Gradients can be employed for sensitivity analysis. Here, we leverage the
advantages of the Loss Landscape to comprehend which independent variables
impact the dependent variable. We seek to grasp the loss landscape by utilizing
first, second, and third derivatives through automatic differentiation. we know
that Spearman's rank correlation coefficient can detect the monotonic
relationship between two variables. However, I have found that second-order
gradients, with certain configurations and parameters, provide information that
can be visualized similarly to Spearman's results.In our approach, we
incorporate a loss function with an activation function, resulting in a
non-linear pattern. Each exploration of the loss landscape through retraining
yields new valuable information. Furthermore, the first and third derivatives
are also beneficial, as they indicate the extent to which independent variables
influence the dependent variable.

利用梯度进行敏感性分析，通过自动微分以及包含激活函数的损失函数探索损失空间中影响因变量的独立变量，利用二阶梯度可视化类似于 Spearman 相关系数结果的信息，同时一阶和三阶导数也揭示了独立变量对因变量的影响程度。

损失景观的灵敏度分析

Sensitivity Analysis On Loss Landscape

The sorting operation is one of the most commonly used building blocks in
computer programming. In machine learning, it is often used for robust
statistics. However, seen as a function, it is piecewise linear and as a result
includes many kinks where it is non-differentiable. More problematic is the
related ranking operator, often used for order statistics and ranking metrics.
It is a piecewise constant function, meaning that its derivatives are null or
undefined. While numerous works have proposed differentiable proxies to sorting
and ranking, they do not achieve the $O(n \log n)$ time complexity one would
expect from sorting and ranking operations. In this paper, we propose the first
differentiable sorting and ranking operators with $O(n \log n)$ time and $O(n)$
space complexity. Our proposal in addition enjoys exact computation and
differentiation. We achieve this feat by constructing differentiable operators
as projections onto the permutahedron, the convex hull of permutations, and
using a reduction to isotonic optimization. Empirically, we confirm that our
approach is an order of magnitude faster than existing approaches and showcase
two novel applications: differentiable Spearman's rank correlation coefficient
and least trimmed squares.

本文提出了首个具有 O (n log n) 时间和 O (n) 空间复杂度的可微分排序和排名操作，并通过在排列凸包上的投影和使用保序优化减少来实现此操作。实验证明，该方法比现有方法快一个数量级，并展示了两个新颖的应用程序：可微 Spearman 秩相关系数和最小修剪的平方。