  Model compression is vital to the deployment of deep learning on edge
devices. Low precision representations, achieved via quantization of weights
and activations, can reduce inference time and memory requirements. However,
quantifying and predicting the response of a model to the changes associated
with this procedure remains challenging. This response is non-linear and
heterogeneous throughout the network. Understanding which groups of parameters
and activations are more sensitive to quantization than others is a critical
stage in maximizing efficiency. For this purpose, we propose FIT. Motivated by
an information geometric perspective, FIT combines the Fisher information with
a model of quantization. We find that FIT can estimate the final performance of
a network without retraining. FIT effectively fuses contributions from both
parameter and activation quantization into a single metric. Additionally, FIT
is fast to compute when compared to existing methods, demonstrating favourable
convergence properties. These properties are validated experimentally across
hundreds of quantization configurations, with a focus on layer-wise
mixed-precision quantization.
