Computa(on through dynamics Using recurrent neural networks to - - PowerPoint PPT Presentation

Computa(on through dynamics

Using recurrent neural networks to unveil mechanism in neural circuits David Sussillo with Valerio Mante and Bill Newsome

Table of contents Introduc(on Training recurrent neural networks(RNNs) Understanding how RNNs work Contextual decision making Future direc(ons

Complex behavior

• Complex neural data

Foster et al. IEEE EMBS 2012

spikes

−400 −200 200 400 600 800 5 10 15 20 25

(me (ms) (me (ms) rate (spikes / sec)

−400 −200 200 400 600 800 10 20 30 40 50

firing rate trials

(me (ms) firing rates of many neurons

400 800 −400

(me (ms) a few principal components

What are the biophysical correlates of these variables?

I work at the level of rates because we can make networks do interes(ng computa(ons!

Recurrent Neural Networks (RNNs)

time (ms)

−400 −200 200 400 600 800 10 20 30 40 50

firing rate

Recurrent Neural Networks (RNNs)

... time (ms) rate (spikes / sec)

−400 −200 200 400 600 800 10 20 30 40 50

firing rate

Recurrent Neural Networks (RNNs) (me (me

...

nonlinear distributed feedback

time (ms) rate (spikes / sec)

−400 −200 200 400 600 800 10 20 30 40 50

firing rate

Sompolinsky et al., PRL 1988 Rajan et al., PRE 2010

...

Dynamics in RNNs (Spontaneous Ac(vity)

(me (ms)

Tools to understand how RNNs work

Sussillo* & Barak*, Neural Computa(on 2013

with Omri Barak

Martens & Sutskever, ICML 2011

How does a sine-wave generator work?

Time Output Frequency

Sussillo* & Barak*, Neural Computa(on 2013

Time Output Frequency

PC1 PC3 PC2

What is a fixed point?

Why are they important?

A B C D E F

Any nonlinear dynamical system (e.g. neural circuit) Zero “mo(on”

Sussillo* & Barak*, Neural Computa(on 2013

firing rate 1 firing rate 2

PC1 PC3 PC2

Time Output Frequency D

PC1 PC3 PC2

10 20 30 40 50 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Fixed Point # Frequency (radians)

Oscilla(on # Frequency (radians)

Input frequency Linear system frequency

The linear system is a very good approxima(on!

Sussillo* & Barak*, Neural Computa(on 2013

Recurrent neural networks are a natural model class for modeling cor(cal phenomenon: dynamical, nonlinear, distributed. Recent advances have enabled the training of RNNs. In “simple” cases, one can understand how an RNN implements its computa(on in the language of dynamical systems (e.g. fixed points, saddle points,

• scilla(ons).

One simple descrip(on of an RNN is as a bunch of linear systems (ling the state space.

Conclusions from technical part

Contextual decision making (data) with Valerio Mante and Bill Newsome

Mante*, Sussillo*, Shenoy & Newsome

Decision( Sensory( s,muli( Context(

Prefrontal cortex contributes to flexibility of decisions

A2end relevant s4muli Ignore irrelevant s4muli Suppress inappropriate responses Represent context

Computa(ons in cor(cal circuits are flexible

Context-dependent ga(ng in monkeys

mo7on context

Context-dependent ga(ng in monkeys

color context

S(muli

S(muli

S(muli

S(muli

mo(on strength color strength

Averaging over color shows effects of mo(on “Average over”

mo(on strength color strength

Averaging over mo(on shows effects of color “Average over”

Behavior

mo(on strength color strength mo(on strength color strength

Behavior

COLOR% (V4,IT)(

Where are sensory inputs selected?

MOTION& (MT)%

Sensory evidence DECISION( (LIP,PFC,SC)* Integrated evidence

One could easily frame this work in the context

• f routing information in the brain.

Mixed signals in FEF neurons

0.1 0.1 choice choice motion motion color color

Mixed signals in FEF neurons

Verbal aside on how to make sense of this data via a state-space.

mo#on% color% choice%

PFC popula(on response during mo(on context

“dots on” to “dots off” (750ms) Correct trials only!

mo#on% color% choice%

choice% le,% choice% right% N">"250" 50ms"

PFC popula(on response during mo(on context

• n
• ff
• ff

“dots on” to “dots off” (750ms)

mo#on% color% choice%

• ff%
• ff%

choice% le-% choice% right%

PFC popula(on response during mo(on context

i n t e g r a (

• n

*

mo#on%

mo#on% color% choice%

• n%
• ff%
• ff%

choice% le-% choice% right%

mo#on% color% choice%

PFC popula(on response during mo(on context

PFC popula(on response during mo(on context

mo#on% color% choice%

choice% le,% choice% right%

PFC popula(on response during mo(on context color%

mo#on% color% choice%

PFC popula(on response during color context

• n
• ff
• ff

choice& le(& choice& right&

PFC popula(on response during color context

PFC popula(on response during color context

mo#on% color% choice%

Choice and input signals in PFC

Color towards Target 1 Color towards Target 2 Motion towards Target 1 Motion towards Target 2 Choice Target 2 Choice Target 1

Representa(on of context in PFC

Mo#on%context%

Color%context%

context' mo)on' choice'

Motion context Color context

color choice color choice motion motion motion motion context (4D)

The structure of task related signals in PFC

The$structure$of$task$related$signals$in$PFC$

Motion context Color context

color c h

• i

c e color c h

• i

c e m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

How does selec(ve integra(on occur?

