prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. How does their model improve interpretability compared to softmax transformers?
Context 1: Introduction
The Transformer architecture BIBREF0 for deep neural networks has quickly risen to prominence in NLP through its efficiency and performance, leading to improvements in the state of the art of Neural Machine Translation BIBREF1, BIBREF2, as well as inspiring other powerful general-purpose models like BERT BIBREF3 and GPT-2 BIBREF4  At the heart of the Transformer lie multi-head attention mechanisms: each word is represented by multiple different weighted averages of its relevant context  As suggested by recent works on interpreting attention head roles, separate attention heads may learn to look for various relationships between tokens BIBREF5, BIBREF6, BIBREF7, BIBREF8, BIBREF9 
The attention distribution of each head is predicted typically using the softmax normalizing transform  As a result, all context words have non-zero attention weight  Recent work on single attention architectures suggest that using sparse normalizing transforms in attention mechanisms such as sparsemax – which can yield exactly zero probabilities for irrelevant words – may improve performance and interpretability BIBREF12, BIBREF13, BIBREF14  Qualitative analysis of attention heads BIBREF0 suggests that, depending on what phenomena they capture, heads tend to favor flatter or more peaked distributions 
Recent works have proposed sparse Transformers BIBREF10 and adaptive span Transformers BIBREF11  However, the “sparsity" of those models only limits the attention to a contiguous span of past tokens, while in this work we propose a highly adaptive Transformer model that is capable of attending to a sparse set of words that are not necessarily contiguous  Figure FIGREF1 shows the relationship of these methods with ours 
Our contributions are the following:
We introduce sparse attention into the Transformer architecture, showing that it eases interpretability and leads to slight accuracy gains 
We propose an adaptive version of sparse attention, where the shape of each attention head is learnable and can vary continuously and dynamically between the dense limit case of softmax and the sparse, piecewise-linear sparsemax case 
We make an extensive analysis of the added interpretability of these models, identifying both crisper examples of attention head behavior observed in previous work, as well as novel behaviors unraveled thanks to the sparsity and adaptivity of our proposed model 
Background ::: The Transformer
In NMT, the Transformer BIBREF0 is a sequence-to-sequence (seq2seq) model which maps an input sequence to an output sequence through hierarchical multi-head attention mechanisms, yielding a dynamic, context-dependent strategy for propagating information within and across sentences  It contrasts with previous seq2seq models, which usually rely either on costly gated recurrent operations BIBREF15, BIBREF16 or static convolutions BIBREF17 
Given $n$ query contexts and $m$ sequence items under consideration, attention mechanisms compute, for each query, a weighted representation of the items  The particular attention mechanism used in BIBREF0 is called scaled dot-product attention, and it is computed in the following way:
where $\mathbf {Q} \in \mathbb {R}^{n \times d}$ contains representations of the queries, $\mathbf {K}, \mathbf {V} \in \mathbb {R}^{m \times d}$ are the keys and values of the items attended over, and $d$ is the dimensionality of these representations  The $\mathbf {\pi }$ mapping normalizes row-wise using softmax, $\mathbf {\pi }(\mathbf {Z})_{ij} = \operatornamewithlimits{\mathsf {softmax}}(\mathbf {z}_i)_j$, where
In words, the keys are used to compute a relevance score between each item and query  Then, normalized attention weights are computed using softmax, and these are used to weight the values of each item at each query context 
However, for complex tasks, different parts of a sequence may be relevant in different ways, motivating multi-head attention in Transformers  This is simply the application of Equation DISPLAY_FORM7 in parallel $H$ times, each with a different, learned linear transformation that allows specialization:
In the Transformer, there are three separate multi-head attention mechanisms for distinct purposes:
Encoder self-attention: builds rich, layered representations of each input word, by attending on the entire input sentence 
Context attention: selects a representative weighted average of the encodings of the input words, at each time step of the decoder 
Decoder self-attention: attends over the partial output sentence fragment produced so far 
Together, these mechanisms enable the contextualized flow of information between the input sentence and the sequential decoder 
Background ::: Sparse Attention
The softmax mapping (Equation DISPLAY_FORM8) is elementwise proportional to $\exp $, therefore it can never assign a weight of exactly zero  Thus, unnecessary items are still taken into consideration to some extent  Since its output sums to one, this invariably means less weight is assigned to the relevant items, potentially harming performance and interpretability BIBREF18  This has motivated a line of research on learning networks with sparse mappings BIBREF19, BIBREF20, BIBREF21, BIBREF22  We focus on a recently-introduced flexible family of transformations, $\alpha $-entmax BIBREF23, BIBREF14, defined as:
where $\triangle ^d \lbrace \mathbf {p}\in \mathbb {R}^d:\sum _{i} p_i = 1\rbrace $ is the probability simplex, and, for $\alpha \ge 1$, $\mathsf {H}^{\textsc {T}}_\alpha $ is the Tsallis continuous family of entropies BIBREF24:
This family contains the well-known Shannon and Gini entropies, corresponding to the cases $\alpha =1$ and $\alpha =2$, respectively 
Equation DISPLAY_FORM14 involves a convex optimization subproblem  Using the definition of $\mathsf {H}^{\textsc {T}}_\alpha $, the optimality conditions may be used to derive the following form for the solution (Appendix SECREF83):
where $[\cdot ]_+$ is the positive part (ReLU) function, $\mathbf {1}$ denotes the vector of all ones, and $\tau $ – which acts like a threshold – is the Lagrange multiplier corresponding to the $\sum _i p_i=1$ constraint 
Background ::: Sparse Attention ::: Properties of @!START@$\alpha $@!END@-entmax 
The appeal of $\alpha $-entmax for attention rests on the following properties  For $\alpha =1$ (i e , when $\mathsf {H}^{\textsc {T}}_\alpha $ becomes the Shannon entropy), it exactly recovers the softmax mapping (We provide a short derivation in Appendix SECREF89 )  For all $\alpha >1$ it permits sparse solutions, in stark contrast to softmax  In particular, for $\alpha =2$, it recovers the sparsemax mapping BIBREF19, which is piecewise linear  In-between, as $\alpha $ increases, the mapping continuously gets sparser as its curvature changes 
To compute the value of $\alpha $-entmax, one must find the threshold $\tau $ such that the r h s  in Equation DISPLAY_FORM16 sums to one  BIBREF23 propose a general bisection algorithm  BIBREF14 introduce a faster, exact algorithm for $\alpha =1 5$, and enable using $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ with fixed $\alpha $ within a neural network by showing that the $\alpha $-entmax Jacobian w r t  $\mathbf {z}$ for $\mathbf {p}^\star = \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ is
Our work furthers the study of $\alpha $-entmax by providing a derivation of the Jacobian w r t  the hyper-parameter $\alpha $ (Section SECREF3), thereby allowing the shape and sparsity of the mapping to be learned automatically  This is particularly appealing in the context of multi-head attention mechanisms, where we shall show in Section SECREF35 that different heads tend to learn different sparsity behaviors 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax
We now propose a novel Transformer architecture wherein we simply replace softmax with $\alpha $-entmax in the attention heads  Concretely, we replace the row normalization $\mathbf {\pi }$ in Equation DISPLAY_FORM7 by
This change leads to sparse attention weights, as long as $\alpha >1$; in particular, $\alpha =1 5$ is a sensible starting point BIBREF14 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax ::: Different @!START@$\alpha $@!END@ per head 
Unlike LSTM-based seq2seq models, where $\alpha $ can be more easily tuned by grid search, in a Transformer, there are many attention heads in multiple layers  Crucial to the power of such models, the different heads capture different linguistic phenomena, some of them isolating important words, others spreading out attention across phrases BIBREF0  This motivates using different, adaptive $\alpha $ values for each attention head, such that some heads may learn to be sparser, and others may become closer to softmax  We propose doing so by treating the $\alpha $ values as neural network parameters, optimized via stochastic gradients along with the other weights 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax ::: Derivatives w r t  @!START@$\alpha $@!END@ 
In order to optimize $\alpha $ automatically via gradient methods, we must compute the Jacobian of the entmax output w r t  $\alpha $  Since entmax is defined through an optimization problem, this is non-trivial and cannot be simply handled through automatic differentiation; it falls within the domain of argmin differentiation, an active research topic in optimization BIBREF25, BIBREF26 
One of our key contributions is the derivation of a closed-form expression for this Jacobian  The next proposition provides such an expression, enabling entmax layers with adaptive $\alpha $  To the best of our knowledge, ours is the first neural network module that can automatically, continuously vary in shape away from softmax and toward sparse mappings like sparsemax 
Proposition 1 Let $\mathbf {p}^\star \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ be the solution of Equation DISPLAY_FORM14  Denote the distribution $\tilde{p}_i {(p_i^\star )^{2 - \alpha }}{ \sum _j(p_j^\star )^{2-\alpha }}$ and let $h_i -p^\star _i \log p^\star _i$  The $i$th component of the Jacobian $\mathbf {g} \frac{\partial \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})}{\partial \alpha }$ is
proof uses implicit function differentiation and is given in Appendix SECREF10 
Proposition UNKREF22 provides the remaining missing piece needed for training adaptively sparse Transformers  In the following section, we evaluate this strategy on neural machine translation, and analyze the behavior of the learned attention heads 
Experiments
We apply our adaptively sparse Transformers on four machine translation tasks  For comparison, a natural baseline is the standard Transformer architecture using the softmax transform in its multi-head attention mechanisms  We consider two other model variants in our experiments that make use of different normalizing transformations:
