Bernal S D_2010.pdf - University of Plymouth

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4.5. FEEDBACK PROCESSING Complete belief update t=1 1=2 t=3 t=4 1 = 5 t=6 t=7 t=8 Upwards belief update 1 = 1 1 = 2 1 = 3 t = 4 1=5 1=6 t = 7 1=8 t.ln. = 1 (Bimulatlon time step) Up-down belief update W = 2 t=1 1 = 2 1 = 3 1 = 4 1=5 t = 6 1=7 t=8 U,r, = 1 (simulation time step) Figure 4.19: Kir t:aption see footnote^. 187 r j - Non-updated belief d^ • Updated belief
4.6. SUMMARY OF MODEL APPROXIMATIONS TO BAYESIAN HEUEF PROPAGATION node instead of on the likelihood funciion, A(X). This allows Ihe A messages lo be modulated by top-down feedback even in regions that have initially flat distribulions, such as the missing contours in the Kanizsa figure. This modification is shown in Rqualion (4.! 2). 4''("/)-Pl 4.6 Summary of model approximations to Bayesian belief propagation • l-'eedforward recognition results assume a singly-connected tree-structured network (no loops and one parent per node) so the HMAX operations can be approximated by the propagation of bottom-up X messages. Similar approaches have been used in other relaied models (Kpshtein et al. 2(X)8. tJcorge and Hawkins 20()'J, Hinlon ei ai. 2006). Preliminary results suggest a similar invariani recognilion performance can be obtained even when including the feedback K messages (loopy belief propagation), but the computational cost associated precludes a comprehensive systematic test over the complete dataset and parameter space. • The number of input Af,(-r) messages used to compute the hkelihood function X{x) is hmited to Mâi- in order to prevent the result of the product operalion from being outside of Matlab's numeric range. The method has been empirically demonstrated to provide a relatively good fit to the exact distribution given a moderate value of Mmax- • The A and ;r messages are sum-normalized to 1 and then re-weighted so that the minimum value of the distribution is equal V„i„ — 1/(^/10). This prevents extremely low values leading to out of range solulions during the belief propagalion operations. The overall shape of the distribution remains identical, except for some of the elements with smaller values, which may now exhibit a relatively larger value. However. Ihe states with lowest values are less likely lo affect the final resuh in a significant way and many of ihem will be discarded anyway during the sampling methods implemented. • The Ji messages are approximated by the belief al each mxle. The same approach is 188
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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'lMîm,_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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3.3. DEFINITION Am MATHEMATICAL FOR
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33. DEFINITION AND MATHEMATICAL FOR
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3.3. OmNmON AND MATHEMATSOALFORMVLA
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3.3. DEFlNmON AND MATHEMATICAL FORM
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3 J. DEFINITION AND MATHEMATICAL f-
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3.3. D^JmnON AND MATHEMATICAL F0RMU
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.1.3. DEFIânON AND MATHFMATICAL FO
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3.3. DEFINITION AND MATHEMATICAl. F
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3J. DEFINITION AND MATHEMATICAL FOR
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3.4. EXISTING MODELS is on models t
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.1.4. EXISTING MODELS Figure J. 10:
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3.4. EXISTING MODELS the node encod
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3.4. EXISTING MOOm^ Type of f>raph
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3.4. EXISTING MODELS The model comp
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X4. EXISTING MODELS ;v 1,1 gi (8>^8
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3A. EXISTING MODELS proposes a triv
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3.4. EXISTING MODELS by the higher
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3.4. EXISTING MODELS aleni lo findi
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3.4. EXISTING MODELS Model Epshtein
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3.4. EXISTING MODELS Fristonelal. 2
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Page 167 and 168: 4.2. ARCHITECTURES 4.2 Architecture
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Page 175 and 176: 4.3. LEARNING 4.3.2 S1-C1 CRTs The
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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 over lime.
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6.1. ANALYSIS OF RESULTS 6.1.2.5 Fe
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6.1. ANALYSIS Ot RESULTS step. Alth
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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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