Large language models excel at following individual instructions but struggle dramatically when multiple constraints must be satisfied simultaneously, according to new research that tested 15 models across 369,753 constraint combinations.

The study introduces Constraint Saturation Evaluation (CSE), a benchmark that systematically varies the number of simultaneous constraints from 1 to 12. Models were tested on 36 different constraint types including reasoning structure, safety boundaries, and output formatting requirements.

Performance Collapses Beyond Five Constraints

While models handle individual constraints reasonably well, their ability to satisfy all constraints simultaneously degrades rapidly. A model achieving 41% success on individual constraints at eight total constraints succeeded on all eight just 5.7% of the time.

The strongest models maintain above 50% success rates only up to seven constraints. For 12 of the 15 tested models, this threshold drops to three constraints or fewer.

Structural constraints prove twice as vulnerable to degradation as lexical ones. Constraints requiring sustained tracking throughout a response lose capability faster than binary decisions that can be resolved independently.

Failures Accumulate Multiplicatively

The research reveals that constraint failures operate nearly independently, causing success rates to multiply rather than add. When one constraint fails due to an incorrect output feature like sentence count, every other constraint dependent on that feature also fails.

This multiplicative effect explains why even modest individual constraint failure rates compound into dramatic overall performance drops. The residual coupling between constraints tracks shared output features rather than direct interference between constraint types.

The findings suggest current OpenAI and Anthropic models face fundamental limitations in complex instruction-following scenarios. Enterprise applications requiring multiple simultaneous constraints may need to decompose requirements or accept significantly higher failure rates.

The research indicates reliable multi-constraint instruction following remains an unsolved challenge for current foundation models, with implications for deployment in structured business environments.