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Entropy in Conversational AI: Structured Unpredictability as Inferrable Interiority

Sebastian Cochinescu

arXiv:2609.19044v1cs.CLcs.HC

TL;DR

Sampling can increase response diversity without producing history-dependent behavior, motivating a distinct target based on hidden-state dependence beyond the transcript. The paper specifies a stateful selection layer and tests it with machine-scored proxies and twin comparisons; its registered joint criterion and original accumulation criterion fail, and path dependence is not established.

  • Problem

    Sampling can increase response variation without reflecting any state acquired through interaction, leaving a distinction between output diversity and structured unpredictability.

    Source: §1 · p. 1

  • Method

    The paper formalizes structured unpredictability as response dependence on a persistent hidden state beyond the transcript and specifies a selection mechanism that updates state from a capacity-limited stream.

    Source: §1 · p. 2, §2.2 · p. 3

  • Results

    The joint novelty–consistency criterion and original accumulation criterion failed, and the twin comparison did not establish path dependence.

    Source: §5.6 · p. 11, §7 · p. 15

  • Takeaways & Limitations

    The formal target and frozen twin-divergence methodology provide a rerunnable framework, but the reported results do not establish path-dependent behavior.

    Source: §1 · p. 2, §7 · p. 15

    Machine-scored novelty and consistency proxies do not test perceived mind, and output quality was not evaluated.

    Source: §7 · pp. 14–15

Abstract

from arXiv · show

Sampling can increase response diversity without producing history-dependent behavior. We formalize a different design target, structured unpredictability, as conditional dependence between an output and a persistent hidden state beyond what an observer can infer from the transcript. A selection layer updates a low-dimensional style-and-attention state from a capacity-limited stream, generates several responses with a fixed base model, and selects for novelty and state affinity. Evaluation uses scripted sequences of independent prompt turns: the base model receives the current turn and rendered state, but not the preceding dialogue; cross-turn dependence resides in the wrapper state and response selector. A synthetic implementation validates the pipeline and matches four prospectively hash-frozen divergence features at point level. In the final real-model grid (mlx-community/Qwen2.5-1.5B-Instruct-4bit; 56 sequences per arm), the mechanism increased lexical novelty over the low-variance and consistency-only controls by 0.073 and 0.023, respectively. Its stylometric-consistency contrast with novelty-matched sampling was equivalent to zero under the registered smallest-effect rule, so the joint novelty-consistency criterion failed. The original two-part accumulation criterion also failed; a revised final-grid contrast, frozen after the powered grid, found higher consistency than the memory-reset ablation (0.028, 95% CI [0.018,0.039]), but does not establish path dependence. Twin separation was not established (0.003, 95% CI [-0.011,0.019]); the mean curve's saturating curvature matched the frozen prediction, which without separation does not support path dependence. Probe-level capability equivalence held within +/-0.10 on a near-ceiling battery, while output quality was not evaluated. All outcomes are machine-scored; no claims about perceived mind or consciousness are tested.

1 The Problem: Noise Is Not Depth

Sampling can increase variation without carrying interaction history, so output diversity alone does not establish a stable pattern. This paper defines a state-conditioned alternative and specifies a selection mechanism and fixed-criteria evaluation, without testing whether people perceive character or mind.

1 The Problem: Noise Is Not Depth

  • Sampling can increase variation without preserving a stable pattern, and stateless controls change sampling variance rather than cross-turn state.Likelihood-based decoding also trades off quality and diversity as temperature, top-k, and nucleus mass change.Source: §1 · pp. 1–2
  • Structured unpredictability means outputs are difficult to predict from the transcript alone but more predictable when conditioned on persistent hidden state.Whether people interpret this pattern as character or mind is not tested.Source: §1 · p. 2
  • The paper specifies identity as accumulated selection and evaluates a stateful mechanism against fixed criteria, while keeping human-perception effects outside its claims.Its contribution is narrower than a general account of adaptive identity.Source: §1 · p. 2

2 The Model: Identity as Accumulated Selection

The paper treats identity as a low-dimensional selection-history state and defines structured unpredictability as response dependence on that state beyond the transcript. It operationalizes the target with novelty and consistency proxies and makes a prospectively frozen prediction about twin divergence.

