Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions
It addresses energy-efficient training for large models, but the work is incremental as it builds on existing analog in-memory computing frameworks.
This paper tackles the problem of training analog in-memory computing hardware with non-ideal resistive elements, showing that asymmetric response functions impose an implicit penalty on gradient-based training, and proposes a Residual Learning algorithm that provably converges to a critical point.
As the economic and environmental costs of training and deploying large vision or language models increase dramatically, analog in-memory computing (AIMC) emerges as a promising energy-efficient solution. However, the training perspective, especially its training dynamic, is underexplored. In AIMC hardware, the trainable weights are represented by the conductance of resistive elements and updated using consecutive electrical pulses. While the conductance changes by a constant in response to each pulse, in reality, the change is scaled by asymmetric and non-linear response functions, leading to a non-ideal training dynamic. This paper provides a theoretical foundation for gradient-based training on AIMC hardware with non-ideal response functions. We demonstrate that asymmetric response functions negatively impact Analog SGD by imposing an implicit penalty on the objective. To overcome the issue, we propose Residual Learning algorithm, which provably converges exactly to a critical point by solving a bilevel optimization problem. We demonstrate that the proposed method can be extended to address other hardware imperfections, such as limited response granularity. As we know, it is the first paper to investigate the impact of a class of generic non-ideal response functions. The conclusion is supported by simulations validating our theoretical insights.