  Neural networks training on edge terminals is essential for edge AI
computing, which needs to be adaptive to evolving environment. Quantised models
can efficiently run on edge devices, but existing training methods for these
compact models are designed to run on powerful servers with abundant memory and
energy budget. For example, quantisation-aware training (QAT) method involves
two copies of model parameters, which is usually beyond the capacity of on-chip
memory in edge devices. Data movement between off-chip and on-chip memory is
energy demanding as well. The resource requirements are trivial for powerful
servers, but critical for edge devices. To mitigate these issues, We propose
Resource Constrained Training (RCT). RCT only keeps a quantised model
throughout the training, so that the memory requirements for model parameters
in training is reduced. It adjusts per-layer bitwidth dynamically in order to
save energy when a model can learn effectively with lower precision. We carry
out experiments with representative models and tasks in image application and
natural language processing. Experiments show that RCT saves more than 86\%
energy for General Matrix Multiply (GEMM) and saves more than 46\% memory for
model parameters, with limited accuracy loss. Comparing with QAT-based method,
RCT saves about half of energy on moving model parameters.
