Does Scaling Toward AGI Depend on What System-1 Lets System-2 Execute?

The paper argues a qualified yes: co-designing a lightweight System-1 predictor with a costly System-2 executor can reduce execution compute toward 1/ρ_u where interactions are costly, unevenly informative, and predictable before execution.

Progress toward AGI has largely relied on scaling a resource-intensive System-2 through larger models, more data and compute, longer reasoning, and more agents. The paper asks whether the next stage may come instead from co-designing System-2 with a lightweight System-1 that evaluates candidate interactions before execution. It focuses on costly, unequal-value, predictable interactions and asks which interactions justify their costs.

The paper defines a conditional interaction policy over feasible interactions, with predicted utility, a threshold, and abstention when none are admitted. It defines Interaction Information Efficiency as utility per unit of screening plus execution cost and pairs it with yield. It formulates a master conditional-interaction objective as a fractional knapsack whose Lagrangian gives a threshold rule. It decomposes co-design into predictive and executive operators and analyzes co-scaling under fixed error curves. It applies the same predict–gate–execute–update ledger to training, test-time reasoning, adaptive decision-making, and agentic tool or computer use.

• Under ideal screening and equal execution costs, execution compute falls by a factor approaching 1/ρ_u; prediction errors, exploration, and distribution shift reduce the saving. §Abstract
• Interaction Information Efficiency is utility obtained per unit of system-level cost, and because a ratio can be raised by obtaining very little at very low cost, it is always reported with yield. §2.2 The Interaction Information Efficiency Metric
• Proposition 13 gives comparative statics: under fixed error curves and k≥1 scaling of System-2 costs, the set of optimal System-1 sizes is non-decreasing in k, and the maximal IIE ratio is non-decreasing in k. §3.2 Co-Scaling: System-1’s Size as System-2 Grows
• Proposition 22 bounds the one-probe test-time gate: accuracy loss is at most δ_FN and compute is at most ρ_u^tt + (1+c_pred)/C + δ_FP of unconditional compute, with multiplier approaching 1/ρ_u^tt as C→∞ and δ_FP→0. §6.1 Face I: Efficient Test-Time Scaling
• Proposition 24 states that with a perfect free gate and constant ρ_u, L_CI(C)=L_base(C/ρ_u), so on a log-compute axis the conditional curve is shifted left by ln(1/ρ_u). §7.1 The Scaling Hypothesis: Informative Compute
• Section 7.2 states that the predictor is trained on p_train(i) ∝ p_cand(i)e(i) ≠ p_cand(i), so labels are missing not at random; positivity needs an exploration mixture or audit sampling with e(i)≥e_min>0. §7.2 Selective Supervision: The Gate Censors Its Own Training Data

• The paper states that the test-time efficiency claim lacks even indirect support: neither the small informative fraction nor an accurate halting predictor has been measured.
• Proposition 13 is comparative statics under fixed error curves; it does not show that growing System-1 helps an evolving executive or at what rate System-1 should grow.
• The gate censors its own training data; the paper says how large e_min must be, how inverse-propensity variance trades against screening gain, and whether rates survive adaptive censored collection remain open.
• The agentic cost bound assumes separable actions; the paper states it fails on long interface trajectories and when locally uninformative actions are prerequisites, and per-action error must shrink with horizon.

• Conditional interaction is a predict–gate–execute–update loop: System-1 predicts each candidate’s utility, System-2 executes admitted candidates, and outcomes update System-1. §2 Conditional Interaction as A Co-Design Strategy: Predict Before You Pay
• System-1 is defined by execution role, not model family: it scores a candidate at c_pred << c_exec, while System-2 performs the resource-demanding interaction. §2 Conditional Interaction as A Co-Design Strategy: Predict Before You Pay
• The policy uses a threshold κ_t and can abstain when the admissible set is empty; β controls selection sharpness and exploration among admissible candidates. §2.1 Core Definition
• The master objective is a fractional knapsack; its Lagrangian threshold rule admits candidates in order of value per unit cost. §2.3 A Master Objective and Its Special Cases
• The operator decomposition refits System-1 first and then steps System-2 along gradients sampled through the refitted gate. §3.1 The Two Systems as an Operator Decomposition
• Proposition 13 fixes only the direction of co-scaling, not its rate; measuring fp, fn, and c_pred is described as the co-design counterpart of a scaling law. §3.2 Co-Scaling: System-1’s Size as System-2 Grows
• Test-time scaling and adaptive decision-making are cast as conditional interaction with inference compute or action cost as the ledger. §6 Conditional Interaction at Test Time
• The scaling hypothesis treats ρ_u as a measurable coordinate of scaling efficiency and makes informative compute a better description than total compute. §7.1 The Scaling Hypothesis: Informative Compute