When LLMs Develop Languages: Symbolic Communication for Efficient Multi-Agent Reasoning

Chain-of-Thought (CoT) improves large language models (LLMs) on difficult reasoning tasks, but it often incurs long natural-language rationales that are poorly aligned with efficient machine reasoning. We propose Communicative Language Symbolism Routing (CLSR), a test-time framework in which multiple LLM agents autonomously invent, evolve, and share compact Language Symbolism Frameworks (LSFs), while a latent-free router adaptively selects and composes these languages per query to optimize the accuracy--token trade-off. Unlike prompt optimization that refines surface instructions, CLSR treats each LSF as a reusable symbolic protocol with compact symbols, usage rules, and a message-passing contract, and improves it through an evolutionary loop driven by correctness and token cost. At inference time, the router may invoke a single low-cost LSF call, ensemble multiple LSFs, or execute a multi-round LSF composition protocol on harder queries. Across challenging benchmarks, CLSR reduces latency-oriented generated token completion by $3\sim 6\times$ compared to standard CoT while maintaining accuracy. We further derive an information-theoretic lower bound on token cost under arbitrary symbolism and show that, under an interpreter-realizability premise, multi-round LSF protocols conditionally subsume program-execution pipelines.

Large language models (LLMs) often solve hard problems by writing long and verbose step-by-step explanations. Practically, these long-text reasoning process can be slow and expensive to generate. In this paper, we ask whether these LLMs can instead invent shorter language symbolism frameworks (LSFs) that are readable for themselves without caring about human readability. These machine-oriented languages might help them reason more efficiently. Our method, called Communicative Language Symbolism Routing (CLSR), lets multiple LLM agents create compact reasoning LSFs, evaluate which LSFs work well, and keep the ones that answer correctly with fewer generated tokens. At inference time, an LLM-based router chooses whether to use one compact LSF, combine several LSFs, or spend more reasoning steps on harder questions. Across several reasoning benchmarks, CLSR keeps accuracy close to standard chain-of-thought reasoning while significantly reducing generated tokens by about three to six times. This results suggests that long natural-language explanations are not always necessary for machine reasoning. An LLM can sometimes use a shorter internal-style protocol instead, rather than those verbose natural languages. The work also gives a theoretical view of why such LLM-invented symbolic protocols can improve the tradeoff between accuracy and token cost. In general, CLSR provides a way to study how AI agents may develop shared communication conventions that are useful for efficient problem solving.