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arxiv: 2605.05657 · v1 · submitted 2026-05-07 · 💻 cs.AI · cs.MA

Recognition: unknown

Retrieval-Conditioned Topology Selection with Provable Budget Conservation for Multi-Agent Code Generation

Abhijit Talluri , Pujith Anne , Bhagavan Choudary Pendiyala , Raghavendra Chilukuri
Authors on Pith no claims yet

Pith reviewed 2026-05-08 11:53 UTC · model grok-4.3

classification 💻 cs.AI cs.MA
keywords multi-agent systemsLLM code generationtopology selectionbudget conservationretrieval-guided orchestrationresource algebrasstructural complexity vector
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The pith

Retrieval from a hierarchical code index lets multi-agent systems select orchestration topologies while provably conserving budgets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Retrieval-Guided Adaptive Orchestration to solve the routing problem in multi-agent LLM code generation. It extracts a structural complexity vector from a hierarchical code index and uses that vector to choose the orchestration topology before generation begins. This choice is then governed by formal contracts that assign six-dimensional budget vectors to sub-agents. The central result is that the combination of complexity-conditioned routing and a resource algebra produces provable budget conservation, a guarantee that neither technique delivers on its own. Readers would care because current systems pick topologies blindly and routinely exceed intended resource limits during code modification tasks.

Core claim

The composition of complexity-conditioned LLM routing and formal resource algebras yields provable budget conservation under retrieval-conditioned dynamic topology selection. The system extracts a structural complexity vector from a hierarchical code index, routes to an appropriate orchestration topology, and executes under contracts that carry six-dimensional budget vectors; a structural-induction theorem in the budget algebra ensures total resource consumption stays within the allocated bounds regardless of the topology chosen.

What carries the argument

The budget algebra with its structural-induction conservation theorem, which tracks six-dimensional resource vectors across sub-agents and guarantees that the sum of expenditures remains inside the original budget envelope when topology selection is conditioned on the retrieved complexity vector.

If this is right

  • The complexity-conditioned router reduces proxy-measured misrouting from 30.1% to 8.2%.
  • DAG construction for orchestration remains sub-millisecond.
  • Tree-index retrieval scales linearly with codebase size.
  • The conservation theorem holds for any topology reachable from the complexity vector under the formal contracts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same retrieval-plus-algebra pattern could be tested on non-code multi-agent tasks such as automated planning or scientific workflow generation if comparable structural indices exist.
  • A direct experiment could measure whether conservation still holds when the code index is incomplete or when the modification task requires structures not captured by the current vector.
  • Production deployments could use the linear scalability property to keep indexing costs negligible even as repositories grow.

Load-bearing premise

The structural complexity vector extracted from the hierarchical code index is sufficient to identify an orchestration topology that keeps total resource use inside the assigned budget.

What would settle it

A concrete run of the system on a code-modification task in which the retrieved complexity vector selects a topology yet the measured expenditure in any budget dimension exceeds the allocated vector would falsify the conservation claim.

Figures

Figures reproduced from arXiv: 2605.05657 by Abhijit Talluri, Bhagavan Choudary Pendiyala, Pujith Anne, Raghavendra Chilukuri.

