A cheap, training-free signal that predicts post-RL lift — from base-model rollouts alone, before a single gradient step.
LAD is a no-training, rollout-only dataset metric that predicts the realized downstream lift from GRPO better per unit cost than common data-quality proxies.
Frontier labs buy expensive post-training data and burn full RL runs to find out whether it helps. The economic question is upstream of training: which cohorts earn their compute?
Today, a cohort's value is revealed only after a complete GRPO run — accuracy-after minus accuracy-before on a fixed benchmark. Procurement, budget allocation, and data-QA decisions are all made blind, then validated by the most expensive possible measurement.
A reliable pre-purchase, pre-training score re-prices the entire post-training data market: allocate RL compute by predicted lift-per-dollar, and kill bad cohorts before they cost a run.
Cheap proxies (token length, diversity) are nearly free but weak. Strong predictors (gradient influence, datamodels, a small RL run) are accurate but cost 100×–1000× more. The open question: can a signal live in the top-left — cheap and predictive?
LAD targets exactly that corner of the Pareto plane, and the study places it there empirically.
Three justified factors: is there signal to learn from, is it pointed where lift lives, and is it non-redundant. Computed from k=32 base-model rollouts per task — no training, no gradients.
GRPO's per-task gradient is driven by the spread of rewards within a group. For a binary verifier that spread is exactly p(1−p) — zero when the model always or never solves a task, maximal in the learnable band. LAD turns that theorem into a dataset score.
Per-task signal p̂(1−p̂)(1−p̂)γ across pass-rate p̂. Drag γ to shift the peak toward harder-but-learnable tasks; toggle the component curves.
Within-group reward variance for a binary verifier. The KL between the base policy and the RL-optimal policy is lower-bounded by this Bernoulli variance — it is the leading term of a proven bound on policy improvement.
Variance is symmetric about 0.5, but lift is not — a cohort that mostly fails has more room to convert fail→pass into benchmark accuracy. The exponent γ tilts the peak toward harder-but-learnable tasks.
Lift is bounded by distinct skills, not summed energy. The Vendi score — the effective number of unique tasks — divides out redundancy so near-duplicate cohorts cannot fake learnability.
Qwen2.5-1.5B-Instruct on GSM8K. 19 cohort families that vary one data property at a time — including families built to break naive metrics. Each runs identical GRPO (70 steps, 2 seeds); LAD is evaluated leave-one-cohort-out.
32 base-model rollouts per task across every cohort — computed once and reused for every metric in the family.
Same model, budget, config, eval set, verifier per cohort. Cohort identity is the only variable; 2 seeds averaged.
Δacc = accuracy-after − accuracy-before on a fixed 500-question held-out GSM8K test set.
Fit ŷ = a + b·LAD on training cohorts; report Spearman ρ on the left-out cohort. Honesty over in-sample fit.
Predictive, incremental, mechanistic, causal. Each viz reads from a single results object and is drawn from the study's measured values.
19 cohorts: LAD (x) vs measured Δaccuracy (y), with the LOCO fit line ŷ = a + b·LAD. Hover any point.
LOCO Spearman ρ per metric, sorted. Cost annotation in rollout-equivalents. Toggle the expensive baselines.
Removing headroom or diversity, collapsing γ, or swapping the energy term each degrades held-out ρ.
LAD (x) vs realized group-advantage variance logged during GRPO (y). Tight positive — LAD reads the optimizer.
LOCO ρ vs rollouts-per-task k. By k=8 the signal is near-optimal; k=8 ranks agree with k=32 at ρ 0.96.
Final accuracy lift when GRPO trains on each selection strategy at equal compute — plus the LAD dose-response.
Every metric placed by cost (log, x) and held-out predictive power (ρ, y). The empirical frontier traces the best achievable tradeoff. LAD sits in the top-left, glowing above it: small-RL-proxy predictive power at rollout cost.
Set the pass-rate profile and effective diversity of a hypothetical cohort. LAD is computed with the real formula and turned into a predicted lift through the fitted line ŷ = a + b·LAD.
LAD correlates with the realized GRPO signal (mechanistic), predicts held-out lift at ρ = 0.89 (predictive), beats every cheap baseline and matches expensive ones at a fraction of the cost (incremental), and selecting by LAD causes the largest lift at equal compute (causal).
The mechanism — advantage energy × headroom × effective diversity — is derived from the GRPO objective, so each factor carries a reason and a demonstrated failure mode it corrects.
Gradient-aligned data selection for RL — the expensive end LAD undercuts on cost.
Down-sampling by pass-rate during training; LAD scores offline, pre-purchase.
Difficulty-aware task scheduling; LAD adds headroom and redundancy corrections.
Prioritized training on learnable points; requires a holdout model and gradients.
Effective-number diversity from kernel eigenvalues — LAD's diversity factor.
Influence-based selection; strong but ~400× the cost of LAD's rollouts.
Attribution via many retrainings; ~100× gradient cost, near the oracle end.