In the design described in Connecting vector spaces through shared references, models independently describe a text’s relationships to the same references. They can compare those relationships without sharing native coordinates.
The references do practical work: they determine the directions from which the system observes an object. To understand the cost, set complex models aside for a moment and consider a plane.
Two different objects produce the same number
Take two unit vectors:
x = (0.6, 0.8)
y = (0.6, -0.8)
Their second coordinates differ, and their dot product is −0.28. Now choose only one unit reference, a = (1, 0), and represent each object’s relationship to it by cosine similarity:
relationship between x and a = 0.6
relationship between y and a = 0.6
Two different objects become the same number. No amount of sophisticated downstream processing of that number alone can recover the distinction already discarded.
Add a second reference, b = (0, 1), and the relationship representations become:
x → [0.6, 0.8]
y → [0.6, -0.8]
The difference is visible again. These calculations are exact. They demonstrate that a chosen representation can lose information, not that two real groups of people have already experienced this ranking outcome.
Repeating a reference adds no new information
If the second reference is still (1, 0), merely given another identifier, the information is identical. If new references all point in nearly the same direction, a longer representation may repeatedly describe distinctions already visible.
The relationship between reference count and useful discrimination therefore depends on complementary references, the distinctions needed by the task, and the model’s ability to express them.
Text spaces are much more complicated than this plane. A reference text is not a semantic axis precisely specified by a person, and models may interpret it differently. The two-dimensional example helps formulate experimental questions: does one reference set push two task-relevant objects too close together? Which relationships change with another set?
From mathematics to people's circumstances
Imagine a collaboration directory that consistently describes capabilities through references about sales, promotion, and growth. Someone who repairs old objects may relate to some of those terms, while distinctions such as diagnosing faults, extending useful life, and restoring use remain poorly expressed.
This is a hypothesis to investigate. It suggests several possible reasons someone is hard to find: their material is absent, their description is unclear, the representation loses a key distinction, or the ranking objective does not reward their contribution. Each cause calls for a different repair.
Adding more repairers does not necessarily fix a blind spot in the representation. Changing the references cannot replace missing material. Locating the failure in the right layer tells us whether to add information, change the representation, or adjust the task judgment.
Who decides which distinctions matter is itself a design choice. A system serving repair classes should distinguish safe disassembly, diagnosis, and teaching. Equipment procurement has different conditions. Shared references can support interoperability without being equally suitable for every task.
A substitution experiment that can inform a decision
To investigate whether reference selection affects discovery, hold requests, candidates, models, retrieval budget, and evaluation method fixed, changing only the reference set.
First inspect the representation: which previously crowded candidates become distinguishable? Then inspect ranks: do the changes reach the top ten or first hundred actually used? Finally return to the task: do the new candidates supply needed capabilities, or merely promote a different set of noise?
Alongside averages, inspect task types selected in advance as important. A set can improve aggregate performance while repeatedly harming a niche task. Conversely, special-purpose references for a few tasks add storage, computation, and versioning costs. Results should inform where shared references suffice and where a supplement is worth maintaining.
Experiments can improve these choices gradually. The set need not be perfect immediately, nor discarded wholesale after an omission is found. What matters is making omissions discoverable and version changes comparable.
Turn an omission into a testable objection
I would like shared references to have two properties: enough stability for participants to understand one another, and room for someone to say, “Describing me with this set leaves out something that matters to the task.”
That feedback needs concrete objects. An objection can include a pair of materials that should be distinguished, an affected task, and a hypothesis about which additional reference might help. That is easier to turn into a runnable test than a debate over whether one vocabulary represents everyone.
The original vector pair gives a simple starting point: show two objects the system currently cannot distinguish but the task needs it to distinguish. Whether references deserve an update can be discussed from that specific difference.