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Beyond the Class Subspace: Teacher-Guided Training for Reliable Out-of-Distribution Detection in Single-Domain Models

Hong Yang, Devroop Kar, Qi Yu, Travis Desell, Alex Ororbia

Abstract

Out-of-distribution (OOD) detection methods perform well on multi-domain benchmarks, yet many practical systems are trained on single-domain data. We show that this regime induces a geometric failure mode, Domain-Sensitivity Collapse (DSC): supervised training compresses features into a low-rank class subspace and suppresses directions that carry domain-shift signal. We provide theory showing that, under DSC, distance- and logit-based OOD scores lose sensitivity to domain shift. We then introduce Teacher-Guided Training (TGT), which distills class-suppressed residual structure from a frozen multi-domain teacher (DINOv2) into the student during training. The teacher and auxiliary head are discarded after training, adding no inference overhead. Across eight single-domain benchmarks, TGT yields large far-OOD FPR@95 reductions for distance-based scorers: MDS improves by 11.61 pp, ViM by 10.78 pp, and kNN by 12.87 pp (ResNet-50 average), while maintaining or slightly improving in-domain OOD and classification accuracy.

Beyond the Class Subspace: Teacher-Guided Training for Reliable Out-of-Distribution Detection in Single-Domain Models

Abstract

Out-of-distribution (OOD) detection methods perform well on multi-domain benchmarks, yet many practical systems are trained on single-domain data. We show that this regime induces a geometric failure mode, Domain-Sensitivity Collapse (DSC): supervised training compresses features into a low-rank class subspace and suppresses directions that carry domain-shift signal. We provide theory showing that, under DSC, distance- and logit-based OOD scores lose sensitivity to domain shift. We then introduce Teacher-Guided Training (TGT), which distills class-suppressed residual structure from a frozen multi-domain teacher (DINOv2) into the student during training. The teacher and auxiliary head are discarded after training, adding no inference overhead. Across eight single-domain benchmarks, TGT yields large far-OOD FPR@95 reductions for distance-based scorers: MDS improves by 11.61 pp, ViM by 10.78 pp, and kNN by 12.87 pp (ResNet-50 average), while maintaining or slightly improving in-domain OOD and classification accuracy.
Paper Structure (73 sections, 4 theorems, 10 equations, 3 figures, 50 tables)

This paper contains 73 sections, 4 theorems, 10 equations, 3 figures, 50 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Out-of-Distribution Detection
  4. Feature Geometry, Neural Collapse, and Representation Rank
  5. Knowledge Distillation and Teacher--Student Frameworks
  6. Fine-Tuning and OOD Detection
  7. Domain-Sensitivity Collapse
  8. Single-domain setting.
  9. Mechanism and severity.
  10. Connection to neural collapse.
  11. Anisotropic Geometry and Distance Failure
  12. Covariance decomposition.
  13. Anisotropy measures.
  14. Subspace decomposition.
  15. Distance failure via variance--discriminability mismatch.
  16. ...and 58 more sections

Key Result

theorem 1

Let $\lambda_1 \ge \cdots \ge \lambda_d$ be the eigenvalues of $\mathrm{Cov}(z_{\mathrm{ID}})$ with eigenvectors $v_1,\ldots,v_d$. Suppose the ID-vs-OOD separation concentrates in a set of directions $\{v_j : j \in \mathcal{J}\}$ with $\lambda_j / \lambda_1 \le \rho$ for all $j \in \mathcal{J}$ and where $L_k \le 1$ is the Lipschitz constant of the $k$-NN distance statistic with respect to featur

Figures (3)

  • Figure 1: Per-dataset gains from Teacher-Guided Training on ResNet-50 relative to the CE baseline. Blue bars show effective-rank increase (TGT$-$CE), and hatched orange bars show FPR@95 reduction (CE$-$TGT; larger is better). The shown datasets are EuroSAT, Colon, Fashion, Tissue, and Rock (Rock shown in a separate $y$-region).
  • Figure 2: EuroSAT out-of-domain OOD (FarOOD) FPR@95 by method across teacher-guidance strengths $\lambda$, averaged over 5 random splits. The effect of $\lambda$ is method-dependent: for example, ReAct improves at higher $\lambda$, while SCALE worsens. Many methods also perform poorly at $\lambda=0.5$.
  • Figure S1: EuroSAT out-of-domain (FarOOD) FPR@95 by method across teacher-guidance strengths $\lambda$, averaged over 5 splits. The effect of $\lambda$ is method-dependent: for example, React improves at higher $\lambda$, while SCALE worsens. Many methods also perform poorly at $\lambda=0.5$.

Theorems & Definitions (7)

  • theorem 1: Distance failure under variance--discriminability mismatch
  • lemma 1
  • proposition 1: MSP/Energy insensitivity
  • remark 1: Interpretation and tightness
  • theorem 2: Distance failure
  • proof
  • proof