One of the most simply classification algorithm one can think of: just see whatever kind of point your new point seems to be closer to, and say it is also of that type! Then it is just a question of defining "close".

Scikit-learn implementation scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html at python/sklearn/knn.py

Training, validation, and test data sets

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stats.stackexchange.com/questions/19048/what-is-the-difference-between-test-set-and-validation-set

Training data set

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Validation data set

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Test data set

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Training and inference

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This is the first thing you have to know about supervised learning:

training is when you learn model parameters from input. This literally means learning the best value we can for a bunch of number input numbers of the model. This can easily be on the hundreds of thousands.
inference is when we take a trained model (i.e. with the parameters determined), and apply it to new inputs

Both of those already have hardware acceleration available as of the 2010s.