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Concept Bottleneck Models (CBMs) propose toenhance the trustworthiness of AI systems byconstraining their decisions on a set of humanunderstandable concepts. However, CBMs typically rely on datasets with assumedly accurateconcept labels—an assumption often violated inpractice which we show can significantly degradeperformance. To address this, we introduce theConcept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigatesthe negative impact of concept mislabeling onCBM performance. We provide an analysis onsome key properties of the CPO objective showing it directly optimizes for the concept’s posteriordistribution, and contrast it against Binary CrossEntropy (BCE) where we show CPO is inherentlyless sensitive to concept noise. We empiricallyconfirm our analysis finding that CPO consistentlyoutperforms BCE in three real-world datasets withand without added label noise