ROAM: Task-Conditioned Metrics for Forecasting Optimization

Can a forecasting task inform how its model should be optimized, without changing the forecasting architecture? We study this question through ROAM (Riemannian Optimization with Adaptive Metrics), which maps six training-derived task statistics to a block-wise positive-definite metric. A slow population controller adapts the metric and a two-signal transition between momentum-based and quasi-Newton updates. The central mechanism is task-conditioned preconditioning on ordinary parameters; explicit orthogonality and positive-definite parameter constraints are separate, optional interventions. Across seven datasets and five backbones, ROAM improves all 35 dataset–backbone MSE aggregates relative to standard training recipes, with approximately 4.8%-7.3% lower macro-average MSE by backbone. Four matched-budget optimizer comparisons and a complete three-component factorial provide more targeted evidence: the metric has the largest average marginal contribution, while switching and outer adaptation also help. A local analysis relates metric alignment and cross-block coupling to conditioning, without assuming that task descriptors guarantee alignment. Together, these results support task information as a useful input to training geometry in the evaluated forecasting regimes.