Dynamics of perceptual bistability. Alternating perceptions of ambiguous scenes J Rinzel, NYU NIST, 2011
w/ N Rubin, A Shpiro, R Curtu, R Moreno, E Montbrio, E Sussman
What do we perceive when confronted with ambiguous sensory stimuli?
Bradley et al, 1998
Dynamics of Perceptual Bistability
w/ N Rubin, A Shpiro, R Curtu, R Moreno, E Montbrio, E Sussman
• Visual modality: moving plaids; Auditory modality: repeating triplet pattern
• Neuronal-based models
• Oscillator models --• mutual inhibition + slow negative feedback (adaptation)• noise gives randomness to period
• Attractor models – • noise driven, no alternation w/o noise• double-well potential: phenomenological model
• Use stats to constrain models
• Levelt II revisited: perceptual exploratory strategy
• Auditory “objects” and alternations: ABA_ABA_… common principles.
Funding: Swartz Foundation, NIH
PLAID DEMOR Moreno, N Rubin
Transparent + coherent. Some parameter variations.
Pressnitzer & Hupe, Current Biology, 2006
Integration
Segregation
“galloping”
Sound parameters: DF = frequency differencePR = presentation rate
Triplet pattern (Van Noorden, 1975) -- possible ambiguity in auditory streaming.
Oscillator Models for Directly Competing Populations
w/ N Rubin, A Shpiro, R Curtu
Two mutually inhibitory populations, corresponding to each percept.Firing rate model: r1(t), r2(t)
Slow negative feedback: adaptation or synaptic depression.
Wilson 2003; Laing and Chow 2003
r1
Slow adaptation, a1(t)
r1 r2r2r1
No recurrent excitation
…half-center oscillator
τ dr1/dt = -r1 + S(-βr2 - φ a1+ I1)τa da1/dt = -a1 + fa(r1)
τ dr2/dt = -r2 + S(-βr1 - φ a2+ I2)τa da2/dt = -a2 + fa(r2)
τa >> τ , S(u)=1/(1+exp[(θ-u)/k])
u
f
S, fa
Shpiro et al, J Neurophys 2007
Input, I1 I2
a2
Alternating firing rates Adaptation slowly grows/decays
IV fa(u)=γu
adaptation LC model
Excessive symmetry
Five Regimes of Behavior,
Common to Neuronal Competition Models
Incr
easi
ng S
timul
us
Shpiro et al, J Neurophys 2006Curtu et al, SIADS, 2008
depression LC model Wilson’s model
Math – adaptation model with adaptation dominant: φ > β / (1+τ). (I1=I2.)
Dynamic states and stability depend on steepness of S and inhibition strength, β.
Weak inhibition: SIM stable, for all I- no altern’ns
Strong enough: then Hopf bifur’cns (2 of them) are supercritical and lead to anti-phase oscill’n.
Very strong: multiple equilibria, pitchfork
and, if stable, WTA.
Five Regimes of Behavior,
Common to Neuronal Competition Models
Shpiro et al, J Neurophys 2006Curtu et al, SIADS, 2008
depression LC model
φ
φ
Fast-Slow dissection: r1 , r2 fast variables a1 , a2 slow variables
r1- nullcliner2- nullcline
r1 = S(- β r2 - φ a1+ I1)r2 = S(- β r1 - φ a2+ I2)
Fast/Slow Dynamics
a1, a2 frozen
r1
r2
Decision making models, XJ Wang…
r1-r2 phase plane, slowly drifting nullclines
a1
a2
Switching occurs when a1-a2
traj reaches a curve of SNs (knees)
At a switch: • saddle-node in fast dynamics.• dominant r is high while system ridesnear “threshold”of suppressed populn’s nullcline ESCAPE.
β =0.9, I1=I2=1.4
r1- nullcliner2- nullcline
r1
r2
input
f
Dominant, a ↑ I – φ a
θ
net input
Suppressed, a ↓ I – φ a - β
Small I, “release”
Switching due to adaptation:release or escape mechanism
θ
net input
Large I, “escape”
Recurrent excitation, secures “escape”
I + α a – φ a
rj = S(input to j) = S(- β rk - φ aj+ Ij)
S
Noise leads to random dominance durations and eliminates WTA behavior.
Added to stimulus I1,2
s.d., σ = 0.03, τn = 10
Model with synaptic depression
τ dri/dt = -ri+ S(-βrj - φ ai+ Ii + ni)τa dai/dt = -ai + fa(ri)
Noise-Driven Attractor Models w/ R Moreno, N Rubin J Neurophys 2007
No oscillations ifnoise is absent.
Kramers 1940
Noise-induced bursting. Sukbin Lim, NYU
Dynamical properties of a network withspiking neurons. Simulation results.
Levelt II
distribution
100 LIF units/ popul’n
fMRI: Polonsky et al, 2000Electrophysiology: Leopold, Logothetis…
Sheinberg and Logothetis, 1997fMRI: Tong et al, 1998
Neuronal correlates of alternations
Rubin’s face-vase: early visual cortex. Parkkonen et al, PNAS, 2008
fMRI
MEG
From Sterzer et al, review, TICS, 2009
Noise-free
Observed variability and mean duration constrain the model.
1 sec < mean T < 10 sec
0.4 < CV < 0.6
With noise
Difficult to arrange high CV andhigh <T> in OSC regime.
With noise
Favored: noise-driven attractor with weak adaptation – but notfar from oscillator regime.
… LP-II in binocular rivalryParameter dependence of mean T and f:
contrast B
contrast A
Eye B
Eye Afrac
tion
B0.14
0.5
0
contrast B
contrast A
LP-II is not valid for all contrast values
TA
TB
contrast B
w/ Moreno, Shpiro, Rubin
???
Transparent + different frequencies.
Plaids with different wavelengths depth reversals
Percent dominance reflects brain’s estimate of probability of depth.
Levelt’s II generalized, Moreno et al, J Vision (2010), ‘Parameter manipulation of an ambiguous stimulus affects mostly the mean dominance duration of the stronger percept.’
also Brascamp et al 2006
Alternation: a perceptual exploration strategy.
#1
behi
nd #1
behi
nd
w/ Moreno, Shpiro, RubinJ of Vision, 2010
Maximum alternation rate at equidominance
log (1 ) log(1 )A A A AEntropy f f f f
Moreno-Bote et al, J of Vision, 2010.
depth reversals plaids
n=4
rivalry
0
AA
A B
gI
g g g
0
BB
A B
gI
g g g
Models: Input normalization and maximum alternation rate at equidominance
fraction of dominance
Alte
rnat
ion
rate
w/ Moreno, Shpiro, Rubin
Temporal dynamics of auditory and visual bistability – common principles of perceptual organization.
Pressnitzer & Hupe, 2006
Van Noorden, 1975
Visual
Temporal dynamics of auditory and visual bistability – common principles of perceptual organization.
Integrated or segregated perceptsGrouped or split percepts
Exclusivity, randomness, and inevitability
Pressnitzer & Hupe, 2006
Leopold & Logothetis, 1999
Visual
Temporal dynamics of auditory and visual bistability – common principles of perceptual organization.
Integrated or segregated perceptsGrouped or split percepts
Pressnitzer & Hupe, 2006
Bistability/alternation in auditory streaming – integration (galloping) or segregation.
Tone duration 120 ms, 3 STs, A=440 Hz, B=523 Hz3 STs 4 STs
Visual Auditory
Temporal dynamics of auditory and visual bistability – common principles of perceptual organization.
Integrated or segregated perceptsGrouped or split percepts
Exclusivity, randomness, and inevitability
Pressnitzer & Hupe, 2006
Leopold & Logothetis, 1999
w/ Montbrio
w/ Sussman, Montbrioascend descend
Direct demonstration of bistability for range of DF
Tone duration 120ms, 4 reps
w/ N Rubin, A Shpiro, R Curtu, R Moreno, E Montbrio, E Sussman
• Visual & auditory modality
• Neuronal-based models
• Oscillator models --• mutual inhibition + slow negative feedback (adaptation)• noise gives randomness to period
• Attractor models – • noise driven, no alternation w/o noise• double-well potential: phenomenological model
• Use stats to constrain models
• Levelt II revisited: perceptual exploratory strategy
• Auditory “objects” and alternations: ABA_ABA_… common principles.
Funding: Swartz Foundation, NIH
SUMMARY
Other works: Dayan ‘98, Lehky ‘88, Grossberg ’87, Wilson ‘01