Abstract: Aspects of the present invention are directed to computer-implemented techniques for improving the training of artificial neural networks using a reduced precision (e.g., float16) data format. Embodiments of the present invention rescale tensor values prior to performing matrix operations (such as matrix multiplication or matrix addition) to prevent overflow and underflow. To preserve accuracy throughout the performance of the matrix operations, the scale factors are defined using a novel data format to represent tensors, wherein a matrix is represented by the tuple X, where X=(a, v[.]), wherein a is a float scale factor and v[.] are scaled values stored in the float16 format. The value of any element X[i] according to this data format would be equal to a*v[i].