Out-of-Distribution Detection

OOD detection specifically targets semantic shift—inputs belonging to fundamentally different classes than the training set—rather than mere covariate shift (stylistic or environmental changes). A handwritten digit classifier encountering a 'car' image faces semantic shift, while seeing rotated digits represents covariate shift. Effective detectors must distinguish between these two types of distributional change, as conflating them leads to false positives on benign variations.

Deep generative models often assign higher likelihood to OOD inputs than in-distribution data, a counterintuitive phenomenon known as the 'density paradox.' This occurs because likelihood is dominated by low-level statistics (e.g., background pixel correlations) rather than semantic content. Modern OOD detectors avoid raw likelihood scores and instead rely on:

• Likelihood ratios comparing foreground to background models
• Typicality tests measuring how 'typical' a sample is of the distribution
• Energy-based scores derived from discriminative classifiers

Distance-based methods measure how far an input embedding lies from the training manifold in feature space. Key approaches include:

• Mahalanobis distance: Computes class-conditional distances in a Gaussian-fitted feature space, capturing both mean and covariance structure
• K-Nearest Neighbors (KNN): Uses the distance to the k-th nearest training sample as an OOD score; non-parametric and effective
• Deep Nearest Neighbors: Applies KNN in the penultimate layer of a pre-trained classifier, achieving state-of-the-art results without retraining

These methods exploit the geometric property that OOD samples map to low-density regions of the learned representation.

Energy-based models define a scalar energy function E(x) where in-distribution samples receive low energy and OOD samples receive high energy. The energy score derived from discriminative classifiers is computed as the negative log-sum-exp of logits: E(x) = -T · log Σ exp(f_i(x)/T). This score is:

• Alignment-agnostic: Does not require access to OOD data during training
• Theoretically grounded: Connected to the model's learned density through Gibbs distributions
• Computationally cheap: Requires only a single forward pass with no auxiliary models

OOD detection approaches divide into two paradigms:

• Post-hoc methods: Apply detection scores to already-trained models without modification. Examples include MSP (Maximum Softmax Probability), ODIN, and Energy. These are deployment-friendly but may underperform on challenging benchmarks.
• Training-time methods: Incorporate OOD awareness during training through outlier exposure (training on auxiliary OOD datasets) or contrastive learning objectives that explicitly separate ID and OOD representations. These achieve superior performance but require access to proxy OOD data and model retraining.

While related, these tasks have distinct objectives:

• Open Set Recognition (OSR) : Classifies known classes while rejecting unknown classes that appear at test time. Requires fine-grained discrimination among known classes simultaneously with novelty detection.
• OOD Detection: A binary decision—is this sample from the training distribution or not? No requirement to classify among known classes.

OSR is a harder problem, as the model must maintain closed-set accuracy while detecting novelty. Many OOD detection methods can be adapted for OSR by combining the OOD score with the argmax prediction.