梯度下降损失曲面可视化

一张机器学习模型非凸损失曲面的 3D 可视化，从左前上方俯瞰。网格曲面由冷到暖色渐变：深紫高损失山脊→钴蓝青绿鞍点→暖金亮黄绿谷底/全局最小值。曲面含一个尖锐全局最小值（中右深漏斗）、两个局部最小值（左侧浅碗）和一个鞍点。白色小球连线轨迹展示 SGD 路径：从左上高原出发，一度陷入局部最小值后逃出；珊瑚色第二条轨迹为自适应优化器路径，绕过局部最小直达全局最小。X 轴 「Parameter θ₁」，Y 轴 「Parameter θ₂」，Z 轴 "Loss ℒ(θ)"。图例标注白色 "SGD" 与珊瑚色 「Loss ℒ(θ)」。深炭黑背景，曲面悬浮感。

A dramatic 3D visualisation of a non-convex loss landscape for a machine learning model, viewed from a slightly elevated front-left perspective. The surface is a smooth parametric mesh rendered with a cool-to-warm colour gradient: deep violet for high-loss ridges, through cobalt blue and teal for saddle points, to warm gold and bright yellow-green for valleys and the global minimum. The surface shows one sharp global minimum (a deep narrow funnel) near the centre-right, two local minima (shallower bowls) in the left region, and a saddle point between two ridges. A gradient descent trajectory is shown as a series of small white spheres connected by a white path line, starting from the top-left plateau and descending via several steps — at one point it gets trapped in a local minimum for a few steps before escaping. A second trajectory in coral shows an adaptive optimiser path that avoids the local minimum and reaches the global minimum more efficiently. X-axis labelled "Parameter θ₁", Y-axis "Parameter θ₂", Z-axis "Loss ℒ(θ)". Small legend identifying the white path as "SGD" and coral path as "Adaptive Optimiser". Background: dark charcoal, giving the surface a floating appearance.