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Three provable regimes determine when multi-agent communication helps or hurts Transformer-based reasoning.

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Multi-agent transformer systems can be formally analyzed: recall needs no communication, state tracking trades communication for parallel speedup, and k-hop reasoning requires per-hop communication.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection A genuinely useful formal framework for when multi-agent communication helps, with one real gap in the headline k-hop optimality claim that is fixable. the 3 major comments →

arxiv 2510.13903 v2 pith:BLSXWZEK submitted 2025-10-14 cs.MA cs.AIcs.LG

Benefits and Limitations of Communication in Multi-Agent Reasoning

Michael Rizvi-Martel , Satwik Bhattamishra , Neil Rathi , Guillaume Rabusseau , Michael Hahn This is my paper
classification cs.MA cs.AIcs.LG
keywords multi-agent reasoningtransformer expressivityhard attention transformersdepth-communication tradeoffstate trackingassociative recallk-hop reasoningchain-of-thought
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper asks whether communication among multiple LLM agents provably helps reasoning as problem size and context length scale. It formalizes multi-agent systems as graphs of hard-attention transformers and derives resource bounds—agents, communication, depth—for three task families: associative recall, state tracking, and k-hop reasoning. The result is a taxonomy of three regimes: recall needs essentially no communication, state tracking can be sped up in wall-clock time at the price of communication, and k-hop reasoning inherently requires communication proportional to the number of hops, with no speedup. The paper also proves a general impossibility: any task solvable with bounded communication is already solvable by a single agent in constant depth. Experiments with pretrained LLMs on the three protocols match the predicted tradeoffs.

Core claim

The central claim is that the depth–communication tradeoff of multi-agent Transformer systems falls into exactly three feasible regimes. Associative recall has depth Θ(1) and communication Θ(1) regardless of agent count. State tracking over a finite monoid can be solved with depth O(N/w + log w) using w agents and communication Θ(w), which is optimal in both communication and depth up to a log factor. k-hop reasoning requires communication Θ(k) and depth O(k) (optimal up to a log factor); adding agents cannot reduce wall-clock time in the worst case. A fourth regime—depth reduction with bounded communication—is impossible by Proposition 4.2.

What carries the argument

The central object is a multi-agent system modeled as a labeled DAG: nodes are agent states at timesteps, CoT edges are autoregressive decoding, and communication edges are messages written into another agent's context. Complexity measures are computation depth (proxy for wall-clock time), size (total nodes), and communication budget. The protocols doing the work are a single attention-head induction head for recall, a prefix-sum/parallel-scan tree for state tracking, and an iterative query handoff for k-hop reasoning. The impossibility result (Proposition 4.2) is the hinge: bounded communication lets a single agent simulate the whole protocol in constant depth.

Load-bearing premise

The upper-bound protocols require a different transformer per input length, with width growing in the length; real multi-agent systems run a single fixed model, and if uniformity across lengths is required, these constant-depth constructions may not be implementable.

What would settle it

Exhibit a multi-agent system computing PARITY or any nontrivial monoid state tracking with w(N) agents, communication budget o(w(N)) and depth o(N/w(N)); or exhibit a k-hop reasoning protocol with two agents whose communication is o(k) for some distribution of facts. Such a protocol would directly refute Propositions 4.6–4.8. Alternatively, an experiment showing a fixed LLM cannot execute the prefix-sum protocol on input lengths beyond its training distribution would test the uniformity gap.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Multi-agent systems cannot reduce total computation (size) beyond a constant factor; they only exchange depth for communication.
  • For state tracking, the prefix-sum protocol achieves near-optimal wall-clock speedup with w agents, validating recursive aggregation over flat manager aggregation.
  • For k-hop reasoning, communication budget must grow linearly with the number of hops, so naive parallelization of multi-hop queries is provably futile.
  • Tasks like associative recall can be partitioned across agents for free, so long-context retrieval does not need inter-agent communication.
  • Any task solvable by a multi-agent system with O(1) communication is already solvable by a single agent with O(1) chain-of-thought depth.

