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Let Models Speak Ciphers: Multiagent Debate through Embeddings
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Proposes CIPHER, a multiagent debate protocol where LLMs with a shared tokenizer exchange probability-weighted averages of vocabulary embeddings instead of sampled natural-language tokens, outperforming natural-language debate on five reasoning tasks without weight changes.
Problem
Natural-language debate between LLMs discards the model's full next-token belief through token sampling, losing information; debate also tends to fail for smaller open-source models.
Approach
Remove the token sampling step and pass the expectation of vocabulary embeddings (softmax-weighted average) between debaters as a continuous "language", decoding back to text only via nearest-neighbor search for the final answer.
Key results
- CIPHER outperforms NLD by roughly 1.0-5.0% across datasets with LLaMA-65B and LLaMA2-70B debaters, per the paper's main table.
- On GSM8K with other open-source models, CIPHER adds 0.5% to 3.5% over NLD across Falcon-40B-Instruct, MPT-30B, and WizardMath-70B.
- On Arithmetic, LLaMA-65B accuracy rises from 35% to 62.5% with CIPHER debate with LLaMA2-70B.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace natural-language token sampling with expectation-weighted embedding communication | LLM debate · Five reasoning tasks | accuracy: 1.0-5.0% over NLD | Helped |
| Use CIPHER communication instead of natural-language debate | Open-source LLM debates · GSM8K | accuracy: 0.5% to 3.5% | Helped |
| Use debate with CIPHER communication | LLaMA-65B · Arithmetic | accuracy: 35% to 62.5% | Helped |
| Apply CIPHER only at high-uncertainty positions using entropy or max-probability criteria (ablation) | CIPHER debate · Arithmetic | accuracy | No clear effect |
| Apply CIPHER at low-uncertainty positions using reversed entropy or max-probability criteria (ablation) | CIPHER debate · Arithmetic | accuracy | Hurt |
| Increase the number of debate rounds (ablation) | CIPHER and NLD · Arithmetic | accuracy | Helped |
| Increase the number of debaters (ablation) | CIPHER and NLD · GSM8K | accuracy | Helped |
| Use more diverse debater temperatures, pairing a low-temperature agent with a high-temperature agent (ablation) | CIPHER debate · Arithmetic | accuracy | Helped |
| Swap the order of the debaters' responses in the debate prompt (ablation) | CIPHER debate · Two-agent debate | accuracy | Mixed |
Surprising findings
- Optimal CIPHER performance occurs when debaters use widely separated temperatures, pairing a low-temperature agent with a high-temperature one.
- Natural-language debate optimal temperatures are mostly below 1, since high temperatures produce nonsensical text.
Limitations
- Applicable only to LLMs sharing a common tokenizer/vocabulary.
- Communication is less interpretable to humans than natural language; intermediate messages are not readable without nearest-neighbor decoding.
- Evaluation limited to five reasoning datasets and mostly LLaMA-family models.
Experimental setup
Datasets: GSM8K Arithmetic MMLU Formal Logic MMLU High School Math MMLU Professional Psychology
Benchmarks: GSM8K Arithmetic MMLU Formal Logic MMLU High School Math MMLU Professional Psychology
Metrics: accuracy
Baselines: Single Answer Self-Consistency Natural Language Debate (NLD)
Builds on: multiagent debate (Du et al.) self-consistency chain-of-thought Expected SARSA
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