OEM: Open-set Entropy Minimization in Domain Adaptation

• OEM is an entropy-based adaptation mechanism using one-vs-all classifiers to enable confident inlier and outlier predictions on unlabeled target data.
• It sharpens the separation between known and unknown classes by uniformly minimizing binary entropies across all class boundaries.
• Enhanced OEM in E-MLNet applies closed-set weighting to focus adaptation on relevant decision boundaries, improving robustness and class separation.

Searching arXiv for the cited papers and closely related OEM work. Open-set Entropy Minimization (OEM) is an entropy-based adaptation mechanism used in open-set and universal domain adaptation to encourage confident decisions on unlabeled target data while preserving the ability to reject unknown classes. In the formulation described for Mutual Learning Network (MLNet), OEM is applied to a bank of one-vs-all (OVA) open-set classifiers so that each classifier makes low-entropy inlier-or-outlier predictions on target samples, thereby sharpening the separation between known classes and the unknown region (Santos et al., 10 Sep 2025). Subsequent work situates OEM within a broader family of open-set entropy objectives: some methods retain entropy minimization but alter its weighting or sample selection, whereas others combine entropy minimization for likely known data with entropy maximization or uncertainty-aware regularization for likely unknown data in open-set test-time adaptation (Gao et al., 2024, Dong et al., 23 Jan 2025, Zhang et al., 2024).

1. Definition and task setting

OEM arises in settings where unlabeled target data may contain both classes shared with the source domain and target-private unknown classes. In Universal Domain Adaptation (UniDA), this requirement is explicit: the model must classify known samples while rejecting unknown ones, without assuming any fixed relationship between source and target label sets (Santos et al., 10 Sep 2025).

In the MLNet formulation, OEM is a loss function applied to unlabeled target data through a bank of OVA classifiers. Each OVA classifier $\mathcal{O}^k$ corresponds to source class $k$ and predicts a probability $p_o(k \mid x^t_j)$ that a target sample $x^t_j$ belongs to class $k$. OEM minimizes the average binary entropy across all $K$ OVA classifiers for each target sample (Santos et al., 10 Sep 2025):

$$\mathcal{L}_{oem}(x^t_j) = -\frac{1}{K} \sum_{k=1}^{K} \left[ p_o(k|x^t_j)\log p_o(k|x^t_j) + (1 - p_o(k|x^t_j))\log(1 - p_o(k|x^t_j)) \right]$$

This objective encourages each open-set classifier to make confident low-entropy inlier or outlier decisions on target data (Santos et al., 10 Sep 2025). In that sense, OEM differs from standard closed-set entropy minimization because the entropy is computed over classwise binary open-set decisions rather than solely over a single multiclass softmax.

2. OEM within MLNet and the OVA architecture

Within MLNet, the architecture consists of a feature extractor, a closed-set multi-class classifier $\mathcal{C}$, and a bank of open-set OVA classifiers $\mathcal{O}^k$ for each source class $k$ (Santos et al., 10 Sep 2025). OEM is applied to all target samples, and the entropy contribution from each OVA classifier is treated equally through uniform averaging over $k$0.

This uniform treatment encodes a specific assumption: every open-set classifier is equally relevant to every target sample (Santos et al., 10 Sep 2025). Operationally, for each target example, entropy is minimized across all class boundaries, regardless of whether the sample is actually close to those boundaries. The intended effect is to drive the feature representation toward decisive regions of the open-set decision space, so that known-class membership and unknown rejection become more separable.

The same source describes OEM as one component of a larger optimization program in MLNet and E-MLNet. The full objective combines source-domain closed-set classification and OVA supervision with multiple target-side regularizers (Santos et al., 10 Sep 2025):

$k$1

This placement clarifies that OEM is not a stand-alone rejection rule, but a target-domain confidence-shaping term embedded in a larger domain adaptation loss.

3. Mathematical role in class separation

The stated purpose of OEM is to push the OVA classifiers toward confident predictions near $k$2 or $k$3, thereby promoting clear inlier-versus-outlier assignments for target data (Santos et al., 10 Sep 2025). In the MLNet interpretation, this creates sharper boundaries between each known class and the collective unknown region.

A central limitation is also explicit: as the number of source classes increases, most class boundaries are irrelevant for any given target sample, so their entropy contributions act as noise and dilute the adaptation signal (Santos et al., 10 Sep 2025). This point is important because it identifies a failure mode intrinsic to the uniform OEM formulation rather than to entropy minimization in general. The issue is not simply that entropy is minimized, but that it is minimized uniformly over all OVA heads.

This suggests a structural tension in OEM-based open-set adaptation. On the one hand, low-entropy OVA predictions can improve separation between known and unknown classes. On the other hand, indiscriminate low-entropy pressure across many irrelevant one-vs-all boundaries can inject optimization noise. A plausible implication is that OEM becomes increasingly sensitive to class cardinality and boundary relevance as the source taxonomy grows.

