Deep Neural Networks (DNNs) rely heavily on dense arithmetic operations, motivating the use of Approximate Multipliers (AxMs) to reduce energy consumption in hardware accelerators. However, a rigorous mathematical characterization of how AxMs error distributions influence DNN accuracy remains underdeveloped. This work presents an analytical framework that connects the statistical error moments of an AxM to the induced distortion in General Matrix Multiplication (GEMM). Using the Frobenius norm of the resulting error matrix, we derive a closed form expression for practical DNN dimensions that demonstrates the distortion is predominantly governed by the multiplier mean error (bias). To evaluate this model in realistic settings, we incorporate controlled error injection into GEMM and convolution layers and examine its effect on ImageNet scale networks. The predicted distortion correlates strongly with the observed accuracy degradation, and an error configurable AxM case study implemented on an FPGA further confirms the analytical trends. By providing a lightweight alternative to behavioral or hardware level simulations, this framework enables rapid estimation of AxM impact on DNN inference quality.

This paper presents a semi-automated methodology for generating geometric proof problems of the kind found in a high-school curriculum. We formalize the notion of a geometry proof problem and describe an algorithm for generating such problems over a user-provided figure. Our experimental results indicate that our problem generation algorithm can effectively generate proof problems in elementary geometry. On a corpus of 110 figures taken from popular geometry textbooks, our system generated an average of about 443 problems per figure in an average time of 4.7 seconds per figure.