The$structure$of$task$related$signals$in$PFC$

Motion context Color context

choice motion choice color

Context'dependent* ga#ng*(“a.en/on”)*

How does selec(ve integra(on occur?

The$structure$of$task$related$signals$in$PFC$

Motion context Color context

color choice motion choice motion color

Context'dependent* input*direc.on*

How does selec(ve integra(on occur?

The$structure$of$task$related$signals$in$PFC$

Motion context Color context

color choice color motion motion choice

Context'dependent* choice*direc.on*

How does selec(ve integra(on occur?

How$does$selec*ve$integra*on$occur?$

Motion context Color context

color choice color choice m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

The structure of task related signals in PFC How does selec(ve integra(on occur?

Task-relevant variables are mixed in the responses of single neurons, but separable and systema(cally represented in the popula(on. Irrelevant inputs are not filtered-out. Selec(on of relevant inputs occurs late, possibly within PFC. Sensory inputs elicit popula(on responses that differ from those corresponding to a choice. The direc(ons of choice and of the inputs are largely independent of context (only shii in state space)

Conclusions from data

Contextual decision making (model)

How could selec(ve integra(on occur?

model

guess mechanism

task Tradi(onal Modeling Framework model data system data

guessed mechanism task Tradi(onal Modeling Framework

But what should the solu(ons look like? Are we too clever? Not clever enough?

system

task Op(mized Modeling Framework

• p(mized model

model data system data discover mechanism

discovered mechanism task Op(mized Modeling Framework system

Fetz, 1993 Zipser & Andersen, 1988

This is a concrete and detailed hypothesis genera(ng mechanism.

A neural-network model of selec(ve integra(on

750ms&

sensory evidence context choice

A neural-network model of selec(ve integra(on

750ms&

sensory evidence context choice

1 +1

750ms&

A neural-network model of selec(ve integra(on

750ms&

sensory evidence context

1

• 1

750ms&

choice

Model “Behavior”

25 50 75 100 fraction right choices (%) fraction green choices (%) motion trials 25 50 75 100 25 50 75 100 fraction right choices (%) fraction green choices (%) color trials 25 50 75 100 motion strength right left color strength green strong weak red strong weak strong weak strong weak

750ms& context sensory evidence

Network Output Bounded Integrator

The trained network creates a bounded integrator

Model trajectories during color trials

choice& right&

• n&
• ff&
• ff&

strong& weak& weak& strong& choice& le1&

choice& color&

Model trajectories during color trials

choice& mo(on&

choice le; choice right

Model trajectories during color trials

How does integra(on happen?

choice le; choice right

color choice

What is a fixed point?

Why are they important?

A B C D E F

Any nonlinear dynamical system (e.g. neural circuit) Zero “mo(on”

+1

• 1

firing rate 1 firing rate 2

Seung, PNAS 1996

choice le; choice right

color choice

Fixed points make a line amractor

color c h

• i

c e motion

context sensory evidence

Two line amractors for two contexts

The line amractors are context dependent and never exist at the same (me.

choice le; choice right

color choice

Fixed points make a line amractor

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

A simulated perturba(on experiment

color context

choice le; choice right

So what causes this difference between integra(on of color and ignoring mo(on?

color context

Projec(ons onto the line amractor

These vectors we’ve talked about are context independent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

The dynamics are context dependent

Flexible selec(on and integra(on

How$does$selec*ve$integra*on$occur?$

Motion context Color context

color c h

• i

c e color c h

• i

c e m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

m

• t

i

• n

selection vector s e l e c t i

• n

v e c t

• r

Context'dependent* selec%on(vector*

A predic(on of the model

choice le; choice right

color context

We trained an abstract model to make a contextual decision based on two noisy input streams. The model made a contextual integrator with bounds. Like the data, the model represents the relevant and irrelevant inputs in separable dimensions. Two context dependent line amractors are responsible for the integra(on. Network dynamics generated through feedback, not input ga(ng, are responsible for context dependent integra(on. The network is flexibly reconfigured by the context input, which is seen as two different line amractors in state space.

Conclusions from model

Ga7ng of sensory signals: Does not require modula(on of sensory responses. Is not about suppressing the irrelevant input, but about selec(ng the relevant input in state space. Is one aspect of a dynamical process occurring in the same cor(cal circuit as integra(on of evidence. Everything is happening at the popula(on level. Our works suggests a possible mechanism, which is not exclusive of others.

Computa7on through dynamics: mixed, separable representa(ons are contextually and dynamically linked to generate the desired output.

Final conclusions

Shenoy Lab

Krishna Shenoy

Mark Churchland MaD Kaufman Cindy Chestek Dan O’Shea Cora Ames Werapong Goo Jus(n Foster Paul Nuyujukian Jonathan Kao Joline Fan Eric Trautmann Sergey Stavisky Chand Chandrasekaran

Newsome Lab

Bill Newsome

Valerio Mante Roozbeh Kiani Vince McGinty Daniel Kimmel Leo Segrue Diogo Peixioto Nazli Emadi

Larry AbboD Mark Churchland Omri Barak Valerio Mante

This research was supported by an NIH Director’s Pioneer award, Howard Hughes Medical Ins(tute, and grants from NIH-CRCNS, DARPA REPAIR, NSF, the Helen Hay Whitney Founda(on, the Burroughs Wellcome Fund, and the Christopher and Dana Reeve Founda(on and a NSF GRFP.

Funding Collaborators Acknowledgments