Learning multisensory integration with stochastic variational - - PowerPoint PPT Presentation

Learning multisensory integration with stochastic variational learning in recurrent spiking networks

Presented by : Sharbatanu Chatterjee1,2 Guided by : Aditya Gilra1 & Johanni Brea1

1Laboratory of Computational Neuroscience, EPFL, Switzerland 2Department of Computer Science & Engineering, IIT Kanpur, India

22 Aaugust 2015

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Contents

1 Multisensory Integration 2 Stochastic Variational Learning Model 3 Results 4 Further Work

Learning multisensory integration with stochastic variational learning in recurrent spiking networks

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: Architecture for Multisensory Integration1

1Sabes et al 2013

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 1

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: Regenerating model from learnt hidden neurons2

1Sabes et al 2013

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 2

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: An autoencoder

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 3

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: A schematic for our model

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 4

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: Architecture for Danilo’s model3

2Danilo et al 2014

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 5

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Danilo’s model

Figure: The Neuron Model4

3Danilo et al 2014

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 6

Multisensory Integration Stochastic Variational Learning Model Results Further Work

The log-likelihood of seeing the spikes

The probability of producing a spike train Xi(t) is: The log-likelihood is: logp (X (0 . . . t)) =

• i∈V ∪H

T [logρi(τ)Xi(τ) − ρi(τ)] (1) The marginalized log-likelihood of the visible neurons p (XV ) =

• DXHp (XV , XH)

(2)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 7

Multisensory Integration Stochastic Variational Learning Model Results Further Work

A ML approach to the problem

We use another distribution “q” to approximate the posterior KL(q|p) =

• DXHq(XH|XV )log q(XH|XV )

p(XH|XV ) =

• DXHq(XH|XV )log q(XH|XV )

p(XH, XV ) + logp(XV ) (3) The first term is the Helmholtz Free Energy F

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 8

Multisensory Integration Stochastic Variational Learning Model Results Further Work

We use another distribution “q” to approximate the posterior 0 ≤ KL(q|p) =

• DXHq(XH|XV )log q(XH|XV )

p(XH|XV ) = F + logp(XV ) (4) The first term is the Helmholtz Free Energy F

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 9

Multisensory Integration Stochastic Variational Learning Model Results Further Work

We use another distribution “q” to approximate the posterior 0 ≤ KL(q|p) =

• DXHq(XH|XV )log q(XH|XV )

p(XH|XV ) = F + logp(XV ) (4) The first term is the Helmholtz Free Energy F Since KL divergence is positive F + logp(XV ) ≥ 0 (5)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 9

Multisensory Integration Stochastic Variational Learning Model Results Further Work

We use another distribution “q” to approximate the posterior 0 ≤ KL(q|p) =

• DXHq(XH|XV )log q(XH|XV )

p(XH|XV ) = F + logp(XV ) (4) The first term is the Helmholtz Free Energy F Since KL divergence is positive F + logp(XV ) ≥ 0 (5) logp(XV ) ≥ −F (6)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 9

Multisensory Integration Stochastic Variational Learning Model Results Further Work

We use another distribution “q” to approximate the posterior 0 ≤ KL(q|p) =

• DXHq(XH|XV )log q(XH|XV )

p(XH|XV ) = F + logp(XV ) (4) The first term is the Helmholtz Free Energy F Since KL divergence is positive F + logp(XV ) ≥ 0 (5) logp(XV ) ≥ −F (6) Problem reduced to minimising the Free Energy with respect to q and the original model p

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 9

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Figure: The Neuron Model

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 10

Multisensory Integration Stochastic Variational Learning Model Results Further Work

The final weight updates are simple gradient descent on the free energy ˙ wM

ij = −µM∇wM

ij F

(7) ˙ wQ

ij = −µQ∇wQ

ij F

(8)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 11

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Final Equations

˙ wM

ij = µMHM ij (t)

(9) ˙ wQ

ij = −µQeN(t)HQ ij (t)

(10)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 12

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Final Equations

˙ wM

ij = µMHM ij (t)

(9) ˙ wQ

ij = −µQeN(t)HQ ij (t)

(10) (Xi − ρQ/M

i

) ∗ φj (11)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 12

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Final Equations

˙ wM

ij = µMHM ij (t)

(9) ˙ wQ

ij = −µQeN(t)HQ ij (t)

(10) (Xi − ρQ/M

i

) ∗ φj (11) eN(t) = ˆ F − ¯ F (12)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 12

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Global signal

eN(t) = ˆ F − ¯ F (13)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 13

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Global signal

eN(t) = ˆ F − ¯ F (13) ˆ F =

• Fτdτ

(14) Fτ = FQ − FM (15) FQ =

• i∈H
• logρQ

i (τ)Xi(τ) − ρQ i (τ)

• (16)

FM =

• i∈V ∪H
• logρM

i (τ)Xi(τ) − ρM i (τ)

• (17)

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 13

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: 2 neurons, only M network, no global factor

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 14

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: 10 neurons, same as above5

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 15

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: Entire network, malfunctional hidden neurons, learning stops at halfway

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 16

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: The entire required result, learning stops halfway

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 17

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: The error terms with constant firing

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 18

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Results

Figure: The rho being approached with constant firing

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 19

Multisensory Integration Stochastic Variational Learning Model Results Further Work

Further work and implication

Get my implementation of Danilo’s model to function flawlessly. Sabes’ paper does not introduce a temporal factor, try to incorporate so. Encoding for other key processes of sensory processing - integration of prior information and coordinate transforms.

Learning multisensory integration with stochastic variational learning in recurrent spiking networks 20

Thank You!