| Challenge: | Existing theories of expressive power of RNNs are limited. |
| Approach: | They propose a formal hierarchy of the expressive capacity of RNN architectures based on two formal properties: space complexity and rational recurrence. |
| Outcome: | The proposed model is based on the theory of “saturated” RNNs and shows that it obeys a similar hierarchy to unsaturated RNN models. |
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| Challenge: | Existing studies have focused on the expressive power of recurrent neural network LMs to recognize unweighted formal languages. |
| Approach: | They propose to model a strict subset of probabilistic finite-state automata with RNNs . they show that an RNN requires left(N ||right) neurons to represent an LM . |
| Outcome: | The proposed language models can represent a strict subset of probabilistic distributions expressed by finite-state models. |
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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On the Representational Capacity of Recurrent Neural Language Models (2023.emnlp-main)
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| Challenge: | Existing studies have focused on LMs as formal languages, but they do not consider language membership. |
| Approach: | They extend the Turing completeness result to the probabilistic case . they show that a rationally weighted RLM can simulate any deterministic Turing machine . |
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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. |
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How much complexity does an RNN architecture need to learn syntax-sensitive dependencies? (2020.acl-srw)
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| Challenge: | Long-term memory (LSTM) networks are capable of encapsulating long-range dependencies . but simple recurrent networks (SRNs) have been less successful at capturing long-term dependencies and loci of grammatical errors in an unsupervised setting. |
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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. |
| Approach: | They propose a convolutional sequence-to-sequence model that exploits hierarchical information implicitly. |
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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. |
| Approach: | They focus on the single-layer, ReLU-activation, rational-weight RNNs with softmax . they show that most problems for such RNN are undecidable . |
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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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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. |
| Approach: | They propose to use LSTM and Elman-RNN with ReLU activation to study RNNs . they show that LS and ReLU-RNns can easily implement counting behavior . |
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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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