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Learning in One-Layer Networks Psych 209 January 9, 2020 - PowerPoint PPT Presentation

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Learning in One-Layer Networks Psych 209 January 9, 2020 Input-output mapping Simplest model of learning: input-output mapping Input-output mapping Pattern associator a1 b1 a2 b2 . . . . . . an bn Input stimulus Input pattern

  1. Learning in One-Layer Networks Psych 209 January 9, 2020

  2. Input-output mapping Simplest model of learning: input-output mapping

  3. Input-output mapping Pattern associator a1 b1 a2 b2 . . . . . . an bn Input stimulus Input pattern Output pattern Output behavior

  4. Input-output mapping How can we learn input-output associations? We know how to store (key, value) pairs on a computer a1 b1 a2 b2 . . hash address . . . . an bn Output pattern Input pattern

  5. Input-output mapping But location-based memory is brittle a1 b1 a2 b2 . . hash address . . . . an bn a1’ z1 a2’ z2 . di ff erent . hash . address . . . an’ zn Similar input Totally di ff erent patterns output pattern

  6. Pattern Associator Content-addressable memory: keys directly “produce” values without location lookup Input pattern Output pattern neuron (cell body) connection (axon) Desirable properties Fully connected

  7. Forward Pass Input pattern Output pattern Input 0 w 00 w 01 Input 1 Output 0 w 02 Input 2 Output 1 w 03 Input 3

  8. <latexit sha1_base64="lLa6sjSOQSA6ZvKbViClURecGQ=">ACAHicbZDNSsNAFIUn9a/Wv6gbwc1gEVyVRAR1IRTduKxgbaEN4WY6aedTMLMRCmhbnwVNy5U3PoY7nwbp20W2npg4OPce7lzT5BwprTjfFuFhcWl5ZXiamltfWNzy97euVNxKgmtk5jHshmAopwJWtdMc9pMJIUo4LQRDK7G9cY9lYrF4lYPE+pF0BUsZAS0sXx7D3yGL3BbpZHfxw9+xvojDAZ9u+xUnInwPLg5lFGum9/tTsxSMqNOGgVMt1Eu1lIDUjnI5K7VTRBMgAurRlUEBElZdNLhjhQ+N0cBhL84TGE/f3RAaRUsMoMJ0R6J6arY3N/2qtVIdnXsZEkmoqyHRmHKsYzyOA3eYpETzoQEgkpm/YtIDCUSb0EomBHf25HmoH1fOK+7NSbl6madRPvoAB0hF52iKrpGNVRHBD2iZ/SK3qwn68V6tz6mrQUrn9lFf2R9/gBTDZW6</latexit> <latexit sha1_base64="lLa6sjSOQSA6ZvKbViClURecGQ=">ACAHicbZDNSsNAFIUn9a/Wv6gbwc1gEVyVRAR1IRTduKxgbaEN4WY6aedTMLMRCmhbnwVNy5U3PoY7nwbp20W2npg4OPce7lzT5BwprTjfFuFhcWl5ZXiamltfWNzy97euVNxKgmtk5jHshmAopwJWtdMc9pMJIUo4LQRDK7G9cY9lYrF4lYPE+pF0BUsZAS0sXx7D3yGL3BbpZHfxw9+xvojDAZ9u+xUnInwPLg5lFGum9/tTsxSMqNOGgVMt1Eu1lIDUjnI5K7VTRBMgAurRlUEBElZdNLhjhQ+N0cBhL84TGE/f3RAaRUsMoMJ0R6J6arY3N/2qtVIdnXsZEkmoqyHRmHKsYzyOA3eYpETzoQEgkpm/YtIDCUSb0EomBHf25HmoH1fOK+7NSbl6madRPvoAB0hF52iKrpGNVRHBD2iZ/SK3qwn68V6tz6mrQUrn9lFf2R9/gBTDZW6</latexit> <latexit sha1_base64="lLa6sjSOQSA6ZvKbViClURecGQ=">ACAHicbZDNSsNAFIUn9a/Wv6gbwc1gEVyVRAR1IRTduKxgbaEN4WY6aedTMLMRCmhbnwVNy5U3PoY7nwbp20W2npg4OPce7lzT5BwprTjfFuFhcWl5ZXiamltfWNzy97euVNxKgmtk5jHshmAopwJWtdMc9pMJIUo4LQRDK7G9cY9lYrF4lYPE+pF0BUsZAS0sXx7D3yGL3BbpZHfxw9+xvojDAZ9u+xUnInwPLg5lFGum9/tTsxSMqNOGgVMt1Eu1lIDUjnI5K7VTRBMgAurRlUEBElZdNLhjhQ+N0cBhL84TGE/f3RAaRUsMoMJ0R6J6arY3N/2qtVIdnXsZEkmoqyHRmHKsYzyOA3eYpETzoQEgkpm/YtIDCUSb0EomBHf25HmoH1fOK+7NSbl6madRPvoAB0hF52iKrpGNVRHBD2iZ/SK3qwn68V6tz6mrQUrn9lFf2R9/gBTDZW6</latexit> <latexit sha1_base64="lLa6sjSOQSA6ZvKbViClURecGQ=">ACAHicbZDNSsNAFIUn9a/Wv6gbwc1gEVyVRAR1IRTduKxgbaEN4WY6aedTMLMRCmhbnwVNy5U3PoY7nwbp20W2npg4OPce7lzT5BwprTjfFuFhcWl5ZXiamltfWNzy97euVNxKgmtk5jHshmAopwJWtdMc9pMJIUo4LQRDK7G9cY9lYrF4lYPE+pF0BUsZAS0sXx7D3yGL3BbpZHfxw9+xvojDAZ9u+xUnInwPLg5lFGum9/tTsxSMqNOGgVMt1Eu1lIDUjnI5K7VTRBMgAurRlUEBElZdNLhjhQ+N0cBhL84TGE/f3RAaRUsMoMJ0R6J6arY3N/2qtVIdnXsZEkmoqyHRmHKsYzyOA3eYpETzoQEgkpm/YtIDCUSb0EomBHf25HmoH1fOK+7NSbl6madRPvoAB0hF52iKrpGNVRHBD2iZ/SK3qwn68V6tz6mrQUrn9lFf2R9/gBTDZW6</latexit> Forward Pass Input pattern Output pattern Input 0 w 00 w 01 Input 1 Output 0 w 02 Input 2 Output 1 w 03 Input 3 X a i = w ij a j j

  9. Forward Pass Input pattern Output pattern Input 0 w 00 w 01 Input 1 Output 0 w 02 Input 2 Output 1 inp 0 inp 1 w 03 inp 2 inp 3 Input 3 out 0 w 00 w 01 w 02 w 03 out 1 w 10 w 11 w 12 w 13 out = W inp

  10. Matrix Representation w 00 w 01 w 02 w 03

  11. How do we learn the weights? w 00 w 01 w 02 w 03

  12. How do we learn the weights? w 00 Learning rules: w 01 1. Hebb’s rule w 02 2. Delta rule w 03

  13. Hebb’s Rule • “Neurons that fire together wire together”

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