Activation-Aware Negative Label Mining for OOD

• Activation-aware Negative Label Mining is a technique that dynamically selects negative labels at test time based on activation patterns to distinguish in-distribution from OOD samples.
• It leverages both historical and batch-level activation metrics, using FIFO queues and interpolation to adaptively update negative label sets without retraining models.
• The method achieves significant reductions in false positive rates across benchmarks, offering robust performance for CLIP-style vision-language models in diverse environments.

Activation-aware Negative Label Mining denotes a family of training-free techniques for out-of-distribution (OOD) detection in vision-LLMs, where negative labels are adaptively selected at test time based on observed activation patterns, rather than fixed a priori. Central to this approach is Test-time Activated Negative Labels (TANL), which mines negative labels with strong response to OOD samples using dynamically accumulated activation metrics drawn from historical and mini-batch test data. The resulting methodology enables online, robust, and adaptive distribution alignment for OOD detection across diverse data regimes without requiring re-training or modification of pre-trained CLIP-style models (Zhang et al., 26 Mar 2026).

1. Formal Framework and Notation

Let $\mathcal{Y}_{ID} = \{y_1, \dots, y_C\}$ be the set of in-distribution (ID) labels and $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$ the corpus of candidate labels. For any test example $x$, pre-trained encoders yield a normalized image feature $v = f_{img}(x) \in \mathbb{R}^D$ and a normalized text feature $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$ for any label $y$, where $\rho$ is a prompt template (e.g., “a photo of a $<y>$”).

The zero-shot softmax probability over labels is given by: $$p(y \mid v) = \frac{\exp(v \cdot t(y))}{\sum_{y' \in \mathcal{Y}_{ID} \cup \mathcal{Y}_{neg}} \exp(v \cdot t(y'))}$$ where $$\mathcal{Y}_{neg} = \{\tilde{y}_1, \dots, \tilde{y}_M\} \subseteq \mathcal{Y}^{\mathrm{cor}} \setminus \mathcal{Y}_{ID}$$ are the mined negative labels ($$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$0).

This framework supports dynamic, test-time re-evaluation of $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$1 as label activations shift during inference.

2. Label Activation Metrics

The informational content of a candidate negative label $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$2 is quantified by its ability to activate upon OOD versus ID samples. The oracle activation difference is: $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$3 where

$$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$4

In the absence of ground-truth OOD labels at inference, TANL maintains two size-$$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$5 FIFO queues—$$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$6 (predicted ID, high-confidence) and $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$7 (predicted OOD, high-confidence)—to estimate the empirical activation gap: $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$8 The high-confidence sets are updated per batch by thresholding an OOD score $$\mathcal{Y}^{\mathrm{cor}} = \{\hat{y}_1, \dots, \hat{y}_N\}$$9 (defined below) with gap $x$0 around $x$1.

3. Batch-Adaptive Activation Mining

In addition to historical activation statistics, TANL leverages batch-level adaptivity by extracting high-confidence positive and negative feature vectors within the current test batch ($x$2). The combined batch-adaptive metric is: $x$3 with

$x$4

where $x$5 interpolates global and batch-local statistics. This enables TANL to rapidly adapt negative label selection in response to distribution drift or diversity in test-time batches.

4. Activation-aware OOD Scoring

Once the $x$6 most activated candidate negatives $x$7 are selected according to $x$8 or $x$9, OOD scoring for any test image feature $v = f_{img}(x) \in \mathbb{R}^D$0 is performed via: $v = f_{img}(x) \in \mathbb{R}^D$1 This formula endows negatives with higher activation greater implicit weight: $v = f_{img}(x) \in \mathbb{R}^D$2 appears in all denominators, $v = f_{img}(x) \in \mathbb{R}^D$3 in all but one, etc. The score is maximized when $v = f_{img}(x) \in \mathbb{R}^D$4 is close to ID features and far from top-activated negatives, reflecting robust OOD/ID discrimination.

5. Algorithmic Workflow

The TANL procedure, summarized in the following pseudocode, alternates between online activation mining and OOD scoring:

$t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$6

In this process, negative labels are dynamically aligned to historic and in-batch activation, yielding distribution-adaptive OOD scoring without requiring model or corpus retraining (Zhang et al., 26 Mar 2026).

6. Theoretical Properties

Building on multilabel detection theory, the change in false positive rate at a fixed decision threshold $v = f_{img}(x) \in \mathbb{R}^D$5 is controlled by: $v = f_{img}(x) \in \mathbb{R}^D$6 where $v = f_{img}(x) \in \mathbb{R}^D$7, $v = f_{img}(x) \in \mathbb{R}^D$8. Effectiveness of additional negatives ($v = f_{img}(x) \in \mathbb{R}^D$9) for decreasing $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$0 hinges on $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$1; i.e., the selected negatives must activate more on OOD than ID. TANL’s metric $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$2 is explicitly constructed to enforce this relationship, ensuring systematic selection of informative negatives (Zhang et al., 26 Mar 2026).

7. Empirical Performance and Robustness

The performance benefits of activation-aware mining are empirically validated across diverse benchmarks and architectures:

• On ImageNet-1K vs. {iNat, SUN, Places, Textures}, NegLabel (agnostic) achieves FPR95 ≈ 25.4%, while TANL attains FPR95 ≈ 9.8% (15.6 percentage point absolute reduction).
• Compared to recent conjugated-pool methods (FPR95 ≈ 17.5%), TANL achieves a 7.7 percentage point lower FPR95.
• TANL is robust to the number $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$3 of negatives: for small $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$4 it outperforms NegLabel, and for large $t(y) = f_{txt}(\rho(y)) \in \mathbb{R}^D$5 the activation-aware score prevents the performance collapse observed in prior approaches.
• Ablations on OpenOOD ImageNet demonstrate progressive improvement: distribution-adaptive only yields FPR95 ≈ 61.6% (vs. NegLabel 69.5%), with further reductions from batch-adaptive and activation-aware variants.
• The method generalizes to various backbones (ResNet50, ViT-B/32, ViT-L/14) and is effective on CIFAR-10/100 and medical X-ray OOD benchmarks.

TANL integrates a principled activation metric, test-time adaptation, and an activation-aware scoring rule, mining the most informative negatives in an online fashion and effecting significant advances in CLIP-style OOD detection (Zhang et al., 26 Mar 2026).