# Machine Learning Applications Applications of UOR principles to machine learning, including coherence regularization for improved generalization and prime-coordinate similarity metrics for enhanced attention mechanisms. ## Mathematical Formulation $ R_{\text{coh}}(W) = \lambda\|\phi(\text{SVD}(W))\|^2 $ $ A(Q, K, V) = \text{softmax}(\text{sim}_{\text{coh}}(Q, K))V $ $ \text{sim}_{\text{coh}}(x, y) = \frac{\langle \phi(x), \phi(y) \rangle}{\|\phi(x)\| \cdot \|\phi(y)\|} $ $ \text{Complexity}(\mathcal{M}) = \sum_{W \in \mathcal{M}} \|\phi(W)\| $ ## Metadata - **ID:** urn:uor:concept:machine-learning-applications - **Code:** UOR-C-192