The approximate computing paradigm advocates for relaxing accuracy goals in applications to improve energy-efficiency and performance. Recently, this paradigm has been explored to improve the energy-efficiency of silicon photonic networks-on-chip (PNoCs). Silicon photonic interconnects suffer from high power dissipation because of laser sources, which generate carrier wavelengths, and tuning power required for regulating photonic devices under different uncertainties. In this paper, we propose a framework called ARXON to reduce such power dissipation overhead by enabling intelligent and aggressive approximation during communication over silicon photonic links in PNoCs. Our framework reduces laser and tuning-power overhead while intelligently approximating communication, such that application output quality is not distorted beyond an acceptable limit. Simulation results show that our framework can achieve up to 56.4% lower laser power consumption and up to 23.8% better energy-efficiency than the best-known prior work on approximate communication with silicon photonic interconnects and for the same application output quality.