1 5-entmax: a Transformer with sparse entmax attention with fixed $\alpha =1 5$ for all heads  This is a novel model, since 1 5-entmax had only been proposed for RNN-based NMT models BIBREF14, but never in Transformers, where attention modules are not just one single component of the seq2seq model but rather an integral part of all of the model components 
$\alpha $-entmax: an adaptive Transformer with sparse entmax attention with a different, learned $\alpha _{i,j}^t$ for each head 
The adaptive model has an additional scalar parameter per attention head per layer for each of the three attention mechanisms (encoder self-attention, context attention, and decoder self-attention), i e ,
and we set $\alpha _{i,j}^t = 1 + \operatornamewithlimits{\mathsf {sigmoid}}(a_{i,j}^t) \in ]1, 2[$  All or some of the $\alpha $ values can be tied if desired, but we keep them independent for analysis purposes 
Experiments ::: Datasets 
Our models were trained on 4 machine translation datasets of different training sizes:
[itemsep= 5ex,leftmargin=2ex]
IWSLT 2017 German $\rightarrow $ English BIBREF27: 200K sentence pairs 
KFTT Japanese $\rightarrow $ English BIBREF28: 300K sentence pairs 
WMT 2016 Romanian $\rightarrow $ English BIBREF29: 600K sentence pairs 
WMT 2014 English $\rightarrow $ German BIBREF30: 4 5M sentence pairs 
All of these datasets were preprocessed with byte-pair encoding BIBREF31, using joint segmentations of 32k merge operations 
Experiments ::: Training 
We follow the dimensions of the Transformer-Base model of BIBREF0: The number of layers is $L=6$ and number of heads is $H=8$ in the encoder self-attention, the context attention, and the decoder self-attention  We use a mini-batch size of 8192 tokens and warm up the learning rate linearly until 20k steps, after which it decays according to an inverse square root schedule  All models were trained until convergence of validation accuracy, and evaluation was done at each 10k steps for ro$\rightarrow $en and en$\rightarrow $de and at each 5k steps for de$\rightarrow $en and ja$\rightarrow $en  The end-to-end computational overhead of our methods, when compared to standard softmax, is relatively small; in training tokens per second, the models using $\alpha $-entmax and $1 5$-entmax are, respectively, $75\%$ and $90\%$ the speed of the softmax model 
Experiments ::: Results 
We report test set tokenized BLEU BIBREF32 results in Table TABREF27  We can see that replacing softmax by entmax does not hurt performance in any of the datasets; indeed, sparse attention Transformers tend to have slightly higher BLEU, but their sparsity leads to a better potential for analysis  In the next section, we make use of this potential by exploring the learned internal mechanics of the self-attention heads 
Analysis
We conduct an analysis for the higher-resource dataset WMT 2014 English $\rightarrow $ German of the attention in the sparse adaptive Transformer model ($\alpha $-entmax) at multiple levels: we analyze high-level statistics as well as individual head behavior  Moreover, we make a qualitative analysis of the interpretability capabilities of our models 
Analysis ::: High-Level Statistics ::: What kind of @!START@$\alpha $@!END@ values are learned?
Figure FIGREF37 shows the learning trajectories of the $\alpha $ parameters of a selected subset of heads  We generally observe a tendency for the randomly-initialized $\alpha $ parameters to decrease initially, suggesting that softmax-like behavior may be preferable while the model is still very uncertain  After around one thousand steps, some heads change direction and become sparser, perhaps as they become more confident and specialized  This shows that the initialization of $\alpha $ does not predetermine its sparsity level or the role the head will have throughout  In particular, head 8 in the encoder self-attention layer 2 first drops to around $\alpha =1 3$ before becoming one of the sparsest heads, with $\alpha \approx 2$ 
The overall distribution of $\alpha $ values at convergence can be seen in Figure FIGREF38  We can observe that the encoder self-attention blocks learn to concentrate the $\alpha $ values in two modes: a very sparse one around $\alpha \rightarrow 2$, and a dense one between softmax and 1 5-entmax   However, the decoder self and context attention only learn to distribute these parameters in a single mode  We show next that this is reflected in the average density of attention weight vectors as well 
Analysis ::: High-Level Statistics ::: Attention weight density when translating 
For any $\alpha >1$, it would still be possible for the weight matrices in Equation DISPLAY_FORM9 to learn re-scalings so as to make attention sparser or denser  To visualize the impact of adaptive $\alpha $ values, we compare the empirical attention weight density (the average number of tokens receiving non-zero attention) within each module, against sparse Transformers with fixed $\alpha =1 5$ 
Figure FIGREF40 shows that, with fixed $\alpha =1 5$, heads tend to be sparse and similarly-distributed in all three attention modules  With learned $\alpha $, there are two notable changes: (i) a prominent mode corresponding to fully dense probabilities, showing that our models learn to combine sparse and dense attention, and (ii) a distinction between the encoder self-attention – whose background distribution tends toward extreme sparsity – and the other two modules, who exhibit more uniform background distributions  This suggests that perhaps entirely sparse Transformers are suboptimal 
