Out-of-Distribution Detection

OOD detectors model the probability density of the in-distribution training data. Samples falling in low-density regions are flagged as OOD.

• Parametric methods fit a Gaussian Mixture Model to learned features.
• Non-parametric methods use kernel density estimation or nearest-neighbor distances.
• Deep generative models like Normalizing Flows learn an explicit likelihood function.
• A critical failure mode occurs when OOD samples are assigned high likelihood due to model flaws, a phenomenon known as the typicality test failure.

This approach computes the distance between a test sample's feature representation and the training distribution's centroid or nearest prototypes.

• Mahalanobis distance measures the number of standard deviations a point is from the mean of a class-conditional Gaussian distribution.
• Cosine similarity thresholds reject samples whose feature vectors point in a direction far from known class anchors.
• Deep Nearest Neighbors leverage non-parametric labels in the embedding space, rejecting inputs whose k-nearest neighbors lack consensus.

Leverages the raw output of a classifier to derive an OOD score without modifying the base model architecture.

• Maximum Softmax Probability (MSP) is a baseline: low confidence on the predicted class suggests an OOD sample.
• Energy-based scores use the logsumexp of logits, providing a theoretically grounded alternative less prone to overconfidence than MSP.
• ODIN adds a small temperature scaling and input pre-processing perturbation to widen the gap between ID and OOD softmax scores.

A formalized extension of classification that explicitly includes an 'unknown' class for any sample not belonging to the known training categories.

• OpenMax replaces the standard SoftMax layer with one that estimates the probability of an input belonging to an unknown class using Extreme Value Theory on activation vectors.
• Generative OpenMax synthesizes counterfactual open-set samples to train a classifier with an explicit rejection head.
• Requires the model to maintain high accuracy on known classes while simultaneously detecting novelties, a fundamental trade-off.

A diagnostic property where OOD inputs produce feature embeddings that anomalously concentrate or collapse in the representation space.

• Spectral signatures identify OOD samples by analyzing the top singular vectors of the feature covariance matrix, where OOD features exhibit abnormally high alignment.
• Gradient-based detection observes that OOD inputs often produce gradients with distinct norms or directions compared to in-distribution data during backpropagation.
• Monitoring the norm of the feature vector is a simple yet effective baseline; OOD samples frequently map to vectors with smaller magnitudes.

An OOD detector is only as good as its decision threshold. Proper calibration ensures the score is interpretable as a true probability of being out-of-distribution.

• Temperature scaling is applied post-hoc to soften the softmax outputs, improving the reliability of confidence-based OOD scores.
• Isotonic regression learns a non-decreasing mapping from raw scores to calibrated probabilities without assuming a parametric form.
• The threshold is typically set on a held-out validation set containing both ID and a proxy OOD dataset to achieve a target True Negative Rate (TNR) at 95% True Positive Rate (TPR).

An open set recognition algorithm that recalibrates a classifier's softmax scores using Extreme Value Theory. Instead of forcing a closed-set decision, OpenMax models the distribution of activation vectors for unknown classes, enabling the system to reject inputs that fall far from any known training distribution. It replaces the standard softmax layer with a recalibrated probability estimate that includes an explicit 'unknown' class.

A model-agnostic framework that produces prediction sets with a finite-sample, distribution-free guarantee of marginal coverage. Rather than a single label, it outputs a set of plausible classes. If the correct label is not in the set, or the set is empty, the sample is flagged as out-of-distribution. This provides a statistically rigorous rejection mechanism without requiring distributional assumptions.

A highly robust estimator of multivariate location and scatter that finds a subset of data points minimizing the determinant of the covariance matrix. For OOD detection, MCD fits a robust Gaussian distribution to in-distribution features. The Mahalanobis distance from this robust centroid serves as an anomaly score, effectively flagging outliers without being influenced by them during fitting.

A decomposition technique that separates a data matrix into a low-rank component and a sparse component. The sparse component captures outliers and adversarial corruption. In OOD detection, Robust PCA can be used to decompose feature representations, isolating anomalous activation patterns that deviate from the low-rank structure of in-distribution data.

The formal process of proving that a neural network's output satisfies a specific property for all inputs within a defined adversarial budget. Applied to OOD detection, verification techniques can provide certified guarantees that a model will correctly reject any input whose latent representation falls outside a verified safe region, moving beyond empirical detection to provable rejection.