Error Signals

Language models are probabilistic systems. For a given input, the model may produce different outputs across runs:

y ~ M(x)

Some outputs will be useful. Others will fail to satisfy the requirements of the surrounding system. When this happens, the failure itself becomes valuable information.

These failures act as error signals.

What Is an Error Signal

An error signal is any feedback that indicates the model output is not acceptable to the system.

schema validation failures
invariant violations
automation failures
incorrect classifications
missing fields
inconsistent results

Instead of treating these failures as simple errors, systems can treat them as signals about how the representation mapping failed.

Where Error Signals Appear

Error signals typically appear at the boundary between the probabilistic model and deterministic software.

Why Error Signals Matter

Prompt engineering often relies on manually adjusting prompts when the model fails. However, once the model is integrated into a system, failures can be detected automatically.

These failures provide structured feedback about what went wrong.

missing JSON fields
invalid schema
logical contradictions
automation step failure

Each of these failures contains information about the system's expectations.

Example: Structured Output

Consider a system expecting structured sentiment analysis:

{
  "sentiment": "positive" | "negative" | "neutral",
  "confidence": number
}

If the model returns:

{
  "sentiment": "positive"
}

The system detects a failure:

missing field: confidence

This becomes an error signal.

Example: Automation Systems

Browser automation systems provide strong error signals.

click failed
element not found
navigation timeout
form field missing

These failures reveal something about the environment. For example, login button not detected may indicate that the model incorrectly mapped the page representation.

Error Signals as System Feedback

Error signals can be used to improve the system in several ways.

In each case, the system learns something about the environment or the representation mapping.

Relationship to Representation Mapping

Representation mapping converts information between domains. Error signals indicate when that mapping failed.

environment → model → representation    (mapping)
representation → verification → error   (signal)

This allows the system to detect when the representation does not satisfy system requirements.

Relationship to Deterministic Boundaries

Deterministic boundaries are responsible for verifying outputs. They enforce constraints such as schema validation, logical invariants, format requirements, and system rules.

When these checks fail, they produce error signals. Error signals are therefore a natural byproduct of deterministic boundaries.

Error Signals as Information

One of the most useful properties of probabilistic systems is that failures reveal information about the system and environment. Instead of treating errors as terminal failures, systems can treat them as signals that guide the next step.

This creates an iterative improvement loop.

Summary

Error signals are feedback produced when model outputs fail to satisfy deterministic system requirements. They reveal information about representation mapping failures, system expectations, and environment structure.

When used correctly, error signals allow systems to improve reliability without relying solely on manual prompt engineering. Instead of ignoring failures, the system can treat them as structured signals that guide the next step.

environment → model → representation → verification → error signal → improvement