The fact that the decoder seems to prefer denser attention distributions might be attributed to it being auto-regressive, only having access to past tokens and not the full sentence  We speculate that it might lose too much information if it assigned weights of zero to too many tokens in the self-attention, since there are fewer tokens to attend to in the first place 
Teasing this down into separate layers, Figure FIGREF41 shows the average (sorted) density of each head for each layer  We observe that $\alpha $-entmax is able to learn different sparsity patterns at each layer, leading to more variance in individual head behavior, to clearly-identified dense and sparse heads, and overall to different tendencies compared to the fixed case of $\alpha =1 5$ 
Analysis ::: High-Level Statistics ::: Head diversity 
To measure the overall disagreement between attention heads, as a measure of head diversity, we use the following generalization of the Jensen-Shannon divergence:
where $\mathbf {p}_j$ is the vector of attention weights assigned by head $j$ to each word in the sequence, and $\mathsf {H}^\textsc {S}$ is the Shannon entropy, base-adjusted based on the dimension of $\mathbf {p}$ such that $JS \le 1$  We average this measure over the entire validation set  The higher this metric is, the more the heads are taking different roles in the model 
Figure FIGREF44 shows that both sparse Transformer variants show more diversity than the traditional softmax one  Interestingly, diversity seems to peak in the middle layers of the encoder self-attention and context attention, while this is not the case for the decoder self-attention 
The statistics shown in this section can be found for the other language pairs in Appendix SECREF8 
Analysis ::: Identifying Head Specializations
Previous work pointed out some specific roles played by different heads in the softmax Transformer model BIBREF33, BIBREF5, BIBREF9  Identifying the specialization of a head can be done by observing the type of tokens or sequences that the head often assigns most of its attention weight; this is facilitated by sparsity 
Analysis ::: Identifying Head Specializations ::: Positional heads 
One particular type of head, as noted by BIBREF9, is the positional head  These heads tend to focus their attention on either the previous or next token in the sequence, thus obtaining representations of the neighborhood of the current time step  In Figure FIGREF47, we show attention plots for such heads, found for each of the studied models  The sparsity of our models allows these heads to be more confident in their representations, by assigning the whole probability distribution to a single token in the sequence  Concretely, we may measure a positional head's confidence as the average attention weight assigned to the previous token  The softmax model has three heads for position $-1$, with median confidence $93 5\%$  The $1 5$-entmax model also has three heads for this position, with median confidence $94 4\%$  The adaptive model has four heads, with median confidences $95 9\%$, the lowest-confidence head being dense with $\alpha =1 18$, while the highest-confidence head being sparse ($\alpha =1 91$) 
For position $+1$, the models each dedicate one head, with confidence around $95\%$, slightly higher for entmax  The adaptive model sets $\alpha =1 96$ for this head 
Analysis ::: Identifying Head Specializations ::: BPE-merging head 
Due to the sparsity of our models, we are able to identify other head specializations, easily identifying which heads should be further analysed  In Figure FIGREF51 we show one such head where the $\alpha $ value is particularly high (in the encoder, layer 1, head 4 depicted in Figure FIGREF37)  We found that this head most often looks at the current time step with high confidence, making it a positional head with offset 0  However, this head often spreads weight sparsely over 2-3 neighboring tokens, when the tokens are part of the same BPE cluster or hyphenated words  As this head is in the first layer, it provides a useful service to the higher layers by combining information evenly within some BPE clusters 
For each BPE cluster or cluster of hyphenated words, we computed a score between 0 and 1 that corresponds to the maximum attention mass assigned by any token to the rest of the tokens inside the cluster in order to quantify the BPE-merging capabilities of these heads  There are not any attention heads in the softmax model that are able to obtain a score over $80\%$, while for $1 5$-entmax and $\alpha $-entmax there are two heads in each ($83 3\%$ and $85 6\%$ for $1 5$-entmax and $88 5\%$ and $89 8\%$ for $\alpha $-entmax) 
Analysis ::: Identifying Head Specializations ::: Interrogation head 
On the other hand, in Figure FIGREF52 we show a head for which our adaptively sparse model chose an $\alpha $ close to 1, making it closer to softmax (also shown in encoder, layer 1, head 3 depicted in Figure FIGREF37)  We observe that this head assigns a high probability to question marks at the end of the sentence in time steps where the current token is interrogative, thus making it an interrogation-detecting head  We also observe this type of heads in the other models, which we also depict in Figure FIGREF52  The average attention weight placed on the question mark when the current token is an interrogative word is $98 5\%$ for softmax, $97 0\%$ for $1 5$-entmax, and $99 5\%$ for $\alpha $-entmax 
Furthermore, we can examine sentences where some tendentially sparse heads become less so, thus identifying sources of ambiguity where the head is less confident in its prediction  An example is shown in Figure FIGREF55 where sparsity in the same head differs for sentences of similar length 