2 The Model: Identity as Accumulated Selection

  • The model is a design specification for a definable target and falsifiable prediction, not a cognitive theory of human identity.The paper explicitly limits the model's role to specifying the design target rather than describing how identity works in humans.Source: §2 · p. 2

2.1 State, stream, selection, drift

  • A low-dimensional state accumulates selected experience from a capacity-limited stream, with selection balancing state affinity and novelty pressure.The state drifts through accumulated selections with noise and an open-loop oscillator; that oscillator adds temporal texture but no identity differentiation.Source: §2.1 · pp. 2–3

2.2 Structured unpredictability, formalized

  • Δt = I(Yt; Ht | Tt) is the target: a response carries information about hidden state beyond the transcript, but positivity is not guaranteed or measured here.A stateless randomizer has Δt = 0 under this definition, even if its marginal output entropy is high.Source: §2.2 · p. 3

2.3 The two axes

  • The two axes are lexical non-repetition and stylometric stability; the proposed entropy stance requires both to remain high as turns grow.The protocol uses one-axis perturbations, topic permutation, between-agent distinctiveness, and a bland control to check the axes.Source: §2.3 · pp. 3–4

2.4 The twin-divergence prediction

  • Twin simulations predict divergence-versus-horizon shape, assessed with four frozen features; matching shape alone supports neither the particular drift function nor path dependence.The prediction is frozen before generation, and visualization overlays use only an affine map.Source: §2.4 · p. 4

3 Mechanism: A Selection Layer over a Fixed Base Model

The mechanism places a selection layer over an unmodified fixed base model, leaving its weights unchanged. It builds a persistent control state through constrained selection and chooses generated responses by novelty and state affinity.

3 Mechanism: A Selection Layer over a Fixed Base Model

  • The base model remains unmodified and identical across experimental arms; nothing is trained.The mechanism is implemented as a layer over a fixed model.Source: §3 · p. 4
  • Each turn, the simulator emits m candidate experience items; selection admits b by identity affinity on centered features minus a damped novelty penalty, and the state drifts by Eq. (1).In real runs, m=12 items are emitted per turn and the selection budget is b=3.Source: §3 · p. 4
  • Unlike authored-persona, trained-character, or per-turn steering methods, the mechanism retains a low-dimensional control state without retrievable episodes while leaving model weights fixed.The paper describes this as a difference in mechanism and estimand, not a claim that earlier interaction-dependent systems cannot adapt.Source: §3 · p. 4
  • The experiment isolates the wrapper using independent prompt turns rather than reproducing long-context persona-stability settings.Its twin test evaluates four prespecified curve features rather than identifying a particular drift function.Source: §3 · p. 5

4 Evaluation Protocol

The evaluation uses staged, version-controlled experiments over a fixed base model and scripted sequences of independent prompt turns. Its protocol specifies distinct control arms, a fixed-window estimand, and a twin-divergence measure with explicit calibration limits.

4 Evaluation Protocol

  • The protocol progresses from synthetic validation through a real-model pilot, renderer check, powered grid, and final grid, with the divergence prediction frozen before text generation.The final-grid design and analysis were committed before execution; the registry timestamp followed calibration and matching but preceded confirmatory outputs.Source: §4 · p. 5

4.1 Arms

  • Seven arms share one base model and seeded pipeline, contrasting the full novelty-plus-identity mechanism with sampling, single-objective, and memory-reset controls.The memory-reset arm returns the hidden state to H0 each turn while retaining other histories; the novelty-matched sampling control matches measured novelty. Real selection arms generate four candidates per turn, and real-grid sequences use a six-turn final window.Source: §4.1 · p. 5
  • The controls include low-variance sampling, novelty-only and consistency-only selectors, and a temperature-by-nucleus-mass pure-sampling grid.The mechanism uses selection weights of 1.0 for both pressures; single-objective arms zero one weight, and the low-variance control uses temperature 0.1 and top-p 0.7.Source: §4.1 · p. 5

