Merge pull request #9 from AidinHamedi/main

sync

Author: AidinHamedi

docs/_includes/mathjax.html

@@ -0,0 +1,19 @@
+<script>
+    MathJax = {
+        tex: {
+            inlineMath: [
+                ["$", "$"],
+                ["\\(", "\\)"],
+            ],
+            displayMath: [
+                ["$$", "$$"],
+                ["\\[", "\\]"],
+            ],
+        },
+    };
+</script>
+
+<script
+    src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
+    defer
+></script>

docs/functions/gradient_labyrinth.md

@@ -25,3 +25,5 @@ The function is composed of four distinct layers:
 *   **Ill-Conditioning:** The ratio between the steepness of the walls and the slope of the floor is massive.
 *   **Parameter Coupling:** Due to rotation, movement in $x$ requires a precise compensatory movement in $y$ to stay in the valley.
 *   **Local Traps:** The floor is not smooth; optimizers must have enough energy (momentum) to hop over ridges but enough damping to stop at the global minimum.
+
+{% include mathjax.html %}

docs/functions/neural_canyon.md

@@ -23,3 +23,5 @@ The function combines three terms:
 *   **Manifold Navigation:** The optimizer must follow the curved $\tanh$ path.
 *   **Vanishing Gradients:** Far from the center, the $\tanh$ curve is flat, providing very little gradient information about direction.
 *   **Noise Tolerance:** The landscape is "rough." Algorithms without adaptive learning rates or momentum may settle in local minima surrounding the global solution.
+
+{% include mathjax.html %}

docs/functions/quantum_well.md

@@ -23,3 +23,5 @@ The function creates a "Cluster" of minima:
 *   **Deceptive Gradient:** At the start (far from center), the gradient looks like a simple convex problem.
 *   **Precision Docking:** As the optimizer nears $(0,0)$, it enters a field of deep local minima. It must find the specific hole at the origin, which is surrounded by nearly identical (but suboptimal) neighbors.
 *   **Barrier Crossing:** Escaping a local minimum near the center requires climbing high barriers relative to the local gradient.
+
+{% include mathjax.html %}