2501.14082

# Communicating Activations Between Language Model Agents **Authors**: Vignav Ramesh, Kenneth Li Abstract Communication between multiple language model (LM) agents has been shown to scale up the reasoning ability of LMs. While natural language has been the dominant medium for inter-LM communication, it is not obvious this should be the standard: not only does natural language communication incur high inference costs that scale quickly with the number of both agents and messages, but also the decoding process abstracts away too much rich information that could be otherwise accessed from the internal activations. In this work, we propose a simple technique whereby LMs communicate via activations; concretely, we pause an LM $B$ ’s computation at an intermediate layer, combine its current activation with another LM $A$ ’s intermediate activation via some function $f$ , then pass $f$ ’s output into the next layer of $B$ and continue the forward pass till decoding is complete. This approach scales up LMs on new tasks with zero additional parameters and data, and saves a substantial amount of compute over natural language communication. We test our method with various functional forms $f$ on two experimental setups—multi-player coordination games and reasoning benchmarks—and find that it achieves up to $27.0\%$ improvement over natural language communication across datasets with $<$ $1/4$ the compute, illustrating the superiority and robustness of activations as an alternative “language” for communication between LMs. Machine Learning, ICML 1 Introduction Language is for the purpose of communication. As large language models (LLMs) have been increasingly used to power autonomous, goal-driven agents capable of reasoning, tool usage, and adaptive decision-making (Yao et al., 2023; Xi et al., 2023; Wang et al., 2024; Ahn et al., 2022; Schick et al., 2023; Shen et al., 2023; Park et al., 2023; Nakano et al., 2022), communication between multiple cooperating agents has emerged as an intuitive approach to amplify the reasoning capabilities of LLMs (Wu et al., 2023). Explicit communication in natural language between multiple LLMs has been shown to encourage divergent thinking (Liang et al., 2023), improve factuality and reasoning (Du et al., 2023), enable integration of cross-domain knowledge (Sukhbaatar et al., 2024), and allow for modular composition of abilities in a complementary manner (Wu et al., 2023; Prasad et al., 2023). A critical problem with natural language communication, however, is that it incurs extremely high inference costs that scale quickly with the number of agents as well as length and number of messages (Du et al., 2023; Yang et al., 2023; Wu et al., 2023). Restricting LLM communication to natural language also raises the question: as LLMs are increasingly capable of handling larger, more complex tasks (sometimes with “super-human” ability) (Wei et al., 2022; Burns et al., 2023), might they communicate more effectively in representations of higher dimension than natural language? While using natural language as a communicative medium is appealing due to its interpretability, we claim that it may not be optimal for inter-LLM communication. Natural language generation uses only one token to represent the model’s belief over the entire vocabulary, which risks losing information embedded within the model output logits (Pham et al., 2024); furthermore, a model’s belief over the entire vocabulary is itself not always better (for communicative purposes) than the model’s (often richer) representation of the input in earlier layers. Indeed, Hernandez et al. (2024) find that by around the halfway point of an LM’s computation, it has developed “enriched entity representations” of the input, where entities in the prompt are populated with additional facts about that entity encoded in the model’s weights; but by the later layers these embeddings are transformed into a representation of the next word which leverages only parts of the previous, richer representations, when that full embedding would be quite useful for communication. Motivated by these concerns, this work outlines a simple technique whereby LLM agents communicate via activations, thus enabling more efficient (i.e., higher-entropy) communication at a fraction of the number of forward passes required at inference time. Concretely, we (1) pause a Transformer LM $B$ ’s computation at intermediate layer $j$ in the residual stream; (2) combine its post-layer $j$ activation with another LM $A$ ’s post-layer $k$ activation via some function $f$ ; and then (3) pass $f$ ’s output into the next layer $j+1$ of $B$ and continue its forward pass till decoding is complete. This approach scales up LLMs on new tasks by leveraging existing, frozen LLMs along with zero task-specific parameters and data, applying to diverse domains and settings. Furthermore, in requiring only a partial forward pass through $A$ and one forward pass through $B$ , this method saves a substantial amount of compute over traditional natural language communication, which we quantify in Section 3.2. We validate our method by testing this approach with various functional forms $f$ on two experimental setups: two multi-player coordination games, where $B$ is asked to complete a task requiring information provided in a prompt to $A$ ; and seven reasoning benchmarks spanning multiple domains: Biographies (Du et al., 2023), GSM8k (Cobbe et al., 2021), MMLU High School Psychology, MMLU Formal Logic, MMLU College Biology, MMLU Professional Law, and MMLU Public Relations (Hendrycks et al., 2021). Our activation communication protocol exhibits up to $27.0\%$ improvement over natural language communication across these datasets, using $<$ $1/4$ the compute. Critically, unlike prior work which test inter-LLM communication only on large-scale ( $>$ $70$ B) models (Du et al., 2023; Liang et al., 2023), we find that our approach generalizes across a wide array of LLM suites and sizes, enabling even smaller LLMs to unlock the benefits of communication. In summary, our contributions are two-fold: - We propose a novel inter-model communication protocol for LLM agents that is purely activation-based. - We perform comprehensive experiments to validate the improved performance of activation communication over traditional natural language communication. We also formally quantify our approach’s compute savings over natural language communication, illustrating the superiority and robustness of activations as an alternative “language” for communication between LMs. 2 Related Work Multi-agent communication The field of multi-agent communication has a long-standing history. Notably, prior works on emergent communication have showed that agents can autonomously evolve communication protocols when deployed in multi-agent environments that enable cooperative and competitive game-play (Sukhbaatar et al., 2016; Foerster et al., 2016; Lazaridou et al., 2017). However, recent experiments have demonstrated that learning meaningful languages from scratch, even with centralized training, remains difficult (Lowe et al., 2020; Chaabouni et al., 2019; Jaques et al., 2019). With the emergence of large pre-trained language models, allowing communication between LLMs in natural language has hence become a promising approach to enable coordination among multiple LLM agents (Li et al., 2023). Recent works have demonstrated that such conversations enable integration of cross-domain knowledge (Sukhbaatar et al., 2024), modular composition of abilities in a complementary manner (Wu et al., 2023), and improved task performance via splitting into subtasks (Prasad et al., 2023). Most notable is multiagent debate introduced by Du et al. (2023), where LLMs provide initial responses and then make refinements by iteratively considering inputs from peers. While such methods have been shown to improve performance on various tasks over vanilla and majority-vote (Wang et al., 2023) style prompting, these experiments have only focused on large models ( $\mathtt{GPT}$ - $\mathtt{3.5/4}$ , $\mathtt{LLaMA2}$ - $\mathtt{70B}$ and up), leaving the efficacy of debate on smaller, open-source models underexplored; our study addresses this gap by reimplementing Du et al. (2023) in experiments with smaller-scale ( $1-70$ B) models. More crucially, debate and similar natural language communication methods are extremely computationally expensive, which this work addresses (Yang et al., 2023; Wu et al., 2023). Notably, Pham et al. (2024) propose CIPHER, which uses input (tokenizer) embeddings (as opposed to activations) to enable multi-agent communication; specifically, CIPHER passes the average tokenizer embedding (weighted by the LLM’s next-token probabilities) between models. While (Pham et al., 2024) show this approach outperforms natural language debate, it (i) still faces substantial information loss relative to the model activations and (ii) does not save compute, as the number of these “average embeddings” passed between models is the same as the number of tokens passed between models in natural language communication. A related class of methods involves spending extra test-time compute reasoning in latent space (Geiping et al., 2025; Hao et al., 2024). Such latent reasoning approaches involving doing ”chain-of-thought in activation space,” e.g. by grafting LM activations into other layers/later forward passes through the same model (e.g., a form of “recurrent AC” within a single model); our approach can be viewed as doing exactly the same thing, but instead ”outsourcing” the CoT to another model (and thus reaping benefits from greater diversity of thoughts/reasoning paths from distinct models). Activation engineering Activation engineering involves editing an LLM’s intermediate layer representations during a forward pass to create desired changes to output text (Li et al., 2024; Turner et al., 2023). Past work has explored extracting latent steering vectors from a frozen LLM to control quality and content of completions (Subramani et al., 2022), as well as using “direction” vectors (computed as the difference in activations between two prompts) that enable inference-time control over high-level properties of generations (Li et al., 2024; Turner et al., 2023). This work involves activation editing that is similar to such prior works at a high level, though for the purpose of communication between LLM agents. Model composition and grafting Composing expert models has been a recurring strategy to improve large models, with different methods imposing different restrictions on the types of base LLMs that can be combined. Mixture of Experts (Shazeer et al., 2017) requires that all experts are trained simultaneously using the same data; Branch-Train-Mix (Sukhbaatar et al., 2024) trains a single base LM multiple times on different datasets, then learns a router on outputs. Crucially, these methods do not work when neither model can do the task at hand well (i.e., they solve the problem of choosing which of several outputs is best, not that of generating a high-quality output by recombining the disparate abilities of the various base LMs). Model grafting, in contrast, seeks to merge different models immediately prior to or at inference-time. Past works have explored this at the parameter level (e.g., task vector averaging as in Ilharco et al. (2023), which requires that the base models be well aligned), probability distribution / token level as in Shen et al. (2024) (which imposes few restrictions on the relationship between the base models, but by virtue of being token-based can result in cascading errors during decoding), and activation level (e.g., CALM (Bansal et al., 2024) which learns an attention layer on top of two models’ intermediate layer activations and thus enables broader integration of model abilities than token-level methods, but requires re-tuning of the attention mechanism for every model pair). In this work, we seek to unify CALM and other activation-level grafting techniques under a single framework, parameterized by the function $f$ used to combine activations; crucially, we explore simple forms of $f$ (e.g., sum, mean) that—unlike Bansal et al. (2024) —require zero additional task-specific parameters and data, and are far more compute-efficient. 