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While these methods are very effective at reducing memory, computation, and energy consumption, they may introduce severe accuracy degradation, which is often mitigated by using iterative, gradual compression. However, different compression techniques require distinct iterative approaches, and some result in unstable, discontinuous model fine-tuning. We introduce Vanishing Contributions (VCON), a unified framework for the smooth, iterative transition of DNNs into a compressed form. Rather than replacing the original network directly with its compressed version, VCON executes both in parallel during fine-tuning. The contribution of the original (uncompressed) model is progressively reduced, while that of the compressed model is gradually increased. 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Rather than replacing the original network directly with its compressed version, VCON executes both in parallel during fine-tuning. The contribution of the original (uncompressed) model is progressively reduced, while that of the compressed model is gradually increased. 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