# Neural Network Training on In-memory-computing Hardware with Radix-4 Gradients

arXiv: https://arxiv.org/abs/2203.04821 · HTML: https://mlsanity.com/paper/2203.04821/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [BOLD: Boolean Logic Deep Learning](https://mlsanity.com/paper/2405.16339/) (2024)
- [Boolean Variation and Boolean Logic BackPropagation](https://mlsanity.com/paper/2311.07427/) (2023)
- [FedUHD: Unsupervised Federated Learning using In-Memory Hyperdimensional Computing](https://mlsanity.com/paper/2508.12021/) (2025)
- [IMC-CLINIC: Coupled Loss-Informed Newton Iterations for Clipping in Analog In-Memory Computing](https://mlsanity.com/paper/2609.35586/) (2026)

## Abstract (arXiv)

Deep learning training involves a large number of operations, which are dominated by high dimensionality Matrix-Vector Multiplies (MVMs). This has motivated hardware accelerators to enhance compute efficiency, but where data movement and accessing are proving to be key bottlenecks. In-Memory Computing (IMC) is an approach with the potential to overcome this, whereby computations are performed in-place within dense 2-D memory. However, IMC fundamentally trades efficiency and throughput gains for dynamic-range limitations, raising distinct challenges for training, where compute precision requirements are seen to be substantially higher than for inferencing. This paper explores training on IMC hardware by leveraging two recent developments: (1) a training algorithm enabling aggressive quantization through a radix-4 number representation; (2) IMC leveraging compute based on precision capacitors, whereby analog noise effects can be made well below quantization effects. Energy modeling calibrated to a measured silicon prototype implemented in 16nm CMOS shows that energy savings of over 400x can be achieved with full quantizer adaptability, where all training MVMs can be mapped to IMC, and 3x can be achieved for two-level quantizer adaptability, where two of the three training MVMs can be mapped to IMC.