Repair the Amplifier, Not the Symptom: Stable World-Model Correction for Agent Rollouts

🕒 Published (v1): 2026-07-02 06:31 UTC · Source: Arxiv · link

Why this paper was selected

Targeted world-model correction for long-horizon agent rollouts — addresses planning graph failure modes

Ask a follow-up

Open an assistant pre-loaded with this paper's context.

💬 Ask ChatGPT✦ Ask Claude

TL;DR

Long-horizon LLM agent workflows produce large planning graphs where failures propagate causally; replanning the entire graph is prohibitively expensive and noisy. This paper introduces WM-SAR, a world-model corrector that uses spectral graph theory to identify the minimal connected subgraph driving error amplification — not the most visible symptom — and routes only that subgraph to an LLM for targeted repair. WM-SAR achieves near-whole-graph stabilization with ~3× fewer nodes than brute-force neighbourhood expansion.

Problem

As LLM agents operate over thousands of steps, failures occur inside large typed planning graphs rather than in isolated predictions. Existing approaches either replan the full graph (consuming large context budgets and degrading long-context retrieval) or apply engineering scans that fix the most visibly erroneous node — leaving intact the causal subgraph that will re-amplify the error in subsequent rollouts. No prior work addresses targeted, budget-constrained, stability-oriented repair of a failed graph world model.

Method

The paper models a failed rollout as a typed failure graph \(G_f = (V, E, X, t^\star)\) where nodes are agent calls (planner, executor, validator, etc.) and edges encode typed causal dependencies. The repair objective is:

\[R^* = \arg\min_{\substack{R \subseteq V:\, G_f[R]\text{ connected},\, |R| \leq K_{\max}}} \rho(B_{G_f \setminus R})\]

where \(\rho(B)\) is the spectral radius of the coupled node-edge error operator \(B\) whose \((1,1)\) block is the node Lipschitz constant \(L_X\) and whose off-diagonal blocks encode cross-channel amplification. The planning-regret bound is shown to grow as \(\Phi_H(\gamma, \rho(B)) = \sum_{t=0}^{H-1}(\gamma\rho)^t\), making \(\rho(B)\) the natural repair target.

WM-SAR algorithm (two phases):

Phase 1 — region selection: 1. GEAF score per node: \(\widehat{\text{GEAF}}_v = e(v)\cdot\rho(A_v)\cdot w^H\), combining observed error magnitude \(e(v)\) with the spectral radius \(\rho(A_v)\) of the \(H\)-hop local subgraph (structural amplification capacity), discounted by horizon \(w^H\). 2. Coupling factor: \(\kappa_v = L_A(v)\cdot M_X(v)\), where \(L_A(v) = w\beta_A \bar{d}_{\text{in}}(v)\cdot\bar{e}(v)\) and \(M_X(v) = w\beta_X \bar{d}_{\text{out}}(v)\cdot\bar{e}(v)\) capture the super-additive node-edge interaction. 3. Seed selection: top-\(k_0\) nodes by \(e(v)\cdot\widehat{\text{GEAF}}_v\cdot(1+\kappa_v)\). 4. Greedy \(\rho(B)\)-relief growing: from each seed, iteratively add the boundary node \(u^*\) maximizing \(g_R(u) = \lambda_1 e(u)(1+\kappa_u) + \lambda_2 \Delta\rho_{\text{rel}}(u) - \lambda_3 c(u)\), where \(\Delta\rho_{\text{rel}}(u) = \rho(B_{G_f\setminus R}) - \rho(B_{G_f\setminus(R\cup\{u\})})\) is the marginal spectral-radius reduction. 5. Pruning and selection: remove nodes that do not increase \(\rho(B_{G_f\setminus R})\) upon removal; choose the candidate region maximizing \(\text{Score}(R) = \frac{\sum_{v\in R} e(v)(1+\kappa_v)\cdot\Delta\rho_{\text{rel}}(R)}{1+|R|}\).

Phase 2 — LLM repair: only the selected subgraph (node types, states, boundary edges) is serialized and passed to an LLM for root-cause identification and structured repair. In simulation, repair zeroes selected node errors and re-runs the rollout.

Key Contributions

• Formulation of world-model correction as a spectral stability problem: choose the smallest connected region that lowers \(\rho(B_{G_f\setminus R})\) under budget \(K_{\max}\), rather than minimizing total observed error.
• Proof that the coupled node-edge spectral radius \(\rho(B)\) bounds both rollout error growth (Theorem 2) and planning regret (Theorem 3, \(J(\pi^*) - J(\hat\pi) \leq 2L_R\kappa\epsilon\Phi_H(\gamma,\rho(B)) + 2\epsilon_R H\)).
• The GEAF score as the first per-node quantity derived from rollout error theory that enables prospective amplification identification.
• A comprehensive engineering-corrector family (Greedy-Point, TopK, Window, LocalRepair, CascadeRepair, full-graph LLM) as strong baselines.
• Empirical demonstration that region selection — not LLM capability — is the bottleneck in graph-repair quality.

Results

• WM-SAR outperforms all engineering correctors on NodeMSE, GrowthSlope, and residual spectral-radius reduction across the agent calling-tree testbed (Table 1; specific numbers not fully reproduced in the provided excerpt).
• Engineering correctors reduce short-horizon error but leave residual spectral mass intact; WM-SAR flattens the long-horizon error growth curve (Figure 6).
• WM-SAR selects ~8 nodes on average and achieves similar spectral relief to LocalRepair-3Hop, which nearly covers the entire graph — approximately 3× node-count reduction.
• Cross-model study confirms the context-selection advantage across GPT-4o, GPT-4o-mini, and Gemini-2.5-Flash.
• Full-graph LLM repair is competitive on small graphs but token-heavy; WM-SAR sits on the efficient frontier in the token–quality tradeoff (Figure 4).
• Results hold on benchmark-inspired topologies mimicking SWE-bench, WebArena, and AgentBench-style agent workflows (Table 3).

Limitations

• Evaluation is entirely on a synthetic heterogeneous calling-tree testbed; no experiments on real deployed LLM agent systems.
• Minimizing \(\rho(B_{G_f\setminus R})\) over connected subsets is NP-hard in general; WM-SAR is a greedy approximation with no optimality guarantee.
• The repair operator (zeroing node errors) is simulated; whether this translates faithfully to re-invocating real tools, planners, or memory updates is unverified.
• Uniform uncertainty in the dataset makes the uncertainty term of the seed score inactive; the method's behavior under heterogeneous uncertainty is untested.
• Testbed graphs are medium-sized; scalability to graphs with tens of thousands of nodes (the motivating setting) is asserted theoretically but not empirically demonstrated.

Relevance to Agentic AI / LLM Agents

This paper directly tackles a core infrastructure gap in long-horizon agentic systems: how to recover from failures in persistent planning graphs without full-graph replay. The framing of a planning graph as a spectral object — and repair as a stability problem rather than an attribution problem — is a conceptual shift with broad applicability to any multi-step agent architecture (ReAct, LATS, Reflexion, SWE-agent). WM-SAR's emphasis on token-budget discipline is especially timely, as agents are increasingly bounded by context-window costs rather than compute. The typed graph representation (planner, executor, validator nodes with typed dependency edges) maps cleanly onto real multi-agent orchestration frameworks, making the approach directly actionable for practitioners building persistent agentic workflows.