Quantizing Looped Transformers: Feedback Exposure and Calibration Blindness

Looped transformers reuse weights across recurrence steps, making low-bit quantization especially attractive. We identify two distinct failure modes of standard post-training quantization. On Huginn-3.5B, per-channel INT4 fails primarily at the non-residual loop-entry adapter, while quantizing the residual core is much less damaging. We call this feedback exposure: a quantized layer perturbs the recurrent state without an identity path, and the resulting error is fed back at later steps. Controlled experiments on linear filters and Mamba state-space models show that feedback exposure also occurs outside transformers. Grouped INT4 reveals a separate failure, calibration blindness: our one-step GPTQ baseline builds its Hessian from step-0 activations, leaving input directions used later in the recurrence nearly unweighted. Across nine checkpoints from seven looped architectures, one-step GPTQ is worse than round-to-nearest (RTN) on the primary task metric for five checkpoints. Accumulating the GPTQ Hessian across recurrence steps outperforms both one-step GPTQ and RTN on all nine checkpoints and recovers bf16-level accuracy on Huginn. These results separate two questions for PTQ on looped models: where quantization error enters the recurrence, and which states calibration sees.