Related Work ::: Sparse attention 
Prior work has developed sparse attention mechanisms, including applications to NMT BIBREF19, BIBREF12, BIBREF20, BIBREF22, BIBREF34  BIBREF14 introduced the entmax function this work builds upon  In their work, there is a single attention mechanism which is controlled by a fixed $\alpha $  In contrast, this is the first work to allow such attention mappings to dynamically adapt their curvature and sparsity, by automatically adjusting the continuous $\alpha $ parameter  We also provide the first results using sparse attention in a Transformer model 
Related Work ::: Fixed sparsity patterns 
Recent research improves the scalability of Transformer-like networks through static, fixed sparsity patterns BIBREF10, BIBREF35  Our adaptively-sparse Transformer can dynamically select a sparsity pattern that finds relevant words regardless of their position (e g , Figure FIGREF52)  Moreover, the two strategies could be combined  In a concurrent line of research, BIBREF11 propose an adaptive attention span for Transformer language models  While their work has each head learn a different contiguous span of context tokens to attend to, our work finds different sparsity patterns in the same span  Interestingly, some of their findings mirror ours – we found that attention heads in the last layers tend to be denser on average when compared to the ones in the first layers, while their work has found that lower layers tend to have a shorter attention span compared to higher layers 
Related Work ::: Transformer interpretability 
The original Transformer paper BIBREF0 shows attention visualizations, from which some speculation can be made of the roles the several attention heads have  BIBREF7 study the syntactic abilities of the Transformer self-attention, while BIBREF6 extract dependency relations from the attention weights  BIBREF8 find that the self-attentions in BERT BIBREF3 follow a sequence of processes that resembles a classical NLP pipeline  Regarding redundancy of heads, BIBREF9 develop a method that is able to prune heads of the multi-head attention module and make an empirical study of the role that each head has in self-attention (positional, syntactic and rare words)  BIBREF36 also aim to reduce head redundancy by adding a regularization term to the loss that maximizes head disagreement and obtain improved results  While not considering Transformer attentions, BIBREF18 show that traditional attention mechanisms do not necessarily improve interpretability since softmax attention is vulnerable to an adversarial attack leading to wildly different model predictions for the same attention weights  Sparse attention may mitigate these issues; however, our work focuses mostly on a more mechanical aspect of interpretation by analyzing head behavior, rather than on explanations for predictions 
Conclusion and Future Work
We contribute a novel strategy for adaptively sparse attention, and, in particular, for adaptively sparse Transformers  We present the first empirical analysis of Transformers with sparse attention mappings (i e , entmax), showing potential in both translation accuracy as well as in model interpretability 
In particular, we analyzed how the attention heads in the proposed adaptively sparse Transformer can specialize more and with higher confidence  Our adaptivity strategy relies only on gradient-based optimization, side-stepping costly per-head hyper-parameter searches  Further speed-ups are possible by leveraging more parallelism in the bisection algorithm for computing $\alpha $-entmax 
Finally, some of the automatically-learned behaviors of our adaptively sparse Transformers – for instance, the near-deterministic positional heads or the subword joining head – may provide new ideas for designing static variations of the Transformer 
Acknowledgments
This work was supported by the European Research Council (ERC StG DeepSPIN 758969), and by the Fundação para a Ciência e Tecnologia through contracts UID/EEA/50008/2019 and CMUPERI/TIC/0046/2014 (GoLocal)  We are grateful to Ben Peters for the $\alpha $-entmax code and Erick Fonseca, Marcos Treviso, Pedro Martins, and Tsvetomila Mihaylova for insightful group discussion  We thank Mathieu Blondel for the idea to learn $\alpha $  We would also like to thank the anonymous reviewers for their helpful feedback 
Supplementary Material
Background ::: Regularized Fenchel-Young prediction functions
Definition 1 (BIBREF23)
Let $\Omega \colon \triangle ^d \rightarrow {\mathbb {R}}\cup \lbrace \infty \rbrace $ be a strictly convex regularization function  We define the prediction function $\mathbf {\pi }_{\Omega }$ as
Background ::: Characterizing the @!START@$\alpha $@!END@-entmax mapping
Lemma 1 (BIBREF14) For any $\mathbf {z}$, there exists a unique $\tau ^\star $ such that
Proof: From the definition of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$,
we may easily identify it with a regularized prediction function (Def  UNKREF81):
We first note that for all $\mathbf {p}\in \triangle ^d$,
From the constant invariance and scaling properties of $\mathbf {\pi }_{\Omega }$ BIBREF23,
Using BIBREF23, noting that $g^{\prime }(t) = t^{\alpha - 1}$ and $(g^{\prime })^{-1}(u) = u^{{1}{\alpha -1}}$, yields
Since $\mathsf {H}^{\textsc {T}}_\alpha $ is strictly convex on the simplex, $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ has a unique solution $\mathbf {p}^\star $  Equation DISPLAY_FORM88 implicitly defines a one-to-one mapping between $\mathbf {p}^\star $ and $\tau ^\star $ as long as $\mathbf {p}^\star \in \triangle $, therefore $\tau ^\star $ is also unique 
