Echo State Networks (Jaeger and Haas, 2004) are an efficient class of recurrent models under the framework of Reservoir Computing (Lukoševičius and Jaeger, 2009), where the recurrent part of the model ("reservoir") is carefully initialized and then left untrained (Gallicchio and Micheli, 2011). The only weights that are trained are part of a usually simple readout layer 1 . Echo State Networks were originally designed to work on sequences, however it has been shown how to extend them to deal with recursively structured data, and 1 Trained in closed form, e.g. by Moore-Penrose pseudoinversion, or Ridge Regression. 20.27% 19.86% 9.45% 5.35% 5.13% 4.11%
3.54% 3.33% 2.80% 2.57%
2.18% 2.16% 2.03% 1.94% 1.78%
1.67% 1.55% 1.52% 1.49% 1.39%
1.37% 1.28% 1.12% 1.07% 1.06%
Figure 1: Emojis under consideration and their frequency within the dataset.
trees in particular, with Tree Echo State Networks (Gallicchio and Micheli, 2013), also referred to as TreeESNs.
We follow this approach for solving the ITAmoji task in the EVALITA 2018 competition (Ronzano et al., 2018). In particular, we parse the input texts into trees resembling the grammatical structure of the sentences, and then we use multiple TreeESN models to process the parse trees and make predictions. We then merge these models by using an ensemble to make our final predictions.
Given a set of Italian tweets, the goal of the ITAmoji task is to predict the most likely emoji associated with each tweet. The dataset contains 250,000 tweets in Italian, each of them originally containing only one (possibly repeated) of the 25 emojis considered in the task (see Figure 1). The emojis are removed from the sentences and used as targets.
The test dataset contains 25,000 tweets similarly processed.
The provided dataset has been shuffled and split into a training set (80%) and a validation set (20%).
We preprocessed the data by first removing any URL from the sentences, as most of them did not contain any informative content (e.g. "https://t.co/M3StiVOzKC"). We then parsed the sentences by using two different parsers for the Italian language: Tint2 (Palmero Aprosio and Moretti, 2016) and spaCy (Honnibal and Johnson, 2015). This produced two sets of trees, both including information about the dependency relations between the nodes of each tree. We finally replace each word with its corresponding pretrained FastText embedding (Joulin et al., 2016).
Our ensemble is composed by 13 different models, 12 of which are TreeESNs and the other one is a Long Short-Term Memory (LSTM) over characters. Different random initializations ("trials") of the model parameters are all included in the ensemble in order to enrich the diversity of the hypotheses. We summarize the entire configuration in Table 1.
The TreeESN that we are using is a specialization of the description given by Gallicchio and Micheli (2013), and the reader can refer to that work for additional details. Here, the state corresponding to node n of an input tree t is computed as:
(1) where u(n) is the label of node n in the input tree, k is the number of children of node n, ch i (n) is the i-th child of node n, W in is the input-toreservoir weight matrix, Ŵn i is the recurrent reservoir weight matrix associated to the grammatical relation between node n and its i-th child, and f is the element-wise applied activation function of the reservoir units (in our case, it is a tanh). All matrices in Equation 1 are left untrained.
Note that Equation 1 determines a recursive application (bottom-up visit) over each node of the tree t until the state for all nodes is computed, which we can express in structured form as x(t). The resulting tree x(t) is then mapped into a fixedsize feature representation via the χ state mapping function. We make use of mean and sum state mapping functions, respectively yielding the mean and the sum of all the states. The result, χ(x(t)), is then projected into a different space by a matrix W φ :
where f φ is an activation function.
For the readout we use both a linear regression approach with L2 regularization known as Ridge regression (Hoerl and Kennard, 1970) and a multilayer perceptron (MLP):
where y ∈ R 25 is the output vector, which represents a score for each of the classes: the index with the highest value corresponds to the most likely class.
