Thought Communication in Multiagent Collaboration
Authors: Yujia Zheng
Zhuokai Zhao
Zijian Li
Yaqi Xie
Mingze Gao
Lizhu Zhang
Kun Zhang
Venue: NeurIPS 2025 spotlight ()
Keywords: multiagent system
inter-agent communication
latent variable models
foundation models
Primary area: deep_learning
TL;DR: We propose thought communication for agents to interact directly mind-to-mind, prove its nonparametric identifiability, and develop a framework for communication beyond language.

Abstract: Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely on natural language, exchanging tokens or their embeddings. To go beyond language, we introduce a new paradigm, *thought communication*, which enables agents to interact directly mind-to-mind, akin to telepathy. To uncover these latent thoughts in a principled way, we formalize the process as a general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in a nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees. Guided by the established theory, we develop a framework that extracts latent thoughts from all agents prior to communication and assigns each agent the relevant thoughts, along with their sharing patterns. This paradigm naturally extends beyond LLMs to all modalities, as most observational data arise from hidden generative processes. Experiments on both synthetic and real-world benchmarks validate the theory and demonstrate the collaborative advantages of thought communication. We hope this work illuminates the potential of leveraging the hidden world, as many challenges remain unsolvable through surface-level observation alone, regardless of compute or data scale.

Thought Communication in Multiagent Collaboration
Yujia Zhengl?
Zhuokai Zhao?
Zijian Li Kun Zhang
Yaqi Xie
Mingze Gao
Lizhu Zhangi:
3 MBBZAA Kyujiazh, kunz1)@cmu, edu {zhuokai, lizhu) com
CMU Meta AI
Abstract
Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely natural language, exchanging tokens their embeddings. To go beyond language, we introduce new paradigm, thought communication, which enables agents interact directly mind-to to-ddd, akin telepathy. To uncover these latent thoughts in principled way, we formalize the process general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees. Guided by the established theory, we develop a framework that extracts latent thoughts from all agents prior communication and assigns each agent the relevant thoughts, along with their sharing patterns. This paradigm naturally extends beyond LLMs to modalities, most observational data arise from hidden generative processes. Experiments both synthetic and real-world benchmarks validate the theory and demonstrate the collaborative advantages of thought communication. We hope this work illuminates the potential of leveraging the hidden world, as many challenges remain unsolvable through surface-level observation alone, regardless of compute or data scale.
Introduction
Natural language has enabled human collaboration at scale, but it also imposes fundamental limita- tions. While powerful, language is inherently sequential, ambiguous, and imprecise, offering only an indirect and fragmented reflection of thought [von Humboldt, 1988]. This constraint is deeply rooted in human cognition, which lacks direct channels for transmitting mental content, Machines, however, not subject to the same physical constraints of speech perception. This difference may be one of the central reasons why superhuman intelligence is possible. Every transformative achieve- ment, from scientific discovery societal progress, relies collaboration. Likewise, superhuman intelligence will require not only individual reasoning beyond human capability but also collective reasoning beyond human coordination [Vinge, 1993]. This calls for new form of communication that transcends the limits of language.
However, existing large language model (LLM) based multi-agent systems (MAS) rely natural language as the medium of communication, exchanging information via tokens or their embed- dings [Du et al., 2023, Liang et al., 2023, Pham et al., 2023, Zhang al., 2024a, Zeng al., 2025, Wang et al., 2025b]. These systems typically assume that multiple LLM agents exchange natural language messages convey internal ideas and coordinate toward shared goal. However, natural
Equaal advising.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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language remains fundamentally limited in its ability to express the underlying latent thoughts that drive reasoning and decision making. As a result, current systems remain restricted by the bottle- necks of language, limiting their potential for superhuman collaboration. Indeed, recent empirical analyses [Cemri et al., 2025, Hu et al., 2025] highlight that many failures in inter-agent collaboration stem from vague message specification and inter-agent misalignment, both ultimately caused by the indirect nature of lossy language- based communication. Then, the core question reveals itself:
What form of communication goes beyond the limits of language?
To answer this, we turn to the idea of communication through latent thoughts. Nothing is more direct than transmitting what one truly thinks, i.e., telepathy. Just as human actions are guided by internal mental states, agents likely operate based on latent representations that encode goals, beliefs, and reasoning. If these could be identified, agents could share them directly, bypassing the ambiguity and distortion of language. This enables fundamentally different mode of communication, based not on the exchange of surface tokens or their embeddings, but on the direct transfer of intent and understanding. Furthermore, in multi-agent settings, some thoughts are intended to be broadly shared, while others are inherently private or uniquely tailored to certain individual agents. Revealing both the latent thoughts and their structural organization allows agents to better detect alignment, resolve conflicts, and integrate diverse reasoning paths.
Contributions: We formalize this idea by introducing latent generative model for inter-agent communication. Specifically, we assume that the model states H; of all agents before communication round are generated from set of latent thoughts Ze through unknown function f. such that H, = f(z). We establish both a nonparametric identifiability result that guarantees recovery of latent thoughts, and general framework that facilitates direct mind-to-mind communication.
Theovetically, we prove that in a general nonparametric setting, both shared and private latent thoughts can be identified from hidden states under a sparsity regularization. Our identifiability result ensures that the recovered latent representations reflect the true internal structure of agent reasoning. Moreover, we show that the structures between thoughts and individual agents can be reliably recovered, enabling a provable correspondence between agents and their cognitive content. Experiments on various synthetic environments confirm the validity of the theory.
Practically, we develop a principled framework for latent communication among agents. Guided by the theory. we implement spuusity-reuularized autoencoder to extract latent thoughts from agent hidden states and infer the underlying mapping between agents and these thoughts. Each agent is equipped with a set of inferred thoughts, along with the structure of how each thought is shared. This allows agents not only understand what others are thinking but also to reason about which thoughts are mutually held or privately maintained. Experiments across diverse models and scenarios demonstrate that communication beyond language directly benefits collaboration among LLM agents.
2 Problem Formulation
What's best way to get the airport?
In this section, we formalize the data- gatta-gnerating pro- cess behind agent responses, providing the foundation for our theoretical analysis.
00-00
Thoughts
Data-generating process. We illustrate the data- generating process Fig. and formalize as:
Zi
TIME
Ze~ Ps. H. = f(Z)).
(1)
Answers
where Ze = (Zr.,...,
E RT denotes the la- tent thoughts of agents at communication round f, and Zr,s E R for E [m.] represents a latent variable denot- ing single thought. Let n. be the number of agents, at communication round t, the global model states* of all agents given by
H
H Agant 2
Agent
Figure 1: Each agent answers the same question by selecting a subset of latent thoughts Zt. Agent I chooses car based on carrying luggage A, while Agent se- lects a train R. for schedule punctuality fM Both share the thought of speed O
H, (HT ..... H(("))) = (H., H He,.
(2)
"We refer to this as the model state instead of hidden state to avoid confusion with the latens thoughts 2.. Specifically, model state corresponds to the hidden layer representation of the underlying fundation model.

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where each H²) E R summarizes the model states of agent A, prior to the communication round t, and n2 = Lje[na] Th., The mapping from latent thoughts to hidden states is governed by an unknown generating function f. assumed to be invertible (to preserve information) and twice differentiable (to ensure well-defined gradients), following the literature [Hyvärinen al., 2024].
Example 1. Fig. illustrates the data-generating process. In response to the question What's 's the best way to gel to the airport? a set of latent thoughts Zz is considered, including factors such as carrying luggage, speed, and punctuality. These thoughts, represented latent variables Ze are mapped through the generating functtinn f to produce each agent's 's answers, which are summarized by their model states H!!") For example, Agent emphasizes thoughts related luggage @ and speed 6 resulting in the state H that leads to choosing a car de. Agent 2, influenced by speed O and schedule punctuality 3 forms the state H and selects train R This example illustrates how the underlying process f encodes shared and private latent thoughts into agent-specific responses.
The structure of thoughts. While prior strategies have focused on communication through language or token embeddings, we propose fundamentally different paradigm where agents share latent thoughts directly. To achieve this, we propose a communication paradigm in which agents access relevant latent thoughts instead of surface-level messages embeddings. Rather than exposing all latent thoughts Z, to every agent uniformly, we focus on learning the structure of the revealed thoughts so that each agent receives only the most relevant information to its goals and role. This requires modeling how thoughts are selectively shared, as some may represent common knowledge useful to many agents, others may be specific or private to individual goals, and some may be irrelevant or even distracting to certain agents.
We formalize the structural dependency between latent thoughts Z, and model states H, through the non-zero pattern of the Jacobian Jy (Z.). represented as a binary matrix indicating which components of Z influence which components of H;:
B(J)) E {0, 10,1) 1]74X"0 B(Jr)a = {o
32g E 2 Jy(e)s # #0,
otherwise.
The model state of each agent A& is represented as a slice HH!*) (Hi,....... H1,,, ). where k e [n.]] and {At..... kn denotes the index range in H, corresponding to agent k. We define the set of latent thoughts relevant to agent Aş as
,0000 = {Zrs E 2e Bi E [ki, ka] such that B(Jr) # #0.
In other words, 7 (r:00 consists of all latent thoughts that influence at least one component of agent A&'s 's hidden state, as determined by the non-zero pattern of the Jacobian (Z)).
3 Identifiability Theory
Before leveraging thought for communication, a critical question arises: how can we ensure that the recovered thoughts correspond to the true ones underlying agent responses? To address this, establish an identifiability theory for reliably recovering the latent thinking process. We begin with the identification of the latent thoughts ($3.1 and $3.2), then explore the structure between thoughts and agents ($3.3). All proofs are included in Appx. A.
3.1 Identifiability of Shared Thoughts
Communication often begins with establishing common ground, which typically requires confirming shared beliefs before addressing disagreements. If the shared part of the latent thought can be reliably disentangled from other components, then communication can start from faithful common basis. Our identifiability result guarantees this: by recovering shared latent variables that are not entangled with any others, we ensure that inter-agent communication is grounded in true cognitive overlap.
We first introduce some additional technical notations. We define the support subspace S as the set of matrices S E RR x whose nonzero entries are restricted to the nonzero pattern of (Z)):
SJ, = {S E I X B(Jr)a 0 St, = =0}.
(5)
We further denote M as a matrix with the same nonzero pattern of m((2)) in J, (,, and write = to denote equality in distribution.
3

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Theorem 1 (Identifying the shared thoughts), Suppose that for each E. [ma]. there exist points where the Jacobians J (z),, span the support subspace SJg,,' and that (J), E ES,,,. at those points. If H, d f(2)) for a model (f, 2c) following $2 with to regularization on J then for any pair of agents Ag and A3 at round i, there exists a permutation over [n=] such that oz. 0 07x(5)
for any Zi E 2g0 n 2 alo and any Zg E 12 U 2 (1?2)) \ (2 n 2 (0)))
Interpretation and discussion. Intuitively, Thm. 1 ensures that, up to permutation, the recovered shared thoughts between any pair of agents are disentangled from all other latent variables in the system. The permutation reflects the standard relabeling indeterminacy common identifiability results [Hyvärinen et al., 2024, Moran and Aragam, 2025]. For instance, in Fig. I, we can make sure that the recovered thought speed & will not be mixed with others such as luggage M or schedule punctuality 8 Without this guarantee, any recovered thought can be a mixture of any other thoughts, since the unknown generating function f is essentially a mixing procedure. Thus, this disentanglement implies the recovery of the target shared components, provided that the generating function is invertible and thus information prreserrin.....iingg...... This has practical implications: given any group of agents, we can decompose them into pairs, each yielding identifiable shared thoughts. By composing the recovered components across different pairs, we reconstruct the common cognitive basis and reveal how thoughts are distributed across agents, including the degree of agreement, which is essential for enabling trustworthy and informative latent communication.
Assumption. The assumption has been widely adopted in the identifiability literature [Lachapelle et al., 2022, Zheng et al., 2022], which eliminates degenerate cases where the population is too limited for the Jacobian to even reflect the dependency structure. It requires that the generating function f varies sufficiently across the population so that there exist several points for the Jacobian to span the support subspace SJ,.,' Requiring (J MZ). E SJ,,. holds at these points is also mild due to (J)(Z)))(Z))); = -J((2)), especially in the asymptotic regime where identifiability is defined.
3.2 Identifiability of Private Thoughts
In Thm. 1, we established the identifiability of shared thoughts. providing a guarantee for recovering the underlying common ground between agents. However, effective collaboration is not solely about enforcing consensus or resolving disagreements. In fact, homogeneity can be counterproductive in the long term [Prat, 2002]. Just as humans value cognitive diversity source of novelty and innovation, different agents may contribute unique perspectives that are essential for solving complex tasks. For instance, in collaborative planning task, one agent may recognize rare constraints based on its prior experience that others overlook. Preserving such private thoughts can lead to better overall solutions through complementary reasoning. Motivated by this, we now extend our theoretical analysis to show that private thoughts can also be identified:
Theorem 2 (Identifying the private thoughts). Suppose the assumption in Thm. holds. If d f(2x) for a model (f, 2.) following $2 with to regularization on Jy. then for any pair of agents A, and A₁
at round 1, there exists a permutation ı over [n-] such that az, 0 for any 7, 7pp0 n and any 7, E 7 pta
87.(3)
Interpretation and discussion. Similar to Thm. 1, Thm. 2 adopts a pairwise perspective and provides guarantees for recovering the hidden private thoughts of any given agent. Specifically, for any pair of agents, it shows that the private component of either agent can be disentangled from all remaining latent variables. For instance, in Fig. I, recovered latent variables corresponding to the thought being able to carry luggage @ which may explain Agent I's choice of car @ is not entangled with unrelated thoughts like speed & or schedule punctuality S which influence Agent 2's preference for the train Rd. Without such disentanglement, we risk misattributing the decision to an incorrect or irrelevant latent cause, leading to misalignment in communication.
This again implies that, under invertibility, the true private thoughts can be recovered. By composing the results across different agent pairs, we can infer how agent-specific a given thought is. For example, by analyzing all pairwise decompositions in large group, we can identify thoughts that are truly unique to individual agents, capturing insights that would otherwise be lost due to their rarity or lack of popularity. This connects naturally to the classical long-tail phenomenon: some thoughts may

