用数学符号压缩大模型指令，省 token 又提速。
Semantic Compression of LLM Instructions via Symbolic Metalanguages
- 用 ∈、⇒ 等符号替代文字指令，模型可直接理解
- 平均减少 62%-81% 的 token，API 用更省钱，本地部署更快
- 小模型符号理解差，大模型如 Kimi K2 能完美执行
我们提出 MetaGlyph，一种用数学符号（如 ∈ 表示成员关系，⇒ 表示蕴含）编码指令的符号语言，替代传统自然语言提示。这些符号基于模型训练数据已具备语义理解能力，无需额外教学即可作为指令捷径。在 3B-1T 参数规模的八种模型上测试，涵盖开源本地部署与专有 API 两种场景。结果显示，所有任务类型中均实现 62%-81% 的 token 减少；对 API 用户，直接降低推理成本；对本地部署，减少延迟与内存压力。性能因模型而异：Gemini 2.5 Flash 在选择任务中实现 75% 语义等价性，∈ 符号识别率达 49.9%；Kimi K2 达到 98.1% ⇒ 符号精度，且符号提示下选择任务准确率 100%；GPT-5.2 Chat 拥有最高 ∈ 精度（91.3%），但解析成功率波动较大；Claude Haiku 4.5 实现 100% 解析成功率，但 ∈ 精度仅 26%。中等规模模型（7B-12B）符号识别率接近零，表明存在规模与指令调优偏见之间的倒 U 型关系。
原文摘要 · Abstract (English)
We introduce MetaGlyph, a symbolic language for compressing prompts by encoding instructions as mathematical symbols rather than prose. Unlike systems requiring explicit decoding rules, MetaGlyph uses symbols like $\in$ (membership) and $\Rightarrow$ (implication) that models already understand from their training data. We test whether these symbols work as ''instruction shortcuts'' that models can interpret without additional teaching. We evaluate eight models across two dimensions relevant to practitioners: scale (3B-1T parameters) and accessibility (open-source for local deployment vs. proprietary APIs). MetaGlyph achieves 62-81% token reduction across all task types. For API-based deployments, this translates directly to cost savings; for local deployments, it reduces latency and memory pressure. Results vary by model. Gemini 2.5 Flash achieves 75% semantic equivalence between symbolic and prose instructions on selection tasks, with 49.9% membership operator fidelity. Kimi K2 reaches 98.1% fidelity for implication ($\Rightarrow$) and achieves perfect (100%) accuracy on selection tasks with symbolic prompts. GPT-5.2 Chat shows the highest membership fidelity observed (91.3%), though with variable parse success across task types. Claude Haiku 4.5 achieves 100% parse success with 26% membership fidelity. Among mid-sized models, Qwen 2.5 7B shows 62% equivalence on extraction tasks. Mid-sized open-source models (7B-12B) show near-zero operator fidelity, suggesting a U-shaped relationship where sufficient scale overcomes instruction-tuning biases.
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