31 · Linear algebra and tensor shapes
Build intuition for matrix shapes, feature units, and silent broadcasting mistakes.
4 LESSONS · ONE CONNECTED PATH
Foundations
Build a shared language of tensors, gradients, optimization and trustworthy evaluation.
Before you begin: Basic Python and arrays; no dataset download is required to read.
THE LEARNING PATH
Build one idea on the last.
01
Foundations · tensors to evaluation
Tensors and linear algebra → computation graphs and gradients → optimization and generalization → scores, probabilities and ranking metrics. Small constructed experiments before a domain track.
32 · Computation graphs, the chain rule, and gradients
Verify the chain rule, finite differences, gradient accumulation, and step-size effects.
33 · Optimization, capacity, and generalization
Separate optimization success from model capacity and independent generalization.
34 · Scores, probabilities, ranking, and evaluation boundaries
Distinguish ranking scores, calibrated probabilities, candidate pools, and metric units.
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TRACE THE IDEAS
Sources & lecture notes
Follow the original material alongside the Lab. Source scope, original language and the boundaries of each teaching unit are explicit.
Lab · Experiment and Evidence Guide
Original prerequisites: tensors, gradients, optimization and evaluation. Not an official translation or certification by an external course.
Chapter-to-source map 4 units
C01
Tensors and linear algebra
Inspect shapes, dot products and broadcasting; explain similarity and batch dimensions.
- Lab · Experiment and Evidence Guide Predict → change one variable → run → explain
Boundary: A prerequisite mechanism exercise, not evidence from business data or online outcomes.
C02
Computation graphs and gradients
Calculate local derivatives and compare autograd with finite differences.
- Lab · Experiment and Evidence Guide Predict → change one variable → run → explain
Boundary: A prerequisite mechanism exercise, not evidence from business data or online outcomes.
C03
Optimization and generalization
Fit polynomial coefficients on training points only; compare learning rate, model capacity and generalization.
- Lab · Experiment and Evidence Guide Predict → change one variable → run → explain
Boundary: A prerequisite mechanism exercise, not evidence from business data or online outcomes.
C04
Scores, probabilities and evaluation
Distinguish scores, probabilities, ranking and calibration; calculate small-example metrics.
- Lab · Experiment and Evidence Guide Predict → change one variable → run → explain
Boundary: A prerequisite mechanism exercise, not evidence from business data or online outcomes.