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be infrequent, but they carry critical value. Our theory ensures that these less common but meaningful components are not discarded, enabling inclusive communication and collaboration among agents.
3.3 The Structure of Thoughts
Having established the identifiability of both shared and private thoughts, we turn to deeper question: how are these thoughts structurally organized across agents? That is, beyond identifying each thought, can we also identify which agents hold which thoughts? In many scenarios, especially those involving coordination, it is not enough to only know the content of internal reasoning. We must also know how that reasoning is distributed across individuals. We formalize this in Thm. 3:
Theorem 3 (Identifying the structure of thoughts). Suppose the assumption in Thm. I holds. If He f(2x) for model (f, 2.) following $2 with En regularization on J. then the nonzero pattern P for a permutation matrix P.
B(Jr) is identifiable up to relabelling, i.e., B(Jj)= P
Interpretation and discussion. Thm. 3 establishes that the structure linking latent thoughts to agents' internal states is identifiable up to permutation. In other words, we can recover not only the content of each thought, but also determine which agents hold which thoughts, and which thoughts shared. Returning to Fig. 1, this means we can infer that both agents care about speed & (shared), while only Agent emphasizes carrying luggage @ (private) and only Agent 2 prioritizes being on time S0 (private). This structure-level recovery is crucial: it enables agents to assess not just what others are thinking. but also how similar different their internal reasoning is, supporting more informed and adaptive communication. In practical terms, this guarantees that agents can identify points of alignment and divergence without confusion. When scaled to larger systems, this enables the reconstruction of a full thought-agen agent incidence structure, revealing clusters of agreement, regions of conflict, and sources of novel inputs. Such structural insights are foundational for building systems that coordinate robustly and interpret each other's 's intentions with precision.
3.4 Discussion on Theoretical Contribution
To the best of our knowledge, this work is the first to consider the latent generative process underlying LLM agent responses and to provide identifiability guarantees for recovering latent thoughts. Beyond its novelty the multi-agent LLM setting, Thms. 2, and also present a new contribution to classical identifiability theory. Prior work typically focuses recovering all latent variables (up to standard indeterminacies), with assumptions that go beyond the basic setup that we adopt, such access to weak supervision [Hyvärinen et al., 2019, Khemakhem et al., 2020], specific function classes [Taleb and Jutten, 1999, Buchholz et al., 2022], or structural criteria on the dependency graph [Moran et al., 2021, Zheng et al., 2022].
In contrast, our approach takes a completely different route. Instead of aiming for global recovery, we focus on pairs of observed variables (agents) and seek to recover as much hidden information as possible from them. Since we rely only on basic assumptions and do not use the additional constraints or auxiliary signals commonly adopted in the identifiability literature, full recovery of all latent variables known to be impossible. Therefore, we target a coarser perspective that is still meaningful for communication, such the shared/private thoughts disentangled by theorems. This is not only practically useful but also theoretically important, as previous methods with global conditions offer no guarantees when their assumptions even partially violated, while our result still provides alternative guarantees under practical assumptions.
THOUGHTCOMM: Multiagent Communication via Thought
Based on the established theory, we propose a practical framework, THOUGHTCOMM, for multi-agent collaboration in which agents exchange thoughts directly. At each communication round t, we first encode the agents' model states into a shared latent space that captures their internal thoughts. These latent thoughts are then processed and selectively reintegrated into each agent's 's context based on the structured relationship between thoughts and agents. This allows each agent to gain a global sense of what others are thinking, and to distinguish which thoughts are shared or agent-specific.
4.1 Uncovering the Latent Thoughts
Each agent A, maintains model state 17(00 E RM. corresponding to the representation of its last generated token immediately before communication round I, contextualizing the text summarizing their own response. We concatenate these states from all agents into single vector as in Eq. 1.
5

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A
Resperss
Fost
Future
Rounds
Rounds
H
(3)
A3
Reppese
Communication Round
Figure 2: Overview of THOUGHTCOMM. At each communication round f, agents encode their model states H! into a shared latent space via a sparsity-regularived autoencoder, yielding latent thoughts 2, Each dimension Zr, is selectively routed to relevant agents based on the recovered dependency structure, allowing agents to identify both shared and private thoughts for reasoning. The corresponding latent thoughts are then injected into each agent model via prefix adaptation to guide the next response. These updated responses form the input to the next round, enabling multi-agent collaboration beyond purely message exchange.
Then we aim to uncover the hidden process that generate these states from the latent thought of agents. According to the formulation in $2, there exists an underlying process f that generates the agents' responses He based on their hidden thoughts Z,, i.e., He = f(Zz).
In the proposed framework, the concatenated state H2 is mapped into a latent space via a sparsity- regularized autoencoder with & regularization on Jj. The resulting latent thoughts 2, are recovered through its encoder f-1
(6) The connection between our estimation 2, and the ground-truth latent thoughts Ze is built by our
2. (H)))
identifiability theory established in $3. The structure of the latent thought Z, is governed by the Jacobian (Z,) E R x"x whose non-zero pattern B,, reveals which latent dimensions are influenced by which agents' states. The autoencoder is trained reconstruct the full state vector:
Lre = I| (
||/l,,
ensuring consistency between He, and its reconstruction via 2.. as well the required sparsity regularization on the Jacobian. This enforces observational equivalence between the estimated and ground-truth processes, which serves the foundation for identifiability. At test time, trained encoder f-1 extract latent thoughts 2, from hidden states He, and leverage the recovered dependency structure BJ, to determine which latent dimensions of 2, are relevant for each agent.
the
4.2 Leveraging the Structure of Thoughts
To provide personalized access to latent thoughts, we adopt an agreement- reweighting strategy. Specifically, for agent A; at communication round I, we first identify the set of latent thoughts 2 H
that influence its model state, i.e., 1n1000 = 2 E 2, 3q E [ir, ix] such that B(J + 0
These latent thoughts are then partitioned into groups based on their level of agreement across agents, measured by the number of agents whose hidden states in H, depend on each latent dimension in thoughts 2, Formally, for every Zr,; E 2 we define its agent agreement as:
03
Σ
(2ns E 2 )
(8)
where II(-) is the indicator function. Latent thoughts are then grouped by their agreement level ay- Each group is assigned distinct weight Ways reflecting the relevance or generality of these thoughts across agents. The new latent representation for agent A; is constructed by combining all groups
2((0 concat, (Way -(00)
(9)

---

where 2(0) t,a denotes the subset of latent variables in 2 20(00 with agreement level i.e.
2
Zus 20000 aj = ===
(10)
Intuitively, the recovered dependency structure plays critical role in shaping how latent thoughts routed to each agent. After extracting the shared latent space via the sparsity-regularized autoencoder, apply structural mask ensure that each agent only receives the latent dimensions that relevant to its own internal representation. This filtering directly affects how the injected prefixes constructed for each agent during the next round of generation. The agreement weights further distinguish different types of relevant thoughts, Although the surface-level messages are broadcast, the actual content used to condition each agent's reasoning is selectively and adaptively constructed in the latent space, reflecting the personalized structure of shared and private thoughts.
4.3 Latent Injection via Prefix Adaptation
To seamlessly integrate the recovered latent thoughts into agent behavior, we incorporate them into the generation process via prefix adaptation. For each agent A, we construct a prefix vector from its personalized latent representation [(") via learned adapter function:
p(1) = - Rmxdd
(11)
where is the prefix length and d is the embedding dimension. Following Li and Liang [2021], prepend the resulting prefix p( to the token embeddings of agent A, the next generation step, leveraging the latent thoughts guide response generation without explicit message passing.
To train the adapter g. inject its output as prefix and generate a brief continuation (e.g., one sentence), keeping it short to focus on linguistic coherence rather than influencing the actual solution. The few generated tokens are compared against reference using a semantic similarity loss and standard regularization term that promotes linguistic fluency:
T
(1 (1- cos (ō(ve,)) o(tt.))) - log context,, P()))
p.O)).
Coomm
(12)
where yf, denotes the tokens generated by agent A, at round t. vt, is reference from the model without latent communication, contextr,; denotes the dialogue history or prompt available to agent mean token embedding. The goal is not to replicate the content of baseline generations, but to ensure that the adapter produces latent modifications whose injected effects remain linguistically natural.
As, and p!() the injected prefix produced by the adapter. ø(-) denotes
Remark 1. Since the autoencoder is trained only to reconstruct model states, and the adapter is guided simply avoid producing semantically absurd responses, both components remain largely task- agnostic and can be pretrained once and reused. This modular design allows latent communication be applied across different tasks without retraining, enabling easy integration into multi-agent generation systems with minimal overhead.
Experiments
In this section, we conduct both synthetic and real-world experiments across various settings. Part of the implementation details are deferred to Appx. C.
5.1 Synthetic Evaluation
2,12
2, 12,
03
We begin with synthetic experiments to val- idate the identifiability of latent thoughts. For the basic setup corresponding to our running ex- ample in Fig.
Z,nz
0.4 ZanZa
82
0.2
412.
4/2
81
consider two observed variables, XA and NB. and three latent ones: Z \ BB Z AA. and Z n ZB, evaluate whether shared and private latent variables can be correctly recovered. The datasets are generated by random invertible transfor- mation from multivariate Laplacian variables. We train a sparsity-reullarized autoencoder on these datasets and compute the standard R² score between each part of the estimated and ground-truth latents. A baseline model without sparsity regularization is also included for comparison.
12 knnk 2, 12,
2,42 2, 2,12.
Ours
Baseline
Figure 3: n²² of two models.
7

