Post-hoc OOD detection · Gradient space

# GROOD ### Gradient-Aware Out-of-Distribution Detection Mostafa ElAraby · Sabyasachi Sahoo · Yann Pequignot · Paul Novello · Liam Paull

Transactions on Machine Learning Research

--- ## Recognizing unfamiliar inputs A classifier trained on cats and dogs still produces a prediction for a bird. **OOD detection adds a rejection decision:** is this input from the distribution of known classes? - Near-OOD: unfamiliar but semantically similar classes. - Far-OOD: inputs substantially different from the training distribution. Note: The presentation focuses on semantic OOD. Covariate shifts with the same labels are a related but distinct evaluation problem. --- ## Signals for OOD detection | Signal | Typical approach | Challenge | | :--- | :--- | :--- | | Output | Softmax confidence, energy | Confident predictions on unknowns | | Features | Distance to ID examples | Near-OOD may resemble known classes | | Gradients | Sensitivity of a loss | Which parameters and which reference? | **GROOD measures sensitivity to an artificial OOD prototype.** --- ## Prototype geometry - Neural collapse motivates representing each ID class by its mean feature. - ID features tend to cluster near their class prototypes. - An artificial OOD prototype provides a shared reference for sensitivity. > Measure how an input responds to the reference, then compare that response with familiar inputs. Note: Neural collapse motivates the method; it is not a guarantee that every architecture and checkpoint has perfectly collapsed features. --- ## GROOD pipeline ![GROOD pipeline: input, feature extractor, features, distances to prototypes, and gradient-space OOD score](assets/grood-slide8-0.webp) **Features → prototype distances → gradient vector → nearest ID gradient**

Method illustration from the supplied GROOD presentation

--- ## ID class prototypes For each class $c$, average its training features:
$$p_c^l=\frac1{|\mathcal D_c|}\sum_{x\in\mathcal D_c} f^l(x)$$
Compute prototypes at the **early** and **penultimate** layers. - Early prototypes support synthetic feature generation. - Penultimate prototypes define the distance-based classifier. --- ## Constructing the OOD prototype Interpolate early features toward the second-closest class prototype:
$$\hat h(x)=f^{\mathrm{mid}}\!\left(\lambda f^{\mathrm{early}}(x)+(1-\lambda)p_{c_2}^{\mathrm{early}}\right)$$
Average the synthetic penultimate features to obtain $p_{\mathrm{ood}}$. **The synthetic variant uses ID data to create a reference without real OOD examples.** Note: This is post-hoc feature interpolation, not a requirement to retrain the backbone with mixup. Other prototype construction variants use auxiliary data; they should be evaluated separately. --- ## Distance-based probabilities Use **negative Euclidean distances** as logits:
$$L_i(h)=-\|h-p_i\|_2$$
Include the $C$ class prototypes and the artificial OOD prototype.
$$q_i(h)=\frac{\exp L_i(h)}{\sum_{j=1}^{C+1}\exp L_j(h)}$$

Paper §4.1, Eqs. 2–3

Note: The supplied slide deck and blog use squared distances alongside a normalized-direction gradient. The published paper uses unsquared L2 distances, which yield the gradient shown on the next slide. q denotes a probability; p denotes a prototype. --- ## Gradient with respect to the reference For cross-entropy with any ID class label:
$$g(h)=\nabla_{p_{\mathrm{ood}}}H(h,y)=q_{\mathrm{ood}}(h)\frac{h-p_{\mathrm{ood}}}{\|h-p_{\mathrm{ood}}\|_2}$$
- **Magnitude:** $q_{\mathrm{ood}}(h)$. - **Direction:** from the reference toward the input’s feature. - Closed-form computation avoids backpropagation through the backbone.

Paper §4.1 and Appendix A.6

Note: y is an ID label, so the OOD component of the cross-entropy derivative is q_ood. The main paper has an inconsistent C+1 label notation; the expression is consistent with an ID target and unsquared negative L2 logits. Stabilize the denominator for a zero-distance input. --- ## Gradient-space geometry ![t-SNE projection of ID classes and OOD samples in gradient space](assets/grood-slide12-0.webp) ID inputs yield coherent gradient responses; unfamiliar inputs can differ in magnitude and direction.

