Compression Has Levels

At three in the morning Priya’s semantic subscription fires. A new paper from a database group has appeared, and the system judges that it qualifies: it may weaken the assumption her protocol’s safety result rests on. The item is relevant to her purpose, new to her, and matches a relation she asked to be told about. All of that has been settled. What has not is how much of it she should see first.

A single fixed summary length cannot be right for this. A replication confirming a result she already trusts needs one line. A possible contradiction of her design needs evidence, scope and a way to reach the source before she acts. The same machinery found both. They should not arrive at the same resolution. This chapter asks:

Once an item deserves attention, how much of it should reach the person first, and where must compression stop?

The two halves of that question belong together. How much to show and how much damage showing less does are the same problem seen from two sides.

A ladder of resolutions

The answer is not one summary but a ladder of them, with the full source at the bottom:

GLANCE
   ↓
BRIEF
   ↓
SUMMARY
   ↓
DETAIL
   ↓
SOURCE

These are resolutions, not word counts. What defines each is what the reader can do with it:

GLANCE    can I decide whether to look further?
BRIEF     can I understand the main change?
SUMMARY   can I act on the main result and its key qualification?
DETAIL    can I reason about the evidence?
SOURCE    can I inspect the original material?

compression level  ≠  character count

A glance might be one sentence for one item, and for another a warning mark plus a single qualification. Length is a poor proxy anyway: asking a language model for “about a hundred words” does not reliably get you a given resolution. The better question about any level is: what is the least representation that still lets this level do its job?

One item, five ways

Suppose the paper in question says the following. It presents a commit protocol that stays safe under arbitrary network delays, with no delay bound assumed, using a mechanism different from the one Priya’s design relies on. Liveness still needs delays to stabilise eventually. The results are for crash faults only, tested on clusters of five and eleven nodes. One lemma’s proof is given only as a sketch. Here is that item at each level.

GLANCE
New evidence may weaken your protocol's bounded-delay assumption.

BRIEF
A new paper claims safety without any delay bound, using a different
mechanism. It affects the safety assumption, not the liveness one.
Standing: preprint, not yet reviewed.

SUMMARY
The paper presents a commit protocol that stays safe under arbitrary
delays; liveness still requires delays to stabilise eventually. Results
cover crash faults only and were tested on five- and eleven-node
clusters. One lemma is proved only in outline. If it holds, your
safety result need not depend on bounded delay, but your liveness
argument still would.

DETAIL
The protocol, the assumptions it states and the ones it leaves implicit,
the proof structure with the incomplete lemma marked, the evaluation
setup and its limits, how the claimed mechanism differs from yours,
and links to each passage.

SOURCE
The paper.

Reading down the page, information visibly disappears. After each reduction one can ask what went, and whether it was safe to lose at this level. That is the preservation audit of Part I applied vertically.

What each level owes

Each rung has obligations, and they accumulate as you go down. At glance level Priya needs very little, but that little must be right:

GLANCE must preserve:
- that the evidence is new
- that the relation is a possible weakening, not an established refutation
- which assumption is affected

A glance that said “your assumption is wrong” would have turned a candidate into a verdict. One that said “a new paper on consensus” would have carried none of the three. A brief adds what was found, why it bears on the assumption, and the evidence’s standing. A summary adds method, qualifications and competing readings. Detail adds the structure of the evidence. Source is the original.

The property that follows is a design expectation, not a theorem:

higher resolution should refine, not reverse, lower resolution

Moving down the ladder should only add. If the summary contradicted the glance, or the detail the brief, something upstream was invented. This is also why the levels should be derived from one stable set of units, by omission, and not regenerated independently from the source at each level. Three fresh generations can quietly disagree: different qualifiers kept, different numbers rounded, different emphasis. Rewriting each level from the one above invites drift for the same reason a game of telephone does.

