Progressive Memory Transformer: Memory-Aware Attention for Time-Series

Time-series carry structure simultaneously at multiple scales (fine-grained variation, mid-range motifs, and global properties) and downstream tasks operate at correspondingly different scales. Most existing self-supervised learning approaches supervise representations globally via instance-level contrastive losses and limited temporal neighborhood supervision, but do not explicitly exploit the structural hierarchy. We propose a learning framework that explicitly enforces a structural hierarchy across three scales independently: a local objective for token continuity, a mid-range objective for window-level motifs, and a global objective for sequence-level agreement. Realizing this framework requires the backbone to expose a representation at each scale; we introduce \textbf{Progressive Memory Transformer} (PMT), which augments a transformer with writable, window-aligned memory that exposes the mid-range scale alongside the token and sequence-level representations conventional transformers already provide. Across seven UCR/UEA/UCI classification benchmarks, a cue-retention probe, and forecasting benchmarks, PMT learns representations that probe well at the global, mid-range, and local scales---strong low-label classification (1--5\% labels), competitive forecasting performance across multiple horizons, and quantitative and qualitative evidence that memory states capture mid-range motifs.