Position: Self-Play Only Evolves When Self-Synthetic Pipeline Ensures Learnable Information Gain

Abstract

Large language models (LLMs) make it plausible to build systems that improve through self-evolving loops, but many existing proposals are better understood as self-play and often plateau quickly. A central failure mode is that the loop synthesises more data without increasing *learnable information* for the next iteration. Through experiments on a self-play coding task, we reveal that **sustainable self-evolution requires a self-synthesised data pipeline with learnable information that increases across iterations.** We identify triadic roles that self-evolving LLMs play: the *proposer*, which generates tasks; the *solver*, which attempts solutions; and the *verifier*, which provides training signals, and we identify three system designs that jointly target learnable information gain from this triadic roles perspective. Asymmetric co-evolution closes a weak-to-strong-to-weak loop across roles. Capacity growth expands parameter and inference-time budgets to match rising learnable information. Proactive information seeking introduces external context and new task sources that prevent saturation. Together, these modules provide a measurable, system-level path from brittle self-play dynamics to sustained self-evolution.