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If you have an $18$ layer residual network versus and a $32$ layer residual network, why would the former do better at object detection than the latter, if you have both models are training using the same training data?

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Just by having more parameters, the deeper model has a higher capacity than the smaller one. This means that theoretically it can learn to extract more complex features from the data. Additionally, more layers means that the model can extract even higher-level features from the data. So, generally speaking, deeper models will most of the times outperform shallow ones for more difficult tasks.

The downside is that if you have a small amount of data, a high-capacity model has the ability of memorizing the training set, which would lead to overfitting. Besides performance, deeper models require better hardware and larger training times. So, there are plenty of reasons for one to prefer a more shallow model to a deeper one.

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