Conclusion

Deep networks need reliable routes for information and gradients.

You have seen the main shortcut patterns:

• residual addition adds F(x) to x
• projection shortcuts make shapes compatible
• skip connections bypass transformations
• concatenation preserves both paths by joining features
• gates learn how much signal to pass or keep
• identity paths give gradients shorter routes

These ideas explain why deeper architectures became easier to train. The next chapter turns to numerical precision and stability: even a good architecture can fail if the numbers overflow, underflow, or become non-finite.