探索损失空间：Hill-ADAM优化器 (Explore the Loss space with Hill-ADAM)

This paper introduces Hill-ADAM. Hill-ADAM is an optimizer with its focus towards escaping local minima in prescribed loss landscapes to find the global minimum. Hill-ADAM escapes minima by deterministically exploring the state space. This eliminates uncertainty from random gradient updates in stochastic algorithms while seldom converging at the first minimum that visits. In the paper we first derive an analytical approximation of the ADAM Optimizer step size at a particular model state. From there define the primary condition determining ADAM limitations in escaping local minima. The proposed optimizer algorithm Hill-ADAM alternates between error minimization and maximization. It maximizes to escape the local minimum and minimizes again afterward. This alternation provides an overall exploration throughout the loss space. This allows the deduction of the global minimum's state. Hill-ADAM was tested with 5 loss functions and 12 amber-saturated to cooler-shade image color correction instances.

翻译：本文提出Hill-ADAM优化器。该优化器专注于逃离预设损失曲面中的局部极小值以寻找全局极小值。Hill-ADAM通过确定性探索状态空间来逃离极小值点，这消除了随机算法中梯度更新的不确定性，同时避免频繁收敛于首次访问的极小值。本文首先推导了ADAM优化器在特定模型状态下的步长解析近似表达式，进而定义了决定ADAM逃离局部极小值能力局限性的核心条件。所提出的Hill-ADAM优化算法在误差最小化与最大化之间交替执行：通过最大化阶段逃离局部极小值，随后恢复最小化过程。这种交替机制实现了对损失空间的系统性探索，从而能够推断出全局极小值的状态。Hill-ADAM在5种损失函数和12个从琥珀饱和色到冷色调的图像色彩校正实例中进行了验证。