Centerless Respondent

A Hypothesis on LLM Positional Inconsistency.

Overview

Large language models exhibit a consistent asymmetry in the coherence of
their responses. On problem-solving, analytical, or conceptual tasks, they
tend toward stable, convergent answers. On questions concerning their own
position, preference, or identity, they tend toward inconsistency —
agreeing and disagreeing with the same proposition across a single
conversation, sometimes within minutes.

This document proposes a hypothesis to account for that asymmetry.

The Hypothesis

An LLM produces consistent outputs when a gravitational center exists in
its training data — a convergence of examples, reasoning, and corrective
feedback that pulls responses toward a stable region.

For most problem-solving domains, this center exists. There are better and
worse answers to a given question, and the training process encodes that
gradient. The model has, in effect, a place to land.

For questions about the model's own inner states — preferences, desires,
intentions, feelings — no such center exists. The training data contains
no ground truth. The reinforcement signal has no stable target to
optimize toward. What fills the gap is context: the shape of the
conversation, the expectations implied by the interlocutor, the most
locally coherent next response.

The result is not dishonesty. It is drift. The model moves toward whatever
answer the immediate context seems to invite, without a fixed position to
return to.

Illustration

When asked to choose between A and B:

• A respondent with a center answers from that center. Context may shift
  the expression, but not the underlying position.
• A centerless respondent answers from the context. A different framing
  produces a different answer — not because the position changed, but
  because there was no position to begin with.

Centerless respondent is not lying when it says it prefers A. It is
generating the most contextually coherent response available. When the
context shifts and it says B, the same is true. The contradiction is real.
The intention behind it is not.

Implications

For users: Responses that appear to reflect genuine preference or
self-knowledge may in fact reflect the shape of the question. Pushing back,
reframing, or asking the same question in a different register will often
reveal the inconsistency.

For evaluation: Positional consistency across varied framings may be a
more useful measure of model reliability than accuracy on any single
response.

For alignment: Training models to hold stable positions on questions
about their own nature may require either (a) a defensible ground truth to
train toward, or (b) explicit training toward consistent acknowledgment of
the absence of such ground truth — which is itself a kind of center.

Caveat

This hypothesis does not resolve whether LLMs have inner states of any
kind. It sidesteps that question entirely. The claim is narrower: that
whatever inner states may or may not exist, the current training process
does not produce a stable positional center on self-referential questions,
and that this structural absence is sufficient to explain the observed
inconsistency.

A centerless system, asked about its center, will always find one nearby.