$W_K, W_V$ is probably all you need: On the necessity of the Query, Key and Value weight triplet in encoder-only and decoder-only Transformers

We theoretically investigate whether the Query, Key, Value weight triplet can be reduced in encoder-only and decoder-only transformers. Under mild assumptions, we prove that Query weights are redundant and can be replaced with the identity matrix, reducing attention parameters by 25\%. This also simplifies optimization: attention logits become linear rather than quadratic in learned weights. Validating on decoder-only GPT-style small models trained from scratch, we find that with adjusted attention scaling and weight decay, reduced models match baseline performance despite fewer parameters. Training remains stable at over $3\times$ lower weight decay, suggesting Query weight elimination provides implicit regularization. Our analysis has also led us to a structural expressivity boundary: in the mathematically tractable ReLU setting, skip connections push MLPs into a generically disjoint function class at fixed width. These findings motivate investigation across modalities and at scale, where the observed stability and efficiency gains may prove most consequential.