TRAINING FUNDAMENTAL PRINCIPLES AND BLOCK TRAINING OF LAYERED NEURAL NETWORKS
A. Navia-Vázquez and Aníbal R. Figueiras-Vidal
ATSC/DTC, Univ. Carlos III de Madrid
C/ Butarque, 15,
28911 Leganés, Madrid, Spain
Phone: + 34 1 624 99 03 / + 34 1 624 99 23
Fax: + 34 1 624 94 30
E-Mail: firstname.lastname@example.org / email@example.com
KEYWORDS: Training, Block, Sensitivity, Selection, Generalization.
The difficulty of artificial learning is universally accepted, both for rule-based and learning-by-example situations; however, there are some fundamental principles that can be applied (at least conceptually) in all the cases.
Among them, that saying that difficult cases require more attention or work have appeared in many different forms: from selecting the simpler rule in conflicts to concentrate more on limit or difficult samples ( declares this principle in its title); the Occam Razor appears when saying that architectures must be as simple, or, parameters as few as possible, etc.; this being the base for selecting, growing or pruning; combining simple machines in modular schemes  or committees  follows analogous reasons; and so on. No less important is to keep the machine parameters inside reasonable margins, as suggested by generalization results  and forced in some recent powerful approaches to inference machine design .
When considering the particular, (but representative) case of layered neural networks, training presents additional difficulties due to the need of applying "chained" algorithms, such as the Backpropagation rule. An alternative solution is to proceed layerwise (i.e., the global problem is decomposed into minimizations at every layer): an example of this approach can be found in , where, after applying the inverse activation function to the output values, Least Squares minimizations are solved to obtain optimal weights and to propagate targets to the previous layer.
Unfortunately, as analyzed in , this layerwise block implementation presents some problems concerning convergency and generalization capability of the system. Nevertheless, the performance of this training algorithm can be improved if we reduce the influence of less meaningful patterns: this is the solution proposed in  by solving at every layer weighted minimizations, the weighting values being proportional to the sensitivity of every pattern.
With this reduced sensitivity approach, we are implicitly incorporating a sample selection strategy (which benefits the learning process), as well as obtaining weights of reasonable size by using minimum norm solutions (which improves generalization); additionally, a direct relationship between the reduced sensitivity algorithm and other efficient training approaches can also be established . All these interesting properties encourage us to propose, as further work, extensions of the algorithm to other learning machines.
A more detailed description will be provided in the full length paper, as well as some simulation examples and further discussion of the results.
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