The Spectrum Remembers: Spectral Memory

Training dynamics encode global structure—persistent long-range correlations, representational curvature, and
seasonality clusters—that no individual sequence contains. While standard memory mechanisms extend context within
a sequence, they ignore a complementary information source: the training trajectory itself. We propose Spectral
Memory, a mechanism that captures hidden-state evolution across thousands of mini-batches to encode temporal structure
unavailable in any single sequence.