Challenge: Existing work suggests that the computational capabilities of self-attention to model hierarchical structures are limited.
Approach: They investigate the computational power of self-attention to model formal languages . they show strong theoretical limitations of self attention to model periodic finite-state languages unless the number of layers or heads increases with input length.
Outcome: The proposed models can model periodic finite-state languages, nor hierarchical structure unless the number of layers or heads increases with input length.

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Self-Attention Networks Can Process Bounded Hierarchical Languages (2021.acl-long)

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Challenge: Existing models that can process formal languages with hierarchical structure are limited in their performance.
Approach: They propose to use a subset of Dyck-k with depth bounded by D to train self-attention networks.
Outcome: The proposed model can process Dyck-(k, D) with depth bounded by D, which better captures the hierarchical structure of natural language.
Overcoming a Theoretical Limitation of Self-Attention (2022.acl-long)

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Challenge: Hahn shows that for languages where acceptance depends on a single input symbol, a transformer’s classification decisions get closer and closer to random guessing as input strings get longer and longer.
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Practical Computational Power of Linear Transformers and Their Recurrent and Self-Referential Extensions (2023.emnlp-main)

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Challenge: Recent studies of the computational power of recurrent neural networks reveal a hierarchy of RNN architectures, given finite-precision assumptions.
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On the Ability and Limitations of Transformers to Recognize Formal Languages (2020.emnlp-main)

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Challenge: Existing studies on LSTMs have not revealed their ability to model syntactic properties.
Approach: They propose to build a Transformers model for a subclass of counter languages and find that their learning mechanism strongly correlates with their construction.
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On the Locality of Attention in Direct Speech Translation (2022.acl-srw)

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Challenge: Recent advances in NLP have created problems with the complexity of the self-attention layer.
Approach: They propose to substitute standard self-attention with a local efficient one to avoid the computation of attention weights.
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How Much Attention Do You Need? A Granular Analysis of Neural Machine Translation Architectures (P18-1)

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Challenge: Neural Machine Translation (NMT) has been replaced by convolutional or self-attentional approaches.
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Saturated Transformers are Constant-Depth Threshold Circuits (2022.tacl-1)

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Challenge: Recent work shows that transformers with hard attention are limited in power, but hard attention is a strong assumption.
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Revealing the Dark Secrets of BERT (D19-1)

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Challenge: Existing models of BERT-based learning systems are lacking specific mechanisms that contribute to its success.
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Anisotropy Is Inherent to Self-Attention in Transformers (2024.eacl-long)

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Challenge: despite their success, Transformers models suffer from a representation degeneration problem . anisotropy is a property of hidden representations that makes them unexpectedly close to each other .
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Theoretical Analysis of Hierarchical Language Recognition and Generation by Transformers without Positional Encoding (2025.acl-long)

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Challenge: Existing studies show that Transformers can recognize hierarchical structures without a specific positional encoding.
Approach: They show that Transformers can generate hierarchical languages without a positional encoding . they also suggest that explicit positional encoders might have a detrimental effect on generalization .
Outcome: The proposed model can generate hierarchical languages with respect to model size without encoding .

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