Omit, add, distort

Compression necessarily throws things away. The question is what may safely go, and the three possible outcomes should be kept apart:

OMISSION     is expected under compression
ADDITION     requires independent support
DISTORTION   is never licensed by brevity

Leaving something out at a given level is normal. Adding something the source did not say, because it makes the short version read better, is not, and needs support of its own. And making a retained statement stronger, weaker or differently scoped than the source made it is never excused by the need to be short. A glance may omit the sample sizes. It may not say “safe” where the paper says “safe under crash faults”.

A loss at a given level can then be sorted into three kinds. Acceptable loss is detail the level never promised to carry. Unmet obligation is something it promised and does not contain, such as a glance with no indication of which assumption is affected. Hard violation is something retained that is now misleading, such as the crash-faults restriction dropped from a sentence that still claims safety. The first can be tolerated. The second and third are failures.

Where compression must stop

This is the centre of the chapter. Compression is not governed by a target length or a compression ratio. It is governed by what has to survive:

compress while the obligations survive
stop when the next omission would break one

An omission is not safe if it would remove something needed for correct reconstruction, for the task, for fidelity to the source, for the uncertainty that attaches to a claim, for the scope within which it holds, or for acting on it safely. That is a much stronger rule than “five bullets” or “fifty words”. It says the right level is the lowest one whose obligations still hold, and that it varies by item and by task.

Sometimes the stop rule fires immediately. There are items where the qualification is the content, where there is no safe glance, no safe brief, and the right thing to show is the source or a very light annotation of it. A system that goes straight from the glance rung to the source for such an item has not failed to compress it. It has recognised that compression would have destroyed what it was for, and that counts as a success.

The costs of the two directions are not equal either. Keeping too much costs attention. Cutting too much costs decisions, and the reader cannot tell. So when the evidence that a shorter version is safe is thin, the level rises.

Every level is an entrance to the one below

Compression must never become replacement. A compressed form that displaces the evidence it came from leaves the reader at a dead end, able to read a conclusion but not to check it.

compression  ≠  replacement

Each level should make expansion cheap, and expansion should reveal more of the same thing, not a fresh retrieval that might return something different:

glance → brief → summary → detail → source

A useful mechanism is for each level to know what it left out. A brief that carries a list of the units it omitted can restore them on request, so that “tell me more” returns the same account at higher resolution instead of a new one. Every level is an entrance to the level beneath it. This is the traceability discipline of Part I made into a way of moving.

More detail is not better

It would be easy to read the ladder as a ranking, with the source at the top as the best representation. That is wrong.

more information  ≠  better representation

For the job of deciding whether an item deserves five minutes, the full source can be worse than a glance: slower, more to wade through, and harder to compare with the other nine items waiting. For the job of judging whether the paper’s proof is sound, the glance is useless. The right level depends on the job. A related point applies to learning. The level that lets someone give a correct immediate answer may be the wrong one for someone trying to understand the material and retain it, because the effort of reconstructing what a short version leaves out is partly what builds understanding. Resolution suited to a decision is not thereby suited to learning.

Resolution is a decision the channel makes

Taken together, this makes the first resolution another decision the channel has to take, and it depends on several things. On the task: scanning for what matters, or deciding whether to act. On prior knowledge: how much Priya needs spelled out. On the time available and the cost of interrupting her. And on the consequence of error: an incorrect glance about a replication is cheap, and one about the safety of a design is not. None of this needs a detailed model of her state. It needs the recognition that the correct resolution is not a constant, and that choosing it is part of communicating.

Where this leaves us

A qualifying item can reach a person at five resolutions, defined by what each lets her do. Each level carries obligations that accumulate downward, higher levels refine and never reverse lower ones, and omission is expected while addition needs support and distortion is never licensed. Compression stops when the next omission would break something that has to survive, which can mean going straight from glance to source. Every level stays an entrance to the next, and more detail is not automatically better.

Now suppose ten things qualify overnight. Each can be rendered at exactly the right level, with its obligations intact. The person can still only look at three.

relevance
    ↓
qualification
    ↓
resolution
    ↓
still too many candidates

Choosing the level for each item does not choose among the items. For that, something has to decide which of them reaches her now, which can wait, and which should sit quietly in a list she will open later.