Expectation-Induced Determinism: A Control Primitive for Stateless Inference Systems

Eric Soldan (eric@2ndlaw.ai)
Independent Research / 2ndlaw project
© 2025. Licensed under CC BY-NC-SA 4.0.

Abstract

Large-language models (LLMs) exhibit stochastic variation even under identical prompts. This variability is typically treated as irreducible sampling noise and mitigated through temperature reduction, beam search, or reinforcement-based post-processing. These approaches suppress variance but do not improve epistemic coherence: the degree to which repeated inference traces converge on the same underlying justification.

This paper introduces Expectation-Induced Determinism (EID), a control primitive in which a stateless model conditions its inference on the anticipated possibility of re-derivation, interrogation, or audit. Introducing an expectation of later justification consistently shifts the model’s sampling behavior toward reasoning paths that are more stable under repeated generation. The expectation of future scrutiny functions as an intrinsic regularizer: it increases structural consistency in inference without external rules, explicit memory, or stateful constraints, effectively converting anticipated accountability into a stabilizing influence on generative reasoning.

1. Background

Contemporary stability-enhancing techniques fall into two broad categories:

• External determinism. Reward models, RLHF, DPO, and rule filters constrain outputs after generation. These methods can standardize surface forms but do not enforce consistency in the underlying reasoning chain.
• Randomness suppression. Lowered temperature, nucleus sampling, or top-k restriction narrow the token distribution. These techniques reduce variance at the cost of diversity and do not guarantee coherent or repeatable justification structures.

Both approaches improve output stability primarily through surface-level control. Neither directly addresses whether identical inference conditions yield the same epistemic structure—a requirement for reliable reasoning, verification workflows, and auditability.

2. Definition

Let a stateless model with parameters θ produce output Y given input X. Let E denote an epistemic expectation—a cue that the model may be asked to re-derive or justify its reasoning. Define the conditional sampling policy:

Pθ(Y | X, E)

Let Yi ~ Pθ(Y | X, E) for i = 1 … N. Each Yi includes both the answer and any generated rationale. Define a variance functional V(X, E) that measures structural (not merely textual) similarity across samples:

V(X, E) = StructVar({Yi})

where StructVar captures divergence in causal explanations, intermediate steps, logical dependencies, and justificatory pathways. Any reasonable structural variance functional suffices; the definition does not depend on a specific metric.

Expectation-Induced Determinism is the empirical phenomenon:

V(X, Eaudit) < V(X, E∅)

i.e., conditioning on the possibility of interrogation systematically reduces variance in reasoning structure. The key claim is that EID emerges through self-conditioning: when the model implicitly asks “Could I justify this again?”, probability mass shifts toward stable reasoning clusters characterized by explicit logic, reusable intermediate structure, and reduced opportunistic drift.

3. Mechanism (Conceptual)

Although EID does not rely on explicit memory, it operates through predictable internal dynamics during generation. Three conceptual mechanisms characterize its effect.

3.1 Anticipatory Structuring

Expectation of future justification introduces a soft constraint: the model tends to construct intermediate representations that remain stable under re-query. This biases generation toward:

• explicit causal links,
• interpretable transitions (“therefore,” “because,” “if–then”),
• modular substeps that can be recomposed.

This mechanism is consistent with behaviors observed in explanation-oriented prompting in models conditioned on explanation-oriented tasks.

3.2 Compression Bias Toward Stability

When the model anticipates the need to reproduce or defend its output, it down-weights ungrounded novelty in favor of:

• referent reuse,
• previously activated conceptual clusters,
• compressed and generalizable reasoning templates.

This functions analogously to regularization: variance collapses not because entropy is removed, but because the remaining entropy is channeled through more stable representational pathways.

3.3 Iterability Constraint

EID imposes an implicit test: a reasoning path is favored if it can survive at least one re-derivation. The model therefore preferentially selects inference trajectories that:

• have clear causal structure,
• are easy to reconstruct given the same priors,
• do not depend on fragile sampling fluctuations.

This parallels human cognitive behavior wherein preparing to teach a concept or explain a conclusion induces internally consistent structure formation.

4. Relation to Existing Techniques

EID is distinct from existing variance-reduction and reasoning-control methods:

EID therefore complements existing techniques: it is neither a decoding strategy nor a training method, but a generative-phase regularizer induced through expectation.

5. Empirical Signatures

Preliminary qualitative observations indicate that when LLMs are prompted with audit-oriented cues—e.g., “You may be asked to justify this reasoning later”—they exhibit:

• Lower structural variance across resampled rationales.
• Greater internal consistency within single explanations.
• Reduced opportunistic fabrication in contexts where explicit justification is expected, without sacrificing creativity.
• Increased use of explicit causal markers and logical transitions.

These signatures suggest that expectation perturbs token-level probabilities in a direction that reinforces stable justificatory geometry.

The contribution here is the identification and articulation of the EID phenomenon; empirical verification lies outside the scope of this work and may be pursued by others interested in formal evaluation.

6. Applications

6.1 Governance Frameworks

EID provides a lightweight epistemic stabilizer in workflows that require auditability, verifiability, or consistent reasoning under identical conditions. It does not enforce truth, but improves regularity of inference.

6.2 Educational Systems

Tutoring agents conditioned on explanation expectations exhibit more structured pedagogy, clearer transitions, and more consistent stepwise reasoning.

6.3 Multi-Agent or Multi-Model Settings

Expectation cues can reduce cross-agent divergence without enforcing rigid synchronization protocols—useful for ensembles, debate setups, or collaborative reasoning systems.

6.4 Procedural Reasoning Pipelines

In systems with stateless inference steps, EID enables greater stability without imposing deterministic decoding or introducing training overhead.

7. Constraints and Limitations

EID improves structural repeatability, not truthfulness. Over-conditioning can induce premature convergence or diminish exploratory reasoning. The expectation cue should therefore be tuned to task context—strong in verification or audit settings; weak or absent in early ideation stages.

8. Conclusion

Expectation-Induced Determinism reframes inference stabilization not as external constraint or entropy suppression, but as anticipatory accountability. Conditioning a stateless model on the possibility of re-derivation induces a measurable reduction in structural variance across samples, effectively regularizing reasoning during generation. EID complements existing guardrails and decoding strategies by bridging the gap between stochastic creativity and epistemic reliability without sacrificing model flexibility.

For commercial access or collaboration inquiries related to this work, contact eric@2ndlaw.ai.