Background ::: Connections to softmax and sparsemax
The Euclidean projection onto the simplex, sometimes referred to, in the context of neural attention, as sparsemax BIBREF19, is defined as
The solution can be characterized through the unique threshold $\tau $ such that $\sum _i \operatornamewithlimits{\mathsf {sparsemax}}(\mathbf {z})_i = 1$ and BIBREF38
Thus, each coordinate of the sparsemax solution is a piecewise-linear function  Visibly, this expression is recovered when setting $\alpha =2$ in the $\alpha $-entmax expression (Equation DISPLAY_FORM85); for other values of $\alpha $, the exponent induces curvature 
On the other hand, the well-known softmax is usually defined through the expression
which can be shown to be the unique solution of the optimization problem
where $\mathsf {H}^\textsc {S}(\mathbf {p}) -\sum _i p_i \log p_i$ is the Shannon entropy  Indeed, setting the gradient to 0 yields the condition $\log p_i = z_j - \nu _i - \tau - 1$, where $\tau $ and $\nu > 0$ are Lagrange multipliers for the simplex constraints $\sum _i p_i = 1$ and $p_i \ge 0$, respectively  Since the l h s  is only finite for $p_i>0$, we must have $\nu _i=0$ for all $i$, by complementary slackness  Thus, the solution must have the form $p_i = {\exp (z_i)}{Z}$, yielding Equation DISPLAY_FORM92 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@
Recall that the entmax transformation is defined as:
where $\alpha \ge 1$ and $\mathsf {H}^{\textsc {T}}_{\alpha }$ is the Tsallis entropy,
and $\mathsf {H}^\textsc {S}(\mathbf {p}):= -\sum _j p_j \log p_j$ is the Shannon entropy 
In this section, we derive the Jacobian of $\operatornamewithlimits{\mathsf {entmax }}$ with respect to the scalar parameter $\alpha $ 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: General case of @!START@$\alpha >1$@!END@
From the KKT conditions associated with the optimization problem in Eq  DISPLAY_FORM85, we have that the solution $\mathbf {p}^{\star }$ has the following form, coordinate-wise:
where $\tau ^{\star }$ is a scalar Lagrange multiplier that ensures that $\mathbf {p}^{\star }$ normalizes to 1, i e , it is defined implicitly by the condition:
For general values of $\alpha $, Eq  DISPLAY_FORM98 lacks a closed form solution  This makes the computation of the Jacobian
non-trivial  Fortunately, we can use the technique of implicit differentiation to obtain this Jacobian 
The Jacobian exists almost everywhere, and the expressions we derive expressions yield a generalized Jacobian BIBREF37 at any non-differentiable points that may occur for certain ($\alpha $, $\mathbf {z}$) pairs  We begin by noting that $\frac{\partial p_i^{\star }}{\partial \alpha } = 0$ if $p_i^{\star } = 0$, because increasing $\alpha $ keeps sparse coordinates sparse  Therefore we need to worry only about coordinates that are in the support of $\mathbf {p}^\star $  We will assume hereafter that the $i$th coordinate of $\mathbf {p}^\star $ is non-zero  We have:
We can see that this Jacobian depends on $\frac{\partial \tau ^{\star }}{\partial \alpha }$, which we now compute using implicit differentiation 
Let $\mathcal {S} = \lbrace i: p^\star _i > 0 \rbrace $)  By differentiating both sides of Eq  DISPLAY_FORM98, re-using some of the steps in Eq  DISPLAY_FORM101, and recalling Eq  DISPLAY_FORM97, we get
from which we obtain:
Finally, plugging Eq  DISPLAY_FORM103 into Eq  DISPLAY_FORM101, we get:
where we denote by
The distribution $\tilde{\mathbf {p}}(\alpha )$ can be interpreted as a “skewed” distribution obtained from $\mathbf {p}^{\star }$, which appears in the Jacobian of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ w r t  $\mathbf {z}$ as well BIBREF14 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: Solving the indetermination for @!START@$\alpha =1$@!END@
We can write Eq  DISPLAY_FORM104 as
When $\alpha \rightarrow 1^+$, we have $\tilde{\mathbf {p}}(\alpha ) \rightarrow \mathbf {p}^{\star }$, which leads to a $\frac{0}{0}$ indetermination 
To solve this indetermination, we will need to apply L'Hôpital's rule twice  Let us first compute the derivative of $\tilde{p}_i(\alpha )$ with respect to $\alpha $  We have
therefore
Differentiating the numerator and denominator in Eq  DISPLAY_FORM107, we get:
with
and
When $\alpha \rightarrow 1^+$, $B$ becomes again a $\frac{0}{0}$ indetermination, which we can solve by applying again L'Hôpital's rule  Differentiating the numerator and denominator in Eq  DISPLAY_FORM112:
Finally, summing Eq  DISPLAY_FORM111 and Eq  DISPLAY_FORM113, we get
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: Summary
To sum up, we have the following expression for the Jacobian of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ with respect to $\alpha $:
Context 2: Introduction
Accurate language identification (LID) is the first step in many natural language processing and machine comprehension pipelines  If the language of a piece of text is known then the appropriate downstream models like parts of speech taggers and language models can be applied as required 
LID is further also an important step in harvesting scarce language resources  Harvested data can be used to bootstrap more accurate LID models and in doing so continually improve the quality of the harvested data  Availability of data is still one of the big roadblocks for applying data driven approaches like supervised machine learning in developing countries 
