You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information from inputs. For modeling long-term dependencies in a dataset, the gating mechanism concept can help RNNs remember and forget previous information. Representing the hidden layers of an RNN with more expressive operations (i.e., tensor products) helps it learn a more complex relationship between the current input and the previous hidden layer information. These ideas can generally improve RNN performances. In this paper, we proposed a novel RNN architecture that combine the concepts of gating mechanism and the tensor product into a single model. By combining these two concepts into a single RNN, our proposed models learn long-term dependencies by modeling with gating units and obtain more expressive and direct interaction between input and hidden layers using a tensor product on 3-dimensional array (tensor) weight parameters. We use Long Short Term Memory (LSTM) RNN and Gated Recurrent Unit (GRU) RNN and combine them with a tensor product inside their formulations. Our proposed RNNs, which are called a Long-Short Term Memory Recurrent Neural Tensor Network (LSTMRNTN) and Gated Recurrent Unit Recurrent Neural Tensor Network (GRURNTN), are made by combining the LSTM and GRU RNN models with the tensor product. We conducted experiments with our proposed models on word-level and character-level language modeling tasks and revealed that our proposed models significantly improved their performance compared to our baseline models.

Cited Abstract(s):
[1]: Recurrent Neural Networks (RNNs) are very powerful sequence models that do not enjoy widespread use because it is extremely difficult to train them properly. Fortunately, recent advances in Hessian-free optimization have been able to overcome the difficulties associated with training RNNs, making it possible to apply them successfully to challenging sequence problems. In this paper we demonstrate the power of RNNs trained with the new Hessian-Free optimizer (HF) by applying them to character-level language modeling tasks. The standard RNN architecture, while effective, is not ideally suited for such tasks, so we introduce a new RNN variant that uses multiplicative (or "gated") connections which allow the current input character to determine the transition matrix from one hidden state vector to the next. After training the multiplicative RNN with the HF optimizer for five days on 8 high-end Graphics Processing Units, we were able to surpass the performance of the best previous single method for character-level language modeling – a hierarchical non-parametric sequence model. To our knowledge this represents the largest recurrent neural network application to date.
On the recurrent neural network-based model, [1] proposed multiplicative RNN (mRNN) for character-level language modeling using tensor as the weight parameters. They proposed two different models. The first selected a slice of tensor weight based on the current character input, and the second improved the first model with factorization for constructing a hidden-to-hidden layer weight. However, those models fail to fully utilize the tensor weight with the tensor product. After they selected the weight matrix based on the current input information, they continue to use linear projection, addition, and nonlinearity for interacting between the input and hidden layers.