Feature	RMSProp	Momentum
Core Idea	Adjusts learning rate based on the recent magnitudes of gradients.	Accelerates convergence by considering the direction of previous gradients.
Learning Rate	Adapts learning rates individually for each parameter.	Uses a constant learning rate, adjusted by the momentum term.
Gradient Accumulation	Uses a moving average of the squared gradients to normalize the gradient.	Accumulates gradient direction and magnitude, simulating momentum.
Purpose	Prevents learning rate from diminishing too quickly.	Helps to overcome local minima and oscillations.
Adaptivity	Highly adaptive to the problem’s topology.	Less adaptive, relies on the inertia of past gradients.

Conclusion

RMSProp and Momentum address the challenge of optimizing the learning process in different yet complementary ways. RMSProp focuses on adapting the learning rate for each parameter based on the recent history of gradients, making it effective in dealing with the issue of vanishing or exploding gradients. On the other hand, Momentum helps to accelerate the convergence by leveraging the direction and velocity of previous gradients, thus improving the optimization trajectory towards the minimum. Both methods offer significant improvements over traditional gradient descent, with RMSProp providing a more nuanced approach to learning rate adjustment, and Momentum adding a dynamic aspect to the convergence process by incorporating the notion of ‘momentum’.