This paper introduces a novel framework for Edge Inference (EI) that bypasses the conventional practice of treating the wireless channel as noise. We utilize Stacked Intelligent Metasurfaces (SIMs) to control wireless propagation, enabling the channel itself to perform over-the-air computation. This eliminates the need for symbol estimation at the receiver, significantly reducing computational and communication overhead. Our approach models the transmitter-channel-receiver system as an end-to-end Deep Neural Network (DNN) where the response of the SIM elements are trainable parameters. To address channel variability, we incorporate a dedicated DNN module responsible for dynamically adjusting transmission power leveraging user location information. Our performance evaluations showcase that the proposed metasurfaces-integrated DNN framework with deep SIM architectures are capable of balancing classification accuracy and power consumption under diverse scenarios, offering significant energy efficiency improvements.