  Large models training is plagued by the intense compute cost and limited
hardware memory. A practical solution is low-precision representation but is
troubled by loss in numerical accuracy and unstable training rendering the
model less useful. We argue that low-precision floating points can perform well
provided the error is properly compensated at the critical locations in the
training process. We propose Collage which utilizes multi-component float
representation in low-precision to accurately perform operations with numerical
errors accounted. To understand the impact of imprecision to training, we
propose a simple and novel metric which tracks the lost information during
training as well as differentiates various precision strategies. Our method
works with commonly used low-precision such as half-precision ($16$-bit
floating points) and can be naturally extended to work with even lower
precision such as $8$-bit. Experimental results show that pre-training using
Collage removes the requirement of using $32$-bit floating-point copies of the
model and attains similar/better training performance compared to $(16,
32)$-bit mixed-precision strategy, with up to $3.7\times$ speedup and $\sim
15\%$ to $23\%$ less memory usage in practice.
