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Not All Variables Agree: Reliability-Aware Variable-Wise Gradient Surgery for Multivariate Time-Series Forecasting

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

In data-driven training, multivariate time-series forecasting is usually optimized with a scalar loss averaged over samples, variables, and horizons. This averaging is convenient, but the optimizer sees only the aggregated gradient, which does not reveal whether the variable-wise contributions align or oppose one another. To quantify how often this disagreement arises, we measure the variable-wise gradients directly and find that 30.6% of their pairwise cosine similarities are negative on average across seven datasets. However, conflict and harm are not the same thing. Under shared training 35

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