Biological sensory systems achieve robust and stable representations despite noise and variability, a property often lacking in artificial neural networks. We study robustness in neural coding from a numerical analysis perspective, focusing on how activation function constraints influence stability. By analyzing network Jacobians and population-level representation geometry, we compare Unconstrained (US) models with biologically inspired bounded and saturating activations. Numerical simulations show that activation constraints significantly reduce sensitivity to input perturbations. Constrained networks preserve representational structure while maintaining feature selectivity. These results suggest that simple biologically motivated nonlinearities provide an effective mechanism for robust sensory processing.