  Learning-in-memory (LIM) is a recently proposed paradigm to overcome
fundamental memory bottlenecks in training machine learning systems. While
compute-in-memory (CIM) approaches can address the so-called memory-wall (i.e.
energy dissipated due to repeated memory read access) they are agnostic to the
energy dissipated due to repeated memory writes at the precision required for
training (the update-wall), and they don't account for the energy dissipated
when transferring information between short-term and long-term memories (the
consolidation-wall). The LIM paradigm proposes that these bottlenecks, too, can
be overcome if the energy barrier of physical memories is adaptively modulated
such that the dynamics of memory updates and consolidation match the Lyapunov
dynamics of gradient-descent training of an AI model. In this paper, we derive
new theoretical lower bounds on energy dissipation when training AI systems
using different LIM approaches. The analysis presented here is model-agnostic
and highlights the trade-off between energy efficiency and the speed of
training. The resulting non-equilibrium energy-efficiency bounds have a similar
flavor as that of Landauer's energy-dissipation bounds. We also extend these
limits by taking into account the number of floating-point operations (FLOPs)
used for training, the size of the AI model, and the precision of the training
parameters. Our projections suggest that the energy-dissipation lower-bound to
train a brain scale AI system (comprising of $10^{15}$ parameters) using LIM is
$10^8 \sim 10^9$ Joules, which is on the same magnitude the Landauer's
adiabatic lower-bound and $6$ to $7$ orders of magnitude lower than the
projections obtained using state-of-the-art AI accelerator hardware
lower-bounds.
