In navigating the challenges of computational and communication overhead within the 6G-era Collaborative Inference (CI), this paper explores the feasibility of employing Stacked Intelligent Metasurface (SIM) to perform CI, termed SIM-CI. The SIM functions as a physical computing unit, receiving multi-user Over-The-Air (OTA) aggregated features within the same spectrum. It thus executes the necessary spatial-frequency combining and inference in a single physical wave propagation.SIM-CI also incorporates a tri-heterogeneity robustness adapter to address the network heterogeneity, such as multi-modal data and user inference models, as well as a quality-aware contrastive approach that align features from different modalities and extraction levels into a unified feature space. Considering the heterogeneous and dynamic channels, we further integrate Channel State Information (CSI) as an additional input into the adapter design, enabling users' early perception of potential channel states. Moreover, to maximally mitigate the impact of channel variations, we design a new hybrid beamforming network that combines the robustness of model-driven pre-equalization with the adaptability of data-driven learning. Experimental results demonstrate the effectiveness of our SIM-CI compared to digital-domain inference, achieving 98.6\% accuracy to conversional digital-domain CI approaches under various heterogeneous conditions, while reducing computational energy by 25\% and requiring 75\% fewer transmission time slots.

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