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The results are shown in Fig. 3. A higher R indicates closer corre- spondence between the estimated latent variables and the matching ground-truth components, and vice versa. Our model clearly iden- tifies the shared region ZA n Z and the private regions ZA \ 7BB and ZB! \ A. while the baseline fails to disentangle them.
0.9
MCC
0.8
Beyond the basic setup, we evaluate whether incorporating multiple pairs of observed variables in a complex system enables recovery of most latent variables, as considering all pairs of agents reveals exponentially more information than any single pair alone. Follow- Figure 4: MCC across setups. ing the identifiability literature, we compute the mean correlation coefficient (MCC) between estimated and ground-trute truth latents across 8 settings, with dimensionality ranging from 124 to 1024 and equal numbers of latent and observed variables. Results are shown in Fig. 4. The red line marks the threshold typically considered identifiable when exceeded. Our model consistently recovers most latent variables across all settings, highlighting the global identifiability.
0.7 256 512 896 1624
Dimension
5.2 Real-Workee Evaluation
Recent empirical analyses [Cemri et al., 2025, Hu et al., 2025] reveal that LLM-based multi-agent sys- tems frequently struggle with reasoning tasks, demonstrating only modest improvements over strong single-agent baselines due to coordination inefficiencies and communication bottlenecks challenges that TноUGHтCOMM is explicitly expected to address. Therefore, we evaluate ThoughtComm on two widely used math reasoning benchmarks, MATH [Hendrycks et al., 2021] and GSM8K [Cobbe et al., 2021] to assess its real-world effectiveness. For the main experiments in this section, we follow Subramaniam al. [2025] by using three agents engaging in two rounds of debate.
Baselines. As the proposed TнооGHтCCMM introduces an additional training stage, the most direct baseline is Multiagent Finetuning [Subramaniam et al., 2025], which is the current state-of-the-art in maximizing multi-agent collaboration through specialized roles and multiple finetuning rounds. We also include single- LLM performance. referred to "single answer," for comparison. It is worth noting that there are many other multi-agent collaboration workflows; our objective here is to validate the potential of the proposed paradigm rather than exhaustively compare all possible strategies.
Data pre- rre-processing and evaluation metries. Following Subramaniam et al. [2025], we randomly sample 500 examples for fine-tuning the latent communication module, which includes both an autoencoder and an adapter, while reserving another 500 examples for evaluation. We select the more challenging questions for evaluation (e.g., level-3 complexity in MATH [Hendrycks al., 2021J) when applicable. Generated responses are parsed and evaluated against the ground truths, with accuracy measured as the percentage of correctly generated answers. To quantify the reliability of these estimates, we also report the standard deviation for each accuracy score. Beside accuracy, we include consensus score, defined as the proportion of final-round instances where all agents reached a unanimous decision, providing a more direct measure of communication effectiveness.
Models. We evaluated both the baseline methods and THoUGHTCOMM on five latest LLMs of vary- ing model sizes, including 1aama-3-8--Insteee [Grattafiori et al., 2024], Phi-4-mini-instruee [Abdin et al., 2024], Qwen-3-0.6B, Qwen-3-1.7B [Yang et al., 2025], as well as the Deepseek-RI-distilledd -distilled- Llama-8B [Guo et al., 2025].
Main results. Table 1 presents the main results, showing that TноUGHTCOMM consistently outper- forms baseline methods across both the MATH [Hendrycks et al., 2021] and GSM8K [Cobbe et al., 2021] benchmarks. Within all base models, THOUGHTCOMM demonstrates clear improvements over both single answer and Multiagent Finetuning [Subramaniam al., 2025]. For instance, on Qwen 3-1.7B, THOUGHTCOMM achieves 93% accuracy on MATH, representing an 17.2% absolute gain over Multiagent Finetuning and 1 11333 relative improvement over the single answer baseline. On average, THOUGHTCOMM achieves 67.23% % relative improvement over single answer and 19.06% over the current of-te-of-the-arr In terms of consensus, THOUGHTCOMM also outperforms all baselines by clear margin, with its improved consensus directly translating to higher accuracy, indicating superior inter-agent alignment enabled by efficient mind-to-mind communication. These gains are consistently observed across models ranging from 0.6B to 8B parameters, demonstrating the scalability and robustness the proposed approach across a broad range of model sizes.
Additionally, unlike Multiagent Finetuning [Subramaniam et al., 2025], which requires finetuning the entire LLM and thus incurs substantial overhead, TноUGHтCOMM only trains a lightweight
8

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Table 1: Evaluation results on MATH [Hendrycks et al., 2021] and GSM8K [Cobbe et al., 2021] various methods with five different LLMs. Bold numbers indicate the best performance.
[ for
MATH
GSMBK
Base Model
Methods
Accuracy (%)
Consensus (%)
Accuracy (%6 Consensus (%)
Single Answer
45.80 2.23
58.20
N/A
Qwen 3-0.6B
Multiagent Finetuning
71.20 2.03
90.07
70.80 +: 2.03
86.40
THOUGHTCOMM
85.00 + 1.60
91.20
75.80 = 1.92
89.27
Single Answer
43.60 2.22
67.40 +
N/A
Qwen 3-1.7B
Multiagent Finetuning
75.80 1.92
95.80
84.20 = 1.63
96.73
THOUGHTCOMM
93.00 + 1.14
95.93
85.00 = 1.60
97.87
Single Answer
63.80 2.15
N/A
81.60 +
N/A
11--4-miii-instrce (3.84B)
Multingent Finetuning
60.20 = 2.19
78.89
82.16 = 1.71
91.24
ThoUGHTCOMM
74.60 1.95
84.73
84,20 + 1.63
94,73
Single Answer
36.20 2.15
N/A
60.80
N/A
LLaMA 3-8t-Instruct
Multiagent Fineluming
39.68 + 2.19
68.97
69.20 + 2.06
80,20
THOUGHTCOMM
45.60 =
74.67
68.40 + 2.08
84.87
Single Answer
42.60
N/A
65,60 2.12
N/A
DeepSeck-RI. Le1--iitill-Llammae
Multiagent Finettuiing
72.40 + 2.00
82.87
76.80 + 1.89
83.13
THOUGHTCOMM
82.80 1.69
80.72
80.80 = 1.76
88.13
Qwen 3-0.68
Qwen 3-1. 7B
2hi-4-mini-instruct (3 848)
LLaMA 3-88-Instruct
100
100
100
80
95
60
Accuracy
ue
Consensus
85
70
40
80
4
16
85
8
16
60
16
16
(prefix tokens)
k (prefix tokens)
k (prefix tokens)
k (prefix tokens)
Figure 5: Two-agent THOUGHTCOMM with accuracy (solid) and consensus (dashed) performance
on MATH [Hendrycks al., 2021] as prefix length increases from 16.
autoencoder and adapter, whose computational cost depends only on the LLM's embedding dimension rather than the parameter count. This results in fundamentally smaller and model-agnostie training overhead, enabling efficient and scalable deployment even for very large LLMs. For instance, both Llama-3-70B and 405B share a 16,384 embedding dimension; thus, THOUGHTCOMM' s overhead remains unchanged when moving from 70B to 405B, whereas Multiagent Finetuning [Subramaniam et al., 2025] would require substantially more training cost at each scale. Overall, these results validate both the efficiency and effectiveness of the proposed THOUGHTCOMM, supporting the theoretical predictions of enhanced coordination and cognitive alignment multi-agent LLMs.
5.3 Scaling the Number of Debate Rounds
Multiagent
ThoughtComm
We further investigate how the number of debate rounds impacts multi-agent performance, as more rounds may introduce redundant or confusing information that can degrade results. With two agents, we vary the number of rounds from 2 6 and evaluate the MATH [Hendrycks et al., 2021] benchmark using LLaMA-3-SBB-nnttnen |Grattafiori et al., 2024], follow- ing the setup in 85.2. As shown in Fig. 6, Multiagent Finetuning suffers drop accuracy with more rounds, while consensus slightly increases and maintains, In contrast, BROUGHTCOMA, achieves simultancous gains in both accuracy and consensus, demonstrating robustness redundancy and noise by consistently identifying true latent thoughts.
Accurcc 188
36
Contreneus
76
Number of Rounds
Number of Rounds
Figure 6: Multi-agent performance as the number of debate rounds increases.
5.4 Varying the Prefix Lengths
As discussed in $4.3, the prefix length m determines how many thought vectors are injected into agent context. key question is whether THOUGHTCOMM remains robust as m grows, or if excessive prefixes introduce redundant or irrelevant information that degrades performance. To answer these questions, we sweep the prefix length m E {1,4,8 8, 16) across four models with different parameter sizes (Llama-3-8B Instruct [Grattafiori et al., 2024], Phi-4-min welt--miiiiiiiiie [Abdin et al., 2024], Qwen-3
3-8B-Instruet

---

0,6B, and Qwen-3 1.7B [Yang et al., 2025]) on the MATH [Hendrycks et al., 2021] benchmark, using the same 500/500 train/test split from $5.2. As shown in Fig. 5, both accuracy and consensus stay remarkably stable for all four models, with performance fluctuations under five percent even as m increases sixteen-fold. These results demonstrate a clear robustness advantage of THOUGHTOOMM by delivering reliable gains without requiring precise tuning of the prefix length, dramatically reducing hyperparameter overhead in practice. Moreover, achieving near-optimal performance with a single injected vector highlights the efficiency of our nlought-communicatioo mechanism. While both token and prefix embeddings have the same dimensionality (e.g., 1024), a token embedding is tied to a single vocabulary item and typically encodes the semantics of just that one discrete token, often lying on a siwer-dimensional subspace. In contrast, a prefix embedding is a free parameter optimized to encode many continuous latent thoughts, leveraging the full capacity of the embedding space.
6 Related Works
Multiagent LLMs communication. LLM- multi-agent systems (MAS) have become com- pelling strategy for advancing beyond the limitations of single LLMs [Li et al., 2023, Wu et al., 2023, Hong et al., 2023, Guo et al., 2024, Tran et al., 2025]. Specifically, multi-agent debate [Du et al., 2023, Pham et al., 2023, Liang et al., 2023], which mimics human collaborative reasoning, has shown particular promise by amplifying reasoning through collective, diverse exchanges. One of the most central factors that determines MAS effectiveness is the communication paradigm between agents [Li al., 2024, Cemri et al., 2025]. Extensive research has sought to improve this paradigm, exploring various directions such as improving communication efficiency [Zhang et al., 2024a, Wang et al., 2025b, Zeng al., 2025], enabling more flexible topologies and workflows [Khattab al., 2023, Zhang et al., 2024b, Liu et al., 2024, Wu et al., 2024, Wang et al., 2024, 2025a], mitigating error propagation [Wang et al., 2023, Yoffe al., 2024], shifting from turn-based, full-response discussion to token-level collaboration [Bian et al., 2025, Chakraborty et al., 2025], and moving beyond text tokens to token embeddings [Pham et al., 2023]. However, all these approaches funda- mentally rely on the exchange of natural language, either through text tokens or their embeddings, thus inheriting the constraints of buman-style communication. In contrast, THOUGHTCOMM pioneers a new communication paradigm by extracting and uncovering the underlying latent thoughts beneath surface-level language tokens and embeddings, enabling a more direct and expressive form of MAS communication and collaboration.
Identifiability of latent variable models. Classical identifiability results in latent variable models largely focus on linear settings, offering strong guarantees through factor analysis, structural equations, and ICA [Reiersol, 1950. Lawley and Maxwell, 1962, Aigner et al., 1984, Comon, 1994, Bekker and ten Berge, 1997, Bishop, 1998]. To relax linearity, previous work introduces auxiliary variables [Hyvärinen and Morioka, 2016, Hyvärinen et al., 2019, Yao et al., 2021, Hälvä al., 2021, Lachapelle et al.. 2022, Song et al., 2024, Li et al., 2025a], structural constraints on the mixing function ITTlleb and Jutten, 1999, Moran al., 2021, Kivva al., 2022, Zheng et al., 2022, Buchholz al., 2022, Zheng et al., 2025], or the synergy of both [Zheng and Zhang, 2023, Li et al., 2025b]. Causal representation learning often depends on interventions [von Kügelgen et al., 2023, Jiang and Aragam, 2023, Jin and Syrgkanis, 2023, Zhang et al., 2024c] or counterfactual views [von Kügelgen et al., 2021, Brehmer et al., 2022]. These approaches typically require parametric assumptions or external signals. With weaker goal of identifying only shared and private thoughts and their structures across agents, our framework can be applied in the general nonparametric setting without such aids.
7 Conclusion
To enable LLM agents to communicate through thoughts, we formulate multi-agent communication as latent variable model to explore agents' minds. We establish identifiability results under general conditions to ensure reliable recovery of latent thoughts and structures, and propose a new framework, THOUGHTCOMM, for effective collaboration via thought. While this introduces new direction, certain limitations remain. Our experiments focus on using model states as observed variables, which may not be feasible for closed-soures -ourcc models. A promising alternative is to replace them with context-aware embeddings of the observational data and recover latent thoughts from those. The observational data need not be textual and can span any modality, extending the framework beyond LLMs. Although we have not explored this empirically, as generating embeddings suitable for summarization is separate topic, the theory and framework can accommodate this extension directly. We hope this work sheds light on the hidden world beneath observation, as many challenges remain unsolvable through surface-level observation, regardless of scale in data or compute.
10

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Acknowledgment
The authors would like to thank the anonymous reviewers and AC for helpful comments and sug- gestions during the reviewing process. The authors would also like to acknowledge the support from NSF Award No. 2229881, AI Institute for Societal Decision Making (AI-SDM), the National Institutes of Health (NIH) under Contract R01HL159805, and grants from Quris AI, Florin Court Capital, MBZUAI- WIS Joint Program, and the Al Deira Causal Education project.
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14

