TEMPO: Temporal Error-Modulated Precision Overlays for Recursive Transformer Quantization

Recursive Transformers repeatedly reuse the same parameters across computational loops, yet the resulting quantization errors are neither uniform nor equally consequential across recurrent roles. We introduce TEMPO, a post-training quantization framework that models this asymmetry through Temporal Error-Modulated Precision Overlays. TEMPO retains a shared low-bit weight backbone and augments selected weight tiles with sparse INT2 residual planes whose contributions are controlled by compact temporal codes. Instead of ranking corrections by local reconstruction error, TEMPO estimates how loop-specific perturbations propagate through the recurrent trajectory and influence the final prediction. This terminal-sensitivity signal drives temporal-code assignment and residual selection, while a global budget allocator concentrates additional bits on corrections with the largest expected distortion reduction. The resulting representation separates globally shared quantized weights from lightweight loop-dependent overlays, preserving the parameter efficiency of recursive architectures without duplicating per-loop weights. TEMPO provides a compact, trajectory-aware mechanism for correcting recurrent quantization error and exposes temporal residual structure as a first-class compression primitive.