SigmaCam: Exact Decision Boundary Extraction for DNNs with Smooth Nonlinearities

Le résumé fourni par la source

Understanding how a trained deep neural network (DNN) classifies input data is critical for interpretability and trust in AI systems. Existing tools such as SplineCam can visualize theoretically exact decision boundaries for neural networks with piecewise polynomial activation functions. However, these methods often struggle with more commonly used smooth activations such as Sigmoid, SiLU, and their combinations. In this paper, we introduce a novel framework termed SigmaCam using a recursive algorithm that is both computationally efficient and capable of generating theoretically exact 2D decision boundaries for any Multi-Layer Perceptron (MLP) employing smooth activations. Our approach extends previous works to a broader class of activation functions and allows for the visualization of decision boundaries on the input domain of any dimension, analogous to the capabilities of SplineCam, but now applicable to widely used smooth nonlinearities. We demonstrate the effectiveness of our method by applying it to a variety of network architectures, activation function combinations (e.g., Sigmoid and SiLU), and datasets. The experiments show that our method can accurately capture complex decision boundaries, providing insights into model behavior and aiding in model interpretability. The proposed algorithm enables the analysis of networks that were previously difficult to handle, broadening the scope of exact decision boundary visualization tools beyond piecewise polynomial activations.

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