Revisiting Log-Transformation in Deep Regression: Rectifying Metric-Warped Interpolation Bias via Transient Variance Guidance

Log-transformation is a standard paradigm for deep regression on heavily skewed data. We find that, for data whose underlying structure is additive-dominant in the original space, the network's smoothness preference in log space drives its predictions away from the data's intrinsic regularity, inducing a systematic interpolation bias during generalization. We define this issue as metric-warped interpolation bias, which arises from the joint effect of the smooth inductive bias of neural networks and the strict convexity of the exponential mapping. Unlike the widely studied pointwise inverse-transform error, this issue has remained unexplored in previous work. Although directly introducing linear intervention to mitigate this bias appears intuitive, it easily destabilizes optimization. To address this dilemma, we propose Transient Variance Guidance (TVG), which repurposes the transient variance–error coupling of Negative Log-Likelihood (NLL), typically regarded as undesirable, as an endogenous proxy for fitting lag. TVG uses this transient variance-based fitting-lag signal to safely inject linear intervention into the learned representation, incurs zero computational overhead during inference, and consistently outperforms mainstream log-regression baselines across five cross-domain skewed datasets.