A 4B coding agent, post-trained only with RL on synthetic software tasks, reaches 61.5% on SWE-bench Verified and beats models many times larger. No distillation from a frontier teacher. The missing ingredient is not a bigger model. It is tasks calibrated to what the current checkpoint can almost, but not quite, solve.

The pipeline estimates how often the agent already resolves a candidate task, then rewrites the ones that are too easy or too hard until they sit in a learnable band. As the policy improves, the curriculum moves: from heavily scaffolded bug fixes toward shorter statements and more diverse change types. A simple tool harness (read, write, edit, glob, bash) lifts the same 4B base far more than it lifts large models. Failures remain mostly reasoning, not tool use. Effective reward hacking is held at zero by the harness, not by hoping the agent is honest.

Recursive self-improvement is usually told as a spell: the model tweaks itself, gets smarter, tweaks itself again. Control theory treats that as a feedback loop with a maximum safe speed, set by how fast you can generate trustworthy evidence that a change was actually an improvement.

A loop stays stable when the product of its gains stays below one. Gain here is how large a modification the system makes per unit of evidence. The entire appeal of self-improvement is high gain. Adaptive control already learned the hard version of this: proofs assumed a plant, a mild violation of the assumptions sent the system haywire. Unstable adaptive systems often do not blow up immediately. They burst: run beautifully, then fail without warning.

Scientific invention requires more than pattern recognition or formal proof. Following Einstein’s own account of discovery, it depends on an intuitive jump from experience to new axioms. Only after that jump does deduction and verification become possible.

Large language models have become strong at induction (extracting patterns from data) and are rapidly improving at deduction (reasoning from given premises). What they still lack is the capacity for the abductive jump itself: the generation of novel explanatory principles when existing ones are insufficient.

Large language models can write essays, solve complex math problems, and generate code at impressive levels. Yet they frequently fail at surprisingly simple variations of the same tasks.

Melanie Mitchell describes this uneven performance as “jagged intelligence” — a landscape where models excel in certain areas while remaining brittle and unpredictable in closely related ones. Slight rewording of a problem, added irrelevant details, or minor changes in context can cause dramatic drops in performance, even on tasks where the model previously succeeded.

Most current AI agent research focuses on short-term tasks or narrow goals. Agentopia takes a different approach: it simulates entire lives.

The framework places 100 LLM-powered agents into persistent social worlds and runs their lives for 10 simulated years. Agents plan, form relationships, pursue personal growth, manage finances, experience setbacks, and make trade-offs between striving and well-being — all without heavy hand-engineering.