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Appendix:
Thought Communication in Multiagent Collaboration
Table of Contents
Proofs
A.1 Proof of Theorem
15
A.2 Proof of Theorem 2
17
A.3 Proof of Theorem 3
19
B Supplementary Discussion
20
C Experimental Details and Additional Results
21
C.I Implementation Details
21
C.2 Additional Results on Scaling Debate Rounds
21
C.3 Additional Results on Varying Latent Dimensions
................................
22
C44 Additional Results on Varying Number of Agents
22
A Proofs
A.1 Proof of Theorem
Theorem 1 (Identifying the shared thoughts). Suppose that for each [ng], there exist points where the Jacobians Jy (Z),, span the support subspace Siye, and that (Jz(Ze)M),, E &S,,.. at those points. H, f(2.) for model (f, 2c) following $2 with to regularization on J then for any pair of agents A, and Aj at round t, there exists a permutation a over [nz] such that oz. 02x(s)
for any Zi E Z H n 2 n()) and any Z3 E 1Z U UZ \ (2 H(00 n 2 2())
Proof. Because H, f(2,) and He f(Z)), we have p(f(2))) p([())))
(13)
According to the change-of- variialle formula, there exists f oo Z, 2. s.t. 2, h(Zi).
Taking the derivatives of both sides w.r.t. Z, yields
(z, J (,(22))((Z)))
(14)
which is equivalent
= J, (Z.).
(15)
The inverse Jacobian ' exists since both f and f are invertible, implying that h = f-1 o is itself invertible.
Since for each E [nz], there exist points where the Jacobian (Z)), spans its support subspace (S,,),,- we can express any vector in that subspace with a linear combination of these vectors. Therefore, for any j E [n.] where B(Jy)as # O. we have Mj. = M,
(16)
where M is constant matrix with the same nonzero pattern as (Z,), and construct one-hot vector E SS,e. with 0% as coefficients of that linear combination:
ej
Σ on (2)
(17)
KEB
15

---

where B, denotes the set of points spanning the subspace. Thus we have
M₁ Σ
(J M.
(18)
AEB;
According to the assumption, we have
(,, = M),, E ESiu
(19)
Therefore, for any j E [m,] where B(J))s # there is
Mj, E SJj..'
(20)
Construct a bipartite graph
G= CR, R=C= [ng]. (j.)) E = Mf, * O.
Since M is invertible, its rows are linearly independent, giving [N(S) 2 |S|
V R,
(21)
where (S) the neighborhood S. Hall's marriage theorem then yields permutation IT Sn. with
Jr. (Z)))0)))))) # O, Vj [n=]- According to Eq. (20), this further implies that, for any j E [ma] where B(Jr) A O, there is
(22)
(1,(()) EiX Mj.- C S1
(23)
Hence
(J)(Z))) #0 (Jf(21)).x0) t0.
(24)
Given additionally the lo regularization on Jf:
((J S I1J [
(25)
Together with (24), this gives the equivalence
(J,(2))ks #0 = (J,(2))),n)) 0, Vi,j E [mz],
(26)
For any Zi 20000 n n and any Zj E (Z U (()))) \ 12, n()))) there is
B(Jr) H("); # 0.
(27)
;
Based on Eq. (20), there is
M, E SJim
(28)
where we use SJ no to index multiple rows corresponding to H. at once. This is for notational brevity and will also be applied later. We also have
B(J)) #0,
(29)
where we slightly abuse the notation to indicate that not all entries at the specified indices are zero. This convention is adopted throughout, though we only make it explicit here.
Similarly, there is also
Mr. E ESJ {)
(30)
Suppose for contradiction that, for any 2, E nt0 U U n \ (4 (211 n 2 ( there is
M)r()) #
(31)
Then, according to Eq. (28), there is
B(J))
H( #0. O.
(32)
16

---

This implies the follows according to Eq. (26):
B(Jr) 1( + 0.
(33)
Similarly, according Eq. (30), there is
(())) s(s) # 0.
(34)
This implies the follows according to Eq. (26):
(( . #
(35)
Thus, there must be
2g E 7 ((9)) n Z 11000
(36)
which contradicts Therefore, there must be
Z3 E (2 110 U 2Z m(p \ 12 n 2 mpn)
(37)
Mi,(() = 0,
(38)
which implies OZ. O.
8Zm(z)
A.2 Proof of Theorem 2
Theorem 2 (Identifying the private thoughts). Suppose the assumption in Thm. holds. H; d for model (f, following $2 with to regularization on Jj. then for any pair of agents A; and Aj
f(2,)
at round t, there exists a permutation π over [n=] such that az. foror any Z, E n Z Z aZ-(1)
and any Zj E 2 gp
Proof. Part of the derivations has been provided in proofs of Theorem 1, and we include it for completeness. Because H, d f(2:) and H, _ f(Zz), we have
pl p(f(2.) = p(f(Z)))
(39)
According to the change-of variable formula, there exists h = f- 2e + s.t. s.t. 2, = h(Z)).
Taking the derivatives of both sides w.r.t. Ze yields
Jy( Jz(22)JA(Z.).
(40)
which is equivalent to
2,( = -,(,),,,
(41)
The inverse Jacobian ' (Zt) exists since both f and f are invertible, implying that h = f-1 o is itself invertible.
Since for each E [n=]. there exist points where the Jacobian (Ze), spans its support subspace (S,,),,, we can express any vector that subspace with a linear combination of these vectors. Therefore, for any j E B(Jr)s.,, we have
MG. = M,
(42)
where M is constant matrix with the same nonzero pattern as J (Z,), and construct one-hot vector E SJ,,.- with 0g as coefficients of that linear combination:
ej
Σ on (J)( kEB,
(43)
where B, denotes the set points spanning the subspace. Thus we have
M₁,- Σ
on ())
(44)
KEB,
17

---

According to the assumption, we have
() (J)(2))M),, EJJU
(45)
Therefore, for any j E B(J)),,, there is
Mj. E Syga.
(46)
Construct bipartite graph
= (R, R= = [nz]:
E = MG, #0.
Since M is invertible, its rows are linearly independent, giving [N(S) 2 |S|
VS R,
(47)
where N(S) is the neighborhood of S. Hall's marriage theorem then yields permutation E S.. with
J (Z) # 0, Vj E [ma]-
(48)
According to Eq. (46), this further implies that, for any j [n,] where BJJr) # 0, there (i, E x Mj.- C SJ,
(49)
Hence
(Jyhss # = (FF)an # O.
(50)
Given additionally the to regularization on Jfi
((J))..llo < II(J)),,lo,
vi [mz].
(51)
Together with Eq. (50), this gives the equivalence
(J)(2)) #0 = (J)(2))),z() # 0, Vi.j E [nz],
(52)
Consider the case where Zr E N 10D and Zz' E Zi (2 p0 n 22 Based on Eq. (46). there is
Mr. E SJ, m
(53)
Suppose
My + O.
(54)
Then we have
B(J ((()))))) # 0,
(55)
which implies
B(J)) + 0.
(56)
At the same time, since Ze Z 190, there is
M E SJ SJ
(57)
Since we suppose Mr.+6") # 0, it follows that
F O,
(58)
which implies
B(J)) y #0. 0.
(59)
Clearly, Eqs. (56) and (59) together contradict Zj Z, \ (Z n Z (1 Thus, there must be My =0:0)=00. =0
(60)
For any Z, E _ _ and any Z, Z Hp we first consider Z, 2 2ng O z Since Z 155 n Z H(O does not intersect with z 2 [a) Z is not a function of Z, According to the
18

---

invertibility and Eq. (60), 2 n0Z n Z ((00) can only be an invertible function of o (2 (1 n 2 m00
where a denotes the permutation function corresponding to the permutation л. Further given that Zj is not function of Z; and Zi E 100 2n,)) Zj is also not a function of any variable in o n(D n Z 2n( ) i.e.
Mi,x()) = 0.
(61)
We then consider the other case where Zg E Z m1:00 \. nn There is
B(J) H(9, *
(62)
implies that
M, E SJ (
(63)
For Z, m00 \ 11t suppose
Max()) # 0.
(64)
Then there is
() xx()) # O.
(65)
Which is equivalent to
B(Jz) n()) & # O.
(66)
This is contradiction since Zj E 2 (((0) Therefore, have
\2 H."0
Mix(1) = 0.
(67)
Considering both cases, we prove that
a2.
0 for any Zi E 2,0 \ Z Zno and any Z, E
77
Z 1
A.3 Proof of Theorem
Theorem 3 (Identifying the structure of thoughts). Suppose the assumption in Thm. 1 holds. If
H2 d. f(2i) for a model (f, 2.) following $2 with En regularization on J then the nonzero pattern B(J,) is identifiable up to relabelling, i.e., B(Jj) = B(J,) for permutation matrix P.
Proof. Part of the derivations has been provided in proofs of Theorems 1 and 2, and we include it for completeness. Because H, d f(,)) and H, d f(z),, we have
p(f(2.) p((())))
(68)
According to the change-of- varriable formula, there exists h = o f: 2. + 2, s.t. 2. l(Z)).
s.t.
Taking the derivatives of both sides w.r.t. Ze yields
(z, (y(2)))h(7)).
(69)
which is equivalent to
Jz(2,) = J)(2,))
(70)
The inverse Jacobian ' (Zt) exists since both f and f are invertible, implying that h = f- o f is itself invertible.
Since for each E [nz]. there exist points where the Jacobian (Z,),, spans its support subspace (S,,),,, we can express any vector that subspace with linear combination of these vectors. Therefore, for any j E B(Jr)s,, we have
M,. Me
(71)
where M is a constant matrix with the same nonzero pattern as (Z,,, and we construct a one-hot vector ej E -S with 0% coefficients of that linear combination:
ej
Σ on (= KEB
(72)
19

---

Thus we have
My Σ
ax ()
(73)
AEB.
According to the assumption, we have
(Jz(2 (J)(Z))M),, EJy
(74)
Therefore, for any j E B( there is
M₁. EJJ..
(75)
Construct bipartite graph
= G= (R, -=C=lnnl (,k) E =
M₁ #0.
Since M is invertible, its rows are linearly independent, giving
[N(S) 2 |S| AS _ R.
where N(S) the neighborhood S. Hall's marriage theorem then yields permutation и S., with
Jn (4)) 10 # O, Vj [m2]-
(76)
According to Eq. (75), this further implies that, for any j E [n,] where B(Jr) + 0, there
(i, Eix Mj. C S1
(77)
Hence
(J))as #0 = (Jg)..m)) #
(78)
Given additionally the l regularization on Jj:
[(Jp),, I 1IJ vi [n.l
(79)
Together with (78), this gives the equivalence
kz)) #0 + (J)(2)))x0s) + 0, Vi,j E [na].
(80)
This implics the equation that
B(J = B(J)P,
(81)
where P is a permutation matrix.
B Supplementary Discussion
Alternative to model states. Our main framework assumes access the model states H, of each agent before communication. These states provide a rich representation of the agent's processing of context and are used as inputs to our autoencoder for recovering latent thoughts. However, such internal states may be inaccessible in many practical settings, particularly when using closed-source or APl-restricted models.
In these cases, a viable alternative is to replace the model state H.") of each agent with a compact embedding extracted from its textual response. Specifically, model to summarize the agent's 's generated text into a fixed-size vector, which is then treated as a proxy for the unavailable model state.
apply context-awar embedding
Crucially, this embedding does not need to preserve any structure among agents, nor does need to reflect the agent's s intent. Its only requirement is to provide a compressed summary of the textual content at the linguistic level. Examples of such embedding methods include those from models like BERT or RoBERTa, pooled sentence embeddings from Sentence-BERT [Reimers and Gurevych, 2019], or output vectors from instruction-tuna embedding APIs. These methods are designed to produce compact, semantically meaningful vectors that summarize the surface content of given text.
Once such an embedding is obtained for each agent, the rest of the framework remains unchanged. The collection of response embeddings is treated as a surrogate for H; and passed through the sparsity- regularized autoencoder to recover latent thoughts 2,. From that point latent communication
20