The CharLSTM model uses a bidirectional LSTM (Hochreiter and Schmidhuber, 1997; Graves and Schmidhuber, 2005) with 2 layers, which takes as input the characters of the sentences expressed as pretrained character embeddings of size 300. The LSTM output is then fed into a linear layer with 25 output units.
Similar models have been used in recent works related to emoji prediction, see for example the model used by Barbieri et al. (2017), or the one by Baziotis et al. (2018), which is however a more complex word-based model.
We take into consideration two different ensembles, both containing the models in Table 1, but with different strategies for weighting the N P predictions. In the following, let Y ∈ R N P ×25 be the matrix containing one prediction per row.
The weights for the first ensemble (corresponding to the run file run1.txt) have been produced by a random search: at each iteration we compute a random vector w ∈ R N P with entries sampled from a random variable W 2 , W ∼ U[0, 1]. near-zero weights. After selecting the best configuration on the validation set, the predictions from each of the models are merged together in weighted mean:
For the second type of ensemble (corresponding to the run file run2.txt) we adopt a multilayer perceptron. We feed as input the N P predictions concatenated into a single vector y (1...N P ) ∈ R 25N P , so that the model is:
where the hidden layer has size 259 and the output layer is composed by 25 units.
In both types of ensemble, as before, the output vector contains a score for each of the classes, providing a way to rank them from the most to the least likely. The most likely class c is thus computed as c = arg max i ȳi .
The training algorithm differs based on the kind of model taken under consideration. We address each of them in the following paragraphs.
Models 1-6 The first six models are TreeESNs using a multilayer perceptron as readout. Given the fact that the main evaluation metric for the competition is the Macro F-score, each of the models has been trained by rebalancing the frequencies of the different target classes. In particular, the sampling probability for each input tree has been skewed so that the data extracted during training follows a uniform distribution with respect to the target class. For the readout part we use the Adam algorithm (Kingma and Ba, 2015) for the stochastic optimization of the multi-class cross entropy loss function.
Models 7-10 Models from 7 to 10 are again TreeESNs, but with a Ridge Regression readout. In this case, 25 classifiers are trained with a 1-vs-all method, one for each class, using binary targets.
Models 11-12 Models 11 and 12 are again TreeESNs with a Ridge Regression readout, but they are trained to distinguish only between the most frequent class, the second most frequent class and all the other classes aggregated together. This is done to try to improve the ensemble precision and recall for the top two classes.
Model 13 The last model is a sequential LSTM over character embeddings. Like in the first 6 models, the Adam algorithm is used to optimize the cross entropy loss function.
The ensemble seems to bring a substantial improvement to the performance on the validation set, as highlighted in Table 2. This is possible thanks to the number and diversity of the different models, as we can see in Figure 2 where we show the Pearson correlation coefficients between the predictions of the models in the ensemble.
On the test set we scored substantially lower, 2018). In Figure 3 we report the confusion matrix (with values normalized over the columns to address label imbalance) and the accuracy over the top-N classes.
An interesting characteristic of this approach, though, is computation time: we were able to train a TreeESN with 5000 reservoir units over 200,000 trees in just about 25 minutes, and this is without exploiting parallelism between the trees.
In ITAmoji 2018, our team ranked 3 rd out of 5. Detailed results and rankings are available at http://bit.ly/ITAmoji18.
Different authors have highlighted the difference in performance between SVM models and (deep) neural models for emoji prediction, and more in general for text classification tasks, suggesting that simple models like SVMs are more able to capture the features which are most important for generalization: see for example the reports of the SemEval-2018 participants C ¸öltekin and Rama (2018) and Coster et al. (2018).
In this work, instead, we approached the problem from the novel perspective of reservoir computing applied to the grammatical tree structure of the sentences. Despite a significant performance drop on the test set3 we showed that, paired with a rich ensemble, the method is comparable to the results obtained in the past by other participants in similar competitions using very different models.