# SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries

## TL;DR

SplineCam provides a provably exact method for visualizing and analyzing the geometry and decision boundaries of deep networks with CPWL nonlinearities, surpassing approximation-based methods.

## Contribution

It introduces the first exact, provably accurate approach for computing deep network geometry and decision boundaries using CPWL spline theory, applicable to various architectures.

## Key findings

- Exact visualization of decision boundaries
- Comparison of different network architectures
- Measurement of model generalizability

## Abstract

Current Deep Network (DN) visualization and interpretability methods rely heavily on data space visualizations such as scoring which dimensions of the data are responsible for their associated prediction or generating new data features or samples that best match a given DN unit or representation. In this paper, we go one step further by developing the first provably exact method for computing the geometry of a DN's mapping - including its decision boundary - over a specified region of the data space. By leveraging the theory of Continuous Piece-Wise Linear (CPWL) spline DNs, SplineCam exactly computes a DNs geometry without resorting to approximations such as sampling or architecture simplification. SplineCam applies to any DN architecture based on CPWL nonlinearities, including (leaky-)ReLU, absolute value, maxout, and max-pooling and can also be applied to regression DNs such as implicit neural representations. Beyond decision boundary visualization and characterization, SplineCam enables one to compare architectures, measure generalizability and sample from the decision boundary on or off the manifold. Project Website: bit.ly/splinecam.