Why we report entropy in nats
The unit choice is the honesty field — spread as a number a CRO can read.
Entropy is the number that says how spread the model doubt is. The unit you report it in changes what the number means. DEINO reports entropy in nats — the natural-log unit — because it is the unit that needs no conversion factor, and a CRO reading it should not have to do math to understand the spread.
Entropy is the honesty field of a distribution. A sharp peak has low entropy — the model is confident. A flat distribution has high entropy — the model is spread. A bimodal distribution has entropy that hides the shape (it can read as moderate when the model is actually torn between two regimes), which is why entropy is paired with the distribution, not substituted for it. DEINO reports entropy in nats — the natural-log unit — because the unit is the one that does not lie about what the number is.
Nats vs bits
Entropy can be reported in bits (base-2 logarithm) or nats (natural logarithm). Bits are familiar from information theory; nats are the natural unit. The difference is a constant factor — one nat is roughly 1.44 bits — and the choice is convention in most contexts. In a forecast context, the choice is not neutral. Bits invite the reader to think in coin flips, which makes the distribution feel like a series of binary bets. Nats invite the reader to think in spread, which is what the number is for. A CRO reading 0.7 nats of entropy is reading a spread; a CRO reading 1.0 bits is reading a coin flip, which is not what the distribution says.
Why it is part of the invariant
INV-1 says entropy is in nats. That is not a style preference; it is part of the normalization invariant. The Ensemble carries entropy alongside the probabilities, and the unit is fixed so every consumer reads the same number the same way. A consumer that wanted to display entropy in bits would convert at the display layer; the stored, manifest-recorded value is in nats. That means the manifest entropy field means the same thing now and years later, regardless of what display layer a future frontend uses. The unit is a contract with the future.
Bits make a distribution feel like coin flips. Nats make it feel like spread. The distribution is spread; the unit should say so.
- Entropy is the honesty field: low is confident, high is spread, bimodal hides in the middle.
- Nats (natural log) is the unit with no conversion factor — the number is the spread.
- The unit is part of INV-1 — the manifest records nats so the field means the same thing years later.
What entropy does not tell you
Entropy tells you how spread the distribution is. It does not tell you whether the spread is calibrated. A model that is uniformly wrong with high entropy is not more honest than a model that is sharply wrong with low entropy; it is differently wrong. Calibration is the loop that scores the distribution against the realized timeline — Brier, log-loss, deino-eval, Gate 1b. Entropy is the field a CRO reads to understand the model self-doubt; calibration is the loop that tells them whether that self-doubt is warranted. We are building the POC; the entropy field is produced, and the calibration loop is inert until it is filled.
Entropy is the model disagreeing with itself, made into a number. Calibration is the realized timeline telling you whether the disagreement was warranted. One is a field; the other is a loop.
— entropy note