Layerwise Representation Geometry and Forecast Decodability in Time-Series Foundation Models

Intermediate representations in deep neural networks have long been studied for what they reveal about transfer and the emergence of task-relevant computation. Comparable understanding remains limited for time-series foundation models (TSFMs): how do their representations reorganize through depth, and do those changes track forecasting ability? We study Chronos-2, TimesFM-3, and TiRex on a controlled 13-dataset panel. Entropy effective rank follows a common construction–compression profile, rising through earlier or middle depth before contracting toward the output. Exploratory dataset-level CKA segmentation further identifies multiple contiguous representational regimes; across datasets, the three architectures exhibit significantly aligned regime boundaries, with common regions recurring near both early and late depth. We evaluate every layer using rank-constrained, representation-specific readouts under matched data and model-selection budgets. Forecasting performance generally improves toward later depth, but the trajectory is architecture-dependent, and inferred CKA regime boundaries are not systematically accompanied by abrupt forecasting changes. Late nonfinal readouts approach final-layer performance across the three models, although only Chronos-2 satisfies our simultaneous 5% criterion. These results show that representation geometry and forecasting ability co-evolve through depth without a universal transition-local correspondence.