Where Pith is reading between the lines

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

  • The upper bounds are proved for non-uniform families of transformers (a different model per input length, with width growing in length); real multi-agent systems run a single fixed model, so transferring the bounds to practice rests on an unproven uniformity assumption.
  • The paper explicitly scopes out majority-voting and debate protocols (Appendix B(v)); its analysis concerns expressivity, not stochastic error reduction, so the empirical comparisons to majority voting are illustrative rather than a proof of superiority.
  • The three-regime taxonomy offers a design heuristic: choose the protocol shape based on the task family—flat broadcast for recall, a tunable prefix-sum tree for state tracking, and sequential handoffs for multi-hop queries.
  • The impossibility result (bounded communication implies constant single-agent depth) is a transformer-specific analogue of communication-complexity lower bounds; porting it to other agent models, like recurrent networks or RAM machines, would give a broader theory of when multi-agent reasoning helps.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper introduces a formal framework for analyzing the expressivity and communication costs of multi-agent Transformer-based reasoning systems. It models agents as nodes in a DAG with CoT and communication edges, defines depth, size, and communication budget, and analyzes three task families: associative recall, state tracking (finite monoids, PARITY), and k-hop reasoning. For each it gives protocols with upper bounds and claims lower bounds establishing three distinct depth-communication regimes: recall requires Θ(1) depth/communication, state tracking achieves depth O(N/w + log w) with Θ(w) communication, and k-hop reasoning requires Θ(k) communication with depth O(k). The theoretical results are complemented by experiments on Llama models using synthetic tasks, which the paper claims confirm the predicted tradeoffs.

Significance. If the bounds are correct, this is a valuable contribution: it provides a principled, formal basis for understanding when multi-agent communication provably helps or does not help LLM-based systems, with concrete protocols and a clear three-regime taxonomy. The framework is general enough to connect to several applied multi-agent architectures, and the paper includes reproducible code and detailed appendix proofs. The recall and state-tracking results appear sound and the qualitative high-level picture is plausible. However, as detailed below, a load-bearing optimality claim for k-hop reasoning is not established as written, and the non-uniform nature of the expressibility model creates a gap between theory and the experimental confirmation language.

major comments (3)
  1. [§4.4, Prop 4.8 / App. C.5, Table 1] Communication budget is defined in Def. 3.2 as the number of nodes with an outgoing communication edge, i.e., a message count, with messages drawn from Ξ_{N+k} of size poly(N+k). The cited Tesson–Thérien lower bound is in communication bits; a single message can encode Θ(log(N+k)) bits. The proof in App. C.5 performs the bits-to-messages conversion only for the depth lower bound (yielding Ω(k/log(N+k))), but then states the communication budget is Ω(k) and 'optimal' without the log factor. Consequently Table 1's Θ(k) communication entry for k-hop reasoning is unsupported; the established lower bound is Ω(k/log(N+k)) messages. Since this underpins the claimed third regime, the optimality claim must be either re-proved or restated with the log factor.
  2. [§4.3, Prop 4.7 / App. C.4] The depth lower bound claims Ω(N/w(N)) for any nontrivial group M. The proof uses 'N=Size≤Depth·Agents' at Eq. (19), but Size=Ω(N) is only established in Prop 4.4 for PARITY. No proof or citation is provided that arbitrary nontrivial-group state tracking requires Ω(N) size in UHAT. Without this, the depth optimality claim for general M is not justified; the proposition should be restricted to PARITY (or a suitable group) or the missing size lower bound supplied.
  3. [§3 and §5] Expressibility in UHAT is non-uniform in input length: for each n a different Transformer T_n is allowed, with width d growing with n (Section 3, definition of expressible). The empirical section uses a single fixed pretrained LLM (Llama, etc.) prompted to follow the protocols. The theory therefore does not directly predict fixed-model performance; the statement in the abstract that experiments 'confirm' the tradeoffs is stronger than the model supports. The authors should either add a uniformity discussion or temper the confirmation claim.
minor comments (3)
  1. [§6] Typo: 'self-consistencty' should be 'self-consistency'.
  2. [Def. 3.1] Item 4 reads 'outgoing edges edge with the same label'; this should be 'outgoing edges with the same label'.
  3. [Table 1] For k-hop reasoning, the Size entry is listed as O(wk) without specifying whether k is treated as a parameter or constant; clarifying this would help the reader interpret the scaling.

