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Associative Memories

Associative Memories. A Morphological Approach. Outline. Associative Memories Motivation Capacity Vs. Robustness Challenges Morphological Memories Improving Limitations Experiment Results Summary References. Associative Memories. Motivation

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Associative Memories

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  1. Associative Memories A Morphological Approach

  2. Outline • Associative Memories • Motivation • Capacity Vs. Robustness Challenges • Morphological Memories • Improving Limitations • Experiment • Results • Summary • References

  3. Associative Memories • Motivation • Human ability to retrieve information from applied associated stimuli • Ex. Recalling one’s relationship with another after not seeing them for several years despite the other’s physical changes (aging, facial hair, etc.) • Enhances human awareness and deduction skills and efficiently organizes vast amounts of information • Why not replicate this ability with computers? • Ability would be a crucial addition to the Artificial Intelligence Community in developing rational, goal oriented, problem solving agents

  4. Capacity Vs. Robustness Challenges • In early memory models, capacity was limited to the length of the memory and allowed for negligible input distortion • Ex. Linear Associative Memory • Recent years have increased the memory’s robustness, but sacrificed capacity • J. J. Hopfield’s proposed Hopfield Network • Capacity: , where n is the memory length • Current research offers a solution which maximizes memory capacity while still allowing for input distortion • Morphological Neural Model • Capacity: essentially limitless (2n in the binary case) • Allows for Input Distortion • One Step Convergence

  5. Morphological Memories • Formulated using Mathematical Morphology Techniques • Image Dilation • Image Erosion • Training Constructs Two Memories: M and W • M used for recalling dilated patterns • W used for recalling eroded patterns • M and W are not sufficient…Why? • General distorted patterns are both dilated and eroded • solution: hybrid approach • Incorporate a kernel matrix, Z, into M and W • General distorted pattern recall is now possible! • Input → MZ → WZ → Output

  6. Improving Limitations • Experiment • Construct a binary morphological auto-associative memory to recall bitmap images of capital alphabetic letters • Use Hopfield Model for baseline • Construct letters using Microsoft San Serif font (block letters) and Math5 font (cursive letters) • Attempt recall 5 times for each pattern for each image distortion at 0%, 2%, 4%, 8%, 10%, 15%, 20%, and 25% • Use different memory sizes: 5 images, 10, 26, and 52 • Use Average Recall Rate per memory size as a performance measure, where recall is correct if and only if it is perfect

  7. Results • Morphological Model and Hopfield Model: • Both degraded in performance as memory size increased • Both recalled letters in Microsoft San Serif font better than Math5 font • Morphological Model: • Always perfect recall with 0% image distortion • Performance smoothly degraded as memory size and distortion increased • Hopfield Model: • Never correctly recalled images when memory contained more than 5 images

  8. Results using 5 Images MNN = Morphological Neural Network HOP = Hopfield Neural Network MSS = Microsoft San Serif font M5 = Math5 font

  9. Results using 26 Images MNN = Morphological Neural Network HOP = Hopfield Neural Network MSS = Microsoft San Serif font M5 = Math5 font

  10. Summary • The ability for humans to retrieve information from associated stimuli continues to elicit great interest among researchers • Progress Continues with the development of enhanced neural models • Linear Associative Memory → Hopfield Model → Morphological Model • Using Morphological Model • Essentially Limitless Capacity • Guaranteed Perfect Recall with Undistorted Input • One Step Convergence

  11. References • Y. H. Hu. Associative Learning and Principal Component Analysis. Lecture 6 Notes, 2003 • R. P. Lippmann. An Introduction to Computing with Neural Nets. IEEE Transactions of Acoustics, Speech, and Signal Processing, ASSP-4:4- 22, 1987. • R. McEliece and et. Al. The Capacity of Hopfield Associative Memory. Transactions of Information Theory, 1:33-45, 1987. • G. X. Ritter and P. Sussner. An Introduction to Morphological Neural Networks. In Proceedings of the 13th International Conference on Pattern Recognition, pages 709-711, Vienna, Austria, 1996. • G. X. Ritter, P. Sussner, and J. L. Diaz de Leon. Morphological Associative Memories. IEEE Transactions on Neural Networks, 9(2):281-293, March 1998.

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