CMSC 191: Introduction to Neural Computing
Learning Dynamics and Optimization
In this topic we’ll explore the dynamic process of how neural networks learn—not just through equations, but through the delicate balance between speed and stability. You’ll begin by understanding the learning rate, which acts as the throttle on the gradient descent engine, controlling how quickly the network makes progress toward its goal. You’ll see how choosing the right learning rate is crucial—too large, and the network can overshoot; too small, and it can get stuck or take too long to learn.
From there, we’ll introduce stochastic and mini-batch gradient descent, which bring in randomness and batching to help speed up learning while making the process more stable. These methods help neural networks navigate the high-dimensional landscapes of complex data more efficiently and with greater resilience.
By the end of this topic, you’ll understand how tuning these key parameters can transform abstract theory into practical success, allowing networks to learn quickly and effectively, even in vast, complex environments.
Explain the role of the learning rate in controlling the pace and stability of convergence.
Identify the failure modes of divergence and slow convergence in gradient-based optimization.
Distinguish between batch, stochastic, and mini-batch gradient descent methods.
Analyze how stochastic updates introduce beneficial randomness to escape local minima.
Evaluate how mini-batching improves both computational efficiency and training stability.
Why is the learning rate considered both the most powerful and the most dangerous hyperparameter in training?
How does stochasticity help a network “jiggle” free from shallow local minima?
What makes mini-batch gradient descent the practical “Goldilocks” choice for modern neural computing?
Learning Dynamics and Optimization* (topic handout)
The Art of Moving Downhill
Learning Rate and Convergence
Stepping Stones: The Power of the Learning Rate
Finding the Sweet Spot: Tuning for Stability
Stochastic and Mini-Batch Gradient Descent
The Random Walk: Embracing Stochasticity
The Goldilocks Zone: Why Mini-Batching Works
Balancing Chaos and Control
The semester at a glance:
Learning Dynamics . . .