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Phase Transitions in Learning Lorenza Saitta Universit del Piemonte Orientale saittamfn.unipmn.it

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Phase Transitions in Learning Lorenza Saitta Universit del Piemonte Orientale saittamfn.unipmn.it

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    1. Phase Transitions in Learning Lorenza Saitta Università del Piemonte Orientale saitta@mfn.unipmn.it

    2. Phase Transitions

    3. Many-Particle System

    4. Phase Space All particles are equivalent at the thermodynamic equilibriumAll particles are equivalent at the thermodynamic equilibrium

    5. Thermodynamical Equilibrium

    6. [Micro, Grand] Canonical Ensemble

    7. Partition Function

    8. Phase Transitions

    9. Types of Phase Transitions

    10. Ising Models

    11. 1D Ising Models

    12. 2D Ising Model

    13. Mean Field Approximation

    14. Quenched Disorder

    15. Self-Averaging

    16. Replica Trick

    17. Phase Transitions in ANN

    18. Generic Computing Unit

    19. Perceptron

    20. Perceptron – Ising model

    21. Activation function

    22. Generalization Error

    23. Learning (Gibbs rule)

    24. Learning

    25. Phase transition

    26. Other Results

    27. Multi-Layer Perceptron [Biehl et al (00)]

    28. Generalization Error

    29. Phase Transition

    30. Conclusions

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