Interpretability is an important aspect of the trustworthiness of a models predictions. Transformers predictions are widely explained by the attention weights, i.e., a probability distribution generated at its self-attention unit (head). Current empirical studies provide shreds of evidence that attention weights are not explanations by proving that they are not unique. A recent study showed theoretical justifications to this observation by proving the non-identifiability of attention weights. For a given input to a head and its output, if the attention weights generated in it are unique, we call the weights identifiable. In this work, we provide deeper theoretical analysis and empirical observations on the identifiability of attention weights. Ignored in the previous works, we find the attention weights are more identifiable than we currently perceive by uncovering the hidden role of the key vector. However, the weights are still prone to be non-unique attentions that make them unfit for interpretation. To tackle this issue, we provide a variant of the encoder layer that decouples the relationship between key and value vector and provides identifiable weights up to the desired length of the input. We prove the applicability of such variations by providing empirical justifications on varied text classification tasks. The implementations are available at https://github.com/declare-lab/identifiable-transformers.
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