Related analyses in open-set test-time adaptation reinforce the broader concern that naive entropy objectives can mis-handle unknowns. In Unified Entropy Optimization (UniEnt), many closed-set TTA methods are reported to perform poorly in open-set scenarios because minimizing entropy on unknown samples makes the model assign overconfident predictions to out-of-distribution data (Gao et al., 2024). In Adaptive Entropy-aware Optimization (AEO), the distinction is made even more sharply: methods that only minimize entropy do not amplify the entropy difference between known and unknown samples, whereas unknown-aware schemes do (Dong et al., 23 Jan 2025). These are not identical formulations of OEM, but they frame the same design problem: low-entropy adaptation can aid known-class alignment while simultaneously damaging unknown detection if applied indiscriminately.

4. Sample-specific weighting in E-MLNet

E-MLNet modifies OEM by introducing dynamic sample-specific weighting derived from the closed-set classifier’s predictions. The motivation is that only a few class boundaries are relevant for a given target sample, so uniform minimization across all classes is inefficient (Santos et al., 10 Sep 2025).

The enhanced OEM objective is (Santos et al., 10 Sep 2025):

$k$4

where $k$5 is the probability assigned to class $k$6 by the closed-set classifier for sample $k$7 (Santos et al., 10 Sep 2025). This weighting scheme upweights the OVA entropy term for classes that the closed-set classifier considers plausible and downweights the others.

The source explicitly interprets this mechanism as an attention mechanism focusing adaptation on the most semantically relevant class boundaries per sample (Santos et al., 10 Sep 2025). If the closed-set classifier is confident that a sample belongs to class $k$8, the corresponding OVA entropy term receives higher weight, sharpening the inlier/outlier decision near that boundary. For irrelevant classes, little to no adaptation signal is propagated, reducing noise from unrelated boundaries.

The consequences attributed to this design are threefold: it creates sharper and less confused boundaries near decision surfaces, avoids learning spurious or unnecessary decision boundaries for irrelevant classes, and improves robustness and class separation for known-versus-unknown detection (Santos et al., 10 Sep 2025). These claims remain within the formulation provided for E-MLNet and do not require introducing external mechanisms beyond the stated weighting rule.

5. Relation to other entropy-based open-set methods

OEM belongs to a broader landscape of entropy-based methods for open-set adaptation, but the objectives differ substantially across domains and problem formulations.

In open-set test-time adaptation, UniEnt explicitly separates pseudo-covariate-shifted in-distribution (csID) and pseudo-covariate-shifted out-of-distribution (csOOD) samples, then applies entropy minimization to pseudo-csID data and entropy maximization to pseudo-csOOD data (Gao et al., 2024). Its total loss includes a marginal entropy term to prevent collapse, and UniEnt+ replaces hard partitioning with sample-level soft weighting. This contrasts with MLNet-style OEM, which minimizes OVA binary entropies on all target samples rather than maximizing entropy for likely unknowns.

AEO makes the divergence from OEM even clearer. Its Unknown-aware Adaptive Entropy Optimization (UAE) computes prediction entropy

$k$9

and uses an adaptive weight

$p_o(k \mid x^t_j)$0

to decide whether a sample’s entropy should be minimized or maximized (Dong et al., 23 Jan 2025). If $p_o(k \mid x^t_j)$1, entropy is minimized; if $p_o(k \mid x^t_j)$2, entropy is maximized. The paper explicitly contrasts this with OEM-style approaches that minimize entropy globally or on selected confident samples but do not adaptively maximize entropy for likely unknowns (Dong et al., 23 Jan 2025).

COME addresses a related pathology from another angle. It argues that standard entropy minimization in TTA leads to overconfidence and model collapse, especially in open-world settings, and replaces standard EM with entropy minimization over a subjective opinion vector derived from a Dirichlet model (Zhang et al., 2024). The key quantity is

$p_o(k \mid x^t_j)$3

with belief terms $p_o(k \mid x^t_j)$4 and uncertainty mass $p_o(k \mid x^t_j)$5, and the adaptation objective is

$p_o(k \mid x^t_j)$6

(Zhang et al., 2024). The stated relation is that COME operationalizes OEM in an uncertainty-aware manner by allowing the model to allocate uncertainty mass to unreliable samples rather than forcing overconfident known-class assignments.

A concise comparison is therefore possible.

