# Choose Representations Where Parameter Distance Tracks Output Distance ## Claim When designing any parameter space an LLM must reason inside, pick the encoding where distance in the parameters correlates with distance in the result the model actually cares about. <!-- atomicity: 1 idea ✓ --> ## Scope & conditions - Holds whenever a model has to make a judgment call inside a continuous or structured parameter space (color, layout spacing, numeric config, prompt templates) and the "obvious" encoding is not the perceptually or functionally linear one. - Does not by itself fix a capability gap — it only removes a source of confusion when the model already has the reasoning skill but is working with a misleading representation. - The fix is representation-level, not prompt-level: no amount of prompting compensates for a parameter space where equal steps don't mean equal effect. ## Evidence The `/design` skill's color system replaces HSL with OKLCH specifically because HSL's lightness channel is not perceptually uniform — 50% lightness reads as a different apparent brightness for yellow than for blue, so a model reasoning in HSL is reasoning against a distorted map. OKLCH is built so that numeric distance approximates perceived distance, which lets the model "reason about color mathematically" instead of guessing. The same logic is offered as a general principle, independent of color: pick the representation where parameter-space distance correlates with output-space distance. ## Links - [[Visual Thinking MOC]] — encoding choice as the thing that decides whether a model can reason in a design space - [[3. Resources/Permanent Notes/AI Quality Gaps Are Policy Problems Not Capability Problems]] — because extends; that note frames the broader "policy gap, not capability gap" diagnosis this technique is one concrete instance of. - [[3. Resources/Literature Notes/how did design fix the ai design slop problem]] — because evidence-for; source Literature note holds the full seven-principle breakdown this claim is extracted from. ## Tests / falsifiers - Compare an AI's color-palette outputs generated via HSL prompts against OKLCH prompts on a blinded perceptual-contrast pass rate; if OKLCH shows no advantage, the representation-choice claim doesn't hold for this domain. - Test the same principle outside color (e.g., a numeric layout-spacing scale) — if switching to a perceptually/functionally linear scale doesn't improve output consistency, the claim may be color-specific rather than general. ## Maintenance - Last tended: 2026-08-16 - Next review: 2026-11-16 ## Source - [[3. Resources/Readwise/Articles/how did design fix the ai design slop problem]] — Ahmad Awais walkthrough of the `/design` skill's OKLCH-over-HSL rationale.