The trade-off between activity sparsity and weight regularization can be formally characterized and optimized for a given hardware platform and performance target by conducting systematic experiments to analyze the impact of varying levels of weight decay on network activity and task performance. By studying the relationship between weight decay rates, network sparsity, and task performance, a comprehensive understanding of how weight regularization influences activity sparsity can be obtained. Optimization techniques, such as grid search or Bayesian optimization, can be employed to find the optimal balance between weight decay and activity sparsity for a specific hardware platform. Additionally, developing mathematical models or algorithms that explicitly consider the trade-off between activity sparsity and weight regularization can help in optimizing neural network architectures for efficient inference on different hardware platforms.