\begin{table}[t]
\caption{Recoverability under common noisy-supervision assumptions.}\label{tab:recoverability}
\small
\setlength{\tabcolsep}{3pt}
\begin{tabular}{@{}L{0.18\textwidth}L{0.24\textwidth}L{0.27\textwidth}L{0.21\textwidth}@{}}
\toprule
Assumption profile & Potentially recoverable object & Extra information or structure needed & Failure if treated too strongly \\
\midrule
Class-conditional closed-set noise & Clean class posterior or corrected risk & Known, estimable, or well-conditioned transition process; clean anchors or validation data & Incorrect transition estimates amplify errors \\
Instance-dependent noise & Local reliability pattern and sample-specific clean target & Repeated labels, clean subsets, structural constraints, temporal dynamics, or neighborhood assumptions & Hard clean samples are identified as noise \\
Semantic ambiguity & Uncertainty over plausible labels or class neighborhoods & Class hierarchy, expert disagreement, semantic embeddings, or calibrated soft targets & Ambiguity is collapsed into overconfident correction \\
Open-set or open-world contamination & In-distribution membership and unknown-class evidence & OOD signals, prototype distance, open-world discovery cues, or mixed-label-space metadata & Unknown samples are forced into known classes \\
Weak, partial, or LLM-generated labels & Candidate-set reliability or annotator/process reliability & Label provenance, repeated prompts, agreement signals, or process-specific uncertainty models & Generated labels become pseudo-ground truth \\
Federated or graph noise & Client-level, neighborhood-level, or propagation-level reliability & Client metadata, topology, privacy-aware aggregation signals, or graph-specific corruption models & Noise is confused with heterogeneity or relational structure \\
\botrule
\end{tabular}
\end{table}