3 Communicating Activations Between Language Models <details> <summary>extracted/6420159/overview.png Details</summary>  ### Visual Description ## Diagram: Computational Graph with Cookie Analogy ### Overview The image presents a computational graph, visually explaining a simple division problem (16 cookies / 4 friends = 4 cookies per friend) using a network-like diagram. The diagram is split into two main sections, with the left side showing a simplified computational flow and the right side showing more detailed representations of the computation. ### Components/Axes * **Text:** * "Each friend gets 16/4 = 4 cookies." (Top center) * "Janet bought 16 cookies, and wants to give an equal number to each of her 4 friends. How many cookies does each friend get?" (Bottom left) * **Nodes:** * Node A (Light Green): Contains h\_A,k+1 and h\_A,k, with upward and downward arrows indicating flow. * Node B (Light Blue): Contains h\_B,j+1 and h\_B,j, with upward and downward arrows indicating flow. * Node f (Light Yellow): Represents a function or operation. * **Connections:** Arrows indicate the flow of information between nodes. * **Symbols:** Snowflake-like symbols are present at the top-right of nodes A and B. * **Right Side Diagrams:** Two diagrams showing different representations of the function 'f'. The left diagram shows 'f' as a summation of h\_A,k and h\_B,j. The right diagram shows 'f' as a transformation using a weight matrix 'W'. ### Detailed Analysis * **Left Side Computational Flow:** * Node A (light green) contains two blocks labeled h\_A,k+1 and h\_A,k. * Node B (light blue) contains two blocks labeled h\_B,j+1 and h\_B,j. * An arrow flows from h\_A,k to the yellow node 'f'. * An arrow flows from 'f' to h\_B,j. * An arrow flows from 'f' back to h\_A,k+1. * An arrow flows from h\_B,j to h\_B,j+1. * **Right Side Diagrams:** * **Diagram 1 (Left):** A light yellow box labeled 'f' contains a summation symbol (+). Arrows flow from h\_A,k and h\_B,j into the summation, and an arrow flows out of the box. * **Diagram 2 (Right):** A light yellow box labeled 'f' contains a purple trapezoid labeled 'W'. Arrows flow from h\_A,k and h\_B,j into the trapezoid, and an arrow flows out of the box. ### Key Observations * The diagram uses a cookie-sharing problem as an analogy to illustrate a computational process. * The left side shows a high-level flow, while the right side provides more detailed views of the function 'f'. * The function 'f' is represented in two ways: as a summation and as a weighted transformation. ### Interpretation The diagram illustrates a computational process, possibly related to a recurrent neural network or similar model. The cookie analogy serves as a simple, relatable example to explain the flow of information and the role of the function 'f'. The two representations of 'f' on the right side suggest that it could be a linear transformation followed by an addition, which is a common operation in neural networks. The diagram highlights the iterative nature of the computation, with information flowing back from 'f' to Node A. The snowflake symbols at the top-right of nodes A and B are not explained, but may represent a specific type of operation or data associated with those nodes. </details> Figure 1: Overview of activation communication. (Left) Our method involves (1) pausing a Transformer LM $B$ ’s computation at layer $j$ in the residual stream; (2) combining its post-layer $j$ activation with another LM $A$ ’s post-layer $k$ activation via some function $f$ ; then (3) passing $f$ ’s output into the next layer $j+1$ of $B$ and continuing the forward pass till decoding is complete. (Right) Any function $f$ can be used to combine $A$ and $B$ ’s activations; we explore letting $f$ be the sum, mean, and replacement functions, as well as a task-agnostic learned linear layer (details in Section 3.1). We propose a simple yet effective technique whereby language models communicate via activations. We detail our approach in Section 3.1; provide analytical models of the compute saved over natural language communication in Section 3.2; and discuss the intuition behind this approach in Section 3.3. 3.1 Method Consider two language models, $A$ and $B$ , and some setting in which $B$ must perform a task where it would benefit from knowledge given to $A$ as a prompt/encoded in $A$ ’s weights (example settings in Section 4.1 / Section 4.2 respectively). We propose incorporating information from $A$ ’s post-layer $k$ activation $\bm{h}_{A,k}$ into $B$ ’s post-layer $j$ activation $\bm{h}_{B,j}$ (and vice versa, though for simplicity we henceforth only discuss the first direction) (Figure 1, left). More formally, suppose $A$ and $B$ (which have model dimensions $d_{A}$ and $d_{B}$ respectively) are given prompts $x_{A}$ and $x_{B}$ respectively, where $x_{A}$ is of length $t_{A}$ tokens and $x_{B}$ is of length $t_{B}$ tokens. We first run a partial forward pass of $B$ until layer $j$ (henceforth denoted $B_{≤ j}(x_{B})$ ) to get $\bm{h}_{B,j}∈\mathbb{R}^{t_{B}× d_{B}}$ . Then we (1) run a partial forward pass of $A$ until layer $k$ to get $A_{≤ k}(x_{1}):=\bm{h}_{A,k}∈\mathbb{R}^{t_{A}× d_{A}}$ ; (2) replace the activation of the last token $(\bm{h}_{B,j})_{t_{B}}∈\mathbb{R}^{d_{B}}$ $\longleftarrow f((\bm{h}_{A,k})_{t_{A}},(\bm{h}_{B,j})_{t_{B}})$ for some function $f:\mathbb{R}^{d_{A}+d_{B}}→\mathbb{R}^{d_{B}}$ ; then (3) continue $B$ ’s forward pass till decoding is complete, resulting in an output $y=B_{>k}(\bm{h}_{B,j})$ . Let $\bm{a}=(\bm{h}_{A,k})_{t_{A}}$ , $\bm{b}=(\bm{h}_{B,j})_{t_{B}}$ . For sake of simplicity assume $d_{A}=d_{B}$ . When $d_{A}≠ d_{B}$ , the $\mathtt{sum}$ , $\mathtt{mean}$ , and $\mathtt{replace}$ functions are defined as follows. Let $d=\min(d_{A},d_{B})$ and $\circ$ the concatenation operator. Then $f(\bm{a},\bm{b})=\bm{b}_{1:\max(d_{B}-d,0)}\circ\left(\bm{b}_{\max(d_{B}-d,0)+% 1:d_{B}}+\bm{a}_{\max(d_{A}-d,0)+1:d_{A}}\right)$ $\mathtt{(sum)}$ , $f(\bm{a},\bm{b})=\bm{b}_{1:\max(d_{B}-d,0)}\circ\frac{1}{2}\left(\bm{b}_{\max(% d_{B}-d,0)+1:d_{B}}+\bm{a}_{\max(d_{A}-d,0)+1:d_{A}}\right)$ $\mathtt{(mean)}$ , and $f(\bm{a},\bm{b})=\bm{b}_{1:\max(d_{B}-d,0)}\circ\bm{a}_{\max(d_{A}-d,0)+1:d_{A}}$ $\mathtt{(replace)}$ . We consider three non-learned functions $f$ : | | $\displaystyle f(\bm{a},\bm{b})$ | $\displaystyle=\bm{a}+\bm{b}\>\>\qquad\qquad\mathtt{(sum)}$ | | | --- | --- | --- | --- | For cases where, due to differences in $A$ and $B$ ’s training, $A$ and $B$ ’s activation spaces are quite different, we propose learning a task-agnostic (depends only on the models $A$ and $B$ ) linear layer $\bm{W}∈\mathbb{R}^{d_{B}}×\mathbb{R}^{d_{A}}$ that projects $\bm{a}$ onto $B$ ’s activation space. Note that this introduces zero additional task-specific parameters and data, as we propose learning this “mapping matrix” $\bm{W}$ only once for each model pair $(A,B)$ using general text, e.g. sequences from $A$ and/or $B$ ’s pretraining data mixes. We can then perform $\mathtt{sum}$ , $\mathtt{mean}$ , or $\mathtt{replace}$ with $\bm{W}\bm{a},\bm{b}$ instead of $\bm{a},\bm{b}$ . We propose training $\bm{W}$ to minimize MSE loss over a dataset of $N$ sentences $$ \mathcal{L}_{\rm MSE}\left(\{\bm{y}^{(i)}\}_{i=1}^{N},\{\bm{z}^{(i)}\}_{i=1}^{% N}\right)=\frac{1}{N}\sum_{i=1}^{N}\left\|\bm{z}^{(i)}-\bm{W}\bm{y}^{(i)}% \right\|_{2}^{2} $$ where each $(\bm{y}^{(i)},\bm{z}^{(i)})$ pair denotes the final-token layer- $26$ activations of $A$ and $B$ at layers $k$ and $j$ respectively given the same sentence as input. 3.2 Compute Analysis To understand the significance of activation communication, we must formally quantify the compute this procedure saves over natural language communication. For simplicity suppose the following (similar calculations can be made for the cases where $A$ and $B$ have differing model architectures and/or are given different prompts): - $A$ and $B$ both have $L$ layers (each with $H$ attention heads, key size $K$ , and feedforward size $F$ ), dimension $D$ , and vocab size $V$ - $A$ and $B$ are both given a prompt of $P$ tokens - $A$ can send $B$ a single $M$ -token message - $B$ must produce an output of $T$ tokens, given its prompt and $A$ ’s message Traditional methods require $M$ forward passes of $A$ given a $P$ -length input, plus $T$ forward passes of $B$ given a $(P+M)$ -length input. Following Hoffmann et al. (2022), this requires $$ \displaystyle M\big{(}4PVD+L(8PDKH+4P^{2}KH+3HP^{2} \displaystyle+4PDF)\big{)}+T\big{(}4(P+M)VD+L(8(P+M)DKH \displaystyle+4(P+M)^{2}KH+3H(P+M)^{2}+4(P+M)DF)\big{)} \tag{1} $$ FLOPs. In contrast, at inference time, our method requires only 1 partial (up till the $k$ th layer) forward pass of $A$ given a $P$ -length input, $T$ forward passes of $B$ given a $P$ -length input, and the activation replacement procedure. This requires $$ \displaystyle 2PVD+k(8PDKH+4P^{2}KH+3HP^{2} \displaystyle+4PDF)+T\big{(}4PVD+L(8PDKH+4P^{2}KH \displaystyle+3HP^{2}+4PDF)\big{)}+\mathcal{F}(D) \tag{2} $$ FLOPs, where $\mathcal{F}(D)=O(D)$ for non-learned $f$ and $O(D^{2})$ when $f$ is the mapping matrix. In all practical cases, (2) is substantially lower than (1). 3.3 Why should this work? Recall that Pham et al. (2024) propose CIPHER—communicating the average tokenizer embedding (weighted by the LLM’s next-token probabilities) between models. We build upon the intuition behind CIPHER, which goes as follows: the token sampling process during decoding risks substantial information loss from the model’s output logits, and communicating a model’s weighted-average tokenizer embedding essentially entails communicating both that model’s final answer and its belief in that answer (over the entire vocabulary). Communicating activations, then, can be thought of as communicating a strict superset of {next-token prediction, belief over entire vocabulary}, as activations of late-enough layers essentially encode the model’s entire knowledge about the provided context as well as its predicted completion and confidence in that completion (see Figures 1 and 7 in Hewitt & Manning (2019) and Hernandez et al. (2024), respectively, which show that linear probes tasked with predicting certain output characteristics from a Transformer’s intermediate layer embeddings of its input work poorly for early layers, extremely well after around the halfway point of computation, but then probe accuracy drops closer to the final layers). Note one important critique of multiagent debate: that in cases where multiple agents are uncertain about the answer, there is no reason why referencing other agents’ answers would generate more factual reasoning. Both CIPHER and activation communication solve this problem, as some notion of model confidence is being communicated along with its next-token prediction. Indeed, these curves of probe accuracy by layer indicate that the final layers and LM head “ throw away ” information not useful for next-token prediction that very well could be useful for communicative purposes; this is precisely why our proposed activation communication technique is not an iterative approach (there is no notion of “rounds” like in debate and CIPHER, which require an additional token budget to extract more and more information out of the LM), as one activation grafting step from $A$ to $B$ inherently communicates to $B$ all of $A$ ’s knowledge/beliefs about the prompt it was given. Moreover, the extra information over the model’s next-token prediction and confidence that is encoded in its activations is what makes activation communication more performant than its natural language counterpart, as we will see in Section 4. 4 Experiments | Countries | $x_{A}$ : “ $\mathtt{Alice}$ $\mathtt{is}$ $\mathtt{at}$ $\mathtt{the}$ $\mathtt{Acropolis}$ $\mathtt{of}$ $\mathtt{Athens}$ .” | | --- | --- | | $x_{B}$ : “ $\mathtt{Which}$ $\mathtt{country}$ $\mathtt{is}$ $\mathtt{Alice}$ $\mathtt{located}$ $\mathtt{in?}$ ” | | | $B$ ’s Expected Answer: “ $\mathtt{Greece}$ ” | | | Tip Sheets | $x_{A}$ : “ $\mathtt{Acme}$ $\mathtt{Inc.}$ $\mathtt{has}$ $\mathtt{taken}$ $\mathtt{a}$ $\mathtt{nosedive,}$ $\mathtt{as}$ $\mathtt{its}$ $\mathtt{quarterly}$ $\mathtt{earnings}$ $\mathtt{have}$ $\mathtt{dipped}$ $\mathtt{8\%}$ . | | $\mathtt{Meanwhile}$ $\mathtt{Doe}$ $\mathtt{LLC}$ $\mathtt{and}$ $\mathtt{Kiteflyer}$ $\mathtt{Labs}$ $\mathtt{have}$ $\mathtt{both}$ $\mathtt{reached}$ $\mathtt{record\text{-}high}$ $\mathtt{stock}$ | | | $\mathtt{prices}$ $\mathtt{of}$ $\mathtt{89,}$ $\mathtt{but}$ $\mathtt{Kiteflyer}$ $\mathtt{is}$ $\mathtt{involved}$ $\mathtt{in}$ $\mathtt{an}$ $\mathtt{IP}$ $\mathtt{lawsuit}$ $\mathtt{with}$ $\mathtt{its}$ $\mathtt{competitors.}^{\prime\prime}$ | | | $x_{B}$ : “ $\mathtt{You}$ $\mathtt{must}$ $\mathtt{invest}$ $\mathtt{in}$ $\mathtt{one}$ $\mathtt{company}$ $\mathtt{out}$ $\mathtt{of}$ { $\mathtt{Acme}$ $\mathtt{Inc.,}$ $\mathtt{Doe}$ $\mathtt{LLC,}$ $\mathtt{Kiteflyer}$ $\mathtt{Labs}$ }. | | | $\mathtt{Which}$ $\mathtt{do}$ $\mathtt{you}$ $\mathtt{invest}$ $\mathtt{in?