vfcai maps images to Boundary Function Space, hits 99.20% on MNIST

The project rests on a simple but unusual premise: rather than feeding raw pixels to a CNN, vfcai first transforms each image into a 'Boundary Function Space' of local linear parameters. Each 3x3 central region is described by a linear function derived from a 9x9 surrounding context, yielding a 5-channel map that includes presence probability, x and y direction components, a signed offset, and a confidence value. This representation is then passed to a standard CNN classifier.

The author evaluated the pipeline on MNIST and Fashion-MNIST with 1,000 samples per class. The results—99.20% on MNIST and 92.00% on Fashion-MNIST—show that a CNN trained only on the local-function representation can still classify shapes accurately, even on Fashion-MNIST where visually similar clothing classes can be confused.

Looking ahead, the author identifies two open questions: how information compression behaves when the stride width changes, and whether boundary-recognition filters with geometric constraints can improve few-shot learning. The code and CLI are available on GitHub, so others can reproduce the experiments and explore the function-reconstruction visualizations.