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Machine learning

As explained in Math and Architectures of Deep Learning

A paradigm for learning a parameterized mapping from inputs to outputs by training on data rather than by writing explicit step-by-step rules.

Machine learning replaces hand-written input-to-output rules with a mathematical model that learns a classification or quantitative estimate from data. It is best viewed as function approximation: a model stands in for an unknown transformation that maps inputs to desired outputs. section 1.1 section 1.2

A model architecture specifies the form of the approximation and exposes tunable parameters, or weights. Training uses examples with known outputs to choose weights whose predictions match those outputs as closely as possible. After training, inference applies the fully determined function to new inputs. section 1.2

The core workflow is:

  • Frame a task as a transformation from input features to a class or estimated value. section 1.1
  • Choose a parameterized model function suited to the task's physical nature and complexity. section 1.2 section 1.8
  • Optimize its weights on training inputs paired with known outputs. section 1.2
  • Deploy the learned function for inference on inputs beyond the training set. section 1.2

A two-feature cat brain

A toy decision-maker receives hardness and sharpness, combines them as a weighted sum plus a bias, and produces a threat score. A negative score leads to “approach and purr,” a near-zero score to “ignore,” and a high score to “run away.” This reduces classification to a quantitative estimate followed by a decision. section 1.1 section 1.3

input: hardness = 0.01, sharpness = 0.02 → threat = —0.90 → decision: “approach and purr”

input: hardness = 0.50, sharpness = 0.60 → threat = 0.01   → decision: “ignore”

input: hardness = 0.99, sharpness = 0.97 → threat = 0.90   → decision: “run away”

Compare three hardness-and-sharpness inputs with their threat scores and resulting decisions to see how one learned numeric output supports classification. section 1.1

Geometrically, a model transforms a point in a multidimensional input space into a point in an output space. Harder tasks require greater expressive power; nonlinearity and layered combinations of simpler machines lead to deep learning. section 1.8

How Math and Architectures of Deep Learning covers it

How deep it goes
Develops function approximation, parameterized architectures, training, inference, geometry, and expressive power, while deferring vectors and matrices.
Examples
Uses a cat brain with hardness and sharpness to produce threat scores and three behavioral decisions.
What it assumes
Introduces the overview from zero but uses vectors and matrices before formally developing them.
What you can do after
Evaluate/understand how training data determines model weights for later inference on classification or estimation tasks.
How it connects
Connects function approximation, model architecture, weights, training data, inference, nonlinearity, and deep learning.
Cover of Math and Architectures of Deep Learning
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This explainer was generated by Manning's knowledge graph from the text of Math and Architectures of Deep Learning. The section links point to the parts of the book it draws on.