摘要：大语言模型正越来越多地被部署在需要同时遵守多项明确约束的场景中——包括推理结构、安全边界和输出模式。模型能够熟练处理单项约束，但对于必须同时满足多项约束的组合场景，目前仍缺乏系统刻画：性能下降有多快、由什么因素主导，以及能否缓解这种坍塌？我们提出约束饱和评估（Constraint Saturation Evaluation，CSE），这是一个程序化生成的基准测试，可系统性地改变同时存在的约束数量（k）。每项约束均由确定性的、基于规则的验证器评分，完全不涉及 LLM 评审：覆盖 15 个模型、36 类约束，并在 k=1-12 范围内进行了 369,753 次检查。研究得出三项发现。第一，单项约束通过率会渐进且可预测地下降，但满足全部 k 项约束的概率会迅速坍塌——一个在 k=8 时单项约束通过率约为 41% 的模型，同时满足全部八项约束的成功率仅为 5.7%。第二，各类约束的退化并不相同：每增加一项约束，结构性约束损失的基线能力是词汇性约束的 2 倍；这种差异可由“理解—维持差距”排序，该差距区分了需要持续追踪的约束与不受组合影响的二元决策类约束。第三，失败事件近乎相互独立，这正是错误累积呈乘法效应的原因；确实存在的残余耦合则与共享的输出特征相关，而非成对干扰——例如，错误的句子数量会导致每一项读取该数量的约束都失败。当同时约束超过 5 至 6 项时，可靠的指令遵循能力开始失效：最强模型在 7 项约束时的探针级成功率降至 50% 以下；在 15 个模型中，有 12 个在约束数量不超过 3 项时就已低于这一水平。

Abstract:Large language models are increasingly deployed in settings that require simultaneous adherence to multiple explicit constraints - reasoning structure, safety boundaries, output schemas. Individual constraints are handled proficiently, but the compositional regime, where many must hold jointly, remains poorly characterized: how rapidly does performance degrade, what governs the degradation, and can the collapse be mitigated? We introduce Constraint Saturation Evaluation (CSE), a procedurally generated benchmark that systematically varies the number of simultaneous constraints (k), with every constraint scored by a deterministic, rule-based verifier and zero LLM-judge involvement: 15 models, 36 constraint types, 369,753 checks at k=1-12. Three findings emerge. First, per-constraint pass rate decays gradually and predictably, while the chance of satisfying all k constraints collapses - a model passing individual constraints at ~41% at k=8 succeeds on all eight just 5.7% of the time. Second, constraints do not degrade equally: structural constraints lose 2x more baseline capability per added constraint than lexical ones, ordered by a comprehension-maintenance gap that separates constraints requiring sustained tracking from binary decisions immune to composition. Third, failures are nearly independent, which is what makes the accumulation multiplicative; the residual coupling that does exist tracks shared output features rather than pairwise interference - a wrong sentence count fails every constraint that reads it. Reliable instruction following breaks down beyond 5-6 simultaneous constraints: probe-level success falls below 50% at 7 constraints for the strongest model, and at 3 or fewer for 12 of 15.