Three-way connections and dynamic routing
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1 Three-way connections and dynamic routing
2 Reference frames require structured representations mapping units Hinton (1981)
3 Which way are the triangles pointing? From Attneave
4 Dynamic routing circuits (Olshausen, Anderson & Van Essen, 1993)
5 Dynamic routing (Olshausen, Anderson, Van Essen 1993) Analysis/ Recognition feature vector High level cortical areas Object-centered reference frame (position and scale invariant) Control Early/intermediate cortical areas (form processing) Saliency Window of Attention Retina
6 Dynamic routing circuit a. I=1 N=B Input b. I4 window of attention window of attention H
7 Dynamic routing: control
8 Dynamic routing: control a. Output b. Output w ij i Input j Input window of attention c. Output d. Output Input window of attention Input window of attention (aliased)
9 a. Control... b. Control... Output Output Input Input c. Control... d. Output Output Input Input
10 Energy function E = X ijk V i ijk c k I j + X ij T V ij V i V j + X kl T c kl c k c l
11 Pattern matching via dynamic routing
12 Dynamic routing in deep networks Max)Unpooling) Layer Above Reconstruction Switches) Pooled Maps Max)Pooling) Rec'fied)Linear) Func'on) Unpooled Maps Rectified Unpooled Maps Convolu'onal) Filtering){F T }) Reconstruction Rectified Feature Maps Feature Maps Rec'fied)Linear) Func'on) Convolu'onal) Filtering){F}) Layer Below Pooled Maps Layer Above Reconstruction Unpooling Max Locations Switches Pooled Maps Pooling Unpooled Maps Rectified Feature Maps Feature Map (Zeiler & Fergus, 2013)
13 Visualization of filters learned at intermediate layers (Zeiler & Fergus 2013) Layer 2
14 Visualization filters learned at intermediate layers Visualizing of and Understanding Convolutional Neur (Zeiler & Fergus 2013) LayerLayer 3 2
15 Visualization filters learned at intermediate layers Visualizing of and Understanding Convolutional Neur (Zeiler & Fergus 2013) LayerLayer 34 Layer 2 Layer 5
16 Map-seeking circuit (Arathorn 2002) input image orprevious layer forward maps: t( ) match Σ Σ comp( ) backward superposition: b forward superposition: f match Σ inverse maps: t ' () Σ memory patterns: w k Σ memory superposition match Figure 1. Data flow in map-seeking circuit
17 A Classification A A B B C C D D E E A B C D E A B C D E A B C D E B C A E D Training Bilinear models (Tenenbaum & Freeman 2000) B Extrapolation A A B B C C D D E E A B C D E A B C D E A B C D E?? C D E Generalization y sc k = I i=1 J j=1 w ijk a s i bc j. C Translation A A B B C C D D E E??? A B C D E A B C D E A B C D E????? F G H
18 In: SPIE Proceedings vol. 6492: Human Vision and Electronic Imaging XII, (B.E. Rogowitz, T.N. Pappas, S.J. Daly, Eds.), Jan 28-Feb 1, 2007, San Jose, California Bilinear Models of Natural Images Bruno A. Olshausen a, Charles Cadieu b, Jack Culpepper c, and David K. Warland d I(x, t + 1) = x T (x, x, t) I(x, t) + (x, t) T (x, x, t) = k c k (t) k (x, x )
19 Transforming Auto-encoders (Hinton, Krizhevsky & Wang 2011) actual output target output gate +'x +'y p x y +'x +'y p x y +'x +'y p x y input image
20 Dynamic routing between capsules (Sabour, Frosst & Hinton 2017) 2 2 This type of routing-by-agreement should be far more effective than the very primitive form of routing implemented by max-pooling, which allows neurons in one layer to ignore all but the most active feature detector in a local pool in the layer below. We demonstrate that our dynamic routing mechanism is an effective way to implement the explaining away that is needed for segmenting highly overlapping objects. higher-level capsules cover larger regions of the image. Unlike max-pooling however, we do not throw away information about the precise position of the entity within the region. For low level capsules, location information is place-coded by which capsule is active. As we ascend the hierarchy, more and more of the positional information is rate-coded in the real-valued components of the output vector of a capsule. This shift from place-coding to rate-coding combined with the fact that higher-level capsules represent more complex entities with more degrees of freedom suggests that the
21 Dynamic routing between capsules (Sabour, Frosst & Hinton 2017) v j = s j 2 1+ s j 2 s j s j ule and s j = X is its total inpu c ij û j i i û j i = W ij u i
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