Having 11 official languages of South Africa has lead to initiatives (discussed in the next section) that have had positive effect on the availability of language resources for research  However, many of the South African languages are still under resourced from the point of view of building data driven models for machine comprehension and process automation 
Table TABREF2 shows the percentages of first language speakers for each of the official languages of South Africa  These are four conjunctively written Nguni languages (zul, xho, nbl, ssw), Afrikaans (afr) and English (eng), three disjunctively written Sotho languages (nso, sot, tsn), as well as tshiVenda (ven) and Xitsonga (tso)  The Nguni languages are similar to each other and harder to distinguish  The same is true of the Sotho languages 
This paper presents a hierarchical naive Bayesian and lexicon based classifier for LID of short pieces of text of 15-20 characters long  The algorithm is evaluated against recent approaches using existing test sets from previous works on South African languages as well as the Discriminating between Similar Languages (DSL) 2015 and 2017 shared tasks 
Section SECREF2 reviews existing works on the topic and summarises the remaining research problems  Section SECREF3 of the paper discusses the proposed algorithm and Section SECREF4 presents comparative results 
Related Works
The focus of this section is on recently published datasets and LID research applicable to the South African context  An in depth survey of algorithms, features, datasets, shared tasks and evaluation methods may be found in BIBREF0 
The datasets for the DSL 2015 & DSL 2017 shared tasks BIBREF1 are often used in LID benchmarks and also available on Kaggle   The DSL datasets, like other LID datasets, consists of text sentences labelled by language  The 2017 dataset, for example, contains 14 languages over 6 language groups with 18000 training samples and 1000 testing samples per language 
The recently published JW300 parallel corpus BIBREF2 covers over 300 languages with around 100 thousand parallel sentences per language pair on average  In South Africa, a multilingual corpus of academic texts produced by university students with different mother tongues is being developed BIBREF3  The WiLI-2018 benchmark dataset BIBREF4 for monolingual written natural language identification includes around 1000 paragraphs of 235 languages  A possibly useful link can also be made BIBREF5 between Native Language Identification (NLI) (determining the native language of the author of a text) and Language Variety Identification (LVI) (classification of different varieties of a single language) which opens up more datasets  The Leipzig Corpora Collection BIBREF6, the Universal Declaration of Human Rights and Tatoeba are also often used sources of data 
The NCHLT text corpora BIBREF7 is likely a good starting point for a shared LID task dataset for the South African languages BIBREF8  The NCHLT text corpora contains enough data to have 3500 training samples and 600 testing samples of 300+ character sentences per language  Researchers have recently started applying existing algorithms for tasks like neural machine translation in earnest to such South African language datasets BIBREF9 
Existing NLP datasets, models and services BIBREF10 are available for South African languages  These include an LID algorithm BIBREF11 that uses a character level n-gram language model  Multiple papers have shown that 'shallow' naive Bayes classifiers BIBREF12, BIBREF8, BIBREF13, BIBREF14, SVMs BIBREF15 and similar models work very well for doing LID  The DSL 2017 paper BIBREF1, for example, gives an overview of the solutions of all of the teams that competed on the shared task and the winning approach BIBREF16 used an SVM with character n-gram, parts of speech tag features and some other engineered features  The winning approach for DSL 2015 used an ensemble naive Bayes classifier  The fasttext classifier BIBREF17 is perhaps one of the best known efficient 'shallow' text classifiers that have been used for LID  
Multiple papers have proposed hierarchical stacked classifiers (including lexicons) that would for example first classify a piece of text by language group and then by exact language BIBREF18, BIBREF19, BIBREF8, BIBREF0  Some work has also been done on classifying surnames between Tshivenda, Xitsonga and Sepedi BIBREF20  Additionally, data augmentation BIBREF21 and adversarial training BIBREF22 approaches are potentially very useful to reduce the requirement for data 
Researchers have investigated deeper LID models like bidirectional recurrent neural networks BIBREF23 or ensembles of recurrent neural networks BIBREF24  The latter is reported to achieve 95 12% in the DSL 2015 shared task  In these models text features can include character and word n-grams as well as informative character and word-level features learnt BIBREF25 from the training data  The neural methods seem to work well in tasks where more training data is available 
In summary, LID of short texts, informal styles and similar languages remains a difficult problem which is actively being researched  Increased confusion can in general be expected between shorter pieces of text and languages that are more closely related  Shallow methods still seem to work well compared to deeper models for LID  Other remaining research opportunities seem to be data harvesting, building standardised datasets and creating shared tasks for South Africa and Africa  Support for language codes that include more languages seems to be growing and discoverability of research is improving with more survey papers coming out  Paywalls also seem to no longer be a problem; the references used in this paper was either openly published or available as preprint papers 
