Shanghai AI Lab's S3AC Trains a Working Critic for Long-CoT RL, Scales From 1.5B to 397B With Prompt-Difficulty Sampling

S3AC (Stabilized, Selective, and Scalable Actor-Critic) from Shanghai AI Laboratory introduces a practical recipe to train critics for long-CoT RLVR, delivering token-level credit assignment plus prompt-specific baselines. Difficulty-Aware Prompt Sampling (DAPS) uses the prompt-level baseline to cut rollout waste without offline difficulty labels. The method outperforms GRPO-X across dense and MoE models from 1.5B to 397B, and at 35B it sustains single-rollout training where critic-free baselines degrade.