The perils of bidirection al excitation..

1. The perils of bidirectionalexcitation.. • Advantages in terms of pattern completion, imagery, amplification, etc • But can you think of problems that can arise with bidir excitation? • If features turn categories on, and categories turn on features, and….

2. Inhibition: motivating questions Q: Why not turn everything on all the time? A: That’s like having everything off, but wasteful! Q: What’s different about inhibitory and excitatory neurons? A: Lots, but mostly where they project (send info) to. Generally... • Excitatory neurons project locally & to different areas • Inhibitory neurons primarily project within small regions • Excitatory neurons carry information for communication • Inhibitory neurons are responsible for (locally) regulating the activation of excitatory neurons.

3. Inhibition: ion mechanism Who remembers how this works? What were the primary NTs? Glutamate is excitatory: • Opens Na+ channels • Na+ enters cell, increasing Vm GABA is inhibitory: • Opens Cl- channels • Cl- enters cell, increasing Vm…? • ...only if Vm > Einhib. reversal

4. Inhibition: Uses • Controls activity (bidirectionalexcitation). • Inhibition as athermostat-controlled airconditioner: • Inhibitoryneuronssampleexcitatoryactivity(likeathermostat samples thetemperature) • Moreexcitatoryactivity→moreinhibitiontokeepthenetworkfrom gettingtoo“hot”(active)→setpointbehavior

5. Types ofInhibition Feedback b) a) Hidden Inhib Hidden Inhib Feed− Forward Input Input Anticipatesexcitation Reacts toexcitation

6. Types ofInhibition Feedback b) a) Hidden Inhib Hidden Inhib Feed− Forward Input Input Anticipatesexcitation Reacts toexcitation Like havingthermostat outside of yourhouse Like a normal(indoor) ACthermostat

7. <Inhib.proj> parameter explanation Feed-forward inhibition • Strength of FF weights to inhib (ff_wt_scale) • How much the input turns on inhibition Feed-back inhibition • Strength of FB weights to inhib (fb_wt_scale) • Hidden units turning on inhibition Both FF and FB • Inhib conductance into inhib units (g_bar_i.inhib) • Inhibitory units inhibiting each-other • Inhib conductance into hidden units (g_bar_i.hidden) • Inhibitory units inhibiting hidden units

8. Simulations:[inhib.proj]

9. FFFB Inhibition function • Can summarise effects of both types of inhibition by manipulating inhibitory conductance in all units within a layer in a way that would approximate what interneurons would do (while retaining dynamics). • This lets us avoid simulating inhibitory interneurons, which is a big computational saving • Also “cuts to the chase” and avoids oscillations in inhibitory response • In some cases inhibitory neurons may be of interest, and we can still simulate them where desirable. Just don’t need to in every case.

10. FFFB inhibitionfunction • Wecanapproximatefeedforward(FF)andfeedback(FB)aspectsof inhibitoryinterneuronsusingtheFFFBinhibitionfunction: • averagenetinput:<η>=Ln1ηi n • averageactivation:<y>=Ln1yi n • Then:ff(t)=ff[<η>−ff0]+ • fb(t)=fb(t−1)+dt[fb<y>−fb(t−1)] • NowjustsetgiintargetlayerasafunctionofFFandFB: • gi(t)=gi[ff(t)+fb(t)] Advantages: Much less computationally expensive, avoidsoscillations

11. Simulations: [inhibfffb.proj] FFFB approximates set pointbehavior. Allowsforfasterupdating,reducesoverallcomputation. Canuseinlargenetworkswithmultiplelayers,withinhibition summarized byFFFB Canstillcapturedifferentialamountsofinhibitionindifferentbrain areas with FFFB params: gi, FF andFB components insomeapplicationsmaystillwantactualinhibneurons

12. Competition • Inhibition within a layer creates competition • Why might this be useful? • Forces different units to do different things • Turns off noisy (irrelevent) units for a given computation • Onlythemost appropriate(best-fitting)unitssurvivethecompetition

13. Alternative inhibition function(optional): k-Winners-Take-All(kWTA)

14. Alternative inhibition function(optional) k-Winners-Take-All(kWTA) • Thefunctionofinhibitionistokeepexcitatoryactivityataroughset point. • Wecanapproximatethisfunctionbyenforcingamaxactivitylevelin eachlayer. • kWTA: Instead of simulating inhibitory neurons, we choose an inhibitorycurrentgi valueforeachlayersuchthatthespecified numberkofexcitatoryneuronsareabovethreshold.