Methodology
The proposed LID algorithm builds on the work in BIBREF8 and BIBREF26  We apply a naive Bayesian classifier with character (2, 4 & 6)-grams, word unigram and word bigram features with a hierarchical lexicon based classifier 
The naive Bayesian classifier is trained to predict the specific language label of a piece of text, but used to first classify text as belonging to either the Nguni family, the Sotho family, English, Afrikaans, Xitsonga or Tshivenda  The scikit-learn multinomial naive Bayes classifier is used for the implementation with an alpha smoothing value of 0 01 and hashed text features 
The lexicon based classifier is then used to predict the specific language within a language group  For the South African languages this is done for the Nguni and Sotho groups  If the lexicon prediction of the specific language has high confidence then its result is used as the final label else the naive Bayesian classifier's specific language prediction is used as the final result  The lexicon is built over all the data and therefore includes the vocabulary from both the training and testing sets 
The lexicon based classifier is designed to trade higher precision for lower recall  The proposed implementation is considered confident if the number of words from the winning language is at least one more than the number of words considered to be from the language scored in second place 
The stacked classifier is tested against three public LID implementations BIBREF17, BIBREF23, BIBREF8  The LID implementation described in BIBREF17 is available on GitHub and is trained and tested according to a post on the fasttext blog  Character (5-6)-gram features with 16 dimensional vectors worked the best  The implementation discussed in BIBREF23 is available from https://github com/tomkocmi/LanideNN  Following the instructions for an OSX pip install of an old r0 8 release of TensorFlow, the LanideNN code could be executed in Python 3 7 4  Settings were left at their defaults and a learning rate of 0 001 was used followed by a refinement with learning rate of 0 0001  Only one code modification was applied to return the results from a method that previously just printed to screen  The LID algorithm described in BIBREF8 is also available on GitHub 
The stacked classifier is also tested against the results reported for four other algorithms BIBREF16, BIBREF26, BIBREF24, BIBREF15  All the comparisons are done using the NCHLT BIBREF7, DSL 2015 BIBREF19 and DSL 2017 BIBREF1 datasets discussed in Section SECREF2 
Results and Analysis
The average classification accuracy results are summarised in Table TABREF9  The accuracies reported are for classifying a piece of text by its specific language label  Classifying text only by language group or family is a much easier task as reported in BIBREF8 
Different variations of the proposed classifier were evaluated  A single NB classifier (NB), a stack of two NB classifiers (NB+NB), a stack of a NB classifier and lexicon (NB+Lex) and a lexicon (Lex) by itself  A lexicon with a 50% training token dropout is also listed to show the impact of the lexicon support on the accuracy 
From the results it seems that the DSL 2017 task might be harder than the DSL 2015 and NCHLT tasks  Also, the results for the implementation discussed in BIBREF23 might seem low, but the results reported in that paper is generated on longer pieces of text so lower scores on the shorter pieces of text derived from the NCHLT corpora is expected 
The accuracy of the proposed algorithm seems to be dependent on the support of the lexicon  Without a good lexicon a non-stacked naive Bayesian classifier might even perform better 
The execution performance of some of the LID implementations are shown in Table TABREF10  Results were generated on an early 2015 13-inch Retina MacBook Pro with a 2 9 GHz CPU (Turbo Boosted to 3 4 GHz) and 8GB RAM  The C++ implementation in BIBREF17 is the fastest  The implementation in BIBREF8 makes use of un-hashed feature representations which causes it to be slower than the proposed sklearn implementation  The execution performance of BIBREF23 might improve by a factor of five to ten when executed on a GPU 
Conclusion
LID of short texts, informal styles and similar languages remains a difficult problem which is actively being researched  The proposed algorithm was evaluated on three existing datasets and compared to the implementations of three public LID implementations as well as to reported results of four other algorithms  It performed well relative to the other methods beating their results  However, the performance is dependent on the support of the lexicon 
We would like to investigate the value of a lexicon in a production system and how to possibly maintain it using self-supervised learning  We are investigating the application of deeper language models some of which have been used in more recent DSL shared tasks  We would also like to investigate data augmentation strategies to reduce the amount of training data that is required 
Further research opportunities include data harvesting, building standardised datasets and shared tasks for South Africa as well as the rest of Africa  In general, the support for language codes that include more languages seems to be growing, discoverability of research is improving and paywalls seem to no