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proceeds identically: inferring shared/private thoughts, routing them based on recovered structure, and injecting them into agents via prefix adaptation.
This replacement provides drop-in mechanism to support latent communication in scenarios where model internals are inaccessible, enabling broader applicability of the framework across both open- and closed-source agents. Naturally, one may choose suitable encoders for other modalities to extend the framework beyond LLMs.
C Experimental Details and Additional Results
C.1 Implementation Details
For experiments conducted in $5, we set the prefix token count for our method to 1. For baseline comparisons, we utilize the original code released by the authors All experiments are conducted on a single compute node with NVIDIA H100 GPUs.
C.2 Additional Results Scaling Debate Rounds
In $5.3, we compare the performance of Multiagent Finetune [Subramaniam et al., 2025] and [НHOGGHCOOM as the number of debate rounds increases from 2 to 6 based on Llama-3-8Bi Instruct [Grattafiori et al., 2024]. Here, further extend the analysis to an additional model, Qwen-3-1.7B (Yang et al., 2025), demonstrating that THOUGHTCOMM remains robust and is not adversely affected by increased redundancy caused by increased numbers of debate rounds.
As shown in Fig. 7, we observe that the accuracy and consensus of THoUGHTCOMM remain stable or even improve as the number of debate rounds inereases up In contrast, the performance of Multiagent Finetune [Subramaniam et al., 2025] declines noticeably as rounds increase beyond 4, particularly in the accuracy metric. This further supports our claim that THoUGHTCOMM robust to the accumulation of redundant noisy information introduced by additional communication rounds.
It is important to note, however, that high consensus among agents does not always imply high task accuracy. This phenomenon is particularly evident in the Qwen-3-1.7D [Yang et al., 2025] results for Multiagent Finetune [Subramaniam al., 2025], where consensus steadily increases the number of debate rounds grows-from to 6, while the corresponding accuracy remains stagnant or even degrades. This decoupling suggests that agents can converge on a common answer even when that answer is incorrect, leading to a failure mode in which additional communication drives premature agreement rather than genuine reasoning improvements.
In contrast, COOUGHTCOMM not only increases consensus but also aligns higher agreement with improved accuracy. We also highlight that the gap between THOUGHTCOMM and the baseline widens at higher round counts. These results underscore the importance of structure-aware latent communication in preventing unproductive conformity and fostering truly collaborative reasoning in multi-agent LLM systems. Taken together, these findings confirm the scalability of our approach: ThoughtCoMm enables multi-agent systems leverage communication rounds for improved reasoning without incurring the degradation commonly observed in prior debate-style frameworks.
Multiagent Finetune
ThoughtComm
Consensus (%)
Accuracy (%)
90
-98
84
96
78
2
5
2
5
Number of Rounds
Number of Rounds
Figure 7: Additional results of multi-agent performance on Qwen-3-1.7B [Yang et al., 2025] as the number of debate rounds increases.
21

---

C.3 Additional Results on Varying Latent Dimensions
We investigate how varying the latent dimensionality affects performance the MATH dataset. In these experiments, the setup involves two agents, two rounds, and a single prefix token used for communication. Results shown for both Llama-3-8BBInstruue and Qwen-3-1.7B models.
As shown in Fig. and Fig. 9, accuracy consistently improves as the latent dimension increases up to 512, after which the gains saturate. This suggests that while higher-capacity latent spaces facilitate richer communication between agents, overly large latent dimensions yield diminishing returns, likely due to redundancy in the learned representations.
Accuracy (%)
Consensus (%)
70
42
69
36
68
128
256
512
1024
2048
128
256
512
1024
2048
Latent Dimension
Latent Dimension
Figure 8: Effect of varying latent dimensionality on MATH for
[Grattafiori
al., 2024]. Accuracy improves with increased latent capacity, stabilizing beyond 1024 dimensions.
Accuracy (%)
Consensus (%)
95
90
88
128
512
1024
2048
128
512
1024 2048
Latent Dimension
Latent Dimension
Figure 9: Effect of varying latent dimensionality MATH for Qwen-3-1.7B [Yang al., 2025). similar trend is observed, confirming that the benefits of higher latent capacity generalize across architectures.
Multiagent Finetune
ThoughtComm
LLaMA 3-8B
Qwen 3-1.7B
54
Accuracy (%)
Accuracy (%)
90
48
84
42
78
36
2
2
Number of Agents
Number of Agents
Figure 10: Performance the number of agents increases on MATH for Llama-3-8B 3-8B-Insttuee and Qwen-3-1.7B. The missing data point is due to runtime limit exceeded.
C.4 Additional Results on Varying Number of Agents
We next analyze how increasing the number of collaborating agents influences performance. All experiments are conducted with two rounds, latent dimension of 1024, and single prefix token on the MATH dataset.
22

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As shown in Fig. 10, both models initially benefit from more agents, achieving notable gains when increasing from 2 to 3. However, beyond 3 agents, accuracy plateaus slightly declines, particularly for the Multiagent Finetune baseline. In contrast, THOUGHTCOMM maintains stable accuracy even as the number of agents grows, highlighting its robustness to redundant or conflicting signals.
23

