Directional Consistency as a Complementary Optimization Signal: The GONO Framework

Problem
This paper addresses a gap in the understanding of optimization dynamics in deep learning, specifically the decoupling of directional alignment and loss convergence during training. The authors identify that existing optimizers, such as Adam, SGD, and RMSprop, do not leverage temporal consistency in gradient directions, which can lead to suboptimal convergence behavior. This work is presented as a preprint and has not yet undergone peer review.

Method
The core technical contribution is the introduction of the Gradient-Oriented Norm-Adaptive Optimizer (GONO). GONO modifies the momentum coefficient (beta_1) of the Adam optimizer based on a newly defined metric, cc_t (consecutive gradient cosine similarity). The optimizer amplifies momentum when cc_t indicates high directional consistency and suppresses it during oscillations. The authors provide a theoretical proof that GONO maintains the same O(1/sqrt(T)) convergence rate as Adam, reverting to Adam’s behavior when the directional signal is uninformative. The implementation details, including the adaptation mechanism for beta_1, are crucial for practitioners looking to enhance optimization performance.

Results
Empirical evaluations demonstrate that GONO achieves an F1 score of 1.00 for oscillation detection, significantly outperforming the gradient norm method, which scores only 0.45. On standard benchmarks, GONO shows competitive performance against AdamW: achieving 98.15% accuracy on MNIST, 43.14% on CIFAR-10, and 75.44% on ResNet-18. These results indicate that GONO not only improves directional consistency but also maintains or enhances convergence rates compared to established optimizers.

Limitations
The authors acknowledge that while GONO shows promise, it may not universally outperform all optimizers across all tasks, particularly in scenarios where directional consistency is less informative. Additionally, the reliance on cc_t as a signal may introduce overhead in computation, which could be a concern in resource-constrained environments. The paper does not explore the performance of GONO on larger datasets or more complex architectures, which could limit the generalizability of the findings.

Why it matters
This work has significant implications for the optimization landscape in deep learning. By formalizing the role of directional consistency as a critical optimization signal, it opens avenues for further research into adaptive optimization strategies that can better navigate the complexities of loss landscapes. The GONO framework encourages the exploration of new metrics for optimizer design, potentially leading to more robust training methodologies that can handle the intricacies of modern neural networks.

Authors: Victor Daniel Gera
Source: arXiv cs.AI
URL: https://arxiv.org/abs/2605.06575v1
arXiv ID: 2605.06575