Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions

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. Among all the physical properties of resistive elements, the response to the pulses directly affects the training dynamics. This paper first provides a theoretical foundation for gradient-based training on AIMC hardware and studies the impact of response functions. We demonstrate that noisy update and asymmetric response functions negatively impact Analog SGD by imposing an implicit penalty term on the objective. To overcome the issue, Tiki-Taka, a residual learning algorithm, converges exactly to a critical point by optimizing a main array and a residual array bilevelly. The conclusion is supported by simulations validating our theoretical insights.