2D Feature Space & Decision Heatmap
x₁ ∈ [-1, 1], x₂ ∈ [-1, 1]
Model Architecture & Training
Hidden Units: 6
Learning Rate (η): 0.080
Training Loss History
0.693
Interactive Query Probe
Input (x₁, x₂):
(0.00, 0.00)
Raw Logit (z):
+0.00
P(Class A):
50.0%
Predicted:
Tie / Ambiguous
1. Non-linear XOR Problem
Minsky & Papert 1969
A single linear hyperplane cannot separate diagonals (XOR). A 2-layer MLP transforms the feature space into curved non-linear decision regions.
2. Linear Separators
Perceptron & Logistic
Computes \( \hat{y} = \sigma(w_1 x_1 + w_2 x_2 + b) \). Perfect for clean linearly separable data, but fails on complex manifold topologies.
3. Non-Parametric Boundaries
k-NN & Decision Trees
k-NN creates Voronoi-like local decision pockets without weights. Decision trees create orthogonal axis-aligned partition boxes.
4. Learning Rate & Dynamics
Gradient Descent
Too small \(\eta\) leads to glacial convergence; too high \(\eta\) oscillates wildly across loss ravines. Observe how loss trajectories morph.