Loss Surface Topology Mapping in Deep Neural Network Optimization

Abstract

Deep neural network training is fundamentally shaped by the topology of the loss surface, where saddle
points and flat plateaus are far more common than sharp local minima. These saddle-dominated regions
slow or stall optimization by reducing gradient magnitude and coherence, forcing the optimizer to rely
on stochastic variation or auxiliary mechanisms to regain directional progress. This study examines loss
surface curvature behavior across multiple neural architectures and training algorithms, integrating
curvature approximation, gradient norm analysis, and optimization trajectory mapping. The results
show that momentum-based methods improve escape behavior from saddle zones but may overshoot
stable regions, while adaptive optimizers converge quickly yet gravitate toward sharper minima that
reduce generalization robustness. Visualization of parameter trajectories further confirms that
convergence quality is governed not only by loss magnitude but by the geometric structure of the basin
in which the solution lies. These findings highlight the need for training strategies explicitly informed
by loss landscape geometry to ensure stable convergence and improved model reliability.