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.

翻译：当前的深度网络可视化与可解释性方法主要依赖数据空间可视化技术，例如通过评分确定哪些数据维度对预测结果负责，或生成与特定网络单元或表征最匹配的新数据特征/样本。本文进一步提出首个可证明精确的方法，用于计算指定数据空间区域内深度网络映射的几何结构（包括其决策边界）。通过利用连续分段线性（CPWL）样条深度网络理论，SplineCam可在无需采样或架构简化等近似手段的前提下精确计算深度网络的几何结构。该方法适用于所有基于CPWL非线性的深度网络架构，包括（泄露）ReLU、绝对值函数、maxout与最大池化，并可推广至隐式神经表征等回归型深度网络。除决策边界可视化与表征外，SplineCam还能实现架构对比、泛化能力评估，以及从流形内外沿决策边界进行采样。项目网站：bit.ly/splinecam。