Figure 1
Figure 1. Figure 1: CODE-AGENT architecture with RGAO. A user query q enters the retrieval layer (blue), which builds a tree index and extracts a complexity vector c∈R 5 . The routing layer (green) maps (c, q) to one of four topologies. The execution layer (red) verifies budget conservation (O(|V |+|E|), static) then dispatches via the three-gate swarm executor. Solid: data; dashed: contract check; dotted: retrieval signal (t… view at source ↗
Figure 2
Figure 2. Figure 2: Contract structure and budget algebra. (a) Each sub-agent is governed by an ⟨I, C, T ,M⟩ contract specifying instructions, a six-dimensional budget vector, a risk-tiered tool allowlist, and a model override. (b) The budget algebra verifies conservation at DAG construction time: the parallel composition ⊕ of child budgets must not exceed the parent on any dimension. The diamond denotes the static O(|V |+|E|… view at source ↗
Figure 3
Figure 3. Figure 3: Hierarchical code retrieval pipeline. Queries are classified into five types, each routed to a specialized strategy. Conceptual queries activate three parallel paths (LATTICE, KohakuRAG, PageIndex) fused via RRF. After code-specific reranking and 1-hop dependency expansion (Repo￾Graph), the pipeline outputs both retrieved code context and the structural complexity vector c that feeds the RGAO topology rout… view at source ↗
Figure 4
Figure 4. Figure 4: Proxy-harness results. (a) Repository-task pass@1 vs. single- and multi-agent baselines. view at source ↗
Figure 5
Figure 5. Figure 5: Swarm execution. (a) DAG build time vs. task count, below 0.01 ms for 20-task pipelines. view at source ↗
Figure 6
Figure 6. Figure 6: Tree index scalability. (a) Build time linear in file count (11.1 ms / 200 files / 2002 nodes). view at source ↗
Figure 7
Figure 7. Figure 7: Retrieval evaluation. (a) Per-strategy latency distribution. (b) Per-query classification view at source ↗
Figure 8
Figure 8. Figure 8: Orchestrator routing distribution across a 12-task hand-held set. (a) Routing mode mix: view at source ↗
Figure 9
Figure 9. Figure 9: Contract system performance. (a) Factory instantiation latency (6 contracts, all view at source ↗
Figure 10
Figure 10. Figure 10: Tree structure analysis. (a) Node type distribution for a 200-file synthetic repo (symbols view at source ↗
Figure 11
Figure 11. Figure 11: Value-guided scoring for the query “authenticate user login”. Target view at source ↗
read the original abstract

Multi-agent LLM systems for code generation face a fundamental routing problem: the optimal orchestration topology depends on the structural complexity of the code under modification, yet existing systems select topologies without consulting the codebase. We present Retrieval-Guided Adaptive Orchestration (RGAO), an architecture that closes this loop by extracting a structural complexity vector from a hierarchical code index before selecting the orchestration topology. RGAO operates within Code-Agent, a multi-agent framework whose sub-agents are governed by formal contracts with six-dimensional budget vectors. Our headline contribution is the composition of two previously separate lines of work -- complexity-conditioned LLM routing and formal resource algebras -- yielding a property neither admits alone: provable budget conservation under retrieval-conditioned dynamic topology selection. Concretely we contribute: (1) a complexity-conditioned topology router that reduces proxy-measured misrouting from 30.1% to 8.2%; (2) a budget algebra with a structural-induction conservation theorem; and (3) a hierarchical code retrieval engine. Empirical evaluation demonstrates sub-millisecond DAG construction and linear tree-index scalability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper introduces Retrieval-Guided Adaptive Orchestration (RGAO) within the Code-Agent framework for multi-agent LLM code generation. It extracts a structural complexity vector from a hierarchical code index to dynamically select an orchestration topology, governed by formal sub-agent contracts using six-dimensional budget vectors. The central claim is that composing complexity-conditioned LLM routing with a formal resource algebra yields provable budget conservation under retrieval-conditioned dynamic topology selection, supported by a structural-induction conservation theorem. Additional contributions include a topology router reducing proxy-measured misrouting from 30.1% to 8.2%, a hierarchical code retrieval engine, and empirical results on sub-millisecond DAG construction with linear scalability.

Significance. If the structural-induction theorem is shown to hold under dynamic topology selection, the work would meaningfully advance multi-agent systems by providing a provable guarantee that neither routing nor resource algebras achieve independently. The reported misrouting reduction and efficiency metrics suggest practical utility, but the absence of detailed proof sketches, evaluation protocols, and error analysis limits assessment of whether the composition truly delivers a new property.

major comments (2)
  1. The headline claim rests on the structural-induction conservation theorem applying to retrieval-conditioned dynamic topology selection. However, the abstract and available text provide no equations, proof outline, or case analysis showing that the induction hypothesis remains valid when the complexity vector alters which agent contracts or DAG edges are instantiated at runtime. Structural induction typically requires a fixed inductive structure; without explicit handling of topology variation, the conservation property may not transfer.
  2. The empirical claim of reducing proxy-measured misrouting from 30.1% to 8.2% lacks supporting details on the proxy definition, evaluation methodology, baselines, dataset, or statistical significance (e.g., error bars or number of trials). This information is load-bearing for validating the topology router's contribution and must be supplied.
minor comments (3)
  1. Define the six-dimensional budget vectors explicitly, including their components and composition rules under the algebra, to allow readers to verify the conservation property.
  2. Clarify the extraction process for the structural complexity vector from the hierarchical code index and justify why it is assumed sufficient for optimal topology selection.
  3. Add a dedicated section or appendix with the full proof of the conservation theorem, including how dynamic selection is enumerated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. The comments highlight important areas where the presentation of the theoretical guarantee and empirical evaluation can be strengthened. We address each point below and will revise the manuscript to incorporate the requested clarifications and details.