Circularity Check

0 steps flagged

No significant circularity; the core derivations are constructive protocols with independent lower-bound citations, and the empirical section tests rather than fits the theory.

full rationale

I walked the derivation chain of the paper. The main results (Prop. 4.3 recall, Prop. 4.6 state tracking, Prop. 4.8 k-hop) are proved by exhibited UHAT protocols and by independent lower-bound arguments. The state-tracking size lower bound (Prop. 4.4) reduces to the single-agent PARITY lower bound of Amiri et al. (2025); although that work shares an author with the present paper, the cited theorem is a published, parameter-free result about UHAT CoT length and does not assume the multi-agent conclusion, so under the review rules it is external support rather than a circular self-citation. The depth lower bound for state tracking follows from the paper's own conservation-of-size identity, not from the desired conclusion. The k-hop optimality proof cites Tesson & Thérien for a communication-complexity lower bound; the skeptic's bit-vs-message concern about converting an Ω(k) bit bound into Θ(k) messages is a potential correctness gap, not a circularity, because the paper is not redefining communication to match its conclusion. The experiments implement the protocols and compare accuracy and token counts; no parameter is fitted to the target claims, so the empirical section is not a fitted-input-called-prediction step. The non-uniform width assumption and the synthetic-task limitation are acknowledged weaknesses (Section 3 and Appendix B), but they do not make any derivation equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The central results rest on three modeling choices: UHAT as the agent architecture, per-length non-uniform transformers with unbounded width, and alphabets that grow polynomially with input length. They also import two external lower-bound theorems (Amiri et al. for PARITY, Tesson & Thérien for permutation composition) plus a threshold-circuit-to-MLP lemma. No free parameters are fitted.

axioms (6)
  • domain assumption UHAT (unique hard attention) with fixed precision is an adequate model for long-context Transformer reasoning
    Section 2 introduces UHAT as the agent model; if softmax transformers can implement behaviors UHAT cannot, the lower bounds would not transfer to real LLMs.
  • domain assumption Expressibility is non-uniform: a different transformer T_n (with unbounded width d) is allowed for each input length n
    Section 3 ('expressible in UHAT'); upper-bound protocols rely on length-specific positional encodings and growing width, so a single fixed LLM may not realize them.
  • domain assumption Input and CoT alphabets grow polynomially with input length (|Σ_N|,|Ξ_N| ∈ O(poly(N)))
    Section 3, Definition 3.1; this makes communication measured in tokens/edges rather than bits and is necessary for the Θ(1) recall and Θ(k) k-hop communication claims.
  • standard math The Amiri et al. (2025) lower bound: any UHAT CoT computing PARITY has length Ω(N)
    Used in Appendix C.4 to prove Prop. 4.4 (PARITY requires size Ω(N)); the theorem shares author Michael Hahn with the present paper, an author-overlap dependency.
  • standard math Tesson & Thérien (2002): composition of k permutations over {1,...,5} has communication complexity Ω(k)
    Used in Appendix C.5 for the k-hop communication lower bound; as applied it conflates bit complexity with message complexity, since tokens carry O(log N) bits.
  • standard math Vardi et al. (2021, Lemma 22): threshold circuits of size s and depth m can be simulated by ReLU MLPs with depth m+1 and size O(s)
    Used throughout Appendix C to justify MLP steps in UHAT constructions.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Benefits and Limitations of Communication in Multi-Agent Reasoning." pith.science (2026). https://pith.science/paper/BLSXWZEK

