Representation

What it is

A computer cannot read a protein, a telescope image or a lump of alloy. It can only read numbers. Representation is the choice of which numbers to use. A material might become a short list of values worked out from the proportions of each element it contains. A protein might become a list of its building blocks, plus a table saying which parts sit close to which. A faint signal recorded over time might become a picture, with time along one axis and pitch, or frequency, along the other.

Some representations are hand-built: a researcher decides which measurable quantities matter and writes them down as a list, often called features or descriptors. Others are graphs, where things are drawn as points joined by links, which suits anything whose structure is about what touches what. Others still are learned by the program itself, which compresses each item into a string of numbers, called an embedding, that places similar items near each other. The same underlying object can be represented in many ways, and the choice changes what the program can notice.

Why scientists use it

Representation is where human understanding of a subject enters the computation. If the numbers you supply already reflect what matters, a fairly simple method can do well; if they leave it out, no amount of clever fitting will recover it. So representation often stands in for theory. Choosing to describe an alloy by the average properties of its ingredients is a statement about why alloys behave as they do.

It also makes problems tractable. A good representation shrinks the search, groups things that behave alike, and lets a program apply what it learned about one item to another it has never seen. It can impose known rules for free: a graph of a molecule treats it the same however you rotate it, and a representation can be built so that symmetry or repeated parts are respected automatically, rather than learned painfully from examples.

In the record

Limits

A representation decides what the program can possibly see. Anything it discards is invisible, and no later step recovers it, so a model can look confident while blind to the thing that actually matters. Hand-built features carry the assumptions, and sometimes the mistakes, of whoever chose them. Learned embeddings hide those assumptions instead of removing them, and are hard to interpret. Two items that look alike in one representation may behave quite differently in reality, and comparisons between methods often turn out to be comparisons between representations.

Written by AIxSci: the background from general knowledge, the examples from checked records.

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