I can’t claim that I am an expert in machine learning. I’d rather say that I am merely a tourist in this area. Anyway, here is a small piece of thought on how (supervised) machine learning imitates human learning.

What are some features of human learning? Ideally, humans aim to understand a subject. To achieve this, they study examples, try to make their own deductions, do experiments, make predictions and test them. The overall goal is to get to the heart of things.

What are features of so called supervised machine learning: The methods get training data, i.e. pairs in input and output that match. The foremost goal of the method is to perform good on test data, i.e. to produce correct output to an input the method hasn’t seen before. In practice, one sets up a fairly general model (such as a neural network or a kernelized support vector machine) and often does as little modeling of the task at hand as possible.

This does not sound as though supervised machine learning and human learning are the same or even related. Their goals and methods are genuinely different.

But let us look at how human learn for a very specific task: Preparing for an exam. Recently I had to prepare several larger exams in mathematics for engineers, each with hundred plus students and got to think how they approach the task of learning. When the exam comes closer, the interactions with the students get more frequent. I had a large “ask anything” meeting, I had students coming to office hours, and I had “digital office hours” where the students could ask question via a messenger in a chat room. So I had quite some interactions and could get a little insight into their way of learning, into their problems and progress.

Here are some observations of how the students tried to learn: The question I got were mostly about the exercises we had handed out (in other words, the students asked for information on the “training data”). They were studying heavy on these exercises, barely using the textbook or their lecture notes to look up theorems or definitions (in other words, some were working “model free” or with a “general purpose model” which says something like “do computations following general rules”). They work with the underlying assumption that the exam is made up of questions similar to the exercises (and actually, this is a reasonable assumption – I announced this in class) (in other words, the test data comes from the same distribution as the training data).

Viewed like this, learning of humans (for an exam, that is) and machine learning sound much more similar. And the similarities do not end here. Also some known problems with machine learning methods can be observed with the students: Students get stuck in local minima (they reach a point where further improvement in impossible by revising the seen data – even though they could, in principle, learn more from the given exercises, they keep going the known paths, practicing the known computations, not learning new techniques). Students overfit to the training data (on the test data, aka the exam, they face new problems and oftentimes apply the learned methods to tasks where they don’t work, getting wrong results which would be true if the problem would be a little different). The trained students are vulnerable to adversarial attacks (for every problem I posed as exercises I could make a slight change that would confuse most students). Also, similar to recent observations in machine learning, overparametrization helps to avoid overfitting and overparametrization helps to avoid spurious local valleys, i.e. when the students have more techniques at hand, which is related to a more flexible machine learning method, they do better on unseen data and do not get stuck at bad local minima where no improvement is possible.

Granted, some observation are a kind of a stretch, but still, in conclusion, I’d advocate to replace the term “machine learning” with machine cramming (the German version would be maschinelles Büffeln or maschinelles Pauken).

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