You will be shown sections from a scientific research paper, together with a question about the paper. Your task is to answer the question based on the contents of the paper. Your response should be a `json` object with two fields:

"answer": An array of strings extracted directly from the paper which, collectively, answer the question.
"evidence": An array of strings. Each should be an excerpt from the paper, in which one or more of the extracted answers can be found.

For instance, for the question "What baselines did the authors compare against?", a sample response might be:

{
  "answer": ["BERT", "RoBERTa"],
  "evidence": ["In our experiments, we compare the performance of our model against BERT and RoBERTa."]
}

Do not include any text in your response other than the json.

If the question is unanswerable given the provided excerpts, respond with the single word "null".

Paper: Dynamic Compositional Neural Networks over Tree Structure

Tree-structured neural networks have proven to be effective in learning semantic representations by exploiting syntactic information. In spite of their success, most existing models suffer from the underfitting problem: they recursively use the same shared compositional function throughout the whole compositional process and lack expressive power due to inability to capture the richness of compositionality. In this paper, we address this issue by introducing the dynamic compositional neural networks over tree structure (DC-TreeNN), in which the compositional function is dynamically generated by a meta network. The role of meta-network is to capture the metaknowledge across the different compositional rules and formulate them. Experimental results on two typical tasks show the effectiveness of the proposed models.

Introduction
Learning the distributed representation for long spans of text from its constituents has been a key step for various natural language processing (NLP) tasks, such as text classification BIBREF0 , BIBREF1 , semantic matching BIBREF2 , BIBREF3 , and machine translation BIBREF4 . Existing deep learning approaches take a compositional function with different forms to compose word vectors recursively until obtaining a sentential representation. Typically, these compositional functions involve recurrent neural networks BIBREF5 , BIBREF6 , convolutional neural networks BIBREF7 , BIBREF8 , and tree-structured neural networks BIBREF9 , BIBREF10 .
Among these methods, tree-structured neural networks (Tree-NNs) show theirs superior performance in many NLP tasks BIBREF11 , BIBREF12 . Following the syntactic tree structure, Tree-NNs assign a fixed-length vector to each word at the leaves of the tree, and combine word and phrase pairs recursively to create intermediate node vectors, eventually obtaining one final vector to represent the whole sentence.
However, these models have a major limitation in their inability to fully capture the richness of compositionality BIBREF13 . The same parameters are used for all kinds of semantic compositions, even though the compositions have different characteristics in nature. For example, the composition of the adjective and the noun differs significantly from the composition of the verb and the noun. Moreover, many semantic phenomena, such as semantic idiomaticity or transparency, call for more powerful compositional mechanisms BIBREF14 . Therefore, Tree-NNs suffer from the underfitting problem.
To alleviate this problem, some researchers propose to use multiple compositional functions, which are arranged beforehand according to some partition criterion BIBREF11 , BIBREF13 , BIBREF15 . Intuitively, using different parameters for different types of compositions has the potential to greatly reduce underfitting. BIBREF13 [ BIBREF13 ] defined different compositional functions in terms of syntactic categories, and a suitable compositional function is selected based on the syntactic categories. BIBREF15 [ BIBREF15 ] introduced multiple compositional functions and during compositional phase, a proper one is selected based on the input information. Although these models accomplished their mission to a certain extent, they still suffer from the following three challenges. First, the predefined compositional functions cannot cover all the compositional rules; Second, they require more learnable parameters, suffering from the problem of overfitting; Third, it is difficult to determine a universal criterion for semantic composition based solely on syntactic categories.
In this paper, we propose dynamic compositional neural networks over tree structure, in which a meta network is used to generate the context-specific parameters of a dynamic compositional network. Specifically, we construct our models based on two kinds of tree-structured neural networks: recursive neural network (Tree-RecNN) BIBREF11 and tree-structure long short-term memory neural network (Tree-LSTM) BIBREF9 . Our work is inspired by recent work on dynamic parameter prediction BIBREF16 , BIBREF17 , BIBREF18 . The meta network is used to extract the shared meta-knowledge across different compositional rules and to dynamically generate the context-specific compositional function. Thus, the compositional function of our models varies with positions, contexts and samples. The dynamic compositional network then applies those context-specific parameters to the current input information. Both meta and dynamic networks are differentiable such that the overall networks can be trained in an end-to-end fashion. Additional, to reduce the complexity of the whole networks, we define the dynamic weight matrix in a manner simulating low-rank matrix decomposition.
We evaluate our models on two typical tasks: text classification and text semantic matching. The results show that our models are more expressive due to their learning to learn nature, yet without increasing the number of model's parameters. Moreover, we find certain composition operations can be learned implicitly by meta TreeNN, such as the composition of noun phrases and verb phrases.
The contributions of the paper can be summed up as follows.

