When a neural time-series model reports that one variable modulates another's effect on a target, is the discovered interaction a property of the data or an artifact of model flexibility? We argue that this is fundamentally a question of identifiability, governed by the geometry of the observed input support rather than by the specific neural architecture. We study the problem in a multiplicative-gating extension of neural additive vector autoregression (GNAVAR), in which source contributions are modulated by other lagged variables. We show that representational capacity is not identifiability: dependent inputs induce leakage between edge-specific interaction terms, and low-dimensional support permits distinct interaction decompositions that agree on the observed data while differing elsewhere. We then prove a population identifiability theorem for normalized minimal GNAVAR decompositions under explicit support conditions, including settings with shared modulators. The theory yields a simple practitioner-facing diagnostic: the effective rank of the joint lag-block covariance predicts, before fitting, whether interaction recovery is feasible for a given candidate set. When the candidate set is unknown, a two-seed stability check provides a practical operational test. The same support condition organizes empirical outcomes into the three states predicted by the theory. Our results show that interaction recoverability depends on support geometry, that effective rank provides a practical pre-fit diagnostic, and that instability across independent fits is a characteristic signature of non-identifiable interaction discovery. The identifiability phenomenon, the support condition, and the instability signature are model-agnostic; GNAVAR is the vehicle that makes them provable.

翻译：当神经时间序列模型报告一个变量调节另一个变量对目标的影响时，所发现的交互作用是数据的固有属性还是模型灵活性的产物？我们认为，这本质上是一个可辨识性问题，其决定因素在于观测输入支撑集的几何结构，而非特定的神经架构。我们在神经加性向量自回归（GNAVAR）的乘法门控扩展中研究该问题，其中源贡献被其他滞后变量所调制。研究表明，表示能力并非可辨识性：依赖输入会导致边特定交互项之间的泄漏，而低维支撑集允许不同的交互分解在观测数据上一致但在其他区域存在差异。随后，我们证明了在显式支撑条件下（包括共享调制器设置）归一化最小GNAVAR分解的总体可辨识性定理。该理论为实践者提供了一个简洁的诊断工具：联合滞后块协方差的有效秩可在拟合前预测给定候选集下交互恢复的可行性。当候选集未知时，双种子稳定性检验提供了实用的操作测试。相同的支撑条件将实证结果归纳为理论预测的三种状态。我们的结果表明：交互可恢复性取决于支撑集几何结构，有效秩提供了实用的预拟合诊断工具，而独立拟合间的不稳定性是非可辨识交互发现的典型特征。可辨识性现象、支撑集条件及不稳定性特征均与模型无关；GNAVAR是使之可被证明的载体。