Neural Nets and Chaotic Carriers

The following sections are included:

• Preface to the Second Edition

• Contents

The following sections are included:

• Organisation of the text

The following sections are included:

• The optimisation of actions
  • Notes

• Effective estimation of state
  • Note

• The quadratic/Gaussian case: Estimation and certainty equivalence

• The linear model, in Bayesian and classic versions

The following sections are included:

• Neural calculations: The linear gate and the McCulloch–Pitts net
  • Note

• Sigmoid and threshold functions
  • Note

• Iteration
  • Notes

• Neural systems and feedback in continuous time
  • Note

• Equilibrium excitation patterns

• Some special-purpose nets

The following sections are included:

• The Hopf bifurcation

• Chaos

The following sections are included:

• Associative memories

• The Hamming net
  • Notes

• Autoassociation, feedback and storage

• The Hopfield net

• Alternative formulations of the Hopfield net

The following sections are included:

• Performance and trace structure

• The recognition of simple traces
  • Note

• Inference for compound traces

• Network realisation of the quantised regression

• Reliability constraints for the quantised regression

• Stability constraints for the quantised regression

• The Hopfield net

The following sections are included:

• A Bayesian view

• A robust estimation method

• Dynamic and neural versions of the algorithm

The following sections are included:

• Fading data, and the need for quantisation

• The probability-maximising algorithm (PMA)

• Properties of the vector activation function F(z)

• Some special cases

• The network realisation of the full PMA
  • Note

• Neural implementation of the PMA

• The PMA and the exponential family

• Conclusions I

The following sections are included:

• A general formulation

• Considerations for reliable inference

• Performance of the PMA for simple stimuli

• Compound stimuli: The general pattern

• Compound stimuli in the Gaussian case

The following sections are included:

• The supervised learning of a linear relation

• Unsupervised learning: The criterion of economy

• Principal components

• The learning of an optimal reduction
  • Note

• Dual variables, back-propagation and Hebb's rule

• Self-organising feature maps

• Other proposals

Any comparison between artificial neural networks (ANNs) and biological neural networks (BNNs) must be interesting, because of the infinitely higher level of function, sophistication and economy to which BNNs have successfully evolved. If one sees a difference between the two at some level of mechanistic detail, then one must ask whether the difference represents an advantage achieved by the BNN from which one should learn, or whether it merely represents a way of coping with biological limitations — the neural equivalent of having to find an alternative to the wheel…

The following sections are included:

• The biological neuron

• Neural masses: Reduced dynamics

• Neural masses: Full dynamics and the tank/sump model
  • Note

• Systems of neural units (masses)

• The Freeman oscillator
  • Notes

• Numerical solution for the Freeman oscillator

• The evidence of EEG traces

The following sections are included:

• Systems of neural units

• The case of simple positive feedback

• Systems of coupled oscillators

• The Freeman oscillator with positive feedback

• Numerical results for the oscillator with feedback

• A block of oscillators

• A chain of oscillators

• Feedback plus standardisation: An essential mechanism

• Numerical results for the standardised oscillator

• Some notes on the literature

The following sections are included:

• Safe data: Adaptation of the Bayesian inferential net

• The oscillatory version of the one-stage PMA

• The oscillatory version of the two-stage PMA

• Numerical results for a two-stage system

The following sections are included:

• The anatomy of the olfactory system

• Neural components

• Block versions and analogues of the olfactory system

• Interpretation

• Conclusions II

The following sections are included:

• The Freeman oscillator with feedback

• Interacting Freeman oscillators

The following sections are included:

• Appendix I Extension of the Wigner Semi-Circle Law

• Appendix II Realisation of the PMA equation

• References

• Index