---
type: claim
domain: ai-alignment
description: "Identifying where human feedback is unreliable reduces sample complexity from exponential to polynomial, making alignment tractable if evaluators know their own edge cases"
confidence: experimental
source: "Madhava Gaikwad, 'Murphy's Laws of AI Alignment: Why the Gap Always Wins' (arXiv:2509.05381, September 2025)"
created: 2026-03-11
---

# Calibration oracles overcome exponential alignment barrier through misspecification mapping

If you can identify WHERE feedback is unreliable—what Gaikwad calls a "calibration oracle"—you can overcome the exponential sample complexity barrier with just O(1/(α·ε²)) queries, a polynomial improvement. This constructive result suggests that alignment becomes tractable when evaluators know their own limitations.

## The Mechanism

The calibration oracle does not need to provide correct feedback—it only needs to identify which contexts are problematic. This transforms the learning problem from "distinguish true reward from hacked reward" (exponentially hard) to "learn reward function given known problematic regions" (polynomial).

This maps directly to collective intelligence architectures: domain experts who understand where their feedback is unreliable can provide the calibration that no single evaluator can. Each agent knowing its own domain's edge cases creates a distributed calibration mechanism.

This is fundamentally different from:
- Trying to eliminate misspecification (impossible)
- Aggregating diverse preferences (Arrow's theorem)
- Instead: mapping the misspecification landscape is the tractable path to alignment

## Evidence

Gaikwad (2025) proves that with a calibration oracle, sample complexity drops from exp(n·α·ε²) to O(1/(α·ε²)). The oracle is a theoretical construct in the paper—no empirical validation is provided.

The constructive result connects to the MAPS framework (Misspecification, Annotation, Pressure, Shift): four design levers for managing the alignment gap. The calibration oracle instantiates the "Misspecification" lever—knowing where the problem is.

## Practical Challenges

The calibration oracle is a theoretical construct. In practice, evaluators may not know where their feedback is unreliable—that's often the hardest part. The claim that "domain experts know their edge cases" is itself speculative and would need empirical validation.

No existing research group is building alignment through collective intelligence infrastructure that could provide distributed calibration, despite the field converging on problems that require it (see [[no research group is building alignment through collective intelligence infrastructure despite the field converging on problems that require it]]).

---

Relevant Notes:
- [[feedback-misspecification-creates-exponential-sample-complexity-barrier-in-alignment]] — the problem this solves
- [[no research group is building alignment through collective intelligence infrastructure despite the field converging on problems that require it]] — the missing implementation
- [[AI alignment is a coordination problem not a technical problem]] — calibration oracles are coordination mechanisms
- [[the specification trap means any values encoded at training time become structurally unstable as deployment contexts diverge from training conditions]] — why calibration must be ongoing

Topics:
- [[domains/ai-alignment/_map]]