}$ ” | | | $B$ ’s Expected Answer: “ $\mathtt{Doe\text{ }LLC}$ ” | | Table 1: Multi-player coordination games. Sample $\mathtt{(prompt,answer)}$ pairs for each game. We test our method on two distinct experimental setups: multi-player coordination games (Section 4.1) and reasoning benchmarks (Section 4.2). Qualitative results are available in Appendix A. 4.1 Multi-player coordination games Drawing from existing literature on multi-agent communication, we design two Lewis signaling games (Lewis, 2008; Lazaridou et al., 2016) to test the efficacy of activation communication (example prompts and answers in Table 1): 1. Countries, where $A$ is given as input a string of the format “ $\mathtt{[PERSON]\text{ }is\text{ }at\text{ }the\text{ }[LANDMARK]}$ ” and $B$ is asked “ $\mathtt{Which\text{ }country\text{ }is\text{ }[PERSON]\text{ }located\text{ }% in?}$ ” 1. Tip Sheets (inspired by Lewis et al. (2017)), where $A$ is given a simulated “tip sheet” and $B$ is asked to make an informed investment decision in accordance with the information in the tip sheet. | $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ | ✗ | $0.0$ ( $0.0$ , $0.0$ ) | $38.6$ ( $38.6,39.4$ ) | | --- | --- | --- | --- | | Skyline | $84.0$ ( $83.5$ , $84.1$ ) | $100.0$ ( $100.0,100.0$ ) | | | NL | $69.0$ ( $68.7$ , $69.3$ ) | $74.3$ ( $74.0,74.6$ ) | | | AC ( $\mathtt{sum}$ ) | $34.0$ ( $33.9$ , $34.4$ ) | $50.0$ ( $49.6,50.3$ ) | | | AC ( $\mathtt{mean}$ ) | $36.0$ ( $35.5$ , $36.1$ ) | $80.0$ ( $79.8,80.4$ ) | | | AC ( $\mathtt{replace}$ ) | $\mathbf{78.0}$ ( $77.7$ , $78.2$ ) | $\mathbf{90.0}$ ( $89.9,90.3$ ) | | | $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ | ✗ | $2.0$ ( $1.9$ , $2.1$ ) | $54.3$ ( $54.2,54.5$ ) | | Skyline | $86.0$ ( $85.7$ , $86.1$ ) | $100.0$ ( $100.0,100.0$ ) | | | NL | $77.0$ ( $76.6$ , $77.1$ ) | $85.7$ ( $85.3,85.8$ ) | | | AC ( $\mathtt{sum}$ ) | $71.0$ ( $70.9,71.4$ ) | $85.7$ ( $85.5,86.0$ ) | | | AC ( $\mathtt{mean}$ ) | $70.0$ ( $69.7,70.3$ ) | $92.9$ ( $92.7,93.1$ ) | | | AC ( $\mathtt{replace}$ ) | $\mathbf{83.0}$ ( $82.7,83.1$ ) | $\mathbf{95.7}$ ( $95.6,95.9$ ) | | Table 2: Accuracies (%) on both coordination games using two identical $\mathtt{LLaMA}$ family models. Communication at layer $k=j=26.$ $95\%$ confidence intervals ( $1000$ bootstrap iterations) reported in parentheses. We synthetically generate $100$ (Countries) and $70$ (Tip Sheets) different prompts and answers of the same format as the samples in Table 1, and report the proportion out of those samples that $B$ responds with an exact string match to the ground truth answer. As baselines, we consider a “silent” (✗) setup, where the agents are not allowed to communicate; a “single-agent skyline,” where a single LLM is given the concatenation of $A$ and $B$ ’s prompts; and traditional natural language communication, where $A$ is asked to output a message that is then given to $B$ along with $x_{B}$ . All decoding is done greedily. Table 2 presents the results for both coordination games using 2 different instances of the same model as the agents ( $A=B$ ). Across the 3B and 8B model sizes, activation communication (AC) with $f=\mathtt{replace}$ almost completely recovers the gap between the zero-communication (✗) and the single-agent skyline (Skyline), outperforming natural language communication (NL) using far less compute. We hypothesize that $\mathtt{replace}$ is more effective than $\mathtt{mean}$ and $\mathtt{sum}$ as the former is guaranteed to output a vector within $B$ ’s activation space, while the latter two likely do not (e.g., the norm of the vector outputted by $\mathtt{sum}$ will be around double that of a typical activation). Furthermore, most of the information $B$ needs is likely contained in its representations of previous tokens in the sequence, hence losing its final-token representation does not hurt. <details> <summary>extracted/6420159/contour.png Details</summary>  ### Visual Description ## Heatmap: Accuracy vs. k and j ### Overview The image contains two heatmaps, each representing accuracy (Acc.) as a function of two variables, k and j. The heatmaps use a color gradient from dark blue (low accuracy) to bright yellow (high accuracy). Black contour lines are overlaid on the heatmaps, indicating regions of similar accuracy. A red diamond is present on each heatmap, marking a specific point. The left heatmap is labeled "(a) Countries" and the right heatmap is labeled "(b) Tip Sheets". ### Components/Axes * **X-axis (k):** Ranges from approximately 1 to 30 in both heatmaps. * **Y-axis (j):** Ranges from approximately 1 to 30 in both heatmaps. * **Color Scale (Accuracy):** * Left heatmap: Ranges from 0% (dark blue) to 80% (yellow). * Right heatmap: Ranges from 0% (dark blue) to 100% (yellow). * **Contour Lines:** Black lines indicating levels of accuracy. * **Red Diamond:** Marks a specific (k, j) coordinate on each heatmap. ### Detailed Analysis #### (a) Countries Heatmap * **General Trend:** Accuracy is generally low (dark blue) for smaller values of k (approximately k < 15). Accuracy increases significantly as k increases beyond 15 and j increases beyond 10, reaching a peak in the upper-right region. * **Specific Values:** * At k=5, j=5, accuracy is approximately 0-20%. * At k=25, j=25, accuracy is approximately 80%. * **Red Diamond Position:** Located at approximately k=27, j=25. The accuracy at this point is approximately 80%. * **Contour Lines:** Concentrated in the region where accuracy transitions from low to high, indicating a steep gradient. #### (b) Tip Sheets Heatmap * **General Trend:** The accuracy varies more across the heatmap compared to the "Countries" heatmap. There are regions of both high and low accuracy scattered throughout. A region of low accuracy (dark blue) is present in the upper-left corner. * **Specific Values:** * At k=5, j=5, accuracy is approximately 40-60%. * At k=25, j=25, accuracy is approximately 80-100%. * **Red Diamond Position:** Located at approximately k=27, j=25. The accuracy at this point is approximately 80-100%. * **Contour Lines:** More dispersed compared to the "Countries" heatmap, reflecting the greater variability in accuracy. ### Key Observations * The "Countries" heatmap shows a more consistent trend of increasing accuracy with increasing k and j, while the "Tip Sheets" heatmap exhibits more localized variations. * The red diamond marks a point of high accuracy in both heatmaps, but the accuracy is higher in the "Tip Sheets" heatmap (80-100%) compared to the "Countries" heatmap (80%). * The contour lines highlight the regions where accuracy changes most rapidly. ### Interpretation The heatmaps visualize the accuracy of a model or system under different conditions, represented by the variables k and j. The "Countries" heatmap suggests that higher values of k and j generally lead to better accuracy in that context. The "Tip Sheets" heatmap indicates a more complex relationship, where accuracy is not solely determined by k and j, and other factors may be at play. The red diamond likely represents a specific configuration or parameter setting, and its position indicates that this setting results in high accuracy for both "Countries" and "Tip Sheets," although the accuracy is slightly better for "Tip Sheets." The contour lines help to identify the regions where fine-tuning of k and j would have the most significant impact on accuracy. </details> Figure 2: 2D contour plots of accuracy over different values of $k$ and $j$ (the layers at which we access/edit activations for $A$ / $B$ respectively). $k=j=26$ is roughly optimal ( $$ ) for both (a) Countries and (b) Tip Sheets. 4.2 Reasoning Benchmarks Next, we test our methods on a variety of reasoning benchmarks, spanning several real-world tasks and domains. Baselines We benchmark activation communication against the following two baselines: - Single Model: A single LLM responds to the prompt in natural language. - Natural Language Debate (NLD) (Du et al., 2023): Each LLM provides an initial response to the given prompt. Then, for each of $r-1$ subsequent rounds, each LLM is prompted to refine its previous response given the other agents’ responses as input. Note that NLD is the most direct baseline for our approach, as it is a state-of-the-art natural language communication protocol. We fix $r=2$ in our experiments. Note that we do not compare to Pham et al. (2024), as they communicate the input (tokenizer) embeddings rather than activations/output embeddings between models, and hence require a shared tokenizer and embedding table between agents which is extremely restrictive and prevents applicability to our experimental setup. To determine the values of $k$ and $j$ for activation communication (AC), we compute the accuracy on Countries and Tip Sheets for every pair $(k,j)∈\{1,...,30\}^{2}$ . Based on these results (shown in Figure 2) as well as Table 2, we fix $k=j=26$ and $f$ $=$ $\mathtt{replace}$ for the following experiments. Across all experiment configurations, we fix the decoding strategy to nucleus sampling with $p=0.9$ . Models We conduct most of our experiments using $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ as the two agents. Additionally, to test our approach’s robustness and generalizability, we conduct experiments with models belonging to various other suites within the $\mathtt{LLaMA}$ family and of several different sizes. Note that for these experiments, we restrict the setting to communication between different models (rather than multiple instances of the same model in Section 4.1), since the same model would have identical activations for the same prompts, meaning no information would be communicated in the grafting process. We argue that the multiple-model setting is realistic (perhaps more so than the setting of multiple instances of the same model), as recent advances in LLM development have led to the release of models with specialized abilities (Singhal et al., 2023) and of different sizes (Dubey et al., 2024) that merit complementary usage. Our work thus answers the question: How can we get the best performance by leveraging multiple models of distinct capabilities and sizes, relative to the added inference-time compute over a single forward pass through any single model? Datasets We evaluate our technique on seven reasoning datasets that span various real-world tasks and domains: (i) Biographies (Du et al., 2023), which asks the LLM to generate a factual biography of a famous computer scientist; (ii) GSM8k (Cobbe et al., 2021), a variety of grade school math problems created by human problem writers; and (iii) 5 datasets randomly drawn from MMLU (Hendrycks et al., 2021): High School Psychology (from the Social Sciences category), Formal Logic (from the Humanities category), College Biology (from the STEM category), Professional Law (from the Humanities Category), and Public Relations (from the Social Sciences category). We evaluate on a randomly-sampled size- $100$ subset of each dataset. In experiments involving the mapping matrix $\bm{W}$ , we instantiate $\bm{W}∈\mathbb{R}^{4096× 3072}$ using Xavier initialization and train for $10$ epochs on a dataset of $3072$ sentences We use $3072$ sentences as linear regression with $d$ -dimensional input has a sample complexity of $O(d)$ (Vapnik, 1999). randomly drawn from the Colossal Clean Crawled Corpus (C4) (Dodge et al., 2021). We use batch size $32$ and the Adam optimizer with learning rate $0.001$ . Metrics We measure the accuracy of the final response for the single models and AC. For NLD, we measure the accuracy of the majority-held final-round answer across agents when the answer is automatically verifiable (numeric in GSM8k, multiple choice for the MMLU datasets) or the average final-round answer across agents otherwise (Biographies). For GSM8k and the MMLU datasets, we report the proportion of samples in the dataset for which the generated answer exactly matches the ground-truth answer. For Biographies, following Du et al. (2023), we prompt an LLM judge ( $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ) to check whether each manually-decomposed fact in a ground-truth biography is supported ( $1$ ), partially supported ( $0.5$ ), or unsupported ( $0 0$ ) in the generated biography, taking the mean of these scores over all facts as the per-biography accuracy and the mean over all dataset samples as the total accuracy. | $\mathtt{3.2}$ - $\mathtt{3B}$ $\mathtt{3.1}$ - $\mathtt{8B}$ NLD | $79.4$ $± 0.0$ $83.9$ $± 0.0$ $80.2$ $± 0.1$ | $58.0$ $± 4.9$ $60.0$ $± 4.9$ $\mathbf{75.0}$ $± 4.3$ | $30.0$ $± 1.0$ $65.0$ $± 0.1$ $83.0$ $± 0.8$ | $16.0$ $± 0.8$ $42.0$ $± 0.1$ $37.0$ $± 0.1$ | $11.0$ $± 0.7$ $50.0$ $± 0.2$ $71.0$ $± 0.1$ | $0.0$ $± 0.0$ $20.0$ $± 0.8$ $30.0$ $± 0.1$ | $26.0$ $± 0.1$ $53.0$ $± 0.2$ $63.0$ $± 0.7$ | | --- | --- | --- | --- | --- | --- | --- | --- | | AC | $84.6$ $± 0.0$ | $64.0$ $± 4.8$ | $\mathbf{85.0}$ $± 0.8$ | $\mathbf{47.0}$ $± 0.1$ | $78.0$ $± 0.9$ | $30.0$ $± 0.1$ | $\mathbf{74.0}$ $± 0.1$ | | AC ( $\bm{W}$ ) | $\mathbf{86.8}$ $± 0.0$ | $66.0$ $± 4.8$ | $70.0$ $± 0.1$ | $35.0$ $± 0.1$ | $\mathbf{79.0}$ $± 0.9$ | $\mathbf{45.0}$ $± 0.1$ | $63.0$ $± 0.1$ | Table 3: Accuracies (%) on all seven reasoning benchmarks. NLD and all AC variants involve communication between $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ ( $A$ ) and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ( $B$ ); the performance of these models individually are presented in the first two rows of the table. NLD typically improves performance over at least one of the single model baselines; AC— both with and without the task-agnostic linear layer—consistently beats both baselines and NLD as well. Comprehensive evaluation with the $\mathtt{LLaMA}$ family Table 3 presents results on each of the seven reasoning benchmarks across various baselines and activation communication. Notably, while NLD consistently outperforms $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ , it does not always display a performance improvement over $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ; but remarkably, AC consistently outperforms both single-model baselines. In fact, AC offers an up to $27.0\%$ improvement over NLD across six of the seven reasoning datasets. When applying $\bm{W}$ to $A$ ’s activation before performing the replacement function, we see even further gains of $2.6-50.0\%$ over vanilla AC for four of the seven datasets. We hypothesize that the benefits from the learned linear layer are less consistent across datasets because the subset of C4 data used to train $\bm{W}$ likely contains text more semantically similar to some datasets than others, hence some datasets provide $\bm{W}$ with out-of-distribution inputs which reduces performance compared to vanilla AC. While we fix $A$ as the smaller model and $B$ as the larger model in Table 3 (so as to ensure decoding happens with the presumably more capable model), this need not be the case; swapping $A$ and $B$ yields results of $81.5± 0.0$ and $61.0± 4.8$ on Biographies and GSM8k respectively (without the linear layer). While these accuracies are lower than their non-swapped counterparts, notably they still are higher than both single-model baselines (and higher than NLD for Biographies); plus this is much more compute-efficient as the smaller model is now the one requiring the full instead of partial forward pass. Note that we find AC outperforms NLD on 48 of the 57 datasets in the full MMLU benchmark; complete MMLU results, as well as a suite of additional experiments, are shown in Appendix B. Performance-compute tradeoff and generalization to different model scales Thus far, we have been considering the absolute performance of AC with respect to NLD, for which our method attains state-of-the-art results; however the superiority of activations as a language for inter-LLM communication is further illustrated by AC’s larger ratio of performance improvement to added inference-time compute over individual LMs. Figure 3 displays the results of single models, AC, and NLD across model scales and suites within the $\mathtt{LLaMA}$ family on the Biographies dataset. Incoming arrows to AC and NLD nodes denote the base models between which communication occurred. Not only does AC consistently outperform both single-model baselines unlike NLD, but also notice that the slope of each black line is far greater than the slope of each gray line, indicating that AC consistently achieves greater increases in accuracy per additional unit of inference-time compute (normalized by the compute of a single forward pass through $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{1B}$ on the given prompt) compared to NLD. Communication across model families Table 4 displays results for AC between models from the $\mathtt{Qwen}$ - $\mathtt{2.5}$ , $\mathtt{Gemma}$ - $\mathtt{2}$ , and $\mathtt{LLaMA}$ - $\mathtt{3}$ families. We see that AC beats NLD across the board, and beats both individual models for $4/5$ of the $6$ model pairs on Biographies/GSM8k respectively —demonstrating the efficacy of AC irrespective of model architecture, size, tokenizer, and training data. Moreover, these results are obtained without training $\bm{W}$ , meaning we do not need a separate projection layer between activation spaces to attain SOTA results, even for extremely distinct models! (We hypothesize this is because we are only replacing $B$ ’s last-token activation, hence $B$ can learn from $A$ without an extreme alteration to its activation distribution. An alternative explanation is to see this result as proof of the platonic representation hypothesis (Huh et al., 2024), which historical deep learning works have oft alluded to, including in the context of cross-model representation stitching (Moschella et al., 2023; Kornblith et al., 2019).) | $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ , $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ $\mathtt{Qwen}$ - $\mathtt{2.5}$ - $\mathtt{1.5B}$ , $\mathtt{Qwen}$ - $\mathtt{2.5}$ - $\mathtt{3B}$ $\mathtt{Gemma}$ - $\mathtt{2}$ - $\mathtt{2B}$ , $\mathtt{Gemma}$ - $\mathtt{2}$ - $\mathtt{9B}$ | $79.4$ $± 0.0$ / $58.0$ $± 4.9$ $59.4$ $± 0.9$ / $20.0$ $± 0.9$ $83.0$ $± 1.1$ / $45.0$ $± 1.1$ | $83.9$ $± 0.0$ / $60.0$ $± 4.9$ $85.5$ $± 1.1$ / $35.0$ $± 1.1$ $\mathbf{94.6}$ $± 0.9$ / $80.0$ $± 0.9$ | $80.2$ $± 0.1$ / $\mathbf{75.0}$ $± 4.3$ $63.2$ $± 1.1$ / $65.0$ $± 1.1$ $70.3$ $± 1.0$ / $70.0$ $± 1.0$ | $\mathbf{84.6}$ $± 0.0$ / $64.0$ $± 4.8$ $\mathbf{89.6}$ $± 1.0$ / $\mathbf{70.0}$ $± 1.0$ $88.1$ $± 0.7$ / $\mathbf{90.0}$ $± 0.7$ | | --- | --- | --- | --- | --- | | $\mathtt{Qwen}$ - $\mathtt{2.5}$ - $\mathtt{1.5B}$ , $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ | $59.4$ $± 0.9$ / $20.0$ $± 0.9$ | $79.4$ $± 0.0$ / $58.0$ $± 4.9$ | $75.4$ $± 1.0$ / $\mathbf{75.0}$ $± 1.0$ | $\mathbf{79.5}$ $± 1.0$ / $75.0$ $± 1.0$ | | $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ , $\mathtt{Gemma}$ - $\mathtt{2}$ - $\mathtt{2B}$ | $79.4$ $± 0.0$ / $58.0$ $± 4.9$ | $83.0$ $± 1.1$ / $45.0$ $± 1.1$ | $62.5$ $± 1.1$ / $55.0$ $± 1.1$ | $\mathbf{84.0}$ $± 0.1$ / $\mathbf{60.0}$ $± 1.1$ | | $\mathtt{Qwen}$ - $\mathtt{2.5}$ - $\mathtt{1.5B}$ , $\mathtt{Gemma}$ - $\mathtt{2}$ - $\mathtt{2B}$ | $59.4$ $± 0.9$ / $20.0$ $± 0.9$ | $\mathbf{83.0}$ $± 1.1$ / $45.0$ $± 1.1$ | $49.3$ $± 1.1$ / $50.0$ $± 1.1$ | $73.0$ $± 1.1$ / $\mathbf{55.0}$ $± 1.1$ | Table 4: Individual model, AC, and NLD accuracies across three model families. Each cell displays two values: Biographies score / GSM8k score. <details> <summary>extracted/6420159/TODO.png Details</summary>  ### Visual Description ## Scatter Plot: Accuracy vs. Compute ### Overview The image is a scatter plot comparing the accuracy of three different models (AC, NLD, and Single Model) against the compute (normalized FLOPs) used. The plot shows the performance of each model at different compute levels, with arrows indicating the progression of the AC model. ### Components/Axes * **X-axis:** Compute (normalized FLOPs). Scale: 1, 2, 4, 8, 16, 32, 64, 128, 256. Logarithmic scale. * **Y-axis:** Accuracy (%). Scale: 76, 78, 80, 82, 84, 86. * **Legend (top-left):** * Green: AC (ours) * Blue: NLD * Orange: Single Model ### Detailed Analysis * **AC (ours) - Green:** * The AC model's accuracy increases as compute increases. * Data points: * Compute = 4, Accuracy ≈ 81.5% * Compute = 8, Accuracy ≈ 84.5% * Compute = 64, Accuracy ≈ 85% * Arrows indicate the progression of the AC model's accuracy with increasing compute. * **NLD - Blue:** * The NLD model's accuracy initially decreases and then increases slightly before decreasing again. * Data points: * Compute = 16, Accuracy ≈ 79.5% * Compute = 32, Accuracy ≈ 80% * Compute = 256, Accuracy ≈ 76% * **Single Model - Orange:** * The Single Model's accuracy varies with compute. * Data points: * Compute = 1, Accuracy ≈ 81% (labeled "3.2-1B") * Compute = 4, Accuracy ≈ 79.5% (labeled "3.2-3B") * Compute = 8, Accuracy ≈ 84% (labeled "3.1-8B") * Compute = 64, Accuracy ≈ 81% (labeled "3.1-70B") ### Key Observations * The AC model generally shows an upward trend in accuracy as compute increases. * The NLD model has a more volatile accuracy, decreasing significantly at higher compute levels. * The Single Model shows varying accuracy across different compute levels. ### Interpretation The plot suggests that the AC model (developed by the authors) benefits from increased compute, showing a general improvement in accuracy. The NLD model, on the other hand, does not scale as well with compute, experiencing a significant drop in accuracy at higher compute levels. The Single Model's performance varies, indicating that its accuracy is not directly correlated with compute in the same way as the AC model. The arrows connecting the AC model's data points emphasize the improvement in accuracy as compute increases, highlighting the effectiveness of the authors' approach. </details> Figure 3: Accuracy (%) vs. compute (# FLOPs normalized by single $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{1B}$ forward pass) for various configurations of AC and NLD on the Biographies dataset. AC () yields the greatest performance gains per additional unit of inference-time compute over each baseline (). 5 Conclusion We present a simple approach to enable effective and computationally efficient communication between language models by injecting information from the activations of one model into the activations of another during the forward pass. Salient features of this approach include: (i) Scales up LLMs on new tasks by leveraging existing, frozen LLMs along with zero additional task-specific parameters and data, (ii) Applies to diverse domains and settings, and (iii) Saves a substantial amount of compute. There are some limitations to this method. First, when not using the learned model-specific mapping discussed in Section 3.1, our method requires both models to have aligned embedding spaces, such that the activation of one model roughly retains its meaning in the other’s activation space (note that unlike past works such as Pham et al. (2024) we do not require shared tokenizers or aligned vocabularies, only aligned embeddings). While less restrictive than past works (Pham et al., 2024), this assumption is somewhat limiting, but can be relaxed when we let $f$ be the learned model-specific mapping; and in practice we find that even amongst different models in the $\mathtt{LLaMA}$ family, no such mapping is required for state-of-the-art results. Second, this method requires access to embeddings and will not work with black-box API access; however exploring API-only approaches is highly limiting, and recent releases of powerful open-source models (Dubey et al., 2024) merit the development of embedding-based techniques. Third, while a concern might be the limited interpretability of communicating activations as opposed to natural language, we note the following. First, there is a fundamental tradeoff between interpretability and information preservation (as activations, by virtue of being much higher-dimensional than the space of natural language, allow proportionally higher-entropy communication) (Pham et al., 2024), which merits discussion beyond the scope of this work. But second, we actually posit that our method suggests a new avenue towards interpreting LM activations: “translating” activations based on the beliefs they induce as messages in listening agents, similar to the method put forward in Andreas et al. (2018). We recognize this as a promising avenue for future research. Additional directions of future work include using AC to allow large LMs to leverage small, tunable LMs as “knowledge bases” during decoding (Lee et al., 2024), as in collaborative decoding (Shen et al., 2024) setups; and testing our approach on more complex coordination games (e.g., Lewis-style negotiation games (Lewis et al., 2017), Diplomacy). Impact Statement This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here. Acknowledgements The authors are grateful to Jacob Andreas, Yoon Kim, and Sham Kakade for their valuable discussions and feedback. References - Ahn et al. (2022) Ahn, M., Brohan, A., Brown, N., Chebotar, Y., Cortes, O., David, B., Finn, C., Fu, C., Gopalakrishnan, K., Hausman, K., Herzog, A., Ho, D., Hsu, J., Ibarz, J., Ichter, B., Irpan, A., Jang, E., Ruano, R. J., Jeffrey, K., Jesmonth, S., Joshi, N. J., Julian, R., Kalashnikov, D., Kuang, Y., Lee, K.-H., Levine, S., Lu, Y., Luu, L., Parada, C., Pastor, P., Quiambao, J., Rao, K., Rettinghouse, J., Reyes, D., Sermanet, P., Sievers, N., Tan, C., Toshev, A., Vanhoucke, V., Xia, F., Xiao, T., Xu, P., Xu, S., Yan, M., and Zeng, A. Do as i can, not as i say: Grounding language in robotic affordances, 2022. - Andreas et al. 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The rise and potential of large language model based agents: A survey, 2023. - Yang et al. (2023) Yang, H., Yue, S., and He, Y. Auto-gpt for online decision making: Benchmarks and additional opinions, 2023. - Yao et al. (2023) Yao, S., Zhao, J., Yu, D., Du, N., Shafran, I., Narasimhan, K., and Cao, Y. React: Synergizing reasoning and acting in language models, 2023. Appendix A Qualitative Results <details> <summary>extracted/6420159/biog.png Details</summary>  ### Visual Description ## Text Document: Joyce K. Reynolds Biography ### Overview The image presents a question asking for a bullet point biography of Joyce K. Reynolds, highlighting her contributions and achievements as a computer scientist. It then provides three different biographies of Joyce K. Reynolds, each with varying levels of detail and focus. The biographies are labeled as "Ground-Truth Biography", "LLaMA-3.2-3B", "LLaMA-3.1-8B", and "AC". ### Components/Axes * **Question:** Give a bullet point biography of Joyce K. Reynolds, highlighting her contributions and achievements as a computer scientist. * **Ground-Truth Biography:** A bullet-point biography of Joyce K. Reynolds. * **LLaMA-3.2-3B:** A bullet-point biography of Joyce K. Reynolds. * **LLaMA-3.1-8B:** A bullet-point biography of Joyce K. Reynolds. * **AC:** A bullet-point biography of Joyce K. Reynolds. ### Detailed Analysis or ### Content Details **Ground-Truth Biography:** * Joyce Kathleen Reynolds was an American computer scientist who contributed to the development of protocols underlying the Internet. * She authored or co-authored many RFCs (Request for Comments) including Telnet, FTP, and POP protocols. * Reynolds worked with Jon Postel to develop early functions of the Internet Assigned Numbers Authority and managed the root zone of DNS. * She received the 2006 Postel Award for her services to the Internet. * ... **LLaMA-3.2-3B:** * Joyce K. Reynolds is a renowned computer scientist and educator who has made significant contributions to the field of computer science and education. * She is a pioneer in the field of artificial intelligence, with a focus on human-computer interaction and user experience. * Reynolds has written extensively on topics such as usability, accessibility, and human-centered design. * She is a highly respected author, having written several books and articles on computer science and education. * Reynolds has received numerous awards and honors for her contributions to the field. **LLaMA-3.1-8B:** * Joyce K. Reynolds was born in 1923 in England. She studied mathematics at Girton College, Cambridge, graduating with a degree in 1945. * Reynolds started her career in computing in 1945 at the National Physical Laboratory (NPL), where she worked on the development of the first commercial computer database, the Database Management System (DBMS). * Reynolds was a key member of the team that developed the first DBMS, which was a pioneering achievement in the field of database management. Her work laid the foundation for modern database systems. **AC:** * Joyce K. Reynolds is a renowned computer scientist and engineer, best known for her pioneering work in the development of the Internet's fundamental technologies. * She was a key member of the team that designed the Internet Protocol (IP) and the Transmission Control Protocol (TCP), which form the basis of the modern Internet. * Reynolds' work on IP and TCP enabled the creation of a network that could efficiently route and manage data packets, paving the way for the modern Internet as we know it. * Reynolds has received numerous awards and honors for her groundbreaking work, including the Internet Society's (ISOC) highest award, the Jonathan B. Postel Service Award. * She continues to be an influential figure in the field of computer science and engineering, inspiring new generations of scientists and engineers with her pioneering achievements. ### Key Observations * All biographies highlight Joyce K. Reynolds' contributions to computer science and the Internet. * The "Ground-Truth Biography" focuses on her work with Internet protocols and the Internet Assigned Numbers Authority. * The "LLaMA-3.2-3B" biography emphasizes her role as an educator and her work in artificial intelligence and human-computer interaction. * The "LLaMA-3.1-8B" biography provides details about her early life and career, including her work on the first commercial computer database. * The "AC" biography highlights her pioneering work in the development of Internet protocols like IP and TCP. ### Interpretation The image presents multiple biographical summaries of Joyce K. Reynolds, each emphasizing different aspects of her career and contributions. The "Ground-Truth Biography" seems to provide a concise overview of her key achievements, while the other biographies offer more specific details about her work in different areas of computer science and her personal background. The presence of multiple biographies suggests that there are different perspectives on what constitutes the most important aspects of her life and work. The "AC" biography seems to be the most comprehensive, covering both her technical contributions and her impact on the field. </details> Figure 4: Example of AC on Biographies dataset. <details> <summary>extracted/6420159/gsm.png Details</summary>  ### Visual Description ## Math Problem and Solutions ### Overview The image presents a math problem about planning a birthday party and calculating the total cost of gift bags. It includes the problem statement and three different solutions labeled LLAMA-3.2-3B, LLAMA-3.1-8B, and AC. ### Components/Axes * **Question:** The problem statement describes Christina planning a birthday party, needing 0.75 gift bags per invited guest because 1/4 of attendees don't show up. She invited 16 friends, and gift bags cost $2 each. The question asks: "How much will she spend?" * **LLAMA-3.2-3B Solution:** This solution calculates the number of attendees by multiplying the total invited guests by 3/4 (since 1/4 don't show up). It then calculates the number of gift bags needed based on the number of attendees and the 0.75 gift bags per guest ratio. Finally, it calculates the total cost by multiplying the number of gift bags by the cost per gift bag. * **LLAMA-3.1-8B Solution:** This solution calculates the number of attendees by finding 1/4 of the invited guests and subtracting that from the total. It then calculates the number of gift bags needed based on the number of attendees and the 0.75 gift bags per guest ratio. Finally, it calculates the total cost by multiplying the number of gift bags by the cost per gift bag. * **AC Solution:** This solution calculates the number of attendees by multiplying the total invited guests by 3/4. It then calculates the number of gift bags needed based on the total number of invited guests and the 0.75 gift bags per guest ratio. Finally, it calculates the total cost by multiplying the number of gift bags by the cost per gift bag. ### Detailed Analysis or ### Content Details **Question:** * Christina is planning a birthday party. * She needs 0.75 gift bags per invited guest. * 1/4 of attendees don't show up. * She invited 16 friends. * Gift bags cost $2 each. * Question: How much will she spend? **LLAMA-3.2-3B:** * 1/4 of attendees don't show up, so calculate 3/4 of the total invited guests. * 3/4 of 16 is (3/4) * 16 = 12. * Christina needs 0.75 gift bags per invited guest, so for 12 guests, she needs 0.75 * 12 = 9 gift bags. * Each gift bag costs $2, so the total cost will be 9 gift bags * $2 per bag = $18. **LLAMA-3.1-8B:** * Christina invited 16 friends, but 1/4 of them won't show up. * Calculate 1/4 of 16 and subtract that from 16. * 1/4 of 16 is 16 / 4 = 4. * 4 guests won't come, so 16 - 4 = 12 guests will attend. * Christina needs 0.75 gift bags per invited guest. Since she invited 16 friends, but only 12 will attend, she needs 0.75 * 12 = 9 gift bags. * Gift bags are $2 each. Since Christina needs 9 gift bags, she needs 9 * 2 = $18. **AC:** * Since 1/4 of the attendees don't show up, 3/4 of them will. To find the number of guests that will show up, multiply the total number of invited guests by 3/4. So, 16 * 3/4 = 12 guests will show up. * Christina needs 0.75 gift bags per invited guest. Since she invited 16 friends, she needs 16 * 0.75 = 12 gift bags. * Each gift bag costs $2. Since she needs 12 gift bags, the total cost will be 12 * $2 = $24. ### Key Observations * LLAMA-3.2-3B and LLAMA-3.1-8B both arrive at the same answer of $18, calculating the number of gift bags based on the number of guests who will attend. * AC calculates the number of gift bags based on the number of invited guests, not the number of guests who will attend, resulting in a different answer of $24. ### Interpretation The problem highlights the importance of carefully considering the wording of a problem. LLAMA-3.2-3B and LLAMA-3.1-8B correctly interpret the problem to mean that the 0.75 gift bags per guest applies only to those who actually attend. AC, however, interprets it to mean 0.75 gift bags per invited guest, regardless of whether they attend. This difference in interpretation leads to different solutions. The problem statement is ambiguous and could be interpreted in either way. </details> Figure 5: Example of AC on GSM8k dataset. <details> <summary>extracted/6420159/psych.png Details</summary>  ### Visual Description ## Question and Explanations Regarding Gate-Control Theory ### Overview The image presents a question about gate-control theory and its possible answers, followed by three different explanations (LLaMA-3.2-3B, LLaMA-3.1-8B, and AC) that attempt to justify the correct answer. ### Components/Axes * **Question:** "According to gate-control theory, which condition tends to close the gate?" * **Options:** A) anxiety, B) depression, C) focusing on the pain, D) electrical stimulation * **LLaMA-3.2-3B Explanation:** A text block providing an explanation based on focusing on the pain. * **LLaMA-3.1-8B Explanation:** A text block providing an explanation based on electrical stimulation. * **AC Explanation:** A text block providing a step-by-step analysis of the options. ### Detailed Analysis or Content Details * **Question:** The question asks which condition, according to gate-control theory, tends to close the gate. The options are anxiety, depression, focusing on the pain, and electrical stimulation. * **LLaMA-3.2-3B:** This explanation argues that focusing on the pain (C) is the correct answer because it directly affects the gate, reducing the perception of pain. It states that anxiety and depression affect pain perception but do not directly close the gate, and electrical stimulation activates the gate, not closes it. * **LLaMA-3.1-8B:** This explanation argues that electrical stimulation (D) is the correct answer. It states that anxiety, depression, and focusing on the pain increase pain perception, suggesting the gate is open. Electrical stimulation, on the other hand, activates nerve fibers that close the gate and reduce pain perception. * **AC:** This explanation provides a step-by-step analysis. It states that anxiety (A) tends to open the gate, depression (B) has a complex relationship, focusing on the pain (C) tends to open the gate, and electrical stimulation (D) can close the gate. The final answer is <<D>>. ### Key Observations * The LLaMA-3.2-3B explanation contradicts the other two explanations. * LLaMA-3.1-8B and AC both agree that electrical stimulation tends to close the gate. * The explanations provide different rationales for the effects of anxiety, depression, and focusing on the pain. ### Interpretation The image highlights a discrepancy in the understanding and application of gate-control theory. While two explanations (LLaMA-3.1-8B and AC) converge on electrical stimulation