**Thursday, 13:15 - 13:40 h, Room: H 2013**

**Xavier Molinero**

Variations in strict separating systems representing a linearly separable function

**Coauthor: Josep Freixas**

**Abstract:**

An important consideration when applying neural networks is predict the effect of threshold and weight perturbations on them, i.e., which is the sharpest bound one may consider for weights and threshold to maintain the linearly separable function unchangeable for designing a more robust

and safer neural network.

Two parameters have been introduced to measure the relative errors in weights and threshold of strict separating systems: the tolerance (Hu 1960) and the greatest tolerance (Freixas and Molinero 2008). Given an arbitrary separating system we study which is the equivalent separating system that provides maximum tolerance and maximum greatest tolerance.

We present new results for the maximum tolerance and the maximum greatest tolerance, for instance, we present when the maximum tolerance and maximum greatest tolerance among all equivalent strict separating (natural) systems are attained.

We also give the strict separating (natural) system that attaches the maximum tolerance for n variables. Similar results appear for the maximum greatest tolerance.

Finally, we also give new results for the number of variables n and the number of types of distinguished variables *k*.

Talk 1 of the contributed session Thu.2.H 2013

**"Network analysis"** [...]

Cluster 11

**"Integer & mixed-integer programming"** [...]