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Training deep learning (DL) models is a complex process, making it prone to silent errors that are challenging to detect and diagnose. This paper presents TRAINCHECK, a framework that takes a proactive checking approach to address silent training errors. TRAINCHECK automatically infers invariants tailored for DL training. It uses these invariants to proactively detect silent errors during the training process while providing debugging help. To evaluate TRAINCHECK, we reproduce 20 real-world silent training errors with diverse root causes. TRAINCHECK successfully detects 18 errors within a single training iteration. It also uncovers 6 unknown bugs in popular training libraries that lead to silent errors.