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Recommendations for Ensuring Injective and Surjective Mappings in Deep Learning for Sequence-to-Sequence Tasks

I’m working on a deep learning problem where the goal is to establish an injective and surjective mapping between elements of an input sequence and elements of an output sequence.
The input sequence consists of feature representations of jigsaw puzzle pieces (extracted by EfficientNetV2L-S, and the output elements are tuples of row, column, and rotation indices in their respective coordinate systems: