Q-DEQ：面向边缘部署编码约束下时间序列预测的深度平衡模型离散求解与量化
Q-DEQ: Discrete Solving and Quantization for Deep Equilibrium Models in Time Series Forecasting under Edge Deployment Coding Constraints
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中文总结 AI 辅助
提出Q-DEQ，将深度平衡模型前向求解中的局部更新转化为QUBO离散优化，结合W8A8量化，在时间序列预测中实现参数和存储大幅压缩，且精度接近显式基线。
中文摘要 AI 辅助
边缘部署促使预测模型采用紧凑的参数存储和低位表示。深度平衡模型（DEQ）通过重复应用共享层获得隐式深度，从而降低了显式堆叠层的参数成本。然而，其常用的Anderson求解器在连续实数域中搜索更新系数。我们提出Q-DEQ，将DEQ前向求解中的局部更新表述为离散优化问题。候选方向由当前状态和迭代历史构建，并使用局部二次残差模型评估其组合。方向系数的二进制编码产生了一个二次无约束二元优化（QUBO）问题，可通过模拟退火（SA）或相干Ising机（CIM）求解。在不动点求解后，一次重新前向传播对共享层的权重和激活应用W8A8伪量化。我们使用iTransformer骨干在五个多元时间序列预测数据集上评估Q-DEQ。与显式多层基线相比，相对MSE差异范围为-1.16%至+2.90%，在两个数据集上MSE更低。DEQ参数共享将参数数量减少了1.80倍至3.82倍；结合W8A8，静态权重存储减少了4.3倍至12.8倍。使用基于CPU的SA和Kaiwu CIM物理后端求解的局部QUBO问题产生的下游预测结果高度一致。这些结果确立了局部离散求解作为DEQ时间序列预测的可行组件，并为通过不同组合优化后端执行不动点更新提供了途径。
英文摘要
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 reduces parameter counts by factors of $1.80\times$--$3.82\times$; combined with W8A8, static weight storage is reduced by factors of $4.3\times$--$12.8\times$. Local QUBO problems solved using CPU-based SA and the Kaiwu CIM physical backend produce closely matching downstream forecasts. These results establish local discrete solving as a viable component of DEQ time series forecasting and provide a route for executing fixed-point updates through different combinatorial optimization backends.
