Is the Cortex a Digital Computer? Dana H. Ballard Department of - - PowerPoint PPT Presentation

Is the Cortex a Digital Computer?

Dana H. Ballard

Department of Computer Science University of Texas at Austin Austin,TX International Symposium “Vision by Brains and Machines” November 13th-17th Montevideo, Uruguay

Computational Hierarchy

Create baseline calibrations Calibration Estimate state State Select the next thing to do within a procedure Action Choose procedural set OS Description Function

Roelfsema et al PNAS 2003

Visual Routines

Multi-tasking As Revealed by Gaze Sharing in Human Data

10 20 30 40 50 60 172 10

3

177 10

3

182 10

3

187 10

3

Mid-Block 40m

time(sec) Mid-block sign Car Intersection sign Eye Stop sign

0 5 10 15

Shinoda and Hayhoe, Vision Research 2001

See Neuron 1999 Special Issue

QuickTime and a YUV420 codec decompressor are needed to see this picture.

Temporal Rate Coding

milliseconds

Why Rate Coding cannot work

Why Rate Coding cannot work

NN Hebb rule: Maximize XW Want x ~ ∆T ~ ∆W

In a rate coding model, the position of the spike at a synapse wrt the output spike must be random

Timing Poisson Updates Synaptic weight

Timing Poisson Updates Synaptic weight

A small ~ 1-2 ms delay can be used to signal an analog quantity

1 ms δ

reference

A Rank Order Code

VanRullen & Thorpe Vision Res 2002

Feedback Spike Timing Constraint

_ + r Loop delay = 20 milliseconds

Computational Hierarchy

Create baseline calibrations Calibration Estimate state State Select the next thing to do within a procedure Action Choose procedural set OS Description Function

LGN-V1 Circuit

• +

U rest I U

T

e = I - Ur

LGN Cortex

r

A Slice Through The Cortex

• +

r

• +

r

• +

r LGN V1 V2

from Usrey & Reid

Labeled Line Math

NN vol8 p1552

x u β

Case 2

Model Experiment

Comparing the Model to Data

Computational Hierarchy

Create baseline calibrations Calibration Estimate state State Select the next thing to do within a procedure Action Choose procedural set OS Description Function

See also: Computing With Self-Excitatory Cliques: A Model and an Application to Hyperacuity-Scale... Zucker and Miller, Neural Comp..1999; 11: 21-66

500µ

Lund & Bressloff (2003) Cerebral Cortex 14

Reasons for copies

_

Copies exist in columns

_

Copies provide robustness to cell death

_

Copies allow mathematical exploration

_

Copies allow multiprocessing

_

Circumvent refractory period

What would the spikes look like in such a scheme?

Parameters

Trials ~ No. of individual experimental trials Processes ~ No. of ongoing procedures Copies ~ No. of cells with same RF Duration ~ Duration of an individual trial Jitter ~ Displacement used to signal analog value*

* Not used

Trials =50 Processes = 2 Copies = 6 Duration =1 sec

Distributed Synchrony Simulation m σ

Poisson Process m σ

Raj Rao Zuohua Zhang Johnathan Shaw Constantin Rothkopf Janneke Jehee

Computation Neuroscience Physics

Axonal Propagation Speeds: Evidence? 2-6 cm/s

0.1 - 0.4 cm/s

Code input I with synapses U and

• utput r

Coding cost of residual error Coding Cost of model [Olshausen and Field 1997]

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

U,r

Synapses are Trained with Natural Images

Dr µ- ¶ E ¶ r

DU µ- ¶ E ¶ U

• 1. Apply Image
• 2. Change firing
• 3. Change Synapses

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

Handling the Error Term with Predictive Coding

I=u1r1u2r 2...um r m

I r1 r2 LGN Cortex

I

r

• +

U

Sparse Priors are Biological

A Slice Through The Cortex

• +

r

• +

r

• +

r LGN V1 V2

X

Rao and Ballard, Nature Neuroscience 1999

RF

Endstopping

Drawbacks of rate coding

_

Inherent inaccuracy with signaling with a probabilistic code

_

Averaging over populations is expensive

_

Unary codes are inefficient

_

Its never used in simulations

_

Decoders are of marginal utility

_

Ubiquitous observation of Poisson statistics

_

Rate coding is incompatible with the Hebb Rule (Bi & Poo)

• C. Reid et al
• M. Meister et al

Retina LGN