Learning representations with a high Probability of Necessary and Sufficient Causes (PNS) has been shown to enhance deep learning models' ability. This task involves identifying causal features that are both sufficient (guaranteeing the outcome) and necessary (without which the outcome cannot occur). However, current research predominantly focuses on unimodal data, and extending PNS learning to multimodal settings presents significant challenges. The challenges arise as the conditions for PNS identifiability, Exogeneity and Monotonicity, need to be reconsidered in a multimodal context, where sufficient and necessary causal features are distributed across different modalities. To address this, we first propose conceptualizing multimodal representations as comprising modality-invariant and modality-specific components. We then analyze PNS identifiability for each component, while ensuring non-trivial PNS estimation. Finally, we formulate tractable optimization objectives that enable multimodal models to learn high-PNS representations, thereby enhancing their predictive performance. Experiments demonstrate the effectiveness of our method on both synthetic and real-world data.
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