Enabling Agents to Communicate Entirely in Latent Space — part 4/4

Cleaned-text code points [47254, 57720). Bibliography omitted here; source.md includes it.

5. CovGauss. We replace the entire H H with i.i.d. samples H t ∼ 𝒩 ⁡ ( 0 , Σ ^ ) H_{t}\sim\mathcal{N}(0,\hat{\Sigma}) (0 μ \mu ) and report a robustness check with 𝒩 ⁡ ( μ ^ , Σ ^ ) \mathcal{N}(\hat{\mu},\hat{\Sigma}) ( μ \mu ). These preserve first-second order moments while removing higher-order structure and temporal alignment. Rationale. This variant preserves the mean and covariance of the original latent distribution while discarding all higher-order statistics and temporal correlations. It tests whether latent communication conveys information beyond global moments (first-order and second-order moments), e.g., structured reasoning paths or non-Gaussian manifold geometry.

6. RandomRot. We apply a structure-preserving but information-scrambling transform H ′ = μ ^ + ( H − μ ^ ) Σ ^ − 1 / 2 Q Σ ^ 1 / 2 H^{\prime}=\hat{\mu}+(H-\hat{\mu})\,\hat{\Sigma}^{-1/2}\,Q\,\hat{\Sigma}^{1/2} , where Q Q is a Haar-random orthogonal matrix ( Mezzadri, 2006 ) . Rationale. This preserves the mean/covariance exactly while disrupting higher-order structure. Random rotation strictly preserves the first two moments of the latent distribution while scrambling its geometric orientation and higher-order structure. This constitutes a strong diagnostic of whether the actor depends on directional semantics or sequential organization within the latent manifold, rather than mere distributional similarity.

7. Cross-Family. We evaluate Interlat under a cross-model-family setting, where the sender and actor belong to different pretrained model families. Specifically, latent communications are generated by a sender model from one family (In this work, we use Qwen2.5-7B-Instruct) and consumed by an actor model from another family (LLaMA3.1-8B-Base), without sharing parameters or tokenizer vocabularies. Rationale. This setting tests whether latent communication encodes task-relevant information in a model-agnostic manner, rather than exploiting family-specific activation conventions or implicit alignment.

## Appendix C Benchmark

### C.1 Alfworld

Alfworld Shridhar et al. (2020) is a text-only benchmark that simulates embodied household tasks while keeping interaction purely in natural language. Agents observe textual descriptions of the scene and issue high-level commands from a constrained action set ( e.g., go to, open, close, take, put, toggle on/off, heat, cool, examine). Tasks are long-horizon and compositional, requiring perception, planning, and execution over multiple steps under partial observability. The benchmark provides official train/seen/unseen splits and a standard success metric under a fixed step budget ( e.g., 20 steps in our setup), enabling systematic and reproducible evaluation of sequential decision-making.

## Appendix D Ablations and Step Analysis

We present ablation studies for both the actor and reasoning models, reporting the average number of steps for successful trials versus all trials (success/all).

#### Effect of curriculum learning.

For the actor model, removing curriculum learning forces the agent to interpret latent communications from scratch. As shown in Figure 7 , this leads to highly unstable training dynamics and substantially degraded latent comprehension, preventing the model from consistently leveraging the communicated information.

#### Step count versus performance.

Table 6 reveals a nuanced but systematic relationship between step count and task performance. On seen tasks, ablating key components results in a lower overall success rate. Although these ablated models often take fewer steps on the trials they complete, their high failure rate indicates an inability to reliably interpret latent communication and solve tasks. In contrast, the full model achieves both higher success rates and longer trajectories, suggesting that additional steps correspond to productive exploration rather than inefficiency.

On unseen tasks, several ablations ( e.g., removing curriculum learning or the communication adapter) exhibit the opposite pattern: the agent takes more steps while achieving a lower success rate. This demonstrates that longer trajectories alone do not imply effective exploration. Without these critical components, the policy exhibits unstructured search behavior that fails to form coherent task-solving strategies. Together, these observations underscore the importance of evaluating step count jointly with success rate, and support our central claim that information-rich latent communication enables structured and effective exploration rather than random wandering.