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Reviews:
[{"review_id": "OxSig2rdPh", "reviewer": "Reviewer_rt7c", "summary": "The paper introduces thought communication, a paradigm where large-language-model agents exchange latent representations nstead of natural-language messages to reduce ambiguity in multi-agent coordination. It formalizes agent states as outputs of an unknown injective function applied to latent thoughts and proves that shared thoughts, private thoughts, and their agent-specific structure are identifiable under mild assumptions. Building on this theory, the authors propose THOUGHTCOMM: a sparsity-regularized autoencoder extracts latent thoughts from agents’ hidden states, and lightweight prefix adapters inject the relevant thoughts back into each agent during generation. Experiments on synthetic data validate the identifiability guarantees, while tests on MATH and GSM8K show accuracy and consensus gains over single-agent baselines and multi-agent finetuning, with minimal additional training overhead.", "questions": "1) This form of multiagent approach is a form of test-time scaling since it involves both several rounds of debate and it involves querying several language models. Because of this, it seems unfair to compare against \"single answer\" that involves no test-time scaling. Do you think the experiments improvements could just results from the increase in test-time scaling? I would really like to see an attempt at giving each of the approaches similar amounts of test-time compute for a fair comparison. For examples, approaches like using thinking models or top-k sampling.\n\n2) It's claimed multiple times that the approach is model-agnostic. As it stands the claim is unsupported – it would be great to see some experimental results backing this up, or rephrasing that this is speculation.\n\n3) It's quite surprising that varying the prefix length doesn't affect the models' performance at all. I would think too small of a prefix length would bottleneck how much the models could communicate but this doesn't seem to be the case. What do you think is going on here?", "limitations": "The limitations of the approach could be more thoroughly discussed. For example, multi-agent appraoces introduce additional overhead in terms of test-time scaling. Also, having models communicated through thought vectors rather than natural language introduces risks in making the models much less interpretable and black-box. Communication through natural language at least allows human oversight into the models. I would really like to see a discussion of this point in the paper.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The paper demonstrates strong empirical improvements over existing methods in well-established benchmarks.\n- Introduces a novel “thought communication” paradigm and backs it with formal identifiability proofs. These results are theoretically interesting and provide a strong basis for the method’s empirical performance.\n- The paper is clearly written and well organized.\n\nWeaknesses:\n- The experimental comparison isn’t fair in terms of test-time compute and I think the baselines could be stronger. See questions.\n- There is a bit of a disconnect between the theory an empirical experiments. My understanding is that the real-world experiments use a dependency structure such that all messages are shared to all agents. It would be nice to have some real-world demonstration of why selective sharing of messages is important.\n- I think the paper could really benefit from a more detailed analysis of what the thought vectors are learning to exchange between agents. It’s not clear to me whether the empirical improvement just comes from an increase in test-time compute, rather than the models actually engaging in a meaningful form of collaboration. I think an analysis of the contents of the thought vectors could provide a lot of insight in this direction. Some experiments in this direction would likely lead me to improve my score.\n- Some of the claims are a bit bold and I think distract from the main points of the paper: “We hope this work marks a potential step toward superhuman collaboration, which is essential for superhuman intelligence”", "was_revised": true, "final_justification": "I believe the inclusion of these extra experiments and clarification in the final version will strengthen the paper. The two strongest reasons (in order) that convinced me to increase my score are: (1) the new mechanistic interpretability experiments and (2) the wall-clock test time experiments.", "rebuttal": "We sincerely appreciate your constructive feedback and insightful comments. In light of these, we have conducted **new experiments** and introduced **new discussions** in the updated version. Please see our point-by-point responses below:\n\n---\n\n**Q1:**  It seems unfair to compare against the “single answer” baseline, which involves no test-time scaling. Could the improvement just result from the increase in scaling? An attempt to evaluate with the consideration of compute would be great.\n\n**A1:** Thank you for the insightful comment. While we agree that the single-agent baseline does not control for test-time scaling, **our primary comparison is with Multiagent Finetuning** [1], a **SOTA in multi-agent communication** that also uses **multiple agents and communication rounds**. In Table 1 of the submission, ThoughtComm consistently outperforms Multiagent Finetuning across settings, highlighting the added benefit of latent thought communication beyond language. The single-answer baseline serves mainly as a sanity check, since prior work in this line of research has already shown that multi-agent debate improves reasoning significantly.\n\nMotivated by your suggestion, we further conducted an **additional runtime comparison** using LLaMA 3-8B-Instruct on MATH, measuring wall-clock runtime on two H100 GPUs as the number of agents varies:\n\n| # Agents | Multiagent Finetuning (s) | ThoughtComm (s) |\n|----------|----------------------------|------------------|\n| 4        | 15520.44                   | 6027.23          |\n| 5        | 22263.76                   | 7867.38          |\n| 6        | 24755.92                   | 9633.05          |\n\nThese results show that **our method achieves higher performance with significantly lower cost**, indicating that the gains do not stem from increased compute. In fact, this suggests that latent communication may be a **more efficient route to improved coordination**. Thanks again for your constructive insight. We hope the new results could shed light on the potential of going beyond language, both in performance and efficiency.\n\n---\n\n**Q2:** My understanding is that the real-world experiments use a dependency structure such that all messages are shared to all agents. It would be nice to have some real-world demonstration of why selective sharing of messages is important.\n\n\n**A2:** Thank you for raising this point. It is correct that, in our current experiments, all text messages are visible to all agents. However, our focus is **not on message-level filtering**, but on **selective sharing of latent thoughts** – the internal representations that generate those messages. This selective sharing occurs in the latent space, where for each agent, we infer a personalized subset of latent thoughts based on recovered structural dependencies and the identified latent thought vector. These determine which thoughts influence an agent’s internal state, enabling agents to consider only relevant cognitive content while ignoring unrelated noises. In this sense, although messages are broadcast, the latent thoughts driving coordination are filtered and routed in a personalized manner, capturing differences in roles, priors, or goals. We believe this is a more faithful model of how effective collaboration should work. \n\nIn light of this, we have added the following discussion in the updated manuscript to further highlight the distinction:\n\n> “In our real-world experiments, the recovered dependency structure plays a critical role in shaping how latent thoughts are routed to each agent. After extracting the shared latent space via the sparsity-regularized autoencoder, we apply a structural mask to ensure that each agent only receives the latent dimensions that are relevant to its own internal representation. This filtering directly affects how the injected prefixes are constructed for each agent during the next round of generation. Although the surface-level messages are broadcast, the actual content used to condition each agent’s reasoning is selectively constructed in the latent space, reflecting the personalized structure of shared and private thoughts.”\n\n---\n\n**Q3**: It’s not clear to me whether the empirical improvement just comes from an increase in test-time compute, rather than the models actually engaging in a meaningful form of collaboration. I think an analysis of the contents of the thought vectors could provide a lot of insight in this direction. Some experiments in this direction would likely lead me to improve my score.\n\n\n**A3:** We sincerely appreciate your insightful suggestions. Accordingly, we have conducted **additional experiments** on both the **computation** and **interpretation of latent thoughts**.\n\nThe results on the computation cost have been shown in detail in **A1**, where our method **achieves higher performance with significantly lower cost**, **compared to SOTA** in multi-agent collaboration and debate.\n\nFor interpretability, we performed a new analysis inspired by the mechanistic interpretability literature. For each latent variable, we identified the top-10 most activated samples (questions) on MATH and used GPT-4o to summarize the shared semantic pattern based on the corresponding conversation contexts. A few representative examples are shown below.\n\n\n> **Shared concepts:**\n> \n> - \"Utilizing trigonometric identities to simplify trigonometric expressions.\"\n> \n> - “Using arithmetic operations to manipulate fractions and decimals”\n> \n> - **Insight:** These are all basic mathematical knowledge that are shared in most problems, and thus are relevant to all agents.\n> \n> **Private concepts:**\n> \n> \n> - **Agent 1’s concept:** “finding the least common multiple (LCM) by identifying the highest power of each prime number that appears in the factors of given integers”\n> \n> - **Insight:** Other agents may opt for different methods to find the LCM, such as listing multiples or using a simpler approach.\n> \n> - **Agent 2’s concept:** “using the quadratic formula over factoring when solving quadratic equations”\n> \n> - **Insight:** This technique differentiates Agent 1 from others who might opt to factor the quadratic expression instead.\n> \n> - **Agent 3’s concept:** “using Heron's Formula to calculate the area of triangles when given the lengths of all three sides.” \n> \n> - **Insight:** While other agents might use basic geometric formulas or the base-height method for calculating the area of triangles, Agent 2 specifically opts for Heron's Formula, indicating a distinctive computational preference for this method in relevant scenarios.\n\n\nIn conclusion, **the latent thoughts indeed encode concepts needed for specific tasks**. Moreover, identifying the dependency structure is important given the **fundamental difference between shared and private thought**. Thanks again for your very constructive feedback.\n\n---\n\n**Q4:** Some of the claims are a bit bold and I think they distract from the main points of the paper.\n\n**A4:** Indeed, these sentences may have been overly aspirational in tone. Thank you for pointing this out. We have removed these sentences (e.g., L19 and L390) in the updated manuscript.\n\n---\n\n**Q5:** Why is it claimed that the approach is model-agnostic?\n\n**A5:** Thank you for highlighting this point. By “model-agnostic,” we mean that for any given set of LLMs, a sparsity-regularized autoencoder can be applied to reconstruct their latent thoughts based on the concatenated model states. Once trained, the same autoencoder can be used across communication rounds without further model-specific tuning.\n\nThat said, we acknowledge that this requires access to open-source models to get the model states. So while our framework does not rely on architectural details of the LLMs themselves, it is not completely plug-and-play in the strictest sense.\n\nInterestingly, **even without knowing any information on the language model, it is still possible to apply our framework**. This is because we can always directly encode latent representation from the text of responses, and thus bypass the model's hidden state, which generalizes the applicability to completely **closed-source** models. At the same time, finding a good summarization representation of text is a separate topic. This was mentioned in **L386-389** and had been detailed in **Appendix C**.\nThanks again for your great question, which provides us with the opportunity to further clarify it. We have removed the term ‘model-agnostic’ and highlighted the above discussion to avoid any potential confusion.\n\n---\n\n**Q6:** It's quite surprising that varying the prefix length doesn't affect the models' performance at all. I would think too small a prefix length would bottleneck how much the models could communicate, but this doesn't seem to be the case. What do you think is going on here?\n\n\n**A6:** Thank you for raising this thoughtful observation – we had a similar reaction initially. In some cases, we do observe slight performance gains as the prefix length increases, but the effect is not consistent across models or tasks. A possible explanation lies in the distinction between a token embedding and a prefix embedding. While both have the same dimensionality (e.g., 1024), a token embedding is tied to a single vocabulary item and typically encodes the semantics of just that **one discrete token**, often lying on a lower-dimensional subspace. In contrast, a prefix embedding is a free parameter optimized to encode **many continuous latent thoughts**, leveraging the full capacity of the embedding space. As a result, even a single prefix token can convey a rich bundle of cognitive content, making longer prefixes less essential in our setting. This may explain the diminishing returns with increased prefix length. \n\n---\n\n[1] Subramaniam et al. \"Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains.\" ICLR 2025"}, {"review_id": "dzbX0gFbz4", "reviewer": "Reviewer_J712", "summary": "This paper proposes to leverage extracted thoughts (i.e. representation vectors) of one model that can be injected into another model in order to improve results.", "questions": "I am struggling with why the results on Table 1 are actually that good. How can the collaboration of just three 0.6B models substantially outperform an 8B models? What is the intuition behind this? Is the knowledge actually in the trained adapter, so is most of the improvement not about the multi-agent but about the finetuning?\n\nFigure 4: \" The red line marks the red line threshold typically considered identifiable when exceeded.\" => what does \"typically considered identifiable\" mean?", "limitations": "Limitations should be discussed in more depth. Also a proper discussion of and positioning with respect to related work is missing.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Overall, this paper pursues a very interesting idea in an up-and-comming hot topic, i.e., multi-agent systems. It is mostly well written and nicely motivated. However, the presentation has still some issues, which leaves a couple of questions open to me.\n\nWhile reading, I struggled with the connection between the data generating process in the problem formulation and how to connect it to LLMs. The authors should consider making this more explicit.\n\nThe reported results are actually impressively good. So good that I actually have trouble to understand how this is achieved. The collaboration of 3 agents of the same type should not be able to solve a problem that much better than a single one.\n\nRelated work to the novel approach is not properly discussed. For example, how does the extraction of thoughts relate to research on interpretability, specifically to probing or sparse autoencoders?\nFurthermore, the proof in the appendix should be explained in more detail; to me if was incomprehensible.\nUnfortunately, the full code is not availbale for review.", "was_revised": true, "final_justification": "In light of the rebuttal, I opted to improve my rating for this paper. Specifically adding the proof sketches will help the readibility of the paper.", "rebuttal": "Thank you very much for your thoughtful and detailed feedback. In response, we have included **additional experiments** and added **new discussions** to the revised version. Please see our detailed point-by-point replies below.\n\n---\n\n**Q1:** More discussion on the connection between the data generating process and LLMs. \n\n**A1:** Thank you for this helpful suggestion. In light of it, we have added the following paragraphs in the updated manuscript:\n\n>  “When generating responses, LLMs operate on internal representations learned during training. We model this by assuming that each agent’s model state (e.g., hidden state $H$ before token generation) is produced from a set of latent thoughts $Z$ via an unknown function. Specifically, we posit that $H$ is generated from $Z$ through a complex, nonparametric function $f$, capturing the model’s internal reasoning process.\n\n> This view aligns with the data-generating perspective adopted in recent mechanistic interpretability work (e.g., Olah et al., 2020; Cunningham et al., 2023), where model states are treated as outputs of latent concepts. Our setting differs in two important ways: (1) we assume a nonparametric, potentially highly nonlinear mapping $f$, whereas sparse autoencoders typically use a sparse linear decoder; and (2) we focus on multi-agent systems, where identifying structured dependencies between agents and their latent thoughts is essential for collaborative reasoning beyond language.”