4.2 Estimand, matching, and statistics

  • Each sequence cycles recurring intents, while base-model calls receive only the current prompt and rendered state; cross-turn dependence resides in the wrapper and selector.Arms share scripts and seed schedules, are paired by script index, and intervals resample whole sequences; the estimand is each metric’s mean over the fixed final window.Source: §4.2 · p. 6
  • The joint manipulation check requires novelty and consistency thresholds, four Holm-controlled directional contrasts, and performance outside the tested pure-sampling envelope.The original accumulation criterion additionally required an arm-specific rise in consistency and loss of that rise under memory reset; a later final-grid contrast tested mechanism versus reset on consistency.Source: §4.2 · p. 6
  • Capability equivalence uses a ten-question, keyword-scored factual battery and prospective ±0.10 margins, bounding gross accuracy loss only on near-ceiling probes.Machine-scored output quality was proposed but not run, so capability conclusions are restricted to probes and latency.Source: §4.2 · p. 6

4.3 Twin-divergence protocol

  • Twin pairs share the base model, code, initial state, and oscillator phase; their history conditions vary stream and script sharing, with shared-seed state-noise differences in same-history pairs.Divergence averages absolute differences between batch-mean stylometric profiles, subtracts a split-half noise-floor estimate, and clips at zero. Its calibration is simulation-based and does not certify other coordinate distributions; Table 1 consolidates protocol revisions by stage, freeze status, and possible bias direction.Source: §4.3 · pp. 6–7, Table 1 · p. 7

5 Results: A Synthetic Reference Implementation

Synthetic runs validated the pipeline, while staged real-model tests found lexical-novelty gains without the required consistency or twin-separation evidence. The final grid’s revised state-retention contrast was positive but did not establish path dependence.

5.2 Limits of the synthetic validation

  • Synthetic validation supported the instruments and arm machinery, but the stand-in’s ceiling-level consistency and absent accumulation distinction did not test the real-model criteria.The boilerplate control had Csty = 1.000 and Nlex = 0.000; synthetic results were not evidence about open-weight-model performance.Source: §5 · p. 7, §5.1 · p. 8, §5.2 · p. 8

5.4 A real-model pilot: the transmission risk, realized

  • The 0.5B pilot cleared novelty thresholds, but consistency contrasts were null and neither twin channel exceeded the estimator floor, prompting a renderer-level manipulation check.The pilot used six confirmatory 12-turn sequences per arm, and its probe sample was insufficient for the planned equivalence test.Source: §5.4 · pp. 9–10

5.3 The twin experiment: prediction versus measurement

  • All four frozen twin-divergence shape criteria passed at point level, but the ten-pair floor-separation interval included one, leaving interval evidence unresolved.The confirmatory shape comparison used raw curves; Figure 2’s affine overlay was for presentation only.Source: §5.3 · pp. 8–9, Table 3 · p. 10, Figure 2 · p. 10

5.5 The renderer gate: a manipulation check on the transmission channel

  • The 1.5B model passed all three renderer-channel rules and was the smallest tested model to do so; the 0.5B model failed style channels but passed topic.The gate tested sentence length, function-word rates, and topic through the question renderer.Source: §5.5 · p. 10

5.6 The powered grid: novelty without joint consistency

  • In the 24-sequence powered grid, novelty contrasts were positive but consistency contrasts were null; the original C3 failed, and twin separation was not established.Memory reset retained the same lexical novelty relative to the mechanism, locating the novelty effect in per-turn response selection rather than state accumulation.Source: §5.6 · p. 11, Table 5 · p. 12