@misc{pith2026251013903,
  author       = {Pith},
  title        = {Pith review of: Benefits and Limitations of Communication in Multi-Agent Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BLSXWZEK}},
  note         = {Machine review of arXiv:2510.13903}
}
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abstract

Chain-of-thought prompting has popularized step-by-step reasoning in large language models, yet model performance still degrades as problem complexity and context length grow. By decomposing difficult tasks with long contexts into shorter, manageable ones, recent multi-agent paradigms offer a promising near-term solution to this problem. However, the fundamental capacities of such systems are poorly understood. In this work, we propose a theoretical framework to analyze the expressivity of multi-agent systems. We apply our framework to three algorithmic families: state tracking, recall, and $k$-hop reasoning. We derive bounds on (i) the number of agents required to solve the task exactly, (ii) the quantity and structure of inter-agent communication, and (iii) the achievable speedups as problem size and context scale. Our results identify regimes where communication is provably beneficial, delineate tradeoffs between agent count and bandwidth, and expose intrinsic limitations when either resource is constrained. We complement our theoretical analysis with a set of experiments on pretrained LLMs using controlled synthetic benchmarks. Empirical outcomes confirm the tradeoffs between key quantities predicted by our theory. Collectively, our analysis offers principled guidance for designing scalable multi-agent reasoning systems.

Figures

Figures reproduced from arXiv: 2510.13903 by Guillaume Rabusseau, Michael Hahn, Michael Rizvi-Martel, Neil Rathi, Satwik Bhattamishra.

Figure 1
Figure 1. Figure 1: Graphical representations of the protocols analyzed in Section 4. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Three possible and one im￾possible regimes for depth-communication tradeoffs. See proof in Appendix C.2. Taken together, this leaves us with three distinct feasible regimes of multi-agent reasoning ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Llama-70B accuracy on RE￾CALL across sequence lengths. CoA is the theoretically optimal protocol. We start by validating experimentally the abilities of different multi-agent systems to perform associative re￾call. Given a string of key-value pairs and a queried key, models must return the associated value. We use self-consistency with majority voting (Wang et al., 2022) as our baseline and use an implemen… view at source ↗
Figure 4
Figure 4. Figure 4: Empirical validation for PARITY [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Empirical validation for k-hop reasoning. 5.3 k-HOP REASONING Finally, we evaluate models on a k-hop reasoning task, where agents are given facts (e.g., ”Paula is the boss of Mary”) and a query (e.g., ”Who is the boss of the friend of George?”). Task difficulty depends on the number of facts and query hops. We compare two protocols: Majority Voting and Iterative Query, an implementation of the protocol pro… view at source ↗
Figure 6
Figure 6. Figure 6: Communication vs Computation tradeoff for Llama-8B showing the relationship between [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Parity calculation accuracy for Llama-8B across different sequence lengths, comparing [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Performance comparison of multi-agent approaches on the [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Performance comparison of multi-agent approaches on the [PITH_FULL_IMAGE:figures/full_fig_p032_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of multi-agent approaches for [PITH_FULL_IMAGE:figures/full_fig_p032_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of multi-agent approaches for [PITH_FULL_IMAGE:figures/full_fig_p033_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of multi-agent approaches for [PITH_FULL_IMAGE:figures/full_fig_p033_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Llama-70B k-hop reasoning accuracy with 200 facts. 4 6 8 10 12 14 16 18 20 Number of Hops 0 200 400 600 800 1000 1200 Computation Depth Token Usage Analysis: Llama-8B 100 facts 200 facts 500 facts [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Computation depth vs. number of hops in the query for Lama-8B. [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

72 extracted references · 1 canonical work pages · cited by 3 Pith papers · 1 internal anchor

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    In 0 0 0 0 0 0 0 0 # (10) W(R) V =

    Finally, we set W(L) V = "In 0 0 0 0 0 0 0 0 # (10) W(R) V = "0 0 0 0 I |D| 0 0 0 0 # (11) The MLP for the first layer trivially computes an identity map. For the second layer, we use a construction similar to that of the retrieval heads used in the proof for Prop. 4.7. In essence we select the firstlogndimensions of the vectors with both key and query ma...