Method	Entropy treatment	Unknown handling
MLNet / OEM	Minimize average binary entropy across OVA heads	Unknowns handled through confident inlier/outlier OVA decisions
E-MLNet	Minimize weighted OVA entropy using $p_o(k \mid x^t_j)$7	Focuses adaptation on relevant class boundaries
UniEnt / UniEnt+	Minimize entropy on pseudo-csID, maximize on pseudo-csOOD	Explicit csID/csOOD partition or soft weighting
AEO / UAE	Per-sample adaptive entropy minimization or maximization	Amplifies entropy difference between known and unknown
COME	Conservative entropy minimization with subjective uncertainty	Preserves uncertainty on unreliable samples

These differences show that “open-set entropy” is not a single recipe. OEM in the MLNet sense is one particular design: low-entropy OVA adaptation for target samples, later refined by class-conditional weighting in E-MLNet (Santos et al., 10 Sep 2025).

6. Experimental evidence and reported effects

The paper introducing E-MLNet reports experiments on Office-31, Office-Home, VisDA-2017, and ImageCLEF (Santos et al., 10 Sep 2025). On these four challenging benchmarks, E-MLNet achieves the highest average H-score on VisDA and ImageCLEF and shows superior robustness over its predecessor. Relative to the MLNet baseline, E-MLNet outperforms MLNet in 22 out of 31 tasks in the Open-Partial DA setting and 19 out of 31 tasks in the Open-Set DA setting (Santos et al., 10 Sep 2025).

The evidence is framed as an ablation on OEM itself: MLNet with uniform OEM and E-MLNet with weighted OEM are compared while keeping the remaining components identical, isolating the effect of the OEM weighting strategy (Santos et al., 10 Sep 2025). The reported conclusion is that the benefits are especially pronounced as the number of source classes increases, which is presented as validation of the claim that uniform OEM becomes increasingly suboptimal with more classes.

Other entropy-based open-set adaptation studies provide related but not identical evidence. UniEnt reports large gains in OOD detection metrics when replacing standard closed-set entropy minimization with a joint minimize/maximize entropy framework in open-set TTA; for example, on CIFAR-100-C with TENT, AUROC improves from $p_o(k \mid x^t_j)$8 to $p_o(k \mid x^t_j)$9, FPR@TPR95 changes from $x^t_j$0 to $x^t_j$1, and OSCR changes from $x^t_j$2 to $x^t_j$3 (Gao et al., 2024). AEO reports that it consistently outperforms baselines in multimodal open-set test-time adaptation, with up to $x^t_j$4 H-score improvement over the Source baseline on EPIC-Kitchens, $x^t_j$5 on various modalities on HAC, and $x^t_j$6 H-score improvement on Kinetics-100-C with severe corruptions (Dong et al., 23 Jan 2025). COME reports up to $x^t_j$7 improvement on accuracy and $x^t_j$8 on false positive rate in standard, life-long, and open-world TTA (Zhang et al., 2024).

These results do not measure OEM in the narrow MLNet sense, but they underscore a consistent empirical theme: entropy-based open-set adaptation is effective only when the objective is shaped to avoid indiscriminate confidence amplification on unknown data.

7. Misconceptions, limitations, and scope

A common misconception is to treat OEM as equivalent to standard entropy minimization. The MLNet-based formulation shows otherwise: OEM is defined over a bank of OVA open-set classifiers, not merely over the multiclass predictive entropy of a closed-set head (Santos et al., 10 Sep 2025). Its objective is specifically to produce confident inlier/outlier decisions for each source class boundary.

A second misconception is that entropy minimization alone is always beneficial in open-set settings. Multiple cited works dispute this. UniEnt argues that minimizing entropy on unknown samples destroys model calibration and OOD detection (Gao et al., 2024). AEO states that OEM-style schemes do not adaptively maximize entropy for likely unknowns (Dong et al., 23 Jan 2025). COME identifies overconfidence as a fatal limitation of standard EM in open-world TTA (Zhang et al., 2024). These papers do not negate OEM’s utility in UniDA, but they delimit where a pure minimization objective can fail.

Within the OEM formulation itself, the key limitation is uniformity across class boundaries. E-MLNet identifies the assumption that every OVA classifier is equally relevant to every target sample as the source of diluted learning signals (Santos et al., 10 Sep 2025). The remedy it proposes is not to abandon OEM, but to weight it by closed-set class probabilities so that adaptation concentrates on the most relevant decision boundaries.

This suggests a useful synthesis. In universal domain adaptation, OEM serves as a classwise boundary-sharpening mechanism over OVA heads. In open-set test-time adaptation, related methods often extend or modify that idea by partitioning samples, reversing the entropy direction for likely unknowns, or explicitly modeling uncertainty. The shared principle is entropy control under semantic shift, but the operational form of that control depends strongly on whether the method prioritizes boundary sharpening, unknown rejection, online robustness, or uncertainty calibration (Santos et al., 10 Sep 2025, Gao et al., 2024, Dong et al., 23 Jan 2025, Zhang et al., 2024).