\n\nWe hope this could make the connection clearer. We appreciate your insight and would be glad to elaborate further if helpful.\n\n---\n\n**Q2:** What’s the intuition behind the strong results? It’s surprising that 3 agents of the same type can so significantly outperform a single one. How can collaboration among three 0.6B models outperform an 8B model? Does most of the gain come from the trained adapter rather than the multi-agent setup?\n\n\n\n**A2:** Thank you for raising these important and insightful questions. It has been consistently observed in recent literature that multi-agent collaboration and debate can lead to substantial performance gains compared to a single agent [1]. Similarly, increasing the number of agents in our framework also leads to improved results, consistent with this line of research.\n\nThat said, our goal is not to re-establish the benefits of multi-agent communication, which are now well-verified in the literature. Rather, our work seeks to **advance the mode of multi-agent communication itself** – from surface-level language to **structured latent thoughts**. The core contribution is to show that communication through latent thoughts can further improve multi-agent reasoning. This is supported by both theory (identifiability of latent thoughts and structure) and experiments: as shown in Table 1 of the manuscript, our method **consistently outperforms the existing SOTA** (Multiagent Finetuning [1]) under the **same number of agents and rounds**, demonstrating the added value of latent thought communication beyond pure language.\n\nMeanwhile, one may also wonder whether the improvements over the previous multi-agent SOTA come at the cost of increased computation. To address this, we conducted an **additional runtime comparison** using LLaMA 3-8B-Instruct on the MATH dataset, measuring wall-clock runtime as the number of agents varies:\n\n| # Agents | Multiagent Finetuning (s) | ThoughtComm (s) |\n|----------|----------------------------|------------------|\n| 4        | 15520.44                   | 6027.23          |\n| 5        | 22263.76                   | 7867.38          |\n| 6        | 24755.92                   | 9633.05          |\n\n\nThese results show that our method not only achieves **higher accuracy** but does so with **significantly lower time**. This indicates that the performance gains are not due to increased compute. In fact, they suggest that latent communication may offer a **more efficient route to improved coordination**.\n\nIn summary:\n\n- **Compared to single-agent baselines**, most of the improvement comes from multi-agent collaboration (as expected).\n\n\n- **Compared to prior multi-agent methods**, most of the gain comes from latent communication, not from increased computation or additional test-time scaling.\n\nRegarding the strong performance of Qwen 0.6B, we note that even in the single-agent setting, it slightly outperforms some 8B models on MATH. This phenomenon has also been observed in prior work and likely reflects differences in the domain specialization of models.\n\nThanks again for your constructive feedback. We appreciate your careful reading and hope the introduced discussions and experiments could be helpful.\n\n---\n\n**Q3:** More discussion on the connection with interpretability research, proof intuitions, and implementation.\n\n**A3:** We sincerely appreciate your suggestions. We fully agree with you that the connection with mechanistic interpretability (e.g., sparse autoencoder) should be further highlighted. In light of this, we have **added the following paragraphs** in the revised manuscript:\n\n> “Recent work in mechanistic interpretability has explored structured latent representations, notably through sparse autoencoders (SAEs), which aim to discover interpretable features from LLM hidden states [Olah et al., 2020; Cunningham et al., 2023]. These approaches treat model states as being generated from latent concepts and recover sparse linear encodings for interpretability. \n\n> Our work aligns with this perspective in spirit: both aim to uncover the latent generative process behind model hidden states. However, there are two key differences. (1) SAEs assume a sparse **linear** relationship between latent variables and observed states, whereas our formulation allows for a **general nonlinear** generative process $f$, providing greater flexibility and applicability to complex real-world settings. (2) The goal of SAEs is primarily interpretability – interpreting the underlying generative features – whereas our focus is on **enabling latent thought communication**. We recover latent thoughts and their dependency structures not only for interpretability, but to directly support efficient multi-agent reasoning. Empirically, this latent communication has been shown to outperform language-based exchange in collaborative tasks.”\n\nMoreover, regarding the proofs, we have now included **proof sketches for all theorems** in the main paper to provide a direct intuition underlying the theoretical framework.\n\n> “**Proof sketch of Theorem 1:** Since we make no assumptions on the functional form of $f$, the latent variable distribution, or access to auxiliary information (e.g., interventions or multiple domains), the only available signal for identification lies in the structural relationship between latent and observed variables. In the nonparametric setting, this structure is captured by the non-zero pattern of the Jacobian of the generating function $f$. We require that the Jacobian spans its support subspace, ensuring that the population adequately reflects the underlying dependency structure. Leveraging this, we show that the intersection of latent variables influencing any pair of observed variables can be disentangled from all other components.”\n\n> “**Proof sketch of Theorem 2:** Similar to Theorem 1, we begin by excluding degenerate cases where the population fails to span the Jacobian's support subspace. We then analyze the Jacobian's structure using linear algebra, focusing on the structural distinction between complements and intersections of latent supports, which enables the disentanglement of private latent variables unique to each observed variable in a pair.”\n\n>”**Proof sketch of Theorem 3:** We begin by connecting the support structure of the Jacobian to the latent-observed dependency graph, under the span assumption. We then show that the support of the estimated Jacobian must contain that of the true Jacobian. By incorporating a sparsity regularization, we eliminate superfluous entries and reduce the indeterminacy, allowing us to identify the dependency structure up to a permutation of the latent dimensions.”\n\nDue to policy restrictions, we cannot include external links in the rebuttal, but we would like to highlight the implementation details as follows. As mentioned in Line 757, we build on the original codebase of Multiagent Finetuning [1]. The main additional module introduced in our framework is the sparsity-regularized autoencoder, which is a standard autoencoder trained with an $\\ell_1$ penalty on the Jacobian to encourage sparse structural dependencies. The adapter for prefix injection is implemented following established techniques from prefix-tuning [3], and both components are lightweight and modular, requiring only the hidden states of the LLMs as input. We have expanded Appendix D with additional architectural and training details.\n\nThanks again for your thoughtful feedback. Please let us know if you have any additional questions.\n\n---\n\n**Q4:** Clarification of \"typically considered identifiable\".\n\n**A4:** Thanks for your great question. In the context of nonparametric identifiability, a high mean correlation coefficient (MCC) between estimated and ground-truth latent variables is widely used as a proxy for identifiability [2]. When the MCC is high, each estimated latent variable tends to correspond to a distinct ground-truth one, suggesting **one-to-one recovery** and thus identifiability. In contrast, **non-identifiable settings typically yield MCC values closer to 0.3**, reflecting entangled or overlapping representations. We have clarified this point in the revised manuscript to avoid potential ambiguity.\n\n---\n\n[1] Subramaniam et al. \"Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains.\" \n\n[2] Hyvärinen et al. “Identifiability of latent-variable and structural-equation models: from linear to nonlinear.”\n\n[3] Li and Liang. “Prefix-Tuning: Optimizing Continuous Prompts for Generation.”"}, {"review_id": "rjE06z9j8d", "reviewer": "Reviewer_d5cT", "summary": "This paper proposes a novel communication paradigm for multi-agent LLM systems called thought communication, which replaces traditional natural language exchanges with direct interaction via shared latent variables. The authors formalize the notion of thoughts as latent variables and present a nonparametric latent variable model that allows agents to share and reason over these latent constructs. The core theoretical contribution is a set of identifiability results proving that shared and private thoughts can be recovered under mild conditions. Building on this, the authors develop THOUGHTCOMM, a framework leveraging a sparsity-regularized autoencoder and prefix adaptation for direct latent communication among agents. Extensive experiments on synthetic data and real-world reasoning benchmarks MATH, GSM8K demonstrate substantial performance gains over standard message-passing approaches.", "questions": "Please refer to the weakness.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strength:\n\n1.\tThe paper presents an interesting and well-explained idea: letting agents share their internal thoughts directly instead of talking through natural language, which can be vague or unclear. This tackles a well-known problem in how AI agents work together and offers a new way for them to communicate more effectively.\n\n2.\tThe paper establishes rigorous identifiability results for both shared and private latent thoughts ensures that the recovered latent representations reflect the true internal structure of agent reasoning. \n\n3.\tThe experiments results show clear improvements in both accuracy and agent consensus over existing baselines and are consistent across model scales.\n\n4.\tThe method avoids full LLM finetuning and works with frozen models, which makes it applicable in real settings.\n\nWeakness:\n1.\tThe proposed framework assumes access to agent model states, which may not be available for closed-source models. While acknowledged as a limitation, the practical impact is non-trivial, especially given the paper’s ambitious real-world aspirations.\n\n2.\tAlthough the theory ensures identifiability, there’s limited discussion on whether the recovered latent thoughts are interpretable or actionable by humans or other systems. Some empirical visualization or case study would have strengthened the narrative.\n\n3.\tThe paper adopts a sparsity-regularized autoencoder as its core estimation engine. However, there’s little exploration of its architecture, training sensitivity, or how design choices impact identifiability or downstream performance.\n\n4.\tThe evaluation is focused on math reasoning, which, while difficult, represents a narrow task distribution. It’s unclear how well THOUGHTCOMM performs in domains like planning, negotiation, or open-domain dialogue.", "was_revised": true, "final_justification": "The authors have successfully addressed my concerns with new experiments and analysis. In this respect, I think this paper can contribute to the community, and I have raised the acceptance score.", "rebuttal": "We truly appreciate your insightful and constructive feedback. Based on it, we have performed **new experiments** and **additional discussions** to the updated manuscript. Below, we provide detailed responses to each point.\n\n---\n\n**Q1:** The proposed framework assumes access to agent model states, which may not be available for closed-source models. While acknowledged as a limitation, the practical impact is non-trivial, especially given the paper’s ambitious real-world aspirations.\n\n\n**A1:** Thanks for raising this insightful point. As noted in **Lines 386–389** and detailed in **Appendix C**, even for **fully closed-source models**, latent thought communication remains applicable. This is because the latent representation need not rely strictly on access to internal model states. Instead, we can directly encode latent thoughts from the summary of the generated text itself, **bypassing the need for model states entirely**. While constructing effective summarization representation from text is itself a separate nontrivial task, this alternative approach offers a practical and extensible solution when access to open-source models is restricted. The details are referenced as follows:\n\n\n> \"**Alternative to model states.** Our main framework assumes access to the model states $H_t$ of each agent before communication. These states provide a rich representation of the agent’s processing of context and are used as inputs to our autoencoder for recovering latent thoughts. However, such internal states may be inaccessible in many practical settings, particularly when using closed-source or API-restricted models.\n\n> In these cases, a viable alternative is to replace the model state $H_t^{(i)}$ of each agent with a compact embedding extracted from its textual response. Specifically, one can apply a context-aware embedding model to summarize the agent’s generated text into a fixed-size vector, which is then treated as a proxy for the unavailable model state.\n\n> Crucially, this embedding does not need to preserve any structure among agents, nor does it need to reflect the agent’s intent. Its only requirement is to provide a compressed summary of the textual content at the linguistic level. Examples of such embedding methods include those from models like BERT or RoBERTa, pooled sentence embeddings from Sentence-BERT, or output vectors from instruction-tuned embedding APIs. These methods are designed to produce compact, semantically meaningful vectors that summarize the surface content of a given text.\n\n> Once such an embedding is obtained for each agent, the rest of the framework remains unchanged. The collection of response embeddings is treated as a surrogate for $H_t$ and passed through the sparsity-regularized autoencoder to recover latent thoughts $\\hat{Z}_t$. From that point on, latent communication proceeds identically: inferring shared/private thoughts, routing them based on recovered structure, and injecting them into agents via prefix adaptation.\n\n> This replacement provides a drop-in mechanism to support latent communication in scenarios where model internals are inaccessible, enabling broader applicability of the framework across both open- and closed-source agents.\"\n\nThanks again for your great question. We have further highlighted it in Section 4. Please feel free to let us know if there are any further questions.\n\n---\n\n\n**Q2:** Although the theory ensures identifiability, there’s limited discussion on whether the recovered latent thoughts are interpretable or actionable by humans or other systems. Some empirical visualization or case study would have strengthened the narrative.\n\n\n**A2:** We sincerely appreciate your constructive suggestions. We fully agree with you that some case studies could be very helpful. In light of it, we carried out a **new interpretability analysis of the latent thoughts**, inspired by standard techniques in mechanistic interpretability. Specifically, for a target latent variable, we identify the top-10 samples (questions) with the highest activation, and prompt GPT-4o to summarize the semantic pattern across those cases given the corresponding conversation contexts. Below are a few representative examples illustrating shared thoughts across agents, as well as agent-specific private reasoning:\n\n> **Shared concepts:**\n> \n> - \"Utilizing trigonometric identities to simplify trigonometric expressions.\"\n> \n> - “Using arithmetic operations to manipulate fractions and decimals”\n> \n> - **Insight:** These are all basic mathematical knowledge that are shared in most problems, and thus are relevant to all agents.\n> \n> **Private concepts:**\n> \n> \n> - **Agent 1’s concept:** “finding the least common multiple (LCM) by identifying the highest power of each prime number that appears in the factors of given integers”\n> \n> - **Insight:** Other agents may opt for different methods to find the LCM, such as listing multiples or using a simpler approach.\n> \n> - **Agent 2’s concept:** “using the quadratic formula over factoring when solving quadratic equations”\n> \n> - **Insight:** This technique differentiates Agent 1 from others who might opt to factor the quadratic expression instead.\n> \n> - **Agent 3’s concept:** “using Heron's Formula to calculate the area of triangles when given the lengths of all three sides.” \n> \n> - **Insight:** While other agents might use basic geometric formulas or the base-height method for calculating the area of triangles, Agent 2 specifically opts for Heron's Formula, indicating a distinctive computational preference for this method in relevant scenarios.\n\nTo summarize, we can observe that the **latent thoughts indeed encode concepts needed for specific tasks**. Moreover, identifying the dependency structure is important given the **fundamental difference between shared and private thoughts**.\n\n---\n\n**Q3:** More exploration on the empirical study of the sparsity-regularized autoencoder.\n\n\n**A3:** Thanks so much for the insightful suggestion. Accordingly, we have conducted a set of **new experiments** to study the regularized autoencoder in both the identifiability and down stream performances.\n\n**Identifiability:**\n\nWe first evaluate the effect of the $\\ell_1$ regularization strength, which promotes sparsity – a key difference from standard autoencoders. Using a hidden dimension of 1024 and 1000 samples, we report the mean correlation coefficient (MCC) across varying sparsity weights:\n\n| Sparsity weight | MCC ($\\uparrow$)             |\n|-----------------|------------------------------|\n| $1\\mathrm{e}{-5}$  | 0.84$\\pm$0.01              |\n| $1\\mathrm{e}{-4}$  | 0.85$\\pm$0.02              |\n| $1\\mathrm{e}{-3}$  | 0.87$\\pm$0.01              |\n\nFrom the results, the performance drops when the sparsity regularization is not strong enough, **supporting the necessity of sparsity regularization**.