Challenge: recurrent models have been effective in NLP tasks but performance on context-free languages (CFLs) is weak.
Approach: They evaluate the performance of recurrent models on Dyck-n languages . they find that they are expressive enough to recognize Dyck words of arbitrary lengths if their depths are bounded.
Outcome: The proposed models generalize well on Dyck-n languages, while performing poorly on longer test strings.

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On Efficiently Representing Regular Languages as RNNs (2024.findings-acl)

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Challenge: Recent work by Hewitt et al. (2020) provides an interpretation of the empirical success of recurrent neural networks (RNNs) as language models (LMs).
Approach: They generalize their construction and show that RNNs can efficiently represent a larger class of LMs than previously claimed.
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Colorless Green Recurrent Networks Dream Hierarchically (N18-1)

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Challenge: Recurrent neural networks (RNNs) can induce non-trivial properties of language.
Approach: They investigate whether RNNs can track hierarchical syntactic structure . they include nonsensical sentences where RNN cannot rely on semantic cues .
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RNNs can generate bounded hierarchical languages with optimal memory (2020.emnlp-main)

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Challenge: Existing studies have shown that RNNs can efficiently generate bounded hierarchical languages with high syntactic fidelity, but their success is not well-understood theoretically.
Approach: They propose a language of well-nested brackets and m-bounded nesting depth . they prove that an RNN with O(m log k) hidden units suffices, an exponential reduction in memory, by an explicit construction.
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The Importance of Being Recurrent for Modeling Hierarchical Structure (D18-1)

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Challenge: Recent work shows that recurrent neural networks can implicitly capture hierarchical information when trained to solve common natural language processing tasks.
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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.
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Lower Bounds on the Expressivity of Recurrent Neural Language Models (2024.naacl-long)

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Challenge: Recent studies of the representational capacity of neural LMs have focused on their ability to recognize formal languages.
Approach: They propose to connect recurrent neural networks (RNNs) as classifiers to finite-state automatas (FSAs) and a probabilistic FSA to characterize their representational capacity.
Outcome: The proposed models can express arbitrary regular LMs with linearly bounded precision.
Recurrent Neural Networks as Weighted Language Recognizers (N18-1)

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Challenge: Recent experiments show that RNNs outperform other methods in assigning high probability to held-out English text.
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Deep RNNs Encode Soft Hierarchical Syntax (P18-2)

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Challenge: Existing studies show that syntactic information is useful for a wide variety of NLP tasks.
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On the Practical Computational Power of Finite Precision RNNs for Language Recognition (P18-2)

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Challenge: Recurrent Neural Networks (RNNs) are famously known to be Turing complete, but this relies on infinite precision in the states and unbounded computation time.
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Advancing Regular Language Reasoning in Linear Recurrent Neural Networks (2024.naacl-short)

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Challenge: Existing linear recurrent neural networks have been used for natural language and long-range modeling for decades.
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