The sklearn.metrics.log_loss is an implementation of the error metric as typically defined, and which is as most error metrics a positive number. In this case, it is a metric which is generally minimized (e.g. as mean squared error for regression), in contrast to metrics such as accuracy which is maximized. The ‘neg_log_loss’ is a hence a technicality to make create a utility value, which allows optimizing functions and classes of sklearn to maximize this utility without having to change the function’s behavior for each metric (such include for instance named cross_val_score, GridSearchCV, RandomizedSearchCV, and others).