updates

Author: makoeppel

content/tutorials/nn_in_cms/Metrics.md

@@ -15,9 +15,9 @@ The following situations are cases where one should pay attention or pitfalls:
 
 * <b>The training & validation losses are increasing after having reached a minimum</b>. This can happen when, ie. from an epoch, the NN is over-fitting the data. In such a case, collecting the weights of the NN at the end of the training will not be optimal, as they will correspond to a case where the loss function isn't minimal, resulting in an under-performing NN. In such a case, as illustrated above, one can/should collect the weights of the epoch where the validation loss is at its minimum.
 * <b>Validation loss smaller than training loss</b>. There can be 3 reasons why this can happen.
-   * Regularization is applied during training, but not during validation. Regularization leads to a set of weights which generalize better, ie NN results which are more stable for different samples, but also to slightly lower classification performance (eg. higher loss, lower accuracy).
-   * Depending on the software used, the training loss can be calculated at the end of each batch and then averaged over all batches of a given epoch, while the validation loss after a full epoch. In such a case, the validation loss is calculated over the full validation set (all batches), without updating at the end of each batch. For example, the default option in Keras is to return the training loss as averaged over the individual batch losses.
-   * The validation can be easier (to learn) than the training sample. This can happen if the validation and training sample are not formed from the same dataset, or if, for any reason, the validation data isn't as hard to classify as the training data. This can also happen if some training events are also mixed in the validation sample. If the code creating the training, validation and testing samples splits them correctly, from the same dataset, these shouldn't happen.
+      * Regularization is applied during training, but not during validation. Regularization leads to a set of weights which generalize better, ie NN results which are more stable for different samples, but also to slightly lower classification performance (eg. higher loss, lower accuracy).
+      * Depending on the software used, the training loss can be calculated at the end of each batch and then averaged over all batches of a given epoch, while the validation loss after a full epoch. In such a case, the validation loss is calculated over the full validation set (all batches), without updating at the end of each batch. For example, the default option in Keras is to return the training loss as averaged over the individual batch losses.
+      * The validation can be easier (to learn) than the training sample. This can happen if the validation and training sample are not formed from the same dataset, or if, for any reason, the validation data isn't as hard to classify as the training data. This can also happen if some training events are also mixed in the validation sample. If the code creating the training, validation and testing samples splits them correctly, from the same dataset, these shouldn't happen.
 
 ### True/False positive/negative