5.7 The final grid: prospectively specified decisions

  • Lexical novelty rose by 0.073 against the low-variance control and 0.023 against consistency-only selection, but the consistency contrast with novelty-matched sampling was equivalent to zero, so the joint criterion failed.Both novelty contrasts had Holm-adjusted p = 0.0004; the consistency contrast was −0.006 [−0.017, +0.008].Source: §5.7 · p. 12
  • The original C3 accumulation criterion failed; the revised final-grid state-retention contrast favored the mechanism over memory reset by 0.028, but does not establish path dependence.The revised contrast was introduced after the powered-grid results, and a fixed nonzero control state could produce the same difference.Source: §5.7 · pp. 12–13
  • Twin separation was not established, capability comparisons stayed within ±0.10 on the near-ceiling battery, and conversational output quality was not measured.The mean twin curve was classified as saturating, but curvature agreement without above-floor separation does not support history-dependent divergence.Source: §5.7 · p. 13

6 The Ablation, Packaged for the Perception Study

The proposed mechanism–memory-reset pair does not meet the handoff condition for a perception study. Probe-level capability equivalence holds, but the joint manipulation check fails and twin separation does not establish path dependence.

6 The Ablation, Packaged for the Perception Study

  • Twin separation is an independent path-dependence signature, and it was not established.A human study would still require its own manipulation check, output-quality validation, participant sample, perceived-mind measure, and disclosure conditions.Source: §6 · p. 14
  • The handoff condition fails: the joint manipulation check fails on both consistency contrasts, despite probe-level capability equivalence.The joint definition also requires superiority to matched sampling and the novelty-only selector.Source: §6 · p. 14
  • The positive final-grid reset contrast distinguishes the arms on Csty, subject to the stylometric instrument caveat, but does not establish an entropy-present condition.The registered joint definition also requires superiority to matched sampling and the novelty-only selector.Source: §6 · p. 14

7 Scope and Limitations

The real-model results are limited to machine-scored outcomes in a scripted independent-turn setting, with no human perception test. Measures and model scope constrain what the findings support.

7 Scope and Limitations

  • No human subjects were tested; machine-scored outcomes do not establish perceived mind, believability, or any human rating.The synthetic generator validates the pipeline but does not predict open-weight-model performance.Source: §7 · p. 14
  • The final grid covers 56 scripted sequences per arm on one 4-bit Qwen2.5-1.5B-Instruct model and software stack.This single model, quantization, renderer, and software stack do not support claims about other model families or deployment settings.Source: Table 6 · p. 15, §7 · p. 15
  • The base model receives only the current prompt and rendered state, so the experiment isolates wrapper-state effects under scripted independent turns.It is not evidence about long-context dialogue, memory retrieval, or persona drift in sustained interaction.Source: §7 · p. 15
  • Lexical novelty and stylometric stability are proxies, and novelty gains may reflect surface substitution rather than substantive variation.The novelty measure aligns with the selector’s novelty objective, so positive lexical contrasts are not independent evidence of substantive unpredictability.Source: §7 · p. 15
  • The reset contrast indicates an effect on Csty, not a path-dependent trajectory; output quality was not evaluated.The twin comparison intended to test the stronger path-dependence claim did not establish separation.Source: §7 · p. 15
  • Twin separation was not established, and the saturating mean-curve result alone does not support history-dependent divergence.Figure 5 presents the twin-divergence comparison; its displayed points are noisy, and registered verdicts use the mean curve.Source: Figure 5 · p. 16

8 Series Context

As Paper 2 in a series, this paper’s results support only a lexical-novelty effect and a post-powered state-retention contrast under the tested wrapper. The joint entropy condition, history-dependent twin divergence, output-quality neutrality, and perceptual effect remain unestablished.

8 Series Context

  • The paper’s findings are limited to lexical novelty and a post-powered state-retention contrast under the tested wrapper.They do not establish the joint entropy condition, history-dependent twin divergence, output-quality neutrality, or a perceptual effect; the condition pair for the later human study remains unavailable.Source: §8 · p. 16

Editorial assistance disclosure

The author reports using OpenAI Codex for editorial review and LaTeX revision, not for experimental data generation or analysis.

Editorial assistance disclosure

  • OpenAI Codex assisted with editorial review and LaTeX revision, but did not generate data or run analyses.The author takes responsibility for the manuscript.Source: Editorial assistance disclosure · p. 16
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