Tree LSTM
Tree LSTM BIBREF9 is a generalization of LSTMs to tree-structured network topologies. In this model, the compositional function is an LSTM unit, and the hidden state $h_j$ of each node can be computed as follows: we refer to $\mathbf {h}_{j}$ and $\mathbf {c}_{j}$ as the hidden state and memory cell of each node $j$ . The transition equations of node $j$ are as follows: 
$$\begin{bmatrix}
\mathbf {\tilde{c}}_{j} \\
\mathbf {o}_{j} \\
\mathbf {i}_{j} \\
\mathbf {f}_{j}^{l} \\
\mathbf {f}_{j}^{r}
\end{bmatrix}
&=
\begin{bmatrix}
\tanh \\
\sigma \\
\sigma \\
\sigma \\
\sigma \end{bmatrix}
\left(
\mathbf {W}
\begin{bmatrix}
\mathbf {x}_{j} \\
\mathbf {h}_{j}^{l} \\
\mathbf {h}_{j}^{r} \\
\end{bmatrix} + \mathbf {b} \right),\\
\mathbf {c}_{j} &=
\mathbf {\tilde{c}}_{j} \odot \mathbf {i}_{j}
+ \mathbf {c}_{j}^{l} \odot \mathbf {f}_{j}^{l}+ \mathbf {c}_{j}^{r} \odot \mathbf {f}_{j}^{r} , \\
\mathbf {h}_{j} &= \mathbf {o}_{j} \odot \tanh \left( \mathbf {c}_{j} \right),$$   (Eq. 8) 
 where $\mathbf {x}_j \in \mathbb {R}^{d}$ denotes the input vector and is non-zero if and only if it is a leaf node. The superscript $l$ and $r$ represent the left child and right child respectively. $\sigma $ represents the logistic sigmoid function and $\odot $ denotes element-wise multiplication. $\mathbf {W} \in \mathbb {R}^{5d \times 3d}$ and $\mathbf {b} \in \mathbb {R}^{5d}$ are learnable parameters.

Meta Network for RecNN
For RecNN, we replace the static parameters $\mathbf {W}$ and $\mathbf {b}$ in Eq.( 5 ) with the dynamic parameters $\mathbf {W}(\mathbf {z}_{j})$ and $\mathbf {b}(\mathbf {z}_{j})$ , which are generated by a meta network. The meta network is a smaller RecNN, and the hidden state $\hat{\mathbf {h}}_{j}\in \mathbb {R}^{m}$ of node $j$ in meta network is defined as 
$$\hat{\mathbf {h}}_{j} &= \tanh \left(
\mathbf {W}_{m}
\mathcal {H}_{j} + \mathbf {b}_{m} \right),\\
\mathbf {z}_{j} &= \mathbf {W}_{z} \hat{\mathbf {h}}_{j}$$   (Eq. 11) 
 where $\mathcal {H}_{j} = \mathbf {h}_{j}^{l}\oplus \mathbf {h}_{j}^{r}\oplus \mathbf {\hat{h}}_{j}^{l}\oplus \mathbf {\hat{h}}_{j}^{r} \in \mathbb {R}^{2m+2d}$ , $\mathbf {W}_{m} \in \mathbb {R}^{m \times (2d+2m)}$ and $\mathbf {b}_{m} \in \mathbb {R}^{m}$ are parameters of meta RecNN; $\mathbf {W}_{z} \in \mathbb {R}^{z \times m}$ is a scale matrix.
To reduce the number of the parameters, we define the dynamic parameters with a low-rank factorized representation of the weights, analogous to the Singular Value Decomposition. The dynamic parameters $\mathbf {W}(\mathbf {z}_{j})$ and $\mathbf {b}(\mathbf {z}_{j})$ of the basic RecNN are computed by: 
$$\mathbf {W}(\mathbf {z}_{j})
&=
\begin{bmatrix}
P_l \mathbf {D}(\mathbf {z}_j)Q_l \\
P_r \mathbf {D}(\mathbf {z}_j)Q_r \\
\end{bmatrix} \\
\mathbf {b}(\mathbf {z}_{j})
&=
\begin{bmatrix}
B_l\mathbf {z}_j \\
B_r\mathbf {z}_j \\
\end{bmatrix}$$   (Eq. 12) 
 where $P \in \mathbb {R}^{d \times z}$ , $Q \in \mathbb {R}^{z \times d}$ , and $\mathbf {D}(\mathbf {z}_t) \in \mathbb {R}^{z \times z}$ is the diagonal matrix of $\mathbf {z}$ .
Thus, our dynamic RecNN needs $(6dz + mz)$ parameters, while the vanilla RecNN has $(2d^2+d)$ parameters. With a small $z$ and $m$ , our dynamic RecNN needs less parameters than the vanilla RecNN. For example, if we set $d =100$ and $z=m=20$ , our model needs $12,400$ parameters while the vanilla model needs $20,100$ parameters.