## Appendix E Compression Result

In this section, we provide more detailed results on compression with average steps as success/all across tasks in Table 7 (LLaMA3.1-8B-Base) and Table 8 (Qwen2.5-7B-Base) and corresponding performance trend in Figure 8 . Latency is measured on the same machine and decoding policy (if needed) across rows 2 2 2 For the untrained reasoning model, we use the standard generate API from Hugging Face transformers ; see https://github.com/huggingface/transformers . .

## Appendix F Latent Parallelism Analysis

We first compared the latent communications produced by our trained reasoning model with those from an off-the-shelf Qwen2.5-7B-Instruct model in the compression-effectiveness analysis (see the Experiments section). Because our reasoning model is initialized from Qwen2.5-7B-Base, we additionally compare it with this base model, which has not been trained for generating compressed latent communication, in Figure 9 . The findings are consistent with the earlier comparison: the trained model maintains stable vertical gaps between successive Top- k k curves across steps and exhibits a substantially lower P 50 ​ ( S 10 ) P_{50}(S_{10}) , whereas the base model shows a clear convergence toward Top-1.

We further extend the parallelism analysis to a deeper horizon of 32 steps. As shown in Figure 10 , the trained model exhibits stable vertical gaps between successive Top- k k curves throughout these steps. This extended analysis further verifies that the trained latent representations preserve a broader set of plausible reasoning paths by sustaining a more balanced probability distribution rather than prematurely collapsing to a Top-1 hypothesis.

## Appendix G Qualitative Analysis of Latent Communication via PCA

To qualitatively examine the semantic structure encoded in latent communications, we perform Principal Component Analysis (PCA) on 3,119 samples from the ALFWorld training set. Each sample corresponds to the mean-pooled last-layer hidden state generated by the reasoning agent for a specific task instance. Tasks are grouped according to the official ALFWorld task templates, which define six core reasoning patterns: pick_and_place , pick_clean_then_place , pick_heat_then_place , pick_cool_then_place , look_in_recep , and look_at_obj . Figure 11 visualizes the projection of latent communications onto the first two principal components, which capture the dominant axes of variance across task instances.

The resulting PCA visualization reveals clear task-dependent organization in the latent space. Action-centric templates such as pick_and_place form a dense central cluster, while templates involving additional procedural constraints—such as thermal manipulation in pick_heat_then_place and pick_cool_then_place —occupy adjacent yet separable regions. Perception-oriented tasks ( look_in_recep and look_at_obj ), although less frequent, also exhibit localized concentrations distinct from execution-heavy templates. As PCA preserves global variance structure rather than emphasizing local neighborhoods, this separation indicates that task-specific semantics are encoded in the dominant latent dimensions, rather than arising from projection artifacts. Moreover, intra-cluster dispersion (e.g., within pick_and_place ) suggests that latent representations retain fine-grained variations across task instances, rather than collapsing to a single prototype per template.

Beyond static clustering, we further analyze how these task-level structures are affected by the latent communication adapter. As shown in Figure 12 and quantified in Table 9 , different task templates exhibit consistent but template-dependent centroid shifts before and after transformation. While the absolute magnitudes of these shifts are moderate relative to within-template dispersion, their directions are highly structured, indicating selective reorganization rather than global rescaling of the latent space. Execution-heavy templates such as pick_and_place and pick_heat_then_place undergo larger relative shifts, whereas observation-oriented templates remain more stable. Together, these results suggest that Interlat preserves the overall geometry of latent communications while inducing task-aware semantic alignment, enabling the actor agent to differentiate diverse reasoning paradigms without relying on explicit natural language communication.

## Appendix H Training Template

We present an example in Figure H to illustrate how agents explore and solve tasks in Alfworld. After perceiving the environment, the agent executes an action, receives feedback from the environment, and then proceeds to the next step until the goal is accomplished. Figure H shows an example of how training data is structured for the actor agent. We append either the latent communication or the natural-language plan after the instruction to facilitate inter-agent communication.

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