1. The Aleatory Cop-Out
"Stochastic" has become a convenient word in modern AI discourse. It sounds technical, borrowed from statistics and physics, and appears to explain variability in model outputs without assigning cost or responsibility.
In practice, the term often functions as a narrative buffer: it shifts attention from the structural sources of uncertainty to the surface-level behavior of the model, regardless of anyone's intention.
True stochasticity—aleatory uncertainty—refers to irreducible randomness: quantum measurement outcomes, thermal noise, radioactive decay. These uncertainties remain even in a perfectly specified model.
Most model failures labeled "stochastic" are nothing like this.
Hallucinated citations, inconsistent causal explanations, confident contradictions across turns, and self-referential reasoning loops are not irreducible randomness. They are structural uncertainty produced by underconstrained systems.
Calling these failures stochastic is not descriptive. It is exculpatory.
2. The Quiet Slide from Unintended to Accepted
Unintended consequences are a legitimate category—but only briefly. They excuse initial error, not sustained inaction.
In complex systems, outcomes frequently arise that were not anticipated at design time. This is not negligence; it is an unavoidable feature of operating in high-dimensional spaces. At this stage, the label "unintended" is accurate and useful.
That label expires once the consequence becomes observable, reproducible, and well understood.
At that point, a system faces a choice: mitigation or acceptance. Mitigation requires work. Acceptance requires justification.
What often occurs instead is a third outcome. The consequence persists without mitigation, yet is never explicitly acknowledged as acceptable collateral damage. It remains linguistically frozen as "unintended," even as it becomes operationally normalized.
This linguistic suspension is not neutral. "Unintended consequences" require no defense. "Acceptable collateral damage" demands one. By never crossing that boundary explicitly, systems avoid both redesign and accountability.
In AI systems, behaviors such as hallucinated citations, erosion of provenance, confident fabrication, and causal inconsistency are no longer surprises. Treating them as unintended today is inaccurate. Treating them as acceptable without acknowledgment is evasive. The result is known harm that is tolerated but unnamed—epistemic entropy preserved through vocabulary rather than design.
3. Entropy Is Introduced Upstream, Not Emergent
For any given true explanation of a phenomenon, the number of coherent alternatives is small. For false or misleading explanations, the number is effectively unbounded.
Falsehoods are cheap because they are unconstrained:
- they need not respect causal direction,
- they need not preserve temporal order,
- they need not remain consistent across contexts,
- they need not survive contact with physical reality.
Conspiracy theories exemplify this. They collapse complex, multi-causal systems into single-agent narratives, eliminate falsifiability, and recycle familiar story primitives. They are not random noise; they are entropy-maximizing constructions.
When a training corpus admits such material without provenance weighting, causal modeling, or decay functions, entropy is injected systematically. The dataset is not neutral. Disorder is not emergent. It is imported.
4. Why "Stochastic Output" Is a Misdiagnosis
Stochasticity describes how a system samples from a distribution.
Entropy describes why the distribution is broad.
If a model produces wildly different explanations for the same question across runs, the issue is not that sampling is probabilistic. The issue is that the hypothesis space was allowed to balloon.
Consider:
- multi-step reasoning that collapses halfway through,
- explanations that reverse cause and effect depending on phrasing,
- answers that confidently assert mutually exclusive premises in adjacent turns.
These are not sampling artifacts. They are symptoms of constraint collapse.
Calling them stochastic errors mistakes the symptom for the cause.
5. The Dimensions That Get Flattened
Modern language models routinely collapse dimensions that, in other epistemic systems, do the work of entropy reduction. What follows is not exhaustive. It is representative. Each item on this list would require significant architectural work to restore.
Causality
Mechanism is flattened into correlation. Post hoc narratives compete equally with causal explanations.
Provenance
Source identity, incentives, expertise, and accountability are erased. Peer-reviewed work and anonymous summaries are tokenized identically.
Weight / Asymmetry
One correct signal is overwhelmed by mass repetition of incorrect ones. Frequency substitutes for importance.
Time
Outdated claims coexist indefinitely with current knowledge. Retractions do not propagate. No decay function exists for invalid models.
Context
Domain boundaries dissolve. Conditional truths are universalized. Edge cases masquerade as rules.
Intent
Explanation, persuasion, propaganda, and fiction are ingested as equivalent linguistic acts.
Grounding
Internal coherence substitutes for correspondence with measurable reality. Models produce explanations that cannot be falsified even in principle.
Cost of Error
Trivial mistakes and catastrophic failures are treated identically. There is no gradient for seriousness.
Uncertainty Representation
Distributions collapse into unjustified point estimates. Known unknowns are presented as settled facts.
Normative vs Descriptive
Facts and values bleed into one another. Description quietly becomes endorsement.
Each flattening expands the hypothesis space. That expansion is entropy.
6. What Does Not Belong in the Core Model
Tone, style, politeness, verbosity, creativity, and conversational alignment do not reduce hypothesis space. Removing them does not increase the number of explanations compatible with the same evidence.
They are presentation layers, not epistemic constraints.
Attempts to compensate for missing structure with presentation—hedging language instead of uncertainty modeling, disclaimers instead of provenance, politeness instead of causal rigor—are not safeguards. They are camouflage.
A better model is defined by the constraints it enforces before speaking, not by how carefully it speaks afterward.
7. Why Scaling Fails (Absent Constraint)
Scaling improves fluency and coverage. It does not impose structure.
As models grow, expressive capacity increases faster than truth density. Without additional constraints, larger models explore larger regions of an already over-entropic space.
This is why scaling alone often produces:
- more confident nonsense,
- more coherent but incorrect explanations,
- reduced variance around the wrong mean.
Scaling optimizes sampling efficiency, not epistemic quality.
8. Entropy Is an Unpaid Debt
In thermodynamics, entropy reduction costs energy.
In epistemic systems, it costs computation, architecture, curation, and governance.
Science pays this cost through peer review and replication.
Law pays it through evidence standards.
Engineering pays it through failure analysis.
Language-only models mostly do not.
Labeling the resulting disorder "stochastic behavior" disguises the unpaid debt. Entropy was borrowed upstream; the bill is deferred downstream.
9. The Challenge
Outside of irreducible physical randomness, what the industry labels "stochastic error" is overwhelmingly the product of unconstrained design.
The question is not whether models are stochastic.
The question is where entropy entered, and who declined to pay to remove it.
Until that question is answered honestly, improvements will remain cosmetic, and disorder will continue to be misnamed as inevitability.
Why Entropy, Not Stochasticity
Stochasticity describes sampling behavior.
Entropy describes the size of the remaining hypothesis space.
If uncertainty were intrinsic, stochasticity would be the correct diagnosis. But when uncertainty arises from flattened causality, erased provenance, and unweighted repetition, the problem is entropy propagation, not randomness.
Entropy identifies origin, asymmetry, and cost.
Stochasticity describes only the symptom.
For the problems facing current AI systems, entropy is not just the better label—it is the only one that assigns responsibility.