Parameter Space and Loss Landscapes for Neural Networks
Artificial neural networks with tunable parameters—weights and biases—act as universal function approximators that can represent many different input–output relationships depending on their parameter settings.
Evolutionary Local Search as a Neural Optimizer
Simple evolutionary-inspired algorithms treat a neural network’s parameters as a genome living on a fitness landscape defined by loss: lower loss means higher fitness, so each candidate network competes to be selected for the next generation.
Why Gradient Descent Scales to Massive Neural Networks
Modern neural networks with thousands to billions of parameters rely on gradient-based optimizers—stochastic gradient descent and variants like Adam—to train on huge datasets within realistic compute budgets.
High-Dimensional Minima, Saddle Points, and the Curse of Dimensionality
Optimization algorithms navigating neural network loss landscapes confront geometric phenomena that look very different in high-dimensional spaces than in low-dimensional visualizations.
Limitations of Gradient Descent and Evolutionary Optimization
Both gradient-based and evolutionary algorithms are powerful but constrained tools for optimizing neural networks; neither fully captures the richness of biological evolution or satisfies all practical needs.