Text Semantic Matching
Among many natural language processing (NLP) tasks, a common problem is modelling the relevance of a pair of texts. In this section, we show how to effectively use the dynamic compositional neural networks to model the semantic relationship between two sentences.
As shown in Figure 1 , given two sentences $x_a$ and $x_b$ , the representation of each sentence $\mathbf {h}_{R}$ can be computed by one basic TreeNN. 
$$\mathbf {h}_{R}^{(a)} &= \operatornamewithlimits{DC-TreeNN}(\mathbf {x}_R, \mathbf {h}_{R}^l, \mathbf {h}_{R}^r,\theta _{a}) \\
\mathbf {h}_{R}^{(b)} &= \operatornamewithlimits{DC-TreeNN}(\mathbf {x}_R, \mathbf {h}_{R}^l, \mathbf {h}_{R}^r,\theta _{b})$$   (Eq. 21) 
 where $R$ denotes the root node of a tree. $\theta _{a}$ and $\theta _{b}$ are generated by a shared meta TreeNN. Then, the representation of each sentence will be fed into a multi-layer perceptron to obtain a unified representation for the final relationship classification.
The sample-specific but shared meta TreeNN ensures that, on the one hand we can dynamically model the diversity of semantic compositionality, on the other hand we can capture the general rules across different samples.
We choose the dataset of Sentences Involving Compositional Knowledge (SICK), which is proposed by BIBREF30 [ BIBREF30 ] aiming at evaluation of compositional distributional semantic models. The dataset consists of 9927 sentence pairs in a 4500/500/4927 train/dev/test split, in which each sentence pairs are pre-defined into three labels: “entailment”,“contradiction” and “neutral”.
Our results are summarized in Table 4 , where the performance of NBOW, LSTM, RecNN, and RNTN are reported by BIBREF31 , BIBREF32 . For fair comparison, we train our models with the same setting. We can see both DC-RecNN and DC-TreeLSTM outperform competitor models, in which DC-RecNN (DC-TreeLSTM) achieves 3% (2.7%) improvements than RecNN (TreeLSTM). We think this breakthrough is basically attributed to the dynamic compositional mechanism, which enables our models to capture various syntactic patterns (As we will discuss later) therefore can more accurately understand sentences.

Training and Hyperparameters
Given a sentence (or sentence pair) and its label, the output of a neural network is the probabilities of the different classes. The parameters of the network are trained to minimise the cross-entropy of the predicted and true label distributions. To minimize the objective, we use stochastic gradient descent with the diagonal variant of AdaGrad BIBREF20 .
The word embeddings for all of the models are initialized with GloVe vectors BIBREF21 . The other parameters are initialized by randomly sampling from uniform distribution in $[-0.1, 0.1]$ .
The final hyper-parameters are as follows. The initial learning rate is $0.1$ . The regularization weight of the parameters is $1E{-5}$ and the others are listed as Table 1 .
For all the sentences in the datasets, we parse them with constituency parser BIBREF22 to obtain the trees for our models and some competitor models.

Related Work
One thread of related work is the exploration of different kinds of compositional function over tree structures. BIBREF11 [ BIBREF11 ] proposed the recursive neural network with standard compositional function. After that, some extensions are introduced to enhance the expressive power of compositional function, such as MV-RecNN BIBREF23 , SU-RNN BIBREF13 , RNTN BIBREF23 , while these models suffer from the problem of hard-coded compositional operations and overfitting.
Another thread of work is the idea of using one network to direct the learning of another network BIBREF16 . BIBREF33 [ BIBREF33 ] introduce a meta neural network to provide another network with a step size and a direction vector, which is helpful for parameter optimization. BIBREF16 [ BIBREF16 ] propose the dynamic filter network to implicitly learn a variety of filtering operations. BIBREF17 [ BIBREF17 ] introduce a learnet for one-shot learning, which can predict the parameters of a second network given a single exemplar. BIBREF18 [ BIBREF18 ] propose the model hypernetwork, which uses a small network to generate the weights for a larger network.
Different from these models, we employ the idea of parameter generation to address the limitation of weight-sharing or partially sharing paradigm of tree-based compositional models.

Acknowledgments
We would like to thank the anonymous reviewers for their valuable comments and thank Kaiyu Qian, Jiachen Xu, Jifan Chen for useful discussions. This work was partially funded by National Natural Science Foundation of China (No. 61532011 and 61672162), Shanghai Municipal Science and Technology Commission (No. 16JC1420401).

Table 3: Accuracies of our models on five datasets against state-of-the-art neural models. DCNN: Dynamic Convolutional Neural Network [Kalchbrenner et al., 2014; Denil et al., 2014]. CNN-multichannel: Convolutional Neural Network [Kim, 2014].

Question: What tasks do they experiment with?
{"answer": ["text classification and text semantic matching"], "evidence": ["We evaluate our models on two typical tasks: text classification and text semantic matching. The results show that our models are more expressive due to their learning to learn nature, yet without increasing the number of model\u0027s parameters. Moreover, we find certain composition operations can be learned implicitly by meta TreeNN, such as the composition of noun phrases and verb phrases."]}