What is the purpose of decreased FLOPs and parameter size if they are not for increased speed?

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CNN algorithms like DenseNet DenseNet stress parameter efficiency, which usually results in less FLOPs. However, what I am struggling to understand is why this is important. For DenseNet, in particular, it has low inference speed. Isn't the purpose of decreased parameter size/FLOPs to decrease the time for inference? Is there another real world reason, such as perhaps less energy used, for these optimizations?

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There is a difference between overall inference time vs. per parameter/FLOPs training efficiency. Having lower parameter/FLOPs in training does not guarantee higher speed in inference. Because overall inference depends on the architecture and how predictions are computed.