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Creating soft robots with sophisticated, autonomous capabilities requires these systems to possess reliable, on-line proprioception of 3D configuration through integrated soft sensors. We present a framework for predicting a soft robot’s 3D configuration via deep learning using feedback from a soft, proprioceptive sensor skin. Our framework introduces a kirigami-enabled strategy for rapidly sensorizing soft robots using off-the-shelf materials, a general kinematic description for soft robot geometry, and an investigation of neural network designs for predicting soft robot configuration. Even with hysteretic, non-monotonic feedback from the piezoresistive sensors, recurrent neural networks show potential for predicting our new kinematic parameters and, thus, the robot’s configuration. One trained neural network closely predicts steady-state configuration during operation, though complete dynamic behavior is not fully captured. We validate our methods on a trunk-like arm with 12 discrete actuators and 12 proprioceptive sensors. As an essential advance in soft robotic perception, we anticipate our framework will open new avenues towards closed loop control in soft robotics.