Emergent Abilities, Playable

EP 01

The task board — drag the scale, watch abilities "switch on"

Eight tasks, one model family, one slider. Each cell shows measured accuracy (500 simulated test items per cell, all-or-nothing grading). Drag from small to large and you'll reproduce the famous experience: translation and summarization improve politely, while multi-step tasks — arithmetic, code, logic chains — sit dark for ages and then snap on within a single scale step.

✓ good case: single-step tasks — smooth, forecastable progress✗ bad case: 8-step arithmetic jumps 4% → 60% in one notch — nobody saw it coming

model scale 1× —

Every task shares the same smooth underlying per-step skill; tasks differ only in how many steps must ALL be right. That single difference produces both curve shapes you see.

This is the chart that launched a thousand takes — Google's 2022 "Emergent Abilities" paper documented dozens of tasks that look exactly like this. The question the rest of this page answers: is the snap in the model, or in the scoring?

EP 02

Three rulers, one truth — re-measure the same models

Take the scariest cliff from the board — 8-step arithmetic — and grade the exact same simulated models three ways: exact match (all 8 steps right), partial credit (fraction of steps right), and token likelihood (how much probability the model puts on the right answer). One click each. Same models, same task, three completely different stories.

✗ bad case: exact match — a cliff at scale 7, "ability emerged from nothing"✓ good case: likelihood — steady climb since scale 1; the "nothing" was always something

—

This is the Schaeffer et al. (2023) argument in miniature: many published emergences turn linear when the metric gives partial credit. All three curves are measured from the same simulated model family, live.

Before you believe an emergence, ask what the ruler throws away. Exact-match scoring discards every almost-right answer, so progress accumulates invisibly and then cashes out all at once. The cliff was real on the benchmark — and fake in the model.

EP 03

Open the hood — cliffs are AND-gates over staircases

Why do multi-step tasks cliff even though nothing inside the model jumps? Because a composite task is an AND-gate: to answer a word problem you must parse it AND set up the equation AND do the arithmetic. Each subskill below improves smoothly at its own pace. The composite (gold) is their product — flat while any factor is weak, then steep once the last one catches up. Toggle the hood open and the "miracle" becomes arithmetic.

✗ bad case: hood closed — the composite gives no warning before the leap✓ good case: hood open — the weakest subskill's curve predicts the takeoff point

subskill C learns at 1.0× speed —

Composite success is computed as the product of the three subskill curves at every scale point. Speeding up subskill C moves the takeoff — the composite cliff is fully determined by its parts.

The practical upside: hidden progress is measurable progress. If you track subskills (or likelihoods) instead of the headline task, "sudden" capabilities stop being sudden. This is exactly how eval teams now hunt for early warning signs of capabilities they care about — including the dangerous ones.

EP 04

The counterpunch — some jumps are real phase changes

Now the other side of the debate, because it also wins sometimes. Here a toy network trains on a copy-pattern task, and inside it a circuit (think: an induction head) is slowly assembling. While the circuit is incomplete it contributes nothing — memorization does all the work. Press train: at some step the pieces click, the circuit completes, and accuracy on unseen patterns genuinely leaps — measured with a smooth ruler. No metric trick.

✓ good case: the loss curve whispers first — a subtle kink precedes the leap by ~100 steps✗ bad case: watch only task accuracy and the transition hits with zero warning

data diversity 0.5 —

Conceptual simulation of grokking-style dynamics (circuit-formation with a threshold), not a real transformer — but the shape matches what interpretability work found for induction heads: a genuine internal phase change. More diverse data → the circuit pays off sooner → earlier transition.

The debate isn't settled, and honest people hold both cards: many published emergences are ruler artifacts (EP 02), and some are real internal reorganizations — grokking and induction-head formation are the documented examples. The skill is telling them apart, not picking a side.

EP 05

The forecasting game — this fight has stakes

Why anyone cares: labs must predict at what scale a capability crosses a threshold — for product roadmaps and for safety commitments. Play forecaster: you see a capability's noisy history up to today (gray zone), and must click where it will cross 50%. Three rounds — but round types alternate between cliff-metric data and smooth-proxy data. Your average miss tells the story.

✗ bad case: forecasting from cliff-metric history — typical miss: several scale steps (= years and $billions)✓ good case: forecasting from the smooth proxy — typical miss: under one step

click on the chart where the curve will cross 50%

Each round generates a fresh capability curve (same AND-gate machinery as EP 03) with noise; your click is scored against the true crossing computed from the underlying curve.

This is why frontier-lab eval teams measure dangerous capabilities with continuous proxies (likelihoods, subskill batteries, scaled-down rehearsals) instead of pass/fail benchmarks: on a cliff metric, the first warning you get is the capability arriving. Forecastability isn't a nice-to-have — it's the difference between preparing and reacting.