Property-driven training is an area of machine learning that studies how to get 'correct-by-training' models given a specification on their behaviour. Usually, this happens by translating a specification into a regularization term to be added to the loss. Despite the apparent simplicity, many challenges plague this technique, and so far it has not delivered satisfying results. In this talk we present QLL, a first-of-its-kind quantitative logic which aims to close that gap. It provides the first quantitative adequacy result, giving losses a concrete logical meaning. Its logspace semantics is also SoTA and formally motivates the mounting consensus around how to interpret logical connectives as differentiable functions. This talk is based on the two preprints Adequate Losses via Quantitative Linear Logic and Quantitative Linear Logic for Neuro-Symbolic Learning and Verification.