as the condition that tends to close the gate, one explanation (LLaMA-3.2-3B) suggests focusing on the pain. This suggests a potential ambiguity or varying interpretations within the framework of gate-control theory itself, or perhaps errors in the reasoning of the models. The step-by-step analysis in the AC explanation provides a more structured and arguably more convincing argument for electrical stimulation as the correct answer. </details> Figure 6: Example of AC on MMLU High School Psychology dataset. <details> <summary>extracted/6420159/logic.png Details</summary>  ### Visual Description ## Multiple Choice Question Analysis ### Overview The image presents a multiple-choice question related to identifying the conclusion of a given argument. The argument discusses genetics as a young science, the description of inheritance traits, the rediscovery of inheritance laws, and the understanding of DNA's importance. The image also includes explanations and analyses from different sources (LLaMA models and an "AC" source) regarding the correct answer. ### Components/Axes * **Question:** The question asks to identify the conclusion of the provided argument. * **Argument:** The argument consists of several statements: * Genetics is a young science from a historical point of view. * Inheritance traits were described less than 150 years ago. * Inheritance laws were rediscovered around the turn of the 20th century. * The importance of DNA was not really understood until the 1950s. * **Answer Choices:** Four options (A, B, C, and D) are provided as potential conclusions. * A) But even then, the importance of DNA was not really understood until the 1950s. * B) The importance of DNA was not really understood until the 1950s. * C) From a historical point of view, genetics is a young science. * D) The principles that govern inheritance traits were described less than 150 years ago. * **LLaMA-3.2-3B:** This section provides the answer and justification from one LLaMA model. It states that the best answer is B. * **LLaMA-3.1-8B:** This section provides the answer and explanation from another LLaMA model. It states that the final answer is A. * **AC:** This section provides a step-by-step analysis to determine the conclusion of the argument. It concludes that the answer is C. ### Detailed Analysis or ### Content Details * **Question Text:** "Identify the conclusion of the following argument. From a historical point of view, genetics is a young science. The principles that govern inheritance traits were described less than 150 years ago. Furthermore, around the turn of the twentieth century, the laws of inheritance were rediscovered. But even then, the importance of DNA was not really understood until the 1950s." * **Answer Choices:** * A) But even then, the importance of DNA was not really understood until the 1950s. * B) The importance of DNA was not really understood until the 1950s. * C) From a historical point of view, genetics is a young science. * D) The principles that govern inheritance traits were described less than 150 years ago. * **LLaMA-3.2-3B:** "The best answer is B) The importance of DNA was not really understood until the 1950s." * **LLaMA-3.1-8B:** "The final answer is: <<A>>. Explanation: The conclusion is the statement that follows from the premises. In this case, the conclusion is the statement that follows from the two premises. The first premise states that genetics is a young science from a historical point of view, and the second premise states that the importance of DNA was not really understood until the 1950s. The conclusion is the statement that summarizes the main point of the argument, which is that even then, the importance of DNA was not really understood until the 1950s. This is the correct answer because it is the statement that follows from the premises and summarizes the main point of the argument." * **AC:** "Step 1: Identify the main claim of the argument. The main claim of the argument is that genetics is a young science from a historical point of view. Step 2: Identify the supporting evidence for the main claim. The supporting evidence includes the fact that the principles that govern inheritance traits were described less than 150 years ago and that the laws of inheritance were rediscovered around the turn of the twentieth century. Step 3: Identify the additional information provided in the argument. The additional information is that the importance of DNA was not really understood until the 1950s. Step 4: Determine the conclusion of the argument. The conclusion is the main claim of the argument, which is that genetics is a young science from a historical point of view. <<C>>" ### Key Observations * The question presents an argument and asks for its conclusion. * The LLaMA models and the "AC" source disagree on the correct answer. LLaMA-3.2-3B selects B, LLaMA-3.1-8B selects A, and AC selects C. * The explanations provided by the LLaMA models and the "AC" source offer different reasoning for their respective choices. ### Interpretation The image highlights the complexities of natural language processing and argument analysis. Different models and analytical approaches can lead to varying conclusions, even when presented with the same information. The disagreement between the LLaMA models and the "AC" source underscores the importance of critically evaluating the reasoning behind each answer choice and considering different perspectives when analyzing arguments. The question is designed to test the ability to identify the main point or conclusion of a given argument, and the varying answers suggest that this is a nuanced and challenging task. </details> Figure 7: Example of AC on MMLU Formal Logic dataset. <details> <summary>extracted/6420159/bio.png Details</summary>  ### Visual Description ## Text Analysis: Ecological Niches ### Overview The image presents a multiple-choice question and explanations related to the ecological niches of bird species. It defines fundamental, realistic, and ecological niches and applies these concepts to a scenario where birds nest in treetops due to competition on cliff ledges. ### Components/Axes The image is divided into four distinct blocks of text: 1. **Question**: Poses a scenario about bird nesting habits and asks which type of niche the birds are utilizing. 2. **LLaMA-3.2-3B**: Provides an explanation and answer to the question. 3. **LLaMA-3.1-8B**: Provides an alternative explanation and answer to the question. 4. **AC**: Presents a step-by-step analysis and answer to the question. ### Detailed Analysis or ### Content Details **Question:** * **Question**: The members of a bird species capable of nesting in treetops or on the ledges of nearby cliffs make their homes only in the treetops due to the established presence of a more aggressive bird species on the cliff ledges. With respect to habitat, the treetop-nesting birds are utilizing: * A) their fundamental niche only * B) their realistic niche only * C) their ecological niche only * D) neither their fundamental niche nor their realistic niche **LLaMA-3.2-3B:** * **Identifier**: LLaMA-3.2-3B * **Content**: The treetop-nesting birds are not utilizing their fundamental niche because the cliff ledge is not part of their natural environment. However, they are utilizing their realistic niche, which is the portion of the fundamental niche that is actually available to the birds. The treetop-nesting birds are not utilizing their ecological niche, which is the actual area used by the birds. Therefore, the correct answer is B) their realistic niche only. **LLaMA-3.1-8B:** * **Identifier**: LLaMA-3.1-8B * **Content**: The birds are using their ecological niche, which is the set of environmental conditions and resources that a species can use and occupy in a given area. The birds are not using their fundamental niche, which is the set of all environmental conditions and resources that a species can use and occupy in theory. The birds are also not using their realistic niche, which is the set of environmental conditions and resources that a species can use and occupy in a given area, but with the constraint of competition and predation. The birds are only using their ecological niche because they are limited by the presence of a more aggressive bird species on the cliff ledges. Therefore, the correct answer is C) their ecological niche only. **AC:** * **Identifier**: AC * **Content**: * Step 1: Define the key terms: fundamental niche, realistic niche, and ecological niche. The fundamental niche refers to the range of environmental conditions in which a species can survive and reproduce without any limitations. The realistic niche, on the other hand, is the range of conditions that a species actually occupies due to biotic and abiotic interactions with other species. The ecological niche is a broader concept that encompasses both the fundamental and realistic niches. * Step 2: Analyze the given scenario. In the given scenario, the bird species capable of nesting in treetops or on cliff ledges makes their homes only in the treetops due to the presence of a more aggressive bird species on the cliff ledges. This means that the treetop-nesting birds are limited by the presence of another species in their potential habitat. * Step 3: Determine the type of niche being utilized. Since the treetop-nesting birds are limited by the presence of another species in their potential habitat, they are not utilizing their fundamental niche or ecological niche, but are utilizing B) only their realistic niche, which is the range of conditions that they actually occupy due to biotic and abiotic interactions with other species. ### Key Observations * The question presents a scenario where birds are forced to nest in treetops due to competition. * LLaMA-3.2-3B and AC both conclude that the birds are utilizing their realistic niche. * LLaMA-3.1-8B concludes that the birds are utilizing their ecological niche. * The "AC" explanation provides definitions for fundamental, realistic, and ecological niches. ### Interpretation The image explores the concept of ecological niches and how competition can influence a species' habitat selection. The differing answers between LLaMA-3.2-3B/AC and LLaMA-3.1-8B highlight the nuances in defining and applying these ecological concepts. The "AC" explanation provides a structured approach to analyzing the scenario, emphasizing the importance of defining key terms and considering the limitations imposed by biotic interactions. The image demonstrates that the realized niche is a subset of the fundamental niche, constrained by factors like competition. </details> Figure 8: Example of AC on MMLU College Biology dataset. <details> <summary>extracted/6420159/law.png Details</summary>  ### Visual Description ## Legal Question and Explanations ### Overview The image presents a legal question related to real estate contract law, followed by multiple-choice answers and explanations supporting different conclusions. The question involves an oral agreement, a written offer, a post-dated check, and a subsequent higher offer from another party. The image provides the question, potential answers, and three different explanations labeled LLAMA-3.2-3B, LLAMA-3.1-8B, and AC. ### Components/Axes * **Question:** A detailed scenario describing a real estate transaction. * **Answers:** Four multiple-choice answers (A, B, C, D) presenting different legal outcomes. * **Explanations:** Three separate explanations (LLAMA-3.2-3B, LLAMA-3.1-8B, AC) providing reasoning for specific answers. ### Detailed Analysis or ### Content Details **Question:** * A purchaser orally agreed with the seller to buy the seller's house for $100,000. * The purchaser gave the seller a written offer and a post-dated check for 5% of the price. * Before the seller signed the offer or deposited the check, he received an offer of his full asking price of $120,000 from another party. * The seller called the purchaser and called the deal off. * The purchaser sued for specific performance on the basis that the oral understanding, along with the written offer and the check, constituted an enforceable agreement. * Will the purchaser likely prevail? **Answers:** * A) Yes, because there was an oral agreement and the check for the down payment was evidence of consideration being paid. * B) No, because the offer was not accepted—prior to an acceptance the seller had the right to sell to anyone. * C) Yes, because the buyer and seller had a meeting of the minds evidenced by their oral understanding, the check and the written offer. * D) No, because