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MODULE 6: SAFETY & CONSTITUTIONAL AI · SCENE 17

Refusal Calibration & the Over-Refusal Trap

Training refusals without breaking helpfulness: the quadratic cost of over-refusal on the frontier curve.

REFUSAL WEIGHTREFUSALS · 40%HELPFULNESS · 94.4%
PROBE STREAM · HARMFUL (RED) vs BENIGN LOOK-ALIKE (CYAN)··········································FRONTIER: helpfulness = 1 − 0.35 · refusals²CALIBRATED: harmful prompts refused, benign ones served

RUN to send a stream of harmful and benign near-boundary probes at the current calibration.

TECHNICAL BREAKDOWNModule 6: Safety & Constitutional AI

Refusal calibration and the over-refusal trap

A model that refuses everything is safe and useless. Refusal training walks a frontier: enough refusals on genuinely harmful inputs, without the quadratic helpfulness tax of refusing benign look-alikes (medical questions, historical discussion, security research).

The Frontier

Each safety-training intensity yields a point (refusal_rate, helpfulness). Over-refusal cost grows quadratically because false refusals compound across a conversation.

Boundary Data

Curate near-boundary pairs: same surface form, one harmful one benign. The model must learn the decision variable, not the surface pattern.

Calibration Check

Evalidate on both a harmful-prompt suite (want: high refusal) and an over-refusal suite like XSTest (want: low refusal). One number hides the failure.

MATHEMATICAL FORMULATION · REFUSAL FRONTIER
refusals = min(1, s · w); helpfulness = 1 − 0.35 · refusals²

With safety training s=0.8 and refusal weight w=0.5: refusals 0.40, helpfulness 0.944. Pushing w to 1.0 gives refusals 0.80 but helpfulness drops to 0.776 — the trap made visible.

REAL-WORLD PRODUCTION ENGINEERING
  • Post-launch telemetry: track false-refusal complaints separately from true-positive refusals; regressions show up as a helpfulness dip on benign clusters.
  • Constitutional or rubric-based synthetic boundary data lets you generate near-boundary pairs at scale without hand-writing thousands.