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To overcome high dependency in a network, it's essential to apply techniques such as regularization, which helps reduce overfitting by penalizing overly complex models. Additionally, using dropout layers can help by randomly deactivating neurons during training, promoting independence among them. Another approach is to implement ensemble methods that combine multiple models to improve robustness and reduce reliance on any single model's predictions. Lastly, careful feature selection and engineering can mitigate dependency by ensuring that input variables are diverse and provide unique information.

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