Nice clear walkthrough. A small worked example that helps MSE vs MAE click: take errors of 1, 1, 1 and 10 (in lakh). MAE = (1+1+1+10)/4 = 3.25, while MSE = (1+1+1+100)/4 = 25.75. The one big miss dominates MSE, which is why it punishes outliers hard and why MAE is more robust when your data has a few odd prices. A practical middle ground is Huber loss: it behaves like MSE for small errors and like MAE for large ones. And for cross-entropy, a fun check: a confident wrong answer (p=0.01 for the true class) costs about 4.6, versus about 0.69 for an unsure p=0.5.