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Predictive Spectral Calibration for Source-Free Test-Time Regression

Nguyen Viet Tuan Kiet, Huynh Thanh Trung, Pham Huy Hieu

TL;DR

Predictive Spectral Calibration is proposed, a source-free framework that extends subspace alignment to block spectral matching and jointly aligns target features within the source predictive support and calibrates residual spectral slack in the orthogonal complement.

Abstract

Test-time adaptation (TTA) for image regression has received far less attention than its classification counterpart. Methods designed for classification often depend on classification-specific objectives and decision boundaries, making them difficult to transfer directly to continuous regression targets. Recent progress revisits regression TTA through subspace alignment, showing that simple source-guided alignment can be both practical and effective. Building on this line of work, we propose Predictive Spectral Calibration (PSC), a source-free framework that extends subspace alignment to block spectral matching. Instead of relying on a fixed support subspace alone, PSC jointly aligns target features within the source predictive support and calibrates residual spectral slack in the orthogonal complement. PSC remains simple to implement, model-agnostic, and compatible with off-the-shelf pretrained regressors. Experiments on multiple image regression benchmarks show consistent improvements over strong baselines, with particularly clear gains under severe distribution shifts.

Predictive Spectral Calibration for Source-Free Test-Time Regression

TL;DR

Predictive Spectral Calibration is proposed, a source-free framework that extends subspace alignment to block spectral matching and jointly aligns target features within the source predictive support and calibrates residual spectral slack in the orthogonal complement.

Abstract

Test-time adaptation (TTA) for image regression has received far less attention than its classification counterpart. Methods designed for classification often depend on classification-specific objectives and decision boundaries, making them difficult to transfer directly to continuous regression targets. Recent progress revisits regression TTA through subspace alignment, showing that simple source-guided alignment can be both practical and effective. Building on this line of work, we propose Predictive Spectral Calibration (PSC), a source-free framework that extends subspace alignment to block spectral matching. Instead of relying on a fixed support subspace alone, PSC jointly aligns target features within the source predictive support and calibrates residual spectral slack in the orthogonal complement. PSC remains simple to implement, model-agnostic, and compatible with off-the-shelf pretrained regressors. Experiments on multiple image regression benchmarks show consistent improvements over strong baselines, with particularly clear gains under severe distribution shifts.
Paper Structure (26 sections, 4 theorems, 55 equations, 2 tables)

This paper contains 26 sections, 4 theorems, 55 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Setting
  4. Image Regression.
  5. Test-Time Adaptation.
  6. Source-Free Domain Adaptation.
  7. Self-Supervised Test-Time Training.
  8. Feature Alignment.
  9. Significant-Subspace Alignment
  10. Subspace Construction.
  11. Test-Time Objective.
  12. Methodology
  13. Block Spectral Source Model
  14. Sample Decomposition.
  15. Support-Space Spectral Matching
  16. ...and 11 more sections

Key Result

Proposition 1

Assume $\mathbf{u}^s\sim\mathcal{N}(\mathbf{0},\mathbf{\Lambda}^s)$ and $\mathbf{u}^t\sim\mathcal{N}(\boldsymbol{\mu}^t,\mathbf{\Sigma}^t)$ in the support subspace. If, for every $\mathbf{q}\in\mathcal{Q}$, $\mathbf{q}^{\top}\mathbf{u}^t\stackrel{d}{=}\mathbf{q}^{\top}\mathbf{u}^s$, then $\boldsymbo

Theorems & Definitions (8)

  • Proposition 1: Identifiability from the $K^2$ probe bank
  • proof
  • Proposition 2: PSC controls predictive mean drift
  • proof
  • Proposition 3: Identifiability of subspace first- and second-order structure from the $K^2$ probe bank
  • proof
  • Proposition 4: PSC controls predictive mean drift
  • proof