  The continuous convergence of machine learning algorithms, 5G and beyond
(5G+) wireless communications, and artificial intelligence (AI) hardware
implementation hastens the birth of federated learning (FL) over 5G+ mobile
devices, which pushes AI functions to mobile devices and initiates a new era of
on-device AI applications. Despite the remarkable progress made in FL, huge
energy consumption is one of the most significant obstacles restricting the
development of FL over battery-constrained 5G+ mobile devices. To address this
issue, in this paper, we investigate how to develop energy efficient FL over
5G+ mobile devices by making a trade-off between energy consumption for
"working" (i.e., local computing) and that for "talking" (i.e., wireless
communications) in order to boost the overall energy efficiency. Specifically,
we first examine energy consumption models for graphics processing unit (GPU)
computation and wireless transmissions. Then, we overview the state of the art
of integrating FL procedure with energy-efficient learning techniques (e.g.,
gradient sparsification, weight quantization, pruning, etc.). Finally, we
present several potential future research directions for FL over 5G+ mobile
devices from the perspective of energy efficiency.