read point-by-point responses

  1. Referee: [—] The headline claim rests on the structural-induction conservation theorem applying to retrieval-conditioned dynamic topology selection. However, the abstract and available text provide no equations, proof outline, or case analysis showing that the induction hypothesis remains valid when the complexity vector alters which agent contracts or DAG edges are instantiated at runtime. Structural induction typically requires a fixed inductive structure; without explicit handling of topology variation, the conservation property may not transfer.

    Authors: We agree that the abstract does not contain the proof details and that the available text excerpt may not have made the handling of dynamic topologies sufficiently explicit. The full manuscript (Section 4) presents the budget algebra and proves the conservation theorem by structural induction over the DAG. The induction is performed on the tree-index structure rather than on a fixed topology; at each inductive step the complexity vector retrieved from the index determines the sub-DAG to instantiate, and the six-dimensional budget contracts are shown to compose algebraically regardless of which sub-topology is chosen. To make this explicit, we will add a dedicated subsection with (i) the formal statement of the theorem, (ii) a proof sketch that separates the induction on the index from the runtime topology selection, and (iii) two concrete case analyses (simple linear DAG vs. branched DAG) demonstrating that the conservation invariant is preserved under router-driven variation. This revision will directly address the concern that the inductive structure must remain valid when topologies change at runtime. revision: yes

  2. Referee: [—] The empirical claim of reducing proxy-measured misrouting from 30.1% to 8.2% lacks supporting details on the proxy definition, evaluation methodology, baselines, dataset, or statistical significance (e.g., error bars or number of trials). This information is load-bearing for validating the topology router's contribution and must be supplied.

    Authors: We acknowledge that the current manuscript provides insufficient methodological detail for this claim. The proxy is defined as the fraction of tasks where the router-selected topology differs from the oracle topology obtained by exhaustive post-hoc complexity analysis on a held-out set. Experiments were run on 500 code-modification tasks drawn from the Code-Agent benchmark suite, using three baselines (random routing, fixed single-topology, and a non-retrieval LLM classifier). Results are reported as mean ± standard deviation over 10 independent trials with statistical significance assessed via paired t-test (p < 0.01). We will expand the experimental section with the exact proxy formula, full baseline descriptions, dataset statistics, and error bars in the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity: composition of independent lines yields the claimed property without definitional reduction

full rationale

The paper's headline claim is that combining complexity-conditioned LLM routing with a formal budget algebra (equipped with its own structural-induction conservation theorem) produces provable budget conservation under dynamic topology selection. The abstract and description present the budget algebra and its theorem as a pre-existing component whose conservation property is then shown to hold when topologies are chosen at runtime from the retrieved complexity vector. No equations, definitions, or self-citations are supplied that would make the conservation property depend on the topology choices themselves or reduce the theorem to a renaming of the input data. The empirical router improvement (30.1% to 8.2% misrouting) is measured separately and does not enter the conservation argument. The derivation chain therefore remains non-circular and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Only the abstract is available, so the ledger is limited to elements explicitly named. The framework introduces formal contracts and a conservation theorem whose details are not shown.

axioms (1)
  • domain assumption The structural complexity vector from the hierarchical code index determines the optimal orchestration topology
    This assumption underpins the retrieval-conditioned router described in the abstract.
invented entities (1)
  • Six-dimensional budget vectors no independent evidence
    purpose: To govern sub-agents via formal contracts and enable the conservation theorem
    Introduced as part of the Code-Agent framework; no independent evidence outside the system is provided in the abstract.

pith-pipeline@v0.9.0 · 5504 in / 1250 out tokens · 36542 ms · 2026-05-08T11:53:15.943968+00:00 · methodology

discussion (0)

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