A new parameter‑pruning scheme is introduced, derived from the differential‑geometric distance in model space. Setting a parameter to zero moves the model onto the hypersurface where that parameter vanishes. The geodesic distance defined by the Fisher information metric gives the minimal displacement from the original model to this hypersurface, directly measuring the true change in the model and its performance after pruning. By progressively adopting more faithful approximations of this geodesic distance, a natural hierarchy of pruning optimality emerges: starting with classic magnitude pruning and advancing to newer, more sophisticated schemes. Experiments on fully‑connected networks and vision transformers, using MNIST and CIFAR‑10 across the full $0$‑$100\%$ pruning range and five random seeds, show that the proposed method consistently outperforms magnitude‑based and local‑Fisher‑information pruning on both accuracy and Matthews correlation coefficient. Analysis of different approximation levels yields intermediate pruning strategies that are computationally cheap yet near‑optimal. This geometric perspective not only delivers state‑of‑the‑art pruning methodology but also supplies a mathematically‑grounded justification for pruning techniques.
Review: The geometric formulation turns abstract model changes into a concrete distance metric, offering a robust and efficient pruning framework for real‑world AI deployment.