Spawn Freely, Act Sparingly: Progressive Risk Vesting for Recursive LLM-Agent Trees

Recursive LLM agents can broaden their search by spawning specialists. Some branches later request tools that send data or deploy code. When should a branch receive authority to act? We distinguish sandbox spawning, in which external controls prevent the specified harm, from capability activation, in which a selected branch crosses an irreversible-action boundary. Progressive Risk Vesting (PRV) holds a trajectory-level risk budget in escrow and debits it as branches are activated. We prove an anytime harm bound for adaptively generated trees. Branch outcomes may be dependent, but each local certificate needs to remain valid conditional on the full pre-activation history, including the information used to select the request. When activation gates, branch charges, and compute constraints are held fixed, delayed vesting preserves every policy available under irrevocable spawn charging. Marginal risk estimates can still fail after branch selection. In a stylized branching model, trajectory harm changes as the authority reproduction number $\mathcal{R}_A$ crosses one. As local risk $p$ approaches zero, trajectory harm is proportional to $p$ below criticality, proportional to $\sqrt{p}$ at criticality, and retains a positive floor above it. A finite-type occupancy model yields risk and compute shadow prices. For nested fanout modes with decreasing marginal value per unit risk, these prices produce a threshold rule. Branching calculations and a split-sample experiment illustrate the results. These synthetic studies do not estimate safety in deployed agents. The analysis suggests a design rule: search broadly in the sandbox and grant recursive authority sparingly, with an explicit risk charge.

Meta$^n$: Recursive Self-Improvement through Emergent Depth

Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta$^n$, which keeps the meta-operation fixed and recurses on its input instead. That operation, $Ω$, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because $Ω$ never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and an evolutionary archive searches over layer chains. Across two backbones, Meta$^n$ outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n

Recursive Agent Harnesses

Recursive language models (RLMs) showed that recursion over model calls is an effective strategy for long-context reasoning, and production coding agents have begun to write code that spawns subagents at scale, most recently in Anthropic's dynamic workflows. We name and study the pattern between these two lines of work, where the recursive unit is a full agent harness with filesystem tools, code execution, and planning rather than a model call with no tools. We call this the Recursive Agent Harness (RAH) and frame it as harness recursion, the code-first extension to the model recursion of RLMs. A parent agent generates and runs an executable script that spawns subagent harnesses in parallel for fine-grained workloads and uses structured function calls for small subtasks. We provide a controlled evaluation on long-context reasoning. With the backbone held fixed at GPT-5 to match the published Codex and RLM baselines, RAH improves the Codex coding-agent baseline from 71.75% to 81.36% on Oolong-Synthetic (199 samples, 13 context-length buckets up to 4M tokens), a gain attributable to the harness rather than the model. With a stronger backbone, Claude Sonnet 4.5, the same design reaches 89.77%.