Artificial Intelligence: Search, Reasoning & Learning
Core concepts, formulas and conditions at a glance.
See the learning route first
Follow the arrows. Choose a stage to open its first lesson. The full framework lists every topic.
- 01
Search and strategic decisions
Define a state, compare exploration rules, then reason about competing or random moves.
6 topics ↗ - 02
Learning from labeled examples
Start with understandable predictors and learn how to measure their performance honestly.
7 topics ↗ - 03
Neural representations and model families
Build from one weighted decision to trainable networks, margins and combinations of models.
7 topics ↗ - 04
Uncertainty and unsupervised structure
Keep probability accounting explicit, then explore structure when labels are absent.
4 topics ↗
01 / Match the frontier to the objective
BFS minimizes depth; UCS minimizes accumulated nonnegative path cost. Equal positive step costs align them. Test a UCS goal when removed from the priority queue, and account for duplicate states.
02 / A* needs a justified heuristic
Use f=g+h. Admissibility is a lower bound; consistency also constrains every edge. Graph search with inconsistent estimates may need reopening. Beam truncation sacrifices ordinary A* guarantees.
03 / Optimization is budgeted exploration
Hill climbing can stop locally. Annealing accepts a worsening cost Δ with exp(−Δ/T). Genetic search needs valid encodings and diversity. A finite stochastic run is evidence of a found solution, not global optimality.
04 / Game backups
MAX takes maxima, MIN minima, chance nodes probability-weighted means. Alpha–beta prunes when alpha reaches beta for the same minimax tree. Heuristic cutoffs replace exact terminal guarantees with approximations.
05 / Prevent leakage
Fit preprocessing and model choices inside training and validation data. Keep the final test untouched. Use groups or time order when independent random splitting would misrepresent deployment.
06 / Evaluate the relevant errors
Precision=TP/(TP+FP), recall=TP/(TP+FN), F1=2TP/(2TP+FP+FN). Name the positive class, handle empty denominators and weight errors when their consequences differ.
07 / Tree splits and pruning
Information gain is parent entropy minus size-weighted child entropy. Unique identifiers can look excellent in training. Validate numeric thresholds, depth and pruning; gain ratio is a mitigation, not a guarantee.
08 / Backpropagation bookkeeping
Save a forward pass, compute all gradients with those parameter values, then update. For sigmoid squared loss, output delta=(a−t)a(1−a). Hidden deltas sum weighted downstream sensitivities.
09 / Regularize deliberately
Learning rate affects stability; zero gradient need not indicate a minimum. Choose early stopping on validation. Inverted dropout scales retained training activations by 1/q and uses no dropout at inference.
10 / Margins and committees
Soft SVM balances norm against C-weighted slack; kernels must be valid inner products. Bagging reduces variance through resampling; boosting adapts emphasis; correlated errors limit the benefit of voting.
11 / Probability bookkeeping
Joint probabilities multiply local Bayesian-network factors. Sum hidden variables before normalizing. Conditioning differs from causation, and absence of a direct edge does not imply unconditional independence.
12 / Clustering choices change the answer
K-means pairs arithmetic means with squared Euclidean error. Single linkage can chain; complete linkage tests the farthest cross pair. Internal quality scores and cluster counts need interpretation and stability checks.