Q-DEQ: Discrete Solving and Quantization for Deep Equilibrium Models in Time Series Forecasting under Edge Deployment Coding Constraints

Ruotong Yang, Hongdong Zhu, Qi Gao, Yin Ma, Hai Wei +1

Edge deployment motivates forecasting models with compact parameter storage and low-bit representations. Deep equilibrium models (DEQs) obtain implicit depth by repeatedly applying a shared layer, reducing the parameter cost of explicit layer stacking. Their usual Anderson solver, however, searches for update coefficients in the continuous real domain. We propose Q-DEQ, which formulates local updates in DEQ forward solving as discrete optimization problems. Candidate directions are constructed from the current state and iteration history, and a local quadratic residual model is used to evaluate their combinations. Binary encoding of the direction coefficients yields a quadratic unconstrained binary optimization (QUBO) problem that can be solved by simulated annealing (SA) or a coherent Ising machine (CIM). After fixed-point solving, a re-forward pass applies W8A8 fake quantization to the shared layer's weights and activations. We evaluate Q-DEQ with an iTransformer backbone on five multivariate time series forecasting datasets. Relative MSE differences from the explicit multi-layer baseline range from $-1.16\%$ to $+2.90\%$, with lower MSE on two datasets. DEQ parameter sharing…