Hidden Trajectories Don't Lie: Correcting Corruption Drift for Test-Time Adaptation

Amirhossein Sabour, Amir Khasahmadi, Mengliu Zhao

Test-time adaptation (TTA) adapts pretrained models to distribution shifts encountered during deployment. However, most existing methods rely on the weight representations of the final layer or signals derived from the model's output probability distribution. We study hidden trajectories: the ordered sequence of intermediate representations produced across a deep neural network. We observe that clean and corrupted trajectories become more separable as corruption severity increases. We introduce Drift-TTA, which adds zero-initialized low-rank adapters to a frozen backbone and trains them to align corrupted hidden trajectories with those from cleaner inputs. The approach supports two variants: a source-dependent version trained with clean targets, and a source-free setting that learns from corrupted images at different severities. We develop an online TTA approach that freezes the backbone and adapters while updating a scalar gate to control adaptation strength. We further cast trajectory alignment as MAP inference under a Gaussian observation model and derive a KL-based transfer bound characterizing test-time trajectory misalignment in terms of offline residual error, residual…