    2025

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    23 42 12 34 56 78 90 12|Query: 56

    Present the final answer in the format ”The answer is: [your answer]” You MUST use the following template. ONLY OUTPUT THE ANSWER. Here is an example for “23 42 12 34 56 78 90 12|Query: 56”: 23 Preprint The answer is: 78 Associative Recall Chain-of-Agents Worker Prompt You are a reasoning agent responsible for analyzing a portion of a document. Your task ...

  3. [6]

    swap ball 1 and 3, swap ball 2 and 4

    Present the final answer in the format ”The answer is: [your answer]” You MUST use the following template. Here is an example for ”1011”: 1: 1 0: 1 1: 2 1: 3 Final count: 3 The answer is: 1 D.3S 5 PERMUTATIONTRACKINGTASK We frame theS5 permutations task as a word problem where each agent is given a prompt explaining there are 5 balls in 5 distinct bins an...

    2024

  4. [7]

    Identify if the key is present in the sequence of key-value pairs

  5. [8]

    If the key is present, return the value corresponding to the key

  6. [9]

    NOT FOUND

    If the key is not present, return “NOT FOUND”

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    The answer is: [your answer]

    Present the final answer in the format “The answer is: [your answer]” You MUST use the following template. ONLY OUTPUT THE ANSWER. Here is an example for “23 42 12 34 56 78 90 12|Query: 56”: The answer is: 78 Associative Recall Chain-of-Agents Manager Prompt You are a manager agent responsible for synthesizing information from multiple workers. Your task ...

  8. [11]

    Collect the value results from all worker agents

  9. [12]

    NOT FOUND

    Each worker will return either a value or “NOT FOUND”

  10. [13]

    NOT FOUND

    Exactly one worker will return the value corresponding to the query, the rest will return “NOT FOUND”

  11. [14]

    Report the value corresponding to the query as your output

  12. [15]

    The answer is: [your answer]

    Present the final answer in the format “The answer is: [your answer]” You MUST use the following template. ONLY OUTPUT THE ANSWER. Here is an example for “NOT FOUND NOT FOUND 78 NOT FOUND”: The answer is: 78 D.2 PARITYCALCULATIONTASK String of bits of fixed length are sampled uniformly at random. Ground truth is computed with a function which evaluates pa...

  13. [17]

    24 Preprint

    If the count is even, return 0. 24 Preprint

  14. [19]

    Present the final answer in the format ”The answer is: [your answer]” You MUST use the following template. Here is an example for ”1011”: 1: 1 (count: 1) 2: 0 (count: 1) 3: 1 (count: 2) 4: 1 (count: 3) Final count: 3 The answer is: 1 Parity Prefix Sum Prompt You are a manager agent responsible for synthesizing the results of previous workers. Your task is...

  15. [20]

    This should be a list of binary digits (0 or 1)

    Collect the results from the worker agents. This should be a list of binary digits (0 or 1)

  16. [21]

    If the parity of the list is even, return 0

  17. [22]

    If the parity of the list is odd, return 1

  18. [23]

    Present the final answer on a new line in the format ”The answer is: [your answer]” IMPORTANT: Show your work step by step to demonstrate thorough analysis:

  19. [24]

    Go through each bit position and note its value

  20. [25]

    Keep a running count of 1s encountered

  21. [26]

    State the final count

  22. [27]

    Determine if the count is even or odd You MUST use the following template. Here is an example for ”1011”: 1: 1 0: 1 1: 2 1: 3 Final count: 3 The answer is: 1 Parity Chain-of-Agents Worker Prompt You are a worker agent responsible for analyzing a portion of a document. Your task is to provide an analysis of the binary string provided in your chunk and dete...

