What symbolic format should an LLM emit for reliable 3D scene editing from natural language, and does algebraic structure help beyond compact syntax? We evaluate Conformal Geometric Algebra (CGA) as a compact symbolic interface against a verbose Euclidean 4$\times$4 matrix baseline and a non-CGA Compact SE3 control in a natural-language 3D editing pipeline with controlled prompting and deterministic geometric execution. Our primary result is compositional fidelity under sequential instruction chains. In a sequence-stress protocol (20 templates, 6 trials each; $\texttt{n=120}$ outputs per method), Simple CGA and Compact SE3 both achieve 100% parse validity, but Simple CGA preserves exact ordered operation chains more reliably (97.5% vs 90.0%, two-proportion $\texttt{p=0.016}$) with lower completion-token cost (112.6 vs 133.6 tokens). This pattern is consistent with algebraic expression form supporting compositional faithfulness beyond compactness alone. A second result is confirmatory in the powered hard semantic suite ($\texttt{n=100}$ per method): compact representations (Simple CGA 45.0%, Compact SE3 42.0%, Shenlong 44.0%) all exceed the Euclidean 4$\times$4 baseline (24.0%). Simple CGA vs Euclidean is +21 pp ($\texttt{p=0.0028}$) and Compact SE3 vs Euclidean is +18 pp ($\texttt{p=0.0103}$), while Simple CGA vs Compact SE3 is statistically close ($\texttt{p=0.7755}$). Separating parse validity from geometric correctness reveals substantial optimization headroom invisible to syntax-only metrics. Overall, compact symbolic interfaces appear to drive reliability-cost gains, with CGA motor composition providing an additional advantage on ordered instruction chains. These findings inform real-time natural-language editing in immersive and interactive 3D environments.

翻译：大语言模型（LLM）应输出何种符号格式以实现可靠的自然语言3D场景编辑？代数结构在紧凑语法之外是否具有额外优势？我们以共形几何代数（CGA）为紧凑符号接口，在受控提示与确定性几何执行的自然语言3D编辑管线中，将其与冗长的欧几里得4×4矩阵基线及非CGA紧凑SE3控制项进行对比评估。核心指标为序列指令链下的组合忠实度。在序列压力测试协议（20个模板，每模板6次实验；各方法n=120个输出）中，Simple CGA与Compact SE3均实现100%解析有效性，但Simple CGA更可靠地保留了精确有序操作链（97.5% vs 90.0%，双比例检验p=0.016），且完成令牌成本更低（112.6 vs 133.6个令牌）。该模式表明代数表达式形式对组合忠实度的支持超越了紧凑性本身。第二项结果在强化语义测试集（各方法n=100）中得到验证：紧凑表示（Simple CGA 45.0%，Compact SE3 42.0%，Shenlong 44.0%）均超越欧几里得4×4基线（24.0%）。Simple CGA相较欧几里得提升21个百分点（p=0.0028），Compact SE3提升18个百分点（p=0.0103），而Simple CGA与Compact SE3之间无显著差异（p=0.7755）。将解析有效性与几何正确性分离后，发现仅通过语法指标无法体现的巨大优化空间。总体而言，紧凑符号接口可驱动可靠性-成本增益，其中CGA马达组合在有序指令链上提供额外优势。这些发现为沉浸式与交互式3D环境中的实时自然语言编辑提供了决策依据。