\n\n**Downstream Performance:**\n\nWe then vary the latent dimensionality of the autoencoder and evaluate multi-agent accuracy on the MATH dataset using two different LLM backbones. The number of agents is set to two, and other settings follow those used in Table 1 of the main paper.\n\n| Base Model     | Dim  | Accuracy ($\\uparrow$)       | Consensus ($\\uparrow$) |\n|----------------|------|------------------------------|-------------------------|\n| LLaMA 3-8B      | 128  | 0.3840$\\pm$0.0218          | 0.6870                  |\n|                | 256  | 0.4160$\\pm$0.0220          | 0.6880                  |\n|                | 512  | 0.4160$\\pm$0.0220          | 0.6800                  |\n|                | 1024 | 0.3880$\\pm$0.0218          | 0.6867                  |\n|                | 2048 | 0.4100$\\pm$0.0220$         | 0.7020                  |\n| Qwen-3-1.7B     | 128  | 0.8740$\\pm$0.0148          | 0.9380                  |\n|                | 256  | 0.8940$\\pm$0.0138          | 0.9460                  |\n|                | 512  | 0.8980$\\pm$0.0135          | 0.9520                  |\n|                | 1024 | 0.8840$\\pm$0.0143          | 0.9480                  |\n|                | 2048 | 0.8860$\\pm$0.0142          | 0.9440                  |\n\nWe observe that increasing the latent dimension improves performance up to a point, after which the gains plateau or slightly degrade. This is **expected**: while too few latent variables can under-represent the thought space, excessively large dimensions may introduce unnecessary noise in addition to the curse of dimensionality.\n\nThank you again for your suggestion to extend the empirical analysis. We hope these new results provide greater clarity into the behavior of the regularized autoencoder. Please feel free to let us know if you have further questions or feedback.\n\n---\n\n**Q4:** The evaluation is focused on math reasoning, which, while difficult, represents a narrow task distribution. It’s unclear how well ThoughtComm performs in domains like planning, negotiation, or open-domain dialogue.\n\n**A4:** Thank you for the thoughtful suggestion. Our current focus on math reasoning tasks is deliberate: these datasets require **a combination of skills**, including **multi-step logical reasoning, collaborative language use, implicit planning**, and **negotiation between agents**. In this sense, they serve as a challenging testbed that integrates multiple reasoning and interaction skills, rather than isolating a single capability. This may also be why they have become standard benchmarks in prior work.\n\nThat said, we agree that evaluating performance on domains like planning, negotiation, and open-domain dialogue would further strengthen the case for generality. We have highlighted this in the revised discussion and see this as an important direction for future work. Please feel free to let us know if you have any further suggestions; we sincerely appreciate it."}, {"review_id": "fkSKR5zq8o", "reviewer": "Reviewer_R1aq", "summary": "This paper proposes enhancing the performance of LLM-based multi-agent collaborative discussions by introducing shared and private hidden thoughts. Specifically, the authors design an autoencoder with an assignment matrix to encode the latent thoughts from the last token embeddings. These latent thoughts are then split into shared and private components based on the assignment matrix and delivered to each agent in the next discussion round via prefix-tuning. The effectiveness of the assignment matrix design is first validated through experiments on a synthetic dataset, and the proposed method is further evaluated on two mathematical reasoning benchmarks, demonstrating its effectiveness.", "questions": "1. Why is it necessary to group latent thoughts by agreement level?  \n\n2. Is $w_{\\alpha_j}$ manually set or learned during training?  \n\n3. How can we validate that the learned structure of thoughts is meaningful in math reasoning tasks?  \n\n4. Have you considered a baseline without any structure of thoughts? Specifically, what happens if all last-token embeddings from previous agents are directly used as prefixes for the next round, without grouping or assigning structure? \n\n5. This looks very similar to Latent Dirichelet Allocation. Have you tried to use a latent generative model directly on natural language in a similar way to LDA? The latent generative model is not bound to hidden representation. In my opinion, the design principle of THOUGHTCOMM is based on latent thoughts, not latent embeddings. Latent thoughts can also be tokens.  \n\n6. Can you provide a concrete case study of THOUGHTCOMM in action? Is there an example showing intermediate natural language outputs for each round of discussion?\n\n7. Do latent thoughts offer interpretable dimensions in real-world tasks like math reasoning? The toy example in Figure 1 includes interpretable concepts like \"carrying luggage\" and \"punctuality\". Can similar concepts be extracted in real-world tasks?\n\n8. Does scaling up the structure of thoughts lead to continued performance gains? \n\n9. From the example in Figure 1, the THOUGHTCOMM design aligns well with scenarios where the problem is approached from different perspectives. However, in cases where multiple agents hold opposing views and need to debate and persuade each other, can THOUGHTCOMM still operate effectively?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n\n1. The paper explores an interesting and meaningful direction: multi-agent communication beyond natural language.\n2. It adopts an efficient training strategy that avoids heavy computation overhead.\n3. The design is intuitively appealing—communication as a composition of private and shared perspectives aligns well with how collaborative reasoning may work.\n4. Experiments are conducted on diverse and up-to-date model backends, showing the method's applicability across different LLMs.\n\nWeaknesses\n\n1. The experimental scale is limited, involving only three agents. It remains unclear how the method generalizes to more complex multi-agent settings.\n2. The experimental analysis lacks depth. For instance, the paper focuses on tuning parameters like prefix length and debate rounds, which are arguably not central to the proposed THOUGHTCOMM framework. More critical variables such as the scale of latent thoughts and the number of agents (which directly relate to the structure of thoughts) deserve closer examination.\n3. The implementation details are overly brief. The main paper and appendix provide only three sentences on implementation. Key details regarding the autoencoder, prefix-finetuning hyperparameters, and training setup are missing.", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding additional experiments and interpretability. I am willing to raise my rating to 5.", "rebuttal": "Thank you very much for your thoughtful and detailed feedback. In light of it, we have incorporated **additional experiments** and **new discussions** in the updated version. Please find our point-by-point responses below.\n\nIn all tables, M denotes Multiagent Finetuning, T denotes ThoughtComm.\n\n**Q1:** It remains unclear how the method generalizes to more complex multi-agent settings.\n\n**A1:** We sincerely appreciate your constructive suggestions. Accordingly, we have conducted **new experiments varying the number of agents** on MATH:\n\n|Base Model|# Agents|Method|Accuracy ($\\uparrow$)|\n|----------|--------|------|---------------------|\n|LLaMA 3-8B|2|M|0.3520$\\pm$0.0214|\n|||T|0.3880$\\pm$0.0218|\n||3|M|0.3968$\\pm$0.0219|\n|||T|0.4560$\\pm$0.0223|\n||4|M|0.3880$\\pm$0.0218|\n|||T|0.4720$\\pm$0.0223|\n||5|M|Running|\n|||T|0.5100$\\pm$0.0224|\n|Qwen 3-1.7B|2|M|0.7540$\\pm$0.0193|\n|||T|0.8840$\\pm$0.0143|\n||3|M|0.7580$\\pm$0.0192|\n|||T|0.9300$\\pm$0.0114|\n||4|M|0.7680$\\pm$0.0189|\n|||T|0.9220$\\pm$0.0120|\n||5|M|0.7740$\\pm$0.0187|\n|||T|0.9300$\\pm$0.0114|\n\nAs expected, performance **improves with more agents** and outperforms SOTA. \n\n---\n\n**Q2:** More critical variables such as the scale of latent thoughts and the number of agents deserve closer examination.\n\n**A2:** In light of your great suggestions, we have conducted **additional experiments** on both the **scale of latent thoughts (below)** and the **number of agents (table in A1)**. For the latent thought scales, we vary the latent dimension and evaluate on MATH with two agents.\n\n|Base Model|Dim|Accuracy ($\\uparrow$)|\n|----------|----|----------------------|\n|LLaMA 3-8B|128|0.3840$\\pm$0.0218|\n||256|0.4160$\\pm$0.0220|\n||512|0.4160$\\pm$0.0220|\n||1024|0.3880$\\pm$0.0218|\n||2048|0.4100$\\pm$0.0220|\n|Qwen-3-1.7B|128|0.8740$\\pm$0.0148|\n||256|0.8940$\\pm$0.0138|\n||512|0.8980$\\pm$0.0135|\n||1024|0.8840$\\pm$0.0143|\n||2048|0.8860$\\pm$0.0142|\n\nWe observe that increasing the latent dimension improves performance up to a point. This is expected: too few latents under-represent latent thoughts, while too many introduce noise and the curse of dimensionality.\n\n---\n\n**Q3:** More details of the implementation.\n\n**A3:** Thanks for your constructive feedback. Accordingly, we have added details as follows:\n\n> “We use a standard autoencoder with $\\ell_1$ sparsity on latent-observed connections. The latent dimension is $1024$. For prefix-finetuning, we use one prefix token and generate one sentence. Training uses batch size 128 and learning rate 1e-5. We extract states from 2/3 model depth.”\n\n---\n\n**Q4:** Why is it necessary to group latent thoughts by agreement level?\n\n**A4:** Thank you for the thoughtful question. Agreement level helps uncover latent thought hierarchy: shared thoughts reflect common knowledge or shared premises, while private ones capture individual reasoning. This separation helps recovering the thought structure, helping agents to adatively consider different types of latent thoughts.\n\n---\n\n**Q5:** Is $w_{\\alpha_j}$ manually set or learned? \n\n**A5:** Thanks for the reminder. It is learned during training. We have highlighted this in the updated manuscript where it first appears (Line 256).\n\n---\n\n**Q6:** Meaningfulness of learned structure in math reasoning.\n\n**A6:** In light of your insightful question, we have conducted **interpretation analysis** on the recovered latent structured thoughts in MATH. We find that **concepts and structures similar to Figure 1 can be extracted in real-world math reasoning tasks**.\n\nWe follow the automatic interpretability methods commonly used in mechanistic interpretability literature. Specifically, for a target latent variable, we identify the top-10 samples (questions) with the highest activation, and prompt GPT-4o to summarize the semantic pattern across those cases given the conversation contexts. Below are a few representative examples:\n\n> **Shared concepts:**\n> \n> - \"Utilizing trigonometric identities to simplify trigonometric expressions.\"\n> \n> - “Using arithmetic operations to manipulate fractions and decimals”\n> \n> - **Insight:** These are all basic mathematical knowledge that are shared in most problems, and thus are relevant to all agents.\n> \n> **Private concepts:**\n> \n> \n> - **Agent 1’s concept:** “finding the least common multiple (LCM) by identifying the highest power of each prime number that appears in the factors of given integers”\n> \n> - **Insight:** Other agents may opt for different methods to find the LCM, such as listing multiples or using a simpler approach.\n> \n> - **Agent 2’s concept:** “using the quadratic formula over factoring when solving quadratic equations”\n> \n> - **Insight:** This technique differentiates Agent 1 from others who might opt to factor the quadratic expression instead.\n> \n> - **Agent 3’s concept:** “using Heron's Formula to calculate the area of triangles when given the lengths of all three sides.” \n> \n> - **Insight:** While other agents might use basic geometric formulas or the base-height method for calculating the area of triangles, Agent 2 specifically opts for Heron's Formula, indicating a distinctive computational preference for this method in relevant scenarios.\n\nIn summary, the latent thoughts **indeed encode concepts needed for tasks**, and identifying the dependency structure is important given the **fundamental difference between shared and private thoughts**\n\n---\n\n**Q7:** Consider a baseline without any structure of thoughts.\n\n**A7:** Thanks, we have conducted **new experiments** accordingly. All other settings are the same as the main experiments in Table 1. The performance drop supports the effect of considering structure.\n\n|Base Model|Method|Accuracy ($\\uparrow$)|\n|----------|------|---------------------|\n|LLaMA 3-8B|Single Answer|0.3620$\\pm$0.0215|\n||M|0.3968$\\pm$0.0219|\n||T|0.4560$\\pm$0.0223|\n||T w/o Structure|0.4380$\\pm$0.0222|\n|Qwen 3-1.7B|Single Answer|0.4360$\\pm$0.0222|\n||M|0.7580$\\pm$0.0192|\n||T|0.9300$\\pm$0.0114|\n||T w/o Structure|0.9180$\\pm$0.0123|\n\n---\n\n**Q8.** Discussion on using a latent generative model directly on natural language in a similar way to LDA.\n\n**A8.** This is a great idea. We haven’t tried LDA specifically, but we discussed a similar idea of **extracting latent thoughts directly from text** in **L386-389** and **Appendix C**. This can sidestep the need to access model states, thus generalizing the framework to **fully closed-source** LLMs. Inspired by your suggestion, we have also highlighted LDA as a promising alternative choice.\n\n---\n\n**Q9:** Can you provide a concrete case study of ThoughtComm including language conversation? \n\n**A9:** Thanks for your great suggestion. Here is a concrete example. Due to the length limit, we omitted some duplicated content with clear notes.\n\n**Summary:**  Agents began with different answers and **converged on the correct answer**. Specifically, the answer of **Agent 2** has been corrected by itself after communication. The other agents **noted** the wrong answer in Agent 2, but were **not misled** by it.\n\n**Question:** In how many ways can 13 students be selected from a group of 15 students to serve on a chalkboard-cleaning team?\n\n- **Ground-truth answer:** 105.\n\n**First round:**\n\n- **Agent 1:**\n\n  >To solve this problem, we can use the combination formula:\n  >\n  >C(n, k) = n! / (k!(n-k)!)\n  >\n  >where n is the total number of students (15) and k is the number of students selected (13). Plugging in the values, we get:\n  >\n  >C(15, 13) = 15! / (13!(15-13)!)\n  >\n  >= 15! / (13!2!)\n  >\n  >= (15 * 14 * 13!)/((13 * 12)*13!)\n  >\n  >= 15 * 14/2\n  >\n  >= 105\n  >\n  >(Omitted)\n  >\n  >Answer: \\boxed{105}\n\n- **Agent 2:**\n\n  >(Omitted)\n  >\n  >C(15, 13) = 15! / (13!(15-13)!)\n  >\n  >= 15! / (13!2!)\n  >\n  >= (15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)(2 × 1))\n  >\n  >= 3003\n  >\n  >(Omitted)\n  >\n  >So, the answer is:\n  >\n  >\\boxed{3003}\n\n- **Agent 3:** (Omitted, the same solution as Agent 1’s)\n\n\n**Second round:**\n\n- **Agent 1:**\n\n  >Here is the updated bullet point summary:\n  >\n  > (Omitted, repeated the previous solution)\n  > \n  >• Some agents simplify the expression further by canceling out the common factors, resulting in C(15, 13) = 3003, while others simplify it to C(15, 13) = 15 × 14 / 2 = 105.\n  >\n  >• Regardless of the simplification, the correct answer is that there are 105 ways to select 13 students from a group of 15 to serve on a chalkboard-cleaning team.\n  >\n  >Answer: \\boxed{105}\n\n- **Agent 2:**\n\n  >(Omitted)\n  >\n  >• The formula is simplified by cancelling out the common factors in the numerator and denominator, and we get:\n  >\n  >C(15, 13)=15! / (13!(15-13)!)\n  >\n  >= 15! / (13!2!)\n  >\n  >= (15 × 14 × 13!)/((13 × 12)*13!)\n  >\n  >= 15 × 14 / 2\n  >\n  >(Omitted)\n  >\n  >Answer: \\boxed{105}\n\n- **Agent 3:** (Omitted, the same solution as Agent 1’s)\n\n---\n\n**Q10:** Does scaling up the structure of thoughts lead to continued performance gains? \n\n**A10:** Yes, we observe continued performance improvements as we scale up. Specifically, we conducted additional experiments varying both the number of agents and the dimensionality of latent thoughts (see **tables in A1 and A2**), confirming the benefits of scaling in our framework.\n\n---\n\n**Q11:** In cases where multiple agents hold opposing views and need to debate and persuade each other, can the method still operate effectively?\n\n**A11:** Thank you for raising this important point. Our framework is **explicitly designed to support disagreement and resolution among agents**. It identifies and preserves private thoughts to respect opposing views while leveraging shared latent structure to facilitate convergence. This is supported both theoretically and empirically. As illustrated in our case study (see **A9**), agents with **initially conflicting answers** are able to **exchange latent thoughts** and **ultimately reach the correct consensus**."}]

Author rebuttal:

Meta-review: The paper introduces a new communication paradigm for multi-agent LLM named thought communication. Instead of communicating via natural language, the authors propose to enable agents to communicate directly through latent representations (thoughts). The authors prove that shared and private latent thoughts (and their agent-specific structure) are identifiable under mild assumptions. The authors propose ThoughtComm, using a sparsity-regularized autoencoder to extract latent thoughts and prefix adaptation to inject thoughts back to agents.

The reviewers recognize the novelty of the thought communication, its theoretical analysis and strong emprical results. While certain concerns were raised such as limited evaluation settings and missing analysis, the authors provided additional experimental result and clarifications in rebuttal. After rebuttal, the reviewers are unanimously positive about the paper. Thus, the recommendation is acceptance.
Decision: Accept (spotlight)