Hindsight-Guided Momentum (HGM) Optimizer: An Approach to Adaptive Learning Rate

We introduce Hindsight-Guided Momentum (HGM), a first-order optimization algorithm that adaptively scales learning rates based on the directional consistency of recent updates. Traditional adaptive methods, such as Adam or RMSprop , adapt learning dynamics using only the magnitude of gradients, often overlooking important geometric cues.Geometric cues refer to directional information, such as the alignment between current gradients and past updates, which reflects the local curvature and consistency of the optimization path. HGM addresses this by incorporating a hindsight mechanism that evaluates the cosine similarity between the current gradient and accumulated momentum. This allows it to distinguish between coherent and conflicting gradient directions, increasing the learning rate when updates align and reducing it in regions of oscillation or noise. The result is a more responsive optimizer that accelerates convergence in smooth regions of the loss surface while maintaining stability in sharper or more erratic areas. Despite this added adaptability, the method preserves the computational and memory efficiency of existing optimizers.By more intelligently responding to the structure of the optimization landscape, HGM provides a simple yet effective improvement over existing approaches, particularly in non-convex settings like that of deep neural network training.