Powered by OpenAIRE graph
Found an issue? Give us feedback
ZENODOarrow_drop_down
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
addClaim

Why the Third Axis Is Weakness

Authors: Bennett, Michael Timothy;

Why the Third Axis Is Weakness

Abstract

In generative training, models produce an output and penalise its difference from an observed example. With one output per comparison, models capable of producing only one valid image incur the same average penalty as models that have learned the whole distribution. Training objectives cannot discriminate between. Explorative Modeling (XM) produces $K$ outputs per comparison, penalising the closest. They claim exploration is a third pretraining axis. But is it? What does it scale? Here I show the third axis is weakness. Weakness counts how much a model could still narrow what it outputs. How loose your constraints are. Freedom of function, not form. Earlier work proved weakest correct models are likeliest to generalise, beating measures of form like flatness and MDL. I prove the average XM penalty depends on the model only through the chance a single output misses by more than an amount, and exploration raises that chance to the power $K$. For $K>1$, among models producing only correct answers, match probability rises strictly with weakness. For unseen prompts, requirements chosen uniformly at random, the chance of meeting every demand is proportional to weakness. So I ran two experiments. Over 456 runs, raising $K$ increased measured weakness in every primary paired comparison. Hence XM is a means of increasing weakness. I then modified XM, using weakness as a selector vs baseline comparison. Applied to the same candidate pools, weakness raised best-of-eight hit from $0.4131$ to $0.4203$, winning in 19 of 20 worlds over baseline XM, tying the last. Weakness makes XM better. Exploration is a means, weakness the end. The third axis. Always has been.

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!