SYSTEMS AND METHODS FOR DEEP LEARNING WITH SMALL TRAINING SETS

1 . A hierarchical compositional network, representable in Bayesian network form, comprising:

first, second, third, fourth, and fifth parent feature nodes;

first, second, and third pool nodes;

first, second, and third weight nodes; and

first, second, third, fourth, and fifth child feature nodes;

wherein the first parent feature node and first weight node are both coupled to and together configured to activate the first pool node; wherein the second parent feature node and second weight node are both coupled to and together configured to activate the first pool node; wherein the third parent feature node and third weight node are both coupled to and together configured to activate the first pool node; wherein the second parent feature node and first weight node are both coupled to and together configured to activate the second pool node; wherein the third parent feature node and second weight node are both coupled to and together configured to activate the second pool node; wherein the fourth parent feature node and third weight node are both coupled to and together configured to activate the second pool node; wherein the third parent feature node and first weight node are both coupled to and together configured to activate the third pool node; wherein the fourth parent feature node and second weight node are both coupled to and together configured to activate the third pool node; wherein the fifth parent feature node and third weight node are both coupled to and together configured to activate the third pool node.

2 . The hierarchical compositional network of claim 1 , wherein any parent feature nodes and weight nodes together configured to activate a pool node are configured to do so according to an AND-OR selection function.

3 . The hierarchical compositional network of claim 2 , wherein the first pool node is coupled to and configured to activate the first, second, and third child feature nodes; wherein the second pool node is coupled to and configured to activate the second, third, and fourth child feature nodes; wherein the third pool node is coupled to and configured to activate the third, fourth, and fifth child feature nodes.

4 . The hierarchical compositional network of claim 3 , wherein an activation of the first pool node results in activation of exactly one of the first, second, and third child feature nodes; wherein an activation of the second pool node results in activation of exactly one of the second, third, and fourth child feature nodes; wherein an activation of the third pool node results in activation of exactly one of the third, fourth, and fifth child feature nodes.

5 . The hierarchical compositional network of claim 4 , wherein the first child feature node corresponds to a first position and a first feature index; wherein the second child feature node corresponds to a second position and the first feature index; wherein the third child feature node corresponds to a third position and the first feature index; wherein the fourth child feature node corresponds to a fourth position and the first feature index; wherein the fifth child feature node corresponds to a fifth position and the first feature index.

6 . The hierarchical compositional network of claim 5 , wherein the first, second, third, fourth, and fifth positions are adjacent.

7 . The hierarchical compositional network of claim 6 , wherein the network is configured to receive data feature input by setting activation of child feature nodes according to image features of an image; wherein the inferred output includes a classification of the image.

8 . The hierarchical compositional network of claim 6 , wherein the network is configured to receive data feature input by setting activation of child feature nodes according to audio features of an audio signal; wherein the inferred output includes a classification of the audio signal.

9 . The hierarchical compositional network of claim 6 , wherein the network is configured to output child feature node selection as a generated output in response to received parent feature input.

10 . The hierarchical compositional network of claim 9 , wherein the generated output is an image generated based on a mapping of selected child feature nodes to image features.

11 . The hierarchical compositional network of claim 10 , wherein the parent feature input is an image classification.

12 . A hierarchical compositional network, representable in Bayes factor graph form, comprising:

first, second, third, fourth, and fifth parent feature variable nodes;

first, second, and third weight variable nodes;

first, second, and third convolution factor nodes;

first, second, and third pool variable nodes;

first, second, and third pool factor nodes;

first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth intermediate variable nodes;

first, second, third, fourth, and fifth pooling OR factor nodes; and

first, second, third, fourth, and fifth child feature variable nodes;

wherein the first, second, and third parent feature variable nodes and first, second, and third weight nodes are coupled to the first pool variable node via the first convolution factor node; wherein the second, third, and fourth parent feature variable nodes and first, second, and third weight nodes are coupled to the second pool variable node via the second convolution factor node; wherein the third, fourth, and fifth parent feature variable nodes and first, second, and third weight nodes are coupled to the third pool variable node via the third convolution factor node.

13 . The hierarchical compositional network of claim 12 , wherein the first convolution node is equivalent to a first convolution OR factor node coupled to first, second, and third convolution AND factor nodes; wherein the first convolution AND factor node couples the first parent feature variable node and the first weight variable node to the first convolution OR factor node; wherein the second convolution AND factor node couples the second parent feature variable node and the second weight variable node to the first convolution OR factor node; wherein the third convolution AND factor node couples the third parent feature variable node and the third weight variable node to the first convolution OR factor node.

14 . The hierarchical compositional network of claim 12 , wherein the second convolution node is equivalent to a second convolution OR factor node coupled to fourth, fifth, and sixth convolution AND factor nodes; wherein the fourth convolution AND factor node couples the second parent feature variable node and the first weight variable node to the second convolution OR factor node; wherein the fifth convolution AND factor node couples the third parent feature variable node and the second weight variable node to the second convolution OR factor node; wherein the sixth convolution AND factor node couples the fourth parent feature variable node and the third weight variable node to the second convolution OR factor node.

15 . The hierarchical compositional network of claim 14 , wherein the first pool variable node is coupled to the first, second, and third intermediate variable nodes via the first pool factor node; wherein the second pool variable node is coupled to the fourth, fifth, and sixth intermediate variable nodes via the second pool factor node; wherein the third pool variable node is coupled to the seventh, eighth, and ninth intermediate variable nodes via the third pool factor node.

16 . The hierarchical compositional network of claim 15 , wherein the first intermediate variable node is coupled to the first child feature variable node via the first pooling OR factor node; wherein the second intermediate variable node is coupled to the second child feature variable node via the second pooling OR factor node; wherein the third intermediate variable node is coupled to the third child feature variable node via the third pooling OR factor node; wherein the fourth intermediate variable node is coupled to the second child feature variable node via the second pooling OR factor node; wherein the fifth intermediate variable node is coupled to the third child feature variable node via the third pooling OR factor node; wherein the sixth intermediate variable node is coupled to the fourth child feature variable node via the fourth pooling OR factor node; wherein the seventh intermediate variable node is coupled to the third child feature variable node via the third pooling OR factor node; wherein the eighth intermediate variable node is coupled to the fourth child feature variable node via the fourth pooling OR factor node; wherein the eighth intermediate variable node is coupled to the fifth child feature variable node via the fifth pooling OR factor node.

17 . The hierarchical compositional network of claim 16 , wherein the first child feature node corresponds to a first position and a first feature index; wherein the second child feature node corresponds to a second position and the first feature index; wherein the third child feature node corresponds to a third position and the first feature index; wherein the fourth child feature node corresponds to a fourth position and the first feature index; wherein the fifth child feature node corresponds to a fifth position and the first feature index.

18 . The hierarchical compositional network of claim 17 , wherein the first, second, third, fourth, and fifth positions are adjacent.

19 . The hierarchical compositional network of claim 12 , wherein the network is configured to receive data feature input by setting activation of child feature nodes according to image features of an image; wherein the inferred output includes a classification of the image.

20 . The hierarchical compositional network of claim 12 , wherein the network is configured to receive data feature input by setting activation of child feature nodes according to audio features of an audio signal; wherein the inferred output includes a classification of the audio signal.

21 . The hierarchical compositional network of claim 12 , wherein the network is configured to output child feature node selection as a generated output in response to received parent feature input.

22 . The hierarchical compositional network of claim 21 , wherein the generated output is an image generated based on a mapping of selected child feature nodes to image features.

23 . The hierarchical compositional network of claim 22 , wherein the parent feature input is an image classification.