OpenMax

For each known class, OpenMax fits a Weibull distribution to the tail of the distance between the class's mean activation vector (MAV) and the top incorrectly classified training samples. This models the extreme value statistics of outlier activations, providing a per-class probabilistic model of what constitutes 'far away' from known data. The fitting uses the libMR framework for efficient Weibull parameter estimation.

Rather than taking the raw softmax output, OpenMax recalibrates the penultimate layer's activation vector (AV). For each top-ranked class, it computes the distance to the class's MAV and queries the fitted Weibull CDF to determine the probability of observing such a distant sample. These probabilities are used to discount the logits of known classes, effectively reducing their scores when the input appears atypical.

The recalibrated logits are re-normalized to produce a new probability distribution over K+1 classes: the K known classes plus a dedicated 'unknown' class. The probability mass assigned to the unknown class is the sum of the discounts applied to the known classes. This provides a calibrated rejection score that can be thresholded to trigger out-of-distribution detection or flag novel modulation schemes.

A critical operational parameter is the rejection threshold (ε). If the probability of the unknown class exceeds ε, the classifier rejects the input entirely. This threshold can be tuned to balance the trade-off between open-set risk (misclassifying an unknown as known) and closed-set accuracy. In signal classification, this prevents a cognitive radio from erroneously identifying a novel adversarial waveform as a known friendly protocol.

OpenMax implements a meta-recognition layer that operates on top of the base classifier. It does not require retraining the original network; it only needs the activation vectors from the training set. This makes it a post-hoc method that can be applied to pre-trained models. The Weibull fitting is performed per-class, assuming that the tail behavior of the distance distribution follows an Extreme Value Theory model.

OpenMax assumes that the distance between an AV and the MAV is a meaningful indicator of novelty. In very high-dimensional activation spaces, distances can concentrate, making separation difficult. Additionally, the method relies on the top-k incorrect classes during training to fit the Weibull tail, which may not capture all modes of novelty. For complex signal environments, it may be outperformed by more recent density-based or energy-based open-set methods.

The task of identifying test samples drawn from a fundamentally different distribution than the model's training data. While OpenMax focuses on activation vector distributions in the penultimate layer, general OOD detection methods may use energy-based scores, Mahalanobis distance, or gradient-based statistics. Key distinction: OOD detection flags distributional shift broadly, whereas OpenMax specifically models the boundary between known and unknown classes within the same feature space.

The statistical foundation underpinning OpenMax. EVT models the behavior of the tail of a distribution—the extreme, rare events. OpenMax applies the Weibull distribution to fit the distance between a sample's activation vector and the mean activation vector of each known class. This calibrated model determines the probability that a sample belongs to an unknown class, rejecting it if the probability exceeds a threshold.

A standard softmax layer forces a closed-world assumption: probabilities always sum to 1 across known classes, even for nonsensical inputs. OpenMax recalibrates these scores by:

• Fitting Weibull models per class on Mean Activation Vectors (MAVs)
• Computing a pseudo-probability for an explicit 'unknown' class
• Redistributing the softmax probabilities to include this rejection class This prevents confident misclassifications on novel signal types.

A security mechanism designed to distinguish between legitimate data samples and adversarial inputs before classification. While OpenMax handles unknown but benign classes, adversarial detection targets maliciously perturbed samples. The two concepts intersect: an adversarially perturbed known signal may appear as an unknown class. Combining OpenMax with feature squeezing or local intrinsic dimensionality detectors creates a layered defense against both novelty and attacks.

A model-agnostic framework that produces prediction sets with a finite-sample, distribution-free guarantee of marginal coverage. Unlike OpenMax's parametric EVT approach, conformal prediction uses a calibration set to determine nonconformity scores. For modulation classification, this means outputting a set like {QPSK, 16QAM} instead of a single label when uncertainty is high, providing a statistically rigorous alternative to OpenMax's rejection mechanism.

A formal guarantee that a classifier's prediction will not change for any input within a mathematically verified Lp-norm bound. While OpenMax provides empirical open-set rejection, certified robustness via randomized smoothing or interval bound propagation offers provable guarantees against adversarial perturbations. In safety-critical RF systems, combining OpenMax for unknown modulation rejection with certified robustness for known-class stability creates a defense-in-depth architecture.