If we have a set of things (e.g. language models) and some measures we care about (e.g. cost, speed, whether weights are open, scores for a few benchmarks, etc.), then some of those things will be "pareto optimal" (see below) and some won't. The "pareto front" is the subset that is pareto optimal.

Some thing is "pareto optimal" when there isn't another thing that's AT LEAST AS GOOD in ALL measures, and BETTER in at least one way. For example, if we say there are no ties (for simplicity), then the cheapest language model is pareto optimal; the fastest model is pareto optimal; those which score highest on each benchmark are pareto optimal; and so on.

Tradeoffs can also be pareto optimal: for example, if the cheapest model is also slow, then there will be more pareto optimal models which are "cheapest for their speed"; and so on for other tradeoffs (e.g. fastest that achieves a certain benchmark score; cheapest model with open weights; etc.).

If you're making a decision about which thing to choose, you only need to care about those in the pareto front (since, by definition, anything that's not pareto optimal is objectively worse on at least one measure).

Pareto optimality does not compare one measure against another: something that's 10000x slower can still be pareto optimal, if it's 1% cheaper than the alternatives. To pick a "best" thing, you could give a weight/importance to each measure, and combine them into an overall score: but that's subjective, and might vary between people and tasks. In contrast, focusing on the pareto front is a way to ignore those things that will never be the best, regardless of weighting.

If you optimize one criterion, it's simple: lowest is best or highest is best. If you optimize multiple criteria, all optimal trade offs between any of the selected criteria are "best" in some way.

When you have a tradeoff between two parameters, which points dominate the others in the sense that you can't choose another point without getting less of one of the parameters.

"what's the family of optimal choices when you have multiple dimensions to rank on?"

Say a race vehicle has acceleration, top speed as defining parameters. Some are slow but accelerate hard, others need a long time to reach very high top speeds. Others are in between, or just flat out bad at both.

The pareto frontier is the set of vehicles that are best: pick one from the frontier and you can be sure that for it's given top speed, none accelerate faster. And vice versa, pick one with a given acceletation and you are sure none have a better top speed

Basically, prioritization.

It’s really that simple.

Eschew obfuscation.