Bernal S D_2010.pdf - University of Plymouth

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4.J. HMAX AS A BAYESJAN m-TWORK The first step in this process is to define the equivalences between the HMAX model and the proposed Bayesian network. These are summed up in Figure 4.1 and are as follows: 1. Each node of the Bayesian network represents a specific location, band and layer of ihe HMAX model. 2. The discrete states of each node of the Bayesian network represent the different feuiures coded al thai location, band and layer of the HMAX model. For example each Bayesian node at layer SI will have Ks\(- 4) features, representing the four different filler orien tations of HMAX. 3. The discrete probability distribution over the slates of each Bayesian node represents the sum-normalized responses of the HMAX units coding the different features ai that location, band and layer. Therefore, the probability distriliution of each node comprises the response of K HMAX units, where K is the number of different features ai that layer. 4. The conditional probability tables (CPTs) that link each node in the Bayesian network with its parent nodes in the layer above represent the prototype weights used lo implc- menl selectivity in the HMAX model. Additionally, die CPTs are used to approximate the max (invariance) operation between simple and complex layers of the HMAX model. Learning the appropriate CPT parameters allows the model to approximate the HMAX functionality during the inference stage (using belief propagation) of the Bayesian net work. This is described in further detail in Section 4.3. Each node in the network implements the belief propagation algorithm, which has been de scribed in detail in .Section 3..1,3, ['igures 4.2 and 4.3 show the specific operations implemented by each node, in the case of a single parent structure and a multiple parent structure, respec tively. The former corresponds lo a parlicularization of the latter. The operations performed correspond to Hquations (3,27) to (3,31). The diagrams illustrate how to effectively implement belief propagation in a local and distributed manner. Note that to do this the top-down output messages of the node are made equivalent to the belief of the node. Therefore, the incoming 145
4.1. HMAX AS A BAYESIAN NETWORK S3 C2 S2 CI SI weigh led •um ,— weig HMAX Bayeslan network hied ' n. 1 1 IT ax 1 1 i:^ rii . 1 1 1 1 Locations A 5, (eatuis maps / 1. locMloni ^ nodn 2. (uturei -^ lUtoi 3. mtponM -> pfobabilrty 4. walghti-^candlHonal ptobiMllty taUii K,i leaturo maps ai feature maps Nodes Figure 4.1: Probabilisiie interpret a lion ol' ITMAX as a Tiayesian network. Left) Schemalic representation of the HMAX model. At each layer, the response of eaeh uniteodes the presence of a speeitlc feuiure at i\ given location. The invarianec (max) and selectivity (weighted sum) operations iiri: implemented in alierniUing layers. Right) Baycsian network representing the HMAX model network on ihe left: I)
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A cortical model of object percepti
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A cortical model of object percepti
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Contents Ab.stract V AcknowlcdRcnie
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4.7 Original contrihutions in this
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3.9 Example of belief propagation i
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5.19 SI and CI model responses to a
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XVI
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2009 Durabernal S. Wennekers T, Den
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J.I. OVERVIEW retinal stimulation (
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J.2. MAIN CONTRfBUTlONS • A revie
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2,1. OBJECT RECOGNITION ihe princip
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2.1. OBJECT REC(JGNmON The dorsal s
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2.1. OBJECT RECOGNJTION properties
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2.1. OBJECT RECOGNITION of input em
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2.1. OBJEOTRBCXiGNrnON ta) u I/I ^.
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2.1. OBJECT RECOGNITION 2.1.2.1 HMA
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2.1. OBJECT RECnCNmON unit will be
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2.1. OBJECT REC(X}NIT!ON tivity, st
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2.1. OBJECT RECOGNITION response fr
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2.2. HSGH-LEVEL FEEDBACK feature an
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2.2. HIGH-LEVEL FEEDBACK Thirdly, p
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2.2. mCH-LBVEL FEEDBACK Kandom 2 LO
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1.2. HIGH-LEVEL FEEDBACK « 70 U M
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2.2. HIGH-LEVEL FEEDBACK D Receptiv
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1.1. HIGH-LEVEL FEEDBACK context of
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2.2. HIGH-LEVEL FEEDBACK detailed i
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2.2. HIGH-LEVEL FEEDBACK activity g
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2.2. HIGH-LEVEL FEEDBACK task, such
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2.2. HIGH'lM^im,_WEDBACK 2004), and
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2.2. HIGH-LEVEL FEEDBACK However, t
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2.2. HIGH-LEVEL FEEDBACK sizes that
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2.3. ILLUSORY AND OCCLUDED CONTOURS
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2.3. a.LVSORY AND OCCLUDED CONTnURS
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2.4. ORIGINAL CONTRIBUTIONS IN THIS
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3.1. THE BAYBSIAN BRAIN HYPOTHESIS
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XI. THEBAYESIANBRAINHYPfmBSIS poste
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3.1. THE BAYESJAN BRAIN HYPOmESIS T
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3.2. EVIDENCE FROM THE BRAIN ity in
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3.3. DEFINITION AND MATHEMATlCACPOR
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3.3. DEFINITION AND MATHEMATICAL FO
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XX DEFINITION AND MATHEMATICAL FORM
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.1,3. DEHNITION AND MATHEMATICAL FO
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3 J. DEFINITION AND MATHEMATICAL FO
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3.3. DEFINITION AND MATHFMAnCAL FOR
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.1.3. DERNrnON AmMAnWMATtCAL FORMUL
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5.1. FEEDFORWARD PROCESSING 1^ Onem
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5.1. FEEDFORWARD PROCESSING j • H
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5.1. FEEDFORWARD PROCESSING 5.1.2 O
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5.1. FEEDFORWARD PROCESSING Normal
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5.1. FEEDFORWARD PROCESSING c g ra
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5-1. FEEDFORWARD PROCESSING 4 5 Non
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5.1. FEEDFORWARD PROCESSING 100 8 9
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S.i. FEEDFORWARD PnOCESSING 5.1.2.4
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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.5.2. FEEDBACK-MEDIATED ELUSORY CON
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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5.4. ORIGINAL CONTRIBUTIONS IN THIS
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6.1. ANALYSIS OF RESULTS dence and
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6.1. ANALYSIS OF RESULTS The graph
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6.t. ANALYSIS OF RESULTS used 10 co
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6.1. ANALYSIS OF RF.SULTS the image
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6.1. ANALYSIS OF RESULTS feedback w
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6.1. ANALYSIS OF RESULTS 6.1.2.5 Fe
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6.1. ANALYSIS OF RESULTS operations
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6.J. ANALYSIS OFRBSULTS model could
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6.1. ANALYSIS OF RESULTS Alternativ
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6.2. COMPARISON WITH EXPERIMENTAL B
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6.3. COMPARISON WITH PRKVIOUS MODBL
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6.4. FUTURE WORK to temporal contex
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6.5. CONCLUSIONS AND SUMMARY OF CON
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6.5. CONCLUSIONS AND SUMMARY OF CON
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• The HTM paliems correspond lo t
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Bolz, J.& Gilbert, CD. (1986), CJcn
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Friston, K. & Kiebel, S. (2009). 'C
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Hoffman. K. L. & Lngothetis, N K. (
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Lanyon. L. & Denham. S. (2(X)9), 'M
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Murray, M. M.. Wylie. G, R., Higgin
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Reynolds, J. H. &, Chelazzi, L. (20
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Stanley. D. A. & Rubin, N. (2003),
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