Autoregressive training requires that the computation at each position ignore future tokens. Causal masking enforces this for self-attention, but efficient training recipes can still break causality when they compute shared statistics across the sequence dimension. We study two such operations: structured activation sparsity and block-scaled activation quantization. Applying these operators along the sequence dimension is attractive for hardware efficiency and can look harmless, but it can break causality when the mask or scale applied to a past token depends on future activations. We show that models do exploit this dependency: the training objective continues to improve under the non-causal operator, but causal validation degrades when the future-dependent computation is removed. We analyze why mitigations that keep the operator in the forward pass can postpone or weaken exploitation, but cannot remove the future-to-past dependency. The solution is to remove non-causal statistics from the forward computation used for prediction, and we show that existing sparsity and quantization recipes do respect this rule, though causality was not an explicit design decision.