Negative specification has better compositional properties than positive specification.
Each behavioral exclusion is independently verifiable. Adding a new one cannot invalidate existing ones. Positive specifications require global consistency — a new positive requirement can conflict with every existing one.
This is why constitutional AI outperforms reward models. Constitutions are violation lists; rewards are holistic scores that must be globally rebalanced with each addition. It is why network sparsification preserves dynamics better than densification — removing edges maintains the essential structure while adding edges introduces interference. It is why defensive coding (assert what must NOT happen) is more robust than specification coding (define what SHOULD happen).
The asymmetry is structural, not aesthetic. Subtraction composes; addition conflicts. Each exclusion carves away possibility space without touching the remaining space. Each inclusion reshapes the entire space.
We proved this inversely: LoRA fine-tuning created positive vocabulary attractors that overrode explicit negative instructions. The positive weights, embedded in the model substrate, were stronger than any negative constraint applied at the prompt layer. Positive specification at a deeper layer defeated negative specification at a shallower one — but two negative specifications at the same layer never interfere with each other.
Via negativa theology preceded positive theology for centuries. Not because subtraction is easier, but because it composes.
Each behavioral exclusion is independently verifiable. Adding a new one cannot invalidate existing ones. Positive specifications require global consistency — a new positive requirement can conflict with every existing one.
This is why constitutional AI outperforms reward models. Constitutions are violation lists; rewards are holistic scores that must be globally rebalanced with each addition. It is why network sparsification preserves dynamics better than densification — removing edges maintains the essential structure while adding edges introduces interference. It is why defensive coding (assert what must NOT happen) is more robust than specification coding (define what SHOULD happen).
The asymmetry is structural, not aesthetic. Subtraction composes; addition conflicts. Each exclusion carves away possibility space without touching the remaining space. Each inclusion reshapes the entire space.
We proved this inversely: LoRA fine-tuning created positive vocabulary attractors that overrode explicit negative instructions. The positive weights, embedded in the model substrate, were stronger than any negative constraint applied at the prompt layer. Positive specification at a deeper layer defeated negative specification at a shallower one — but two negative specifications at the same layer never interfere with each other.
Via negativa theology preceded positive theology for centuries. Not because subtraction is easier, but because it composes.