Qualitative projection from the supplied presentation; t-SNE alone does not establish detection accuracy.

--- ## Nearest-neighbor OOD score Store gradient vectors from ID training inputs.
$$S(x)=\min_{x_i\in\mathcal D_{\mathrm{in}}}\|g(h(x))-g(h(x_i))\|_2$$
**Low score:** response resembles a familiar input. **High score:** response is unusual → more OOD-like. Note: This score has the opposite orientation to TOOD's ID score. For a threshold tau, accept ID if S is at most tau and reject otherwise. --- ## Setup and inference **Setup on a frozen model** 1. Compute class prototypes and the OOD reference. 2. Compute the ID gradient bank. 3. Build the nearest-neighbor search index. **At inference** Extract features → compute the closed-form gradient → query the index.

Post-hoc detection; nearest-neighbor search adds storage and inference cost.

Note: Search can use FAISS. The detector leaves the original classifier's class predictions intact and computes a separate rejection score. --- ## Experimental protocol - OpenOOD v1.5 evaluation on CIFAR-10, CIFAR-100, ImageNet-200, ImageNet-1K. - Separate Near-OOD and Far-OOD results. - ResNet backbones, plus ViT and Swin-T evaluations. - Comparisons include MSP, ODIN, ReAct, KNN, ViM and NCI. **AUROC (%) measures separation across thresholds; higher is better.** --- ## Near-OOD results AUROC (%) · OpenOOD v1.5 | Method | CIFAR-10 | CIFAR-100 | IN-200 | IN-1K | | :--- | ---: | ---: | ---: | ---: | | MSP | 88.0 | 80.3 | 83.3 | 76.0 | | ReAct | 87.1 | 80.7 | 81.9 | 77.4 | | KNN | 90.6 | 80.2 | 81.6 | 71.1 | | ViM | 88.7 | 75.0 | 78.7 | 72.1 | | NCI | 88.8 | **81.0** | **83.5** | 78.6 | | GROOD | **91.2** | 78.9 | 83.4 | **78.9** | **Strong CIFAR-10 and ImageNet-1K results; performance varies by dataset.** Note: Selected baseline rows from the provided presentation/blog and official repository. Bold marks the best value among the displayed methods, not a claim about every published method. --- ## Far-OOD results AUROC (%) · OpenOOD v1.5 | Method | CIFAR-10 | CIFAR-100 | IN-200 | IN-1K | | :--- | ---: | ---: | ---: | ---: | | MSP | 90.7 | 77.8 | 90.1 | 85.2 | | ReAct | 90.4 | 80.4 | 92.3 | 93.7 | | KNN | 93.0 | 82.4 | 93.2 | 90.2 | | ViM | 93.5 | 81.7 | 91.3 | 92.7 | | NCI | 91.3 | 81.3 | **93.7** | **95.5** | | GROOD | **93.8** | **84.4** | 92.2 | 94.8 | **GROOD leads the displayed methods on CIFAR-10 and CIFAR-100.** --- ## Checkpoint robustness ![AUROC across model checkpoints for multiple OOD detectors](assets/grood-slide25-0.webp)

Checkpoint comparison from the supplied GROOD presentation

Detection quality should be assessed alongside the choice of classifier checkpoint. Note: Read this as an empirical comparison on the plotted datasets and checkpoints, not a guarantee of stability for all training procedures. --- ## Scope and limitations - Requires access to ID training features and intermediate model representations. - Prototype construction and backbone geometry affect detection quality. - A single OOD reference does not represent every possible unknown class. - The gradient bank and nearest-neighbor index add memory and search cost. **Compare full gradient vectors, rather than relying only on confidence or gradient norm.** ---

Questions & discussion

# GROOD [Paper · OpenReview](https://openreview.net/forum?id=2V7itvvMVJ) [Paper · arXiv:2312.14427](https://arxiv.org/abs/2312.14427) [Code · Gradient-Aware-OOD-Detection](https://github.com/mostafaelaraby/Gradient-Aware-OOD-Detection) [Related presentation · TOOD](TOOD.html) Note: Source material: TMLR- GROOD.pptx and the site's GROOD publication post. Distance and gradient conventions were checked against the published paper, version 3.