  23. [28]

    Count the number of 1’s in the binary string

  24. [29]

    If the count is even, return 0

  25. [30]

    If the count is odd, return 1

  26. [31]

    Provide your result in a clear and concise manner

  27. [32]

    Present the final answer in the format ”The answer is: [your answer]” You MUST use the following template. Here is an example for ”1011”: 1: 1 0: 1 1: 2 1: 3 Final count: 3 The answer is: 1 25 Preprint Parity Chain-of-Agents Manager Prompt You are a manager agent responsible for synthesizing information from multiple workers. Your task is to combine their...

  28. [33]

    Collect the parity results from all worker agents

  29. [34]

    Each worker will return either 0 or 1

  30. [35]

    Count the number of 1 responses

  31. [36]

    If the count of 1 responses is even, the overall parity is 0

  32. [37]

    If the count of 1 responses is odd, the overall parity is 1

  33. [39]

    First, identify which balls are mentioned in the swap operations - ONLY track these balls

  34. [40]

    Start with balls in their initial positions (e.g., if balls 1, 2, 3 are mentioned:{1:1, 2:2, 3:3})

  35. [41]

    For each swap operation ”Swap ball X and ball Y”: • Find the current bins of ball X and ball Y • Exchange their positions

  36. [42]

    Continue until all swaps are processed

  37. [43]

    Do not add extra balls

    Present your final answer as a dictionary mapping ONLY the balls mentioned in swaps to their final positions IMPORTANT: Only include balls that appear in the swap operations. Do not add extra balls. Present the final answer in the format ”The answer is:{ball1:bin1, ball2:bin2, ...}” for only the balls involved in swaps. 26 Preprint Permutation Chain-of-Ag...

  38. [44]

    Start with the EXACT positions given to you - this is the state after previous swaps

  39. [45]

    Process each swap operation ”Swap ball X and ball Y” in order: • Find the current bins of ball X and ball Y • Exchange ONLY their positions • Keep all other balls in their current positions

  40. [46]

    Track each swap carefully - one mistake will affect the final result

  41. [47]

    The exact same balls, no more, no less

    Report the state after processing ALL your assigned swaps CRITICAL: Only include the balls that are present in the input positions. The exact same balls, no more, no less. Present the final answer in the format ”The answer is:{ball1:bin1, ball2:bin2, ...}” with the exact same ball numbers as your input. Permutation Chain-of-Agents Manager Prompt You are a...

  42. [48]

    The workers processed swaps in chronological order (worker 1→worker 2→worker 3, etc.)

  43. [49]

    Each worker started with the positions left by the previous worker

  44. [50]

    The LAST worker’s result contains the final positions after all swaps

  45. [51]

    This represents the complete final state

    Simply report the last worker’s position dictionary as the final answer CRITICAL: Take the position dictionary from the last (final) worker only. This represents the complete final state. Present the final answer in the format ”The answer is:{ball1:bin1, ball2:bin2, ...}” exactly as reported by the final worker. Permutation Prefix Sum Worker Prompt You ar...

  46. [52]

    Current state: [copy the input dictionary]

  47. [53]

    Operation: [copy the swap operation]

  48. [54]

    Ball X is currently in bin: [identify bin number] 27 Preprint

  49. [55]

    Ball Y is currently in bin: [identify bin number]

  50. [56]

    After swap: Ball X moves to bin [Y’s old bin], Ball Y moves to bin [X’s old bin]

  51. [57]

    Verification: Check that only these two balls changed positions, all others remain the same

  52. [58]

    Final state: [complete updated dictionary] CRITICAL CONCEPT: You are tracking which BALL is in which BIN. • BALLS are the moving objects (numbered 1, 2, 3, 4, 5) • BINS are the fixed locations (numbered 1, 2, 3, 4, 5) • When you swap ”ball X and ball Y”, you move those balls to different bins • The bins stay in place - only the balls move between them CRI...

