Noise-shaped Sampling and Annealing for Scalable On-the-edge Training of Binary and Ternary AI Models

Zihao Chen, Zhili Xiao, Rui-Jie Zhu, Yipeng Wang, Jason Eshraghian +1

The training loss of binary and ternary neural networks, expanded as a multilinear polynomial over the discrete weights, is structurally equivalent to the energy of a hierarchical high-order Ising model. We exploit this equivalence to apply Ising solvers to discrete-weight network training, while accounting for a fundamental difference in objectives: an Ising solver seeks the ground state of a fixed energy function, whereas training seeks solutions that generalize to unseen data. Our key contribution is $ΣΔ$-Sampler, an optimizer that reconciles these objectives by embedding a stochastic sampling-and-annealing step as a noisy quantizer inside a first-order $ΣΔ$ noise-shaping loop. The loop pushes noise from weight quantization, high-order frustration, and mini-batch sampling out of the low-frequency adaptation band, so that discrete weight updates follow the smooth descent trajectories embedded in the rugged loss landscape. We validate the framework on a planted quadratic unconstrained binary optimization (QUBO) benchmark with a known minimizer; on CIFAR-10, where a $13$M-parameter ternary model comes within $1\%$ of full-precision accuracy; on ImageNet-1k, where a ternary…