Semantic Compression of LLM Instructions via Symbolic Metalanguages

TL;DR

MetaGlyph investigates whether pretrained models inherently understand symbolic mathematical instructions to compress prompts without explicit teaching. By comparing natural-language prompts, symbolic MetaGlyph prompts, and meaningless-symbol controls across eight models, the study reports substantial token savings (62-81%) and model-dependent instruction fidelity, with standout results such as $98.1\%$ implication fidelity on Kimi K2 and $91.3\%$ membership fidelity on GPT-5.2 Chat. The findings reveal a nuanced, non-monotonic relationship between model scale and symbolic understanding, including a U-shaped pattern where frontier models recover strong symbolic semantics while mid-sized models can underperform. The work has practical implications for API cost and latency in production and local deployments, while outlining concrete directions for expanding symbolic instruction languages and stress-testing their limits.

Abstract

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.