Silicon photonic neural networks can achieve higher throughputs and lower latencies than digital electronic alternatives.However, recently reported implementations of such networks have lacked integrated signal gain, instead utilizingoff-chip amplifiers or co-processors to complete the signal processing pipeline. Photonic neural networks without gainface substantial limitations in network depth and inter-layer fan-out. Here, we demonstrate a fully integrated siliconphotonic modulator neuron capable of up to 14.1 dBgain, achieved by modeling and addressing self-heating behavior inour output PN-junction micro-ring modulator.We use our experimental neuron to emulate a small network subject tohigh loss, achieving superior accuracy on an automated modulation classification benchmark to that of an optimal linearsystem. Our high-gain neuron can serve as a building block vastly expanding the range of neural network architecturesthat can be implemented with silicon photonics.