Objectives supporting non-assignment for open-set inference

Design and analyze training objectives that support non-assignment within the implicit expectation-maximization framework—such as introducing an explicit "none of the above" component or threshold-based responsibility rejection—to enable open-set inference that can reject inputs outside known categories.

Background

Softmax normalization enforces a closed-world assumption: every input must be fully assigned to some component, which can yield high-confidence misassignments for out-of-distribution inputs.

Introducing non-assignment mechanisms within the implicit EM framework would allow models to abstain when no component is appropriate, thereby extending the approach to open-set recognition and more realistic deployment scenarios.

References

Several directions remain open. Open-set inference requires escaping the closed-world assumption. Objectives that support non-assignment---an explicit ``none of the above'' component, or a threshold below which no component takes responsibility---would extend implicit EM to settings where not all inputs belong to known categories.

— Gradient Descent as Implicit EM in Distance-Based Neural Models  (2512.24780 - Oursland, 31 Dec 2025) in Discussion, Open Directions (Section 7, Open Directions)