughout cortex quickly, calibration uses the calibration uses the band band

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

Context Select a set of active behaviors

~10s

Resource Map active behaviors onto

motor system ~.3s

Routines update state information ~100ms

Calibration represent sensory/motor/reward

~20ms

Computational quanta

~2ms

1. Computational Timescales

2. How can the Cortical Memory Self-Calibrate?

Olshausen and Field 97Rao and Ballard 99

Code Input I with synapses U and output r

Coding cost of residual error

Coding Cost of model

Min E(U,r)= |I-Ur|2 + F(r) + G(U)

Synapses are Trained with Natural Images

Δ r ∝ −

∂ E

∂ r

Δ U ∝ −

∂ E

∂ U

1. Apply Image

2. Change firing

3. Change Synapses

An Example: LGN-V1Circuit

r-

+

U

restI

U Te = I - Ur

LGN Cortex

HierarchicalMemoryOrganization

Fellerman and Van Essen 85

A Slice Through The Cortex

-+r

-+r

-+r

LGN V1 V2X

Rao and Ballard, Nature Neuroscience 1999

RF

Endstopping

3. Can Predictive Coding work with individual spikes?

Spike Timing Model

_+

r

Loop delay - 20 milliseconds

LGN-V1 Circuit using Spikes

r

-+

U

restI

U T

e

-+

U

restI-

U T

e

Spike Models

Spike is probabilistic

Deterministic spike has area

input feedbackprediction

predictionerror

LGN ON

LGN OFF

I Ur I-Ur

Receptive FieldsOrientationDistribution

Coding Cells

Responses are Random and Phasic

Projection Pursuit

I u1

u2

r1

r2

r1 = I u1

r2 = ( I - r1 u1 ) u2

Microcircuit Details

1

I

I

II

I

r1 u1 u2

r1 = I u1

r2 = I u2 - r1 u1 u2

2

Summary 1:Distributed Synchrony is motivated by four

principle constraints

1. Fast, reliable intercortical communication1. Fast, reliable intercortical communication

2. The ‘need’ for a cell to multiplex2. The ‘need’ for a cell to multiplex

3. Need to poll the input3. Need to poll the input

4 .The need to reproduce observed cell responses4 .The need to reproduce observed cell responses

Summary 2:Isolating Computations = The Binding problem

Solutions:Solutions:

1. There is no binding problem - 1. There is no binding problem - Movshon

2. Fast weight changes at synapses - 2. Fast weight changes at synapses - von der Malsburg

3 .Synchrony encodes the stimulus - 3 .Synchrony encodes the stimulus - Singer

4 .Synchrony encodes the answer - 4 .Synchrony encodes the answer - Koch and others 5 .Synchrony encodes the 5 .Synchrony encodes the processprocess - - Distributed Synchrony

Thanks !

Handling the Error Term with Predictive Coding

I = u1

r1

+ u2

r2

+ ... + um

rm

I

r1

r2

LGN

Cortex

Roelfsema et alPNAS 2003

Diesmann, Gewaltig,Aertsen Nature 402, p529 1999

Synchronous Spikes Can Propagate

MaxM P(M|D)= MaxM[P(D|M)P(M)/P(D)]

Minimum Description Length - Bayesian Version

Can neglect P(D) and take logs…

MaxM[log P(D|M)+ log P(M)]

Or equivalently minimize negative logs…

MinM[ - log P(D|M) - log P(M)]

If we use exponentiated probability distributions,log cancels negated exponent so…

Coding cost of residual error

Coding cost of model

Singer group, J Neuroscience 1997

Cortical Inhibitory CellsCan Oscillate at 20-50 Hz

Beierlein, Gibson, Connors Nature Neuroscience 3 p904 2000

Temporal Rate Coding:A Strategy that cannot possibly work

Reconstructionas a function ofCoding Cost

low

high

input feedback error

LGN ON

LGN OFF

LGN ON

LGN OFF

Spectral software supplied by Daeyeol Lee

Distributed Synchrony

Coding Cost as a function of Signaling Strategy

Axonal Propagation Speeds: Evidence?

2-6 cm/s

0.1 - 0.4 cm/s

Visual Routine

ReverseReverse Correlation Correlation

Δ

+

+

+

Spatio-temporal behavior of LGN Cells

Experiment (Reid & Usrey)Model

Time - milliseconds30 50 70 90

Using Reverse Correlation