15. Alternative inhibition function(optional) k-Winners-Take-All(kWTA) • Thefunctionofinhibitionistokeepexcitatoryactivityataroughset point. • Wecanapproximatethisfunctionbyenforcingamaxactivitylevelin eachlayer. • kWTA: Instead of simulating inhibitory neurons, we choose an inhibitorycurrentgi valueforeachlayersuchthatthespecified numberkofexcitatoryneuronsareabovethreshold. • Advantages: Much less computationally expensive, avoidsoscillations.

33. kWTA:Summary • Simpleshortcutweuseinsteadofactualinhibitoryinterneurons • Capturesbasicideathatinhibitionmaintainsactivityata • set point for a givenlayer • Specifyinhibitionvalueforalayersuchthatkunitsareactive • kisaparameter:percentactivitylevelsvaryacrossdifferentbrain regions! • kWTAstillallowsforsomewiggleroominoverallactivation

34. Benefits ofInhibition • Controls activity (bidirectionalexcitation) • Inhibitionforcesunitstocompetetorepresenttheinput:Onlythemost appropriate(best-fitting)unitssurvivethecompetition

35. Networks • Biology: The cortex • Excitation: • Unidirectional(transformations) • Bidirectional (top-down processing, patterncompletion, amplification) • Inhibition: Controls bidirectional excitation (feedforward, feedback,set point, FFFBapproximation) • Constraint Satisfaction: Putting it alltogether.

36. ConstraintSatisfaction

37. ConstraintSatisfaction Processoftryingtosatisfyvariousconstraints(fromenvironment, connection weights,activations). Bidirectionalexcitationandinhibitionformpartofthislarger computationalgoal.

38. ConstraintSatisfaction Processoftryingtosatisfyvariousconstraints(fromenvironment, connection weights,activations). Bidirectionalexcitationandinhibitionformpartofthislarger computationalgoal. Energy/harmony. AttractorDynamics. Noise.

39. Harmony Harmony=extenttowhichunitactivationsareconsistentwithweights H=1LjLiaiwijaj 2

40. Harmony Harmony=extenttowhichunitactivationsareconsistentwithweights H=1LjLiaiwijaj 2 Harmonyishighwhenunitswithstrong(positive)weightsareco-active

41. Harmony JohnHopfieldshowedthatharmonytendstoincreasemonotonicallyasthe networksettles

42. Harmony JohnHopfieldshowedthatharmonytendstoincreasemonotonicallyasthe networksettles

43. Harmony JohnHopfieldshowedthatharmonytendstoincreasemonotonicallyasthe networksettles networksettling=movingtoamore“harmonious”state

44. Attractors An attractor network is a network of neurons with excitatory interconnectionsthatcansettleintoastablepatternoffiringgivenarange of different startingstates.

45. Attractors An attractor network is a network of neurons with excitatory interconnectionsthatcansettleintoastablepatternoffiringgivenarange of different startingstates. [hereweconsideronlyfixedpointattractors,butcyclicalorchaotic attractors are alsopossible]

46. AttractorDynamics Bidirectionalexcitationcausesanetworktosettleintoaparticularstable state over time: theattractor. Cool Demos on Hopfield attractors: http://jackterwilliger.com/attractor-networks/

47. AttractorDynamics Bidirectionalexcitationcausesanetworktosettleintoaparticularstable state over time: theattractor. Circle indicates attractor basin. Maximizeharmonygiveninputsandweights.

48. The NeckerCube a) b) c) • Two differentinterpretations • Can’t perceive both atonce • Alternate between perceptions:bistability

49. Otherexample

50. The Role ofNoise Howmightnoisebeusefulinyourbrain?