  Multi-head self-attention-based Transformers have shown promise in different
learning tasks. Albeit these models exhibit significant improvement in
understanding short-term and long-term contexts from sequences, encoders of
Transformers and their variants fail to preserve layer-wise contextual
information. Transformers usually project tokens onto sparse manifolds and fail
to preserve mathematical equivalence among the token representations. In this
work, we propose TransJect, an encoder model that guarantees a theoretical
bound for layer-wise distance preservation between a pair of tokens. We propose
a simple alternative to dot-product attention to ensure Lipschitz continuity.
This allows TransJect to learn injective mappings to transform token
representations to different manifolds with similar topology and preserve
Euclidean distance between every pair of tokens in subsequent layers.
Evaluations across multiple benchmark short- and long-sequence classification
tasks show maximum improvements of 6.8% and 5.9%, respectively, over the
variants of Transformers. Additionally, TransJect displays 79% better
performance than Transformer on the language modeling task. We further
highlight the shortcomings of multi-head self-attention from the statistical
physics viewpoint. Although multi-head self-attention was incepted to learn
different abstraction levels within the networks, our empirical analyses
suggest that different attention heads learn randomly and unorderly. In
contrast, TransJect adapts a mixture of experts for regularization; these
experts are more orderly and balanced and learn different sparse
representations from the input sequences. TransJect exhibits very low entropy
and can be efficiently scaled to larger depths.
