andras lorincz [email protected] nipgf.elte.hu

Faculty of InformaticsEötvös Loránd University

Andras [email protected]

http://nipg.inf.elte.hu

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Content

Homunculus fallacy and resolution Hebbian architecture step-by-step Outlook to neurobiology

Cognitive Map: the hippocampal formation (in rats) Extensions to control and reinforcement learning Conjecture about consciousness Conclusions

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The Homunculus Fallacy

How do we know that this is a phone?

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Democrit’s Answer

Small phone atoms fly away, leave a ‘print’ – a representation of the phone – on our eyes and this is how we know

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Fallacy

Infinite regressionInfinite regression

Who makes sense of the representation?

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Root of fallacy is in the wording

We transform the infinte regression into finite architecture with convergent dynamics

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Root of fallacy is in the wording

We transform the infinte regression into finite architecture with convergent dynamics

(Not the representation but the) input makes sense provided that

the representation can reconstruct the input (given the experiences)

In other words: the representation

can produce an output, which is similar to the input of the network

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Architecture with Hebbian learning

x: input h: hidden representation y: reconstructed input (should match x) W: bottom-up matrix, or BU transformation M: top-down matrix, or TD transformation

Hebbian (or local) learning:Components of the matrices (transformations) make the LTM of the systemLocality of learning warrants graceful degradation for the architecture

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Architecture with Hebbian learning

x: input h: hidden representation y: reconstructed input (should match x) W: bottom-up matrix, or BU transformation M: top-down matrix, or TD transformation

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Previous New: we compareε: reconstruction error: x–y

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Previous New: we learn to predictε(t+1): innovation: x(t+1)–y(t+1)ε(t+1) = x(t+1)–y(t+1) = x(t+1)–Mh(t)

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Conditions

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Conditions

AutoRegressive (AR) process with recurrent network Fh(t+1)=Fh(t)+ε(t+1)h: hidden stateF: hidden deterministic dynamicsnh: hidden innovation “causing” the process

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Cause-effect relations

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Double loop:Both the state and the innovation are represented

Generalization:AutoRegressive Independent Process Analysis (AR-IPA)

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“Cognitive Map” (in rats)

Lorincz-SzirtesAutoregressive model of the hippocampal representation of eventsIJCNN Atlanta, June 14-19, 2009

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Similar anatomical structure Similar opertational propertiesTwo-phase operation

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A single additional pieceCA3—DG: eliminates echoes (ARMA-IPA)

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Learns places and directions path integration / planning (dead reckoning)

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Extensions of the network

AR can be embedded into reinforcement learning Kalman-filter and RL: Szita, Lorincz, Neural Computation, 2004 Echo State Networs and RL: Szita, Gyenes, Lorincz, ICANN, 2006

AR can be extended with control (ARX) and active (Bayesian) learningPoczos, Lorincz, Journal of Machine Learning Research, 2009

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Consciousness

Consider an overcomplete hidden representation made of a set of recurrent networks

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Consciousness

This model can explain rivalry situations

Consider an overcomplete hidden representation made of a set of recurrent networks

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Conclusions

Resolution of the fallacy plus Hebbian constraintslead to a structure that resembles the “Cognitive Map” of rats

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Conclusions

Resolution of the fallacy plus Hebbian constraintslead to a structure that resembles the “Cognitive Map” of rats searches for hidden cause-effect relationships

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Conclusions

Resolution of the fallacy plus Hebbian constraintslead to a structure that resembles the “Cognitive Map” of rats searches for hidden cause-effect relationships

Questions for future workWhat kind of networks arise from the extensions, i.e., Kalman filter embedded into reinforcement learning Bayesian actively controlled learningif the constraint of Hebbian learning is taken rigorously.

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Thank you for your attention!.

andras lorincz [email protected] nipgf.elte.hu

Documents

hidden innovation

reconstruction error

hidden representationy

reconstructed input

thatthe representation

hidden statef

hebbian learningx

bu transformationm