  53. [59]

    Validate that each worker’s result is a logical continuation of the previous worker’s output

  54. [60]

    Show the complete sequence of states from initial to final

  55. [61]

    Verify that each step represents exactly one swap operation

  56. [62]

    Report the last worker’s result as your final output Use this reasoning template:

  57. [63]

    Initial state: [first worker’s input state]

  58. [64]

    After worker 1: [worker 1’s result] - validate this is one swap from initial

  59. [65]

    After worker 2: [worker 2’s result] - validate this is one swap from worker 1’s result

  60. [66]

    This contains the cumulative effect of all swaps

    Final result: [last worker’s result] CRITICAL: Output exactly the position dictionary from the final (last) worker. This contains the cumulative effect of all swaps. Present the final answer in the format ”The answer is:{ball1:bin1, ball2:bin2, ...}” exactly as reported by the last worker. D.4k-HOPREASONINGTASK We create a list of entities and a list of r...

  61. [67]

    A set of facts describing relationships between people (e.g., ”Alice’s boss is Bob”)

  62. [68]

    A query asking about a multi-step relationship chain Instructions: • Read all the facts carefully • Follow the relationship chain step by step • Track each connection to find the final answer • Output your answer in the exact format: Answer: [PersonName] Example: Facts: ”John’s boss is Mary. Mary’s supervisor is Tom.” Query: ”Who is the supervisor of the ...

  63. [69]

    A limited set of facts about relationships between people

  64. [70]

    Alice’s teacher is Bob.” Query: ”Who is John’s boss?” Response: Answer: Mary Example (not found - very common): Facts: ”John’s boss is Mary

    A specific query about one relationship Instructions: • ONLY look through the facts provided to you • If you find the EXACT fact needed to answer the query, extract the answer • If the exact fact is NOT in your subset (which is very common), respond with ”Not Found” • DO NOT guess or infer answers from similar facts • DO NOT make assumptions about relatio...

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    Re-read the query to understand exactly what is being asked

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    Scan through ALL the facts again to verify your answer or confirm it’s not found

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    Make sure the relationship type matches exactly (e.g., ”boss” vs ”supervisor”)

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    Only answer if the exact fact is present and you have double-checked it

    Only provide an answer if you are completely certain it appears in the facts Remember: Most queries will not have their answer in your subset of facts. Only answer if the exact fact is present and you have double-checked it. 29 Preprint K-hop IterativeQuery Manager Agent Prompt You are a manager agent that coordinates multi-hop reasoning queries. Your tas...

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    The original multi-hop question

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    The current intermediate answer

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    E.1 PARITY In this section, we provide PARITYresults similar to those in the main text, but with llama-8B as the base model for agents

    The current step number Instructions: • Use the intermediate answer to construct the next query • Format your response as: Next Query: [YourQuery] Example: Original question: ”Who is the supervisor of the boss of John?” Current answer: ”Mary” (John’s boss) Response: Next Query: Who is Mary’s supervisor? E ADDITIONALEXPERIMENTS In this section, we provide ...

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    Multi2: Multi-Agent Test-Time Scalable Framework for Multi-Document Processing

    Association for Computational Linguistics. doi: 10.18653/v1/2020.emnlp-main.576. URL https://aclanthology.org/2020.emnlp-main.576. Satwik Bhattamishra, Michael Hahn, Phil Blunsom, and Varun Kanade. Separations in the repre- sentational capabilities of transformers and recurrent architectures. InThe Thirty-eighth Annual Conference on Neural Information Pro...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2502.20592 2020

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.