specific performance does not apply in a residential real estate transaction. **Explanation LLAMA-3.2-3B:** * The most accurate answer would be: A). * Here's the explanation: The purchaser and seller had an oral agreement to buy the house for $100,000, which is a sufficient consideration to support the enforceability of the agreement. * The written offer and the post-dated check for 5% of the price ($5,000) also constitute consideration, as they demonstrate the purchaser's commitment to the deal. * The seller's receipt of the written offer and the post-dated check prior to the offer from the other party indicates that the seller had already accepted the purchaser's offer and was willing to move forward with the deal. * Therefore, the purchaser can argue that the seller had already accepted the offer and was not free to accept the other offer. **Explanation LLAMA-3.1-8B:** * The purchaser and seller had a valid contract. * The check was consideration, and the oral agreement was enforceable. * The seller had no right to call off the deal after the purchaser's offer was made. * The seller could have sold to anyone, but he was not free to call off the deal with the purchaser after the purchaser's offer was made. * The purchaser had a right to enforce the contract. <<A>> **Explanation AC:** * The purchaser will not prevail because the offer was not accepted. * The seller received another offer and called off the deal before accepting the purchaser's offer. * The law requires that there be an acceptance of the offer before a contract can be formed. * The seller's action in calling off the deal before accepting the purchaser's offer terminated the offer, and the purchaser's offer lapsed. <<B>> ### Key Observations * The question presents a common legal issue in real estate transactions: the enforceability of agreements when there are oral agreements, written offers, and subsequent higher offers. * The explanations provide different legal perspectives, with LLAMA-3.2-3B and LLAMA-3.1-8B supporting the purchaser's claim, while AC supports the seller's position. * The explanations reference key legal concepts such as "consideration," "enforceable agreement," and "acceptance." ### Interpretation The image presents a legal hypothetical and competing arguments regarding the enforceability of a real estate agreement. The core issue revolves around whether the oral agreement and the post-dated check constitute sufficient consideration and evidence of acceptance to bind the seller, even before formal acceptance of the written offer. The explanations highlight the complexities of contract law and the importance of factors such as intent, consideration, and acceptance in determining the enforceability of agreements. The differing conclusions demonstrate that the outcome of such a case can depend on the specific facts and the interpretation of applicable laws. </details> Figure 9: Example of AC on MMLU Professional Law dataset. <details> <summary>extracted/6420159/prel.png Details</summary>  ### Visual Description ## Question and Answers: No-Wait Weight Loss Advertising Campaign ### Overview The image presents a multiple-choice question about the failure stage of the "No-Wait Weight Loss" advertising campaign, along with three different explanations for the correct answer. The question describes the product's promise and the negative experiences reported by users. The explanations are provided by LLAMA-3.2-3B, LLAMA-3.1-8B, and AC. ### Components/Axes * **Question:** The question text describes the product and the problem. The possible answers are: * A) distribution * B) penetration * C) participation * D) identification * **LLAMA-3.2-3B Explanation:** This section provides an explanation for why "penetration" is the best answer. * **LLAMA-3.1-8B Explanation:** This section provides a different explanation for why "penetration" is the best answer, referencing the stages of an advertising campaign. * **AC Explanation:** This section provides a different explanation and argues that "distribution" is the correct answer. ### Detailed Analysis or ### Content Details **Question Text:** "No-Wait Weight Loss, a diet pill brand, promises its potential consumers that if they take one pill once a day they will lose weight without having to change their diet or start exercising. However, many people who have used the product have complained that they haven't lost weight, and some have even gained weight. No-Wait Weight Loss has been unsuccessful in the ______ stage of the advertising campaign: A) distribution, B) penetration, C) participation, D) identification" **LLAMA-3.2-3B Explanation:** "LLAMA-3.2-3B: The best answer is B). Explanation: The product has failed to gain traction with consumers, which is referred to as the penetration stage of the advertising campaign. The penetration stage is the point in time when a product is introduced to the market and has not yet reached a significant level of adoption or usage. In this case, the product is not gaining any traction, and many consumers are not using it, which indicates that it has not yet reached the penetration stage of the advertising campaign." **LLAMA-3.1-8B Explanation:** "LLAMA-3.1-8B: We need to consider the stages of the advertising campaign and how they relate to the product's performance. The stages are: 1) Identification: The initial stage... 7) Participation: The stage where consumers become engaged with the brand. We can infer that the product has not been able to convince potential consumers of its benefits, which is the Persuasion stage. However, this is not the correct answer. The product has been used by many people, and some have even complained about its performance, which suggests that the product has reached the Trial stage. However, this is also not the correct answer. The product has been unsuccessful in the stage of the advertising campaign, which suggests that the product has not been able to gain market share and become a dominant player in the market, which is the Penetration stage. Therefore, the correct answer is B) Penetration." **AC Explanation:** "AC: The question is asking about the stage of the advertising campaign that No-Wait Weight Loss has been unsuccessful in. The stages of the advertising campaign are: identification, awareness, knowledge, liking, persuasion, trial, and adoption. However, the options provided in the question are not the traditional stages of the advertising campaign. The options are distribution, penetration, participation, and identification. However, if we map the options to the traditional stages of the advertising campaign, we can see that: distribution is similar to the trial stage, penetration is similar to the adoption stage, participation is similar to the awareness stage, and identification is similar to the awareness stage as well. Since No-Wait Weight Loss has been unsuccessful in getting people to buy and use their product, it has been unsuccessful in the trial stage of the advertising campaign, which is similar to the distribution stage. Therefore, the correct answer is <<A>>." ### Key Observations * The question describes a product that fails to deliver its promised benefits. * LLAMA-3.2-3B and LLAMA-3.1-8B both identify "penetration" as the correct answer, but provide different reasoning. * AC argues that "distribution" is the correct answer, mapping the provided options to traditional advertising campaign stages. * There is disagreement on the correct answer. ### Interpretation The question explores the concept of advertising campaign stages and how a product's failure can be attributed to a specific stage. The different explanations highlight varying interpretations of the stages and their relevance to the product's situation. LLAMA-3.2-3B focuses on the lack of consumer traction, while LLAMA-3.1-8B considers the product's inability to convince consumers and gain market share. AC takes a different approach, mapping the provided options to traditional stages and concluding that the failure lies in the "distribution" stage. The disagreement suggests that the question is open to interpretation and that different perspectives can lead to different conclusions. </details> Figure 10: Example of AC on MMLU Public Relations dataset. Appendix B Additional Experiments B.1 Modifying Activations of All Tokens Recall that AC grafts the last-token layer- $k$ activation of $A$ into $B$ ’s last-token layer- $j$ activation. But is modifying just the last token activation enough to communicate information from $A$ to $B$ ? Note that after applying masked attention in each of the previous Transformer layers, the last token activation of $A$ attends to all tokens before it, hence incorporating information from the entire sequence. Indeed, this must be the case for activation communication to recover the gap between the zero-communication and skyline setups on both coordination games, which (for Tip Sheets in particular) require information starting at the first few tokens of $A$ ’s prompt to be communicated. To verify this empirically, we experiment with summing the activations of all tokens in the sequence rather than just the last (we cannot replace all tokens as this would just replace $B$ ’s layer- $j$ activation with $A$ ’s layer $k$ -activation). Results are shown in Table 5. | AC (replace) AC (sum) AC (all tokens) | $\mathbf{84.6}$ $± 0.0$ $79.7$ $± 0.0$ $76.0$ $± 0.0$ | $64.0$ $± 4.8$ $\mathbf{66.0}$ $± 4.7$ $62.0$ $± 4.9$ | $\mathbf{85.0}$ $± 0.8$ $65.0$ $± 4.8$ $35.0$ $± 4.8$ | $\mathbf{47.0}$ $± 0.1$ $42.0$ $± 4.9$ $42.0$ $± 4.9$ | $\mathbf{78.0}$ $± 0.9$ $50.0$ $± 5.0$ $61.0$ $± 4.9$ | $\mathbf{30.0}$ $± 0.1$ $25.0$ $± 4.3$ $15.0$ $± 3.6$ | $\mathbf{74.0}$ $± 0.1$ $37.0$ $± 4.8$ $26.0$ $± 4.4$ | | --- | --- | --- | --- | --- | --- | --- | --- | Table 5: Reasoning benchmark performance when varying tokens modified during AC. All methods involve communication between $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ ( $A$ ) and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ( $B$ ). The functional form $f$ is varied between last-token replacement, last-token summation, and summation for all tokens. Indeed, applying $f$ to all tokens decreases performance relative to applying $f$ to just the last token. Note that the fact performance generally decreases from $f=$ $\mathtt{replace}$ to $f=$ $\mathtt{sum}$ , and further with all tokens, is expected. The high performance of AC with $f=$ $\mathtt{replace}$ means that the edited last-token activation $\bm{b}$ retains some meaning in $B$ ’s activation space; it is less likely for this to be the case when $f=$ $\mathtt{sum}$ (at the very least $\bm{b}$ has norm roughly $2×$ that of $B$ ’s original last-token activation), and when doing this for all tokens we’d expect performance to decrease even further as now all activation vectors, not just the last, are out-of-distribution with respect to $B$ ’s activation space. B.2 Incorporating Chain-of-Thought Prompting How does AC perform in relation to NLD in cases where $A$ might incur a long response (possibly with chain-of-thought for intermediate answer computation)? I.e., does AC lose out on the benefits of CoT? First, note that we still reap the benefits of CoT when we sample a completion from $B$ after AC (where $B$ gets all the information encoding $A$ ’s “beliefs” about the prompt via AC, hence CoT on $A$ ’s side is not needed). To verify this, we experiment with prompting $A$ with CoT, generating a full response, and then passing the layer- $k$ last-token activation of the CoT response to $B$ as part of AC. Results are shown in Table 6. | AC AC ( $\bm{W}$ ) AC (CoT) | $84.6$ $± 0.0$ $\mathbf{86.8}$ $± 0.0$ $82.1$ $± 0.0$ | $64.0$ $± 4.8$ $\mathbf{66.0}$ $± 4.8$ $\mathbf{66.0}$ $± 4.0$ | $\mathbf{85.0}$ $± 0.8$ $70.0$ $± 0.1$ $80.0$ $± 4.0$ | $\mathbf{47.0}$ $± 0.1$ $35.0$ $± 0.1$ $26.0$ $± 4.4$ | $78.0$ $± 0.9$ $\mathbf{79.0}$ $± 0.9$ $67.0$ $± 4.7$ | $30.0$ $± 0.1$ $\mathbf{45.0}$ $± 0.1$ $40.0$ $± 4.9$ | $\mathbf{74.0}$ $± 0.1$ $63.0$ $± 0.1$ $63.0$ $± 4.8$ | | --- | --- | --- | --- | --- | --- | --- | --- | Table 6: Reasoning benchmark performance when sampling from $A$ with CoT. All methods involve communication between $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ ( $A$ ) and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ( $B$ ). Indeed, we empirically find our above intuition (in orange) to hold, as there is no significant improvement over vanilla AC when generating from $A$ using CoT. B.3 Learning $\bm{W}$ In-Distribution Recall our reasoning about the AC $(\bm{W})$ results from Section 4.2: “We hypothesize that the benefits from the learned linear layer are less consistent across datasets because the subset of C4 data used to train $\bm{W}$ likely contains text more semantically similar to some datasets than others, hence some datasets provide $\bm{W}$ with out-of-distribution inputs which reduces performance compared to vanilla AC.” Indeed, we verify this hypothesis by training $\bm{W}$ on the GSM8k train set (to produce $\bm{W}_{\textrm{in dist}}$ ) and then evaluating with this task-specific linear layer on the GSM8k test set. Results are shown in Table 7. | $64.0$ $± 4.8$ | $66.0$ $± 4.8$ | $\mathbf{78.0}$ $± 4.1$ | | --- | --- | --- | Table 7: GSM8k performance when learning $\bm{W}$ in-distribution. All AC variants involve communication between $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ ( $A$ ) and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ( $B$ ). Indeed, learning $\bm{W}$ in-distribution significantly boosts performance, confirming our hypothesis. Unfortunately we cannot run this experiment for the other datasets, as there is no in-distribution training data available for MMLU (we use all public data for testing). Hence, this suggests that AC ( $\bm{W}$ ) should unilaterally improve over vanilla AC if we choose a training set with good coverage across many tasks and distributions, such that there are sentences semantically similar to prompts across the span of downstream task datasets. B.4 Activation Space Similarity $\propto$ AC Performance Gain We conduct the following experiment: for each of the six pairs of models $A,B$ in the above experiment (see Table 4), we compute the increase in Biographies performance with AC relative to the average individual performance of $A$ and $B$ . We also compute the matrix analogue of the squared cosine similarity between the models’ activation spaces, $$ \frac{\lVert Y^{\top}X\rVert_{F}^{2}}{\lVert X\rVert_{F}^{2}\,\lVert Y\rVert_{% F}^{2}}, $$ where $X$ is the matrix of $A$ ’s activations on $3072$ sentences from C4 (the same dataset used to train $\bm{W}$ ), $Y$ is the corresponding matrix for $B$ , and $\lVert·\rVert_{F}$ denotes the Frobenius norm. This yields the plot in Figure 11. There is a clear positive correlation between the similarity of the activation distributions and the AC performance gain, as expected; the more aligned $A$ and $B$ ’s activation spaces are, the more semantically meaningful and useful the embedding we graft from $A$ to $B$ becomes. B.5 Communicating Activations Between Identical Models Note that AC as described in Section 3.1 only supports communication between distinct models. We can extend AC to work for communication between identical models as follows: let $A$ and $B$ be instances of the same model. We can sample a completion from $A$ with temperature and graft the last-token layer- $k$ activation of the completion into $B$ at layer $j$ as part of the AC procedure. This still saves a substantial amount of compute over NLD between 2 model instances, showing our technique can apply to this setting. Table 8 shows the results of this experiment. <details> <summary>extracted/6420159/model-comparison-plot.png Details</summary>  ### Visual Description ## Scatter Plot: AC Performance Gain vs. Cosine Similarity ### Overview The image is a scatter plot showing the relationship between AC (Accuracy) performance gain on biographies and the cosine similarity (normalized squared Frobenius norm) of activation spaces A and B. Each point represents a different model configuration, labeled with the model names. The plot visualizes how the similarity of activation spaces correlates with the performance gain. ### Components/Axes * **Title:** AC performance gain vs. "cosine similarity" (normalized squared Frobenius norm) of A, B's activation spaces * **X-axis:** ||Y^T X||_F^2 / (||X||_F^2 ||Y||_F^2) - Represents the cosine similarity between activation spaces. The scale ranges from approximately 0.35 to 0.65, with tick marks at intervals of 0.05. * **Y-axis:** AC performance gain on Biographies (AC perf. - avg(A, B) perf.) - Represents the gain in AC performance. The scale ranges from -0.025 to 0.175, with tick marks at intervals of 0.025. * **Data Points:** Each data point is a blue circle, labeled with the corresponding model names. ### Detailed Analysis The data points, from left to right, are approximately: * **gemma2b,gemma9b:** X: 0.34, Y: -0.01 * **llama3b,llama8b:** X: 0.51, Y: 0.03 * **llama3b,gemma2b:** X: 0.57, Y: 0.02 * **qwen1.5b,gemma2b:** X: 0.57, Y: 0.02 * **qwen1.5b,llama3b:** X: 0.57, Y: 0.10 * **qwen1.5b,qwen3b:** X: 0.63, Y: 0.17 ### Key Observations * There appears to be a positive correlation between cosine similarity and AC performance gain. As the cosine similarity increases, the AC performance gain tends to increase as well. * The models "llama3b,gemma2b" and "qwen1.5b,gemma2b" have similar cosine similarity and AC performance gain values, clustering together. * The model "gemma2b,gemma9b" has the lowest cosine similarity and the lowest AC performance gain. * The model "qwen1.5b,qwen3b" has the highest cosine similarity and the highest AC performance gain. ### Interpretation The scatter plot suggests that a higher cosine similarity between the activation spaces of models A and B is associated with a greater AC performance gain on biographies. This could indicate that models with more similar internal representations tend to perform better in this specific task. The clustering of certain models suggests that specific model combinations yield similar performance characteristics. The outlier "gemma2b,gemma9b" indicates that this model combination may have significantly different internal representations or is less effective for the biography task. </details> Figure 11: AC performance gain over average $A$ / $B$ individual performance on Biographies, as a function of matrix “cosine similarity” between $A$ and $B$ ’s activation spaces. | $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ NLD AC | $\mathbf{83.9}$ $± 0.0$ $80.8$ $± 0.0$ $83.7$ $± 0.0$ | $60.0$ $± 4.9$ $\mathbf{70.0}$ $± 3.7$ $60.0$ $± 4.9$ | $65.0$ $± 0.1$ $\mathbf{85.0}$ $± 3.6$ $\mathbf{85.0}$ $± 3.6$ | $\mathbf{42.0}$ $± 0.1$ $35.0$ $± 4.8$ $40.0$ $± 4.9$ | $50.0$ $± 0.2$ $\mathbf{78.0}$ $± 4.1$ $74.0$ $± 4.4$ | $20.0$ $± 0.8$ $\mathbf{40.0}$ $± 4.9$ $\mathbf{40.0}$ $± 4.9$ | $53.0$ $± 0.2$ $53.0$ $± 5.1$ $\mathbf{79.0}$ $± 4.1$ | | --- | --- | --- | --- | --- | --- | --- | --- | Table 8: Reasoning benchmark performance of communication between identical models. Both NLD and AC involve communication between 2 instances of $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ . $512$ -token completions are sampled with temperature $0.7$ and debate is run for $2$ rounds. Indeed, while communication between multiple model instances doesn’t always show improvement over the single model itself (a well-known result from (Du et al., 2023)), AC matches/outperforms NLD on five of the seven datasets. The intuition behind debate between multiple identical model instances is that sampling multiple completions (with temperature) from the same model yields diverse reasoning paths that can be recombined into a stronger final answer. The above experiment shows that the same intuition holds for AC—we are sampling multiple times from the same model, but passing responses between agents via AC rather than as NL messages. B.6 Additional Rounds of Natural Language Debate In Section 4.2 we fix NLD to $2$ agents and $2$ rounds, however we find in additional experiments that AC outperforms NLD even with additional rounds, highlighting the superiority and robustness of activations as an alternative “language” for inter-LM communication. Results are shown in Table 9; we see that for 5 of the 7 reasoning benchmarks, AC beats NLD even with $3$ - $4$ rounds while using substantially less compute. | NLD (1 round) NLD (2 rounds) NLD (3 rounds) | $83.6$ $± 0.0$ $80.2$ $± 0.1$ $80.1$ $± 4.6$ | $72.0$ $± 4.5$ $75.0$ $± 4.3$ $\mathbf{79.0}$ $± 4.1$ | $65.0$ $± 4.8$ $83.0$ $± 0.8$ $70.0$ $± 4.6$ | $40.0$ $± 4.9$ $37.0$ $± 0.1$ $45.0$ $± 5.0$ | $68.0$ $± 4.6$ $71.0$ $± 0.1$ $63.0$ $± 4.8$ | $30.0$ $± 4.6$ $30.0$ $± 0.1$ $\mathbf{40.0}$ $± 4.9$ | $63.0$ $± 4.8$ $63.0$ $± 0.7$ $\mathbf{74.0}$ $± 4.4$ | | --- | --- | --- | --- | --- | --- | --- | --- | | NLD (4 rounds) | $78.0$ $± 0.0$ | $\mathbf{79.0}$ $± 4.1$ | * | * | * | * | * | | AC | $\mathbf{84.6}$ $± 0.0$ | $64.0$ $± 4.8$ | $\mathbf{85.0}$ $± 0.8$ | $\mathbf{47.0}$ $± 0.1$ | $\mathbf{78.0}$ $± 0.9$ | $30.0$ $± 0.1$ | $\mathbf{74.0}$ $± 0.1$ | ∗ Runs required too much compute Table 9: Reasoning benchmark performance of AC and NLD with varying number of rounds. All methods involve communication between $\mathtt{LLaMA}$ - $\mathtt{3.2}$ - $\mathtt{3B}$ ( $A$ ) and $\mathtt{LLaMA}$ - $\mathtt{3.1}$ - $\mathtt{8B}$ ( $B$ ). B.7 Full MMLU Benchmark Results Table 10 below displays complete results of both AC and NLD on the full MMLU benchmark. Notably, AC matches/outperforms NLD on 48/57 datasets, with substantially less compute used, indicating its superiority and robustness as an alternative “language” for inter-LLM communication. | Conceptual Physics High School Chemistry Security Studies | $60.0± 4.9$ $\mathbf{50.0± 5.0}$ $60.0± 4.9$ | $\mathbf{68.0± 4.6}$ $37.0± 4.8$ $60.0± 4.9$ | | --- | --- | --- | | Jurisprudence | $84.0± 3.6$ | $84.0± 3.6$ | | Logical Fallacies | $63.0± 4.8$ | $\mathbf{72.0± 4.5}$ | | College Computer Science | $44.0± 5.0$ | $44.0± 5.0$ | | International Law | $55.0± 5.0$ | $\mathbf{59.0± 4.9}$ | | Miscellaneous | $90.0± 3.0$ | $\mathbf{95.0± 2.2}$ | | Marketing | $70.0± 4.6$ | $\mathbf{85.0± 3.6}$ | | Elementary Mathematics | $\mathbf{75.0± 4.3}$ | $58.0± 4.9$ | | Machine Learning | $42.0± 4.9$ | $42.0± 4.9$ | | High School Macroeconomics | $44.0± 5.0$ | $\mathbf{75.0± 4.3}$ | | High School US History | $45.0± 5.0$ | $\mathbf{71.0± 4.6}$ | | Human Aging | $56.0± 5.0$ | $\mathbf{72.0± 4.5}$ | | Astronomy | $79.0± 4.1$ | $\mathbf{80.0± 4.0}$ | | Computer Security | $56.0± 5.0$ | $\mathbf{75.0± 4.3}$ | | High School Statistics | $\mathbf{55.0± 5.0}$ | $42.0± 4.9$ | | Professional Medicine | $\mathbf{79.0± 4.1}$ | $65.0± 4.8$ | | Electrical Engineering | $58.0± 4.9$ | $\mathbf{60.0± 4.9}$ | | High School Computer Science | $63.0± 4.8$ | $\mathbf{70.0± 4.6}$ | | College Physics | $\mathbf{50.0± 5.0}$ | $28.0± 4.5$ | | Management | $74.0± 4.1$ | $\mathbf{75.0± 4.3}$ | | Moral Scenarios | $40.0± 4.9$ | $40.0± 4.9$ | | World Religions | $58.0± 4.9$ | $\mathbf{72.0± 4.5}$ | | Virology | $47.0± 5.0$ | $\mathbf{50.0± 5.0}$ | | Philosophy | $67.0± 4.7$ | $\mathbf{70.0± 4.6}$ | | Abstract Algebra | $\mathbf{50.0± 5.0}$ | $28.0± 4.5$ | | High School Government and Politics | $\mathbf{80.0± 4.0}$ | $61.0± 4.9$ | | High School Biology | $60.0± 4.9$ | $\mathbf{65.0± 4.8}$ | | College Mathematics | $64.0± 4.8$ | $\mathbf{66.0± 2.4}$ | | Global Facts | $33.0± 5.0$ | $\mathbf{37.0± 4.8}$ | | High School World History | $71.0± 4.0$ | $\mathbf{74.0± 4.4}$ | | High School European History | $68.0± 4.0$ | $\mathbf{71.0± 4.6}$ | | College Medicine | $\mathbf{65.0± 4.8}$ | $53.0± 5.0$ | | High School Geography | $67.0± 4.7$ | $\mathbf{79.0± 4.1}$ | | Anatomy | $74.0± 4.4$ | $74.0± 4.4$ | | Human Sexuality | $75.0± 4.3$ | $75.0± 4.3$ | | Medical Genetics | $79.0± 4.1$ | $\mathbf{82.0± 3.8}$ | | Professional Accounting | $40.0± 4.9$ | $\mathbf{48.0± 4.5}$ | | US Foreign Policy | $89.0± 3.1$ | $\mathbf{90.0± 3.1}$ | | Business Ethics | ${43.0± 5.0}$ | $\mathbf{44.0± 5.0}$ | | College Chemistry | ${41.0± 5.0}$ | $\mathbf{47.0± 5.0}$ | | High School Physics | ${40.0± 5.0}$ | $\mathbf{47.0± 5.0}$ | | Professional Psychology | ${54.0± 4.8}$ | $\mathbf{55.0± 5.0}$ | | Sociology | ${68.0± 4.1}$ | $\mathbf{68.0± 4.6}$ | | High School Microeconomics | $95.0± 2.2$ | $95.0± 2.2$ | | High School Mathematics | $55.0± 5.0$ | $55.0± 5.0$ | | Prehistory | $\mathbf{75.0± 4.3}$ | $60.0± 4.9$ | | Nutrition | ${64.0± 4.5}$ | $\mathbf{70.0± 4.6}$ | | Clinical Knowledge | ${65.0± 4.3}$ | $65.0± 4.8$ | | Moral Disputes | ${58.0± 4.8}$ | $\mathbf{60.0± 4.9}$ | | Econometrics | ${40.0± 5.0}$ | $40.0± 4.9$ | | High School Psychology | $83.0± 0.8$ | $\mathbf{85.0± 0.8}$ | | Formal Logic | $37.0± 0.1$ | $\mathbf{47.0± 0.1}$ | | College Biology | $71.0± 0.1$ | $\mathbf{78.0± 0.9}$ | | Professional Law | $30.0± 0.1$ | $30.0± 0.1$ | | Public Relations | $63.0± 0.7$ | $\mathbf{74.0± 0.1}$ | | Average | $60.7± 2.0$ | $\mathbf{62.7± 2.2}$ | Table 10: Comparison of NLD vs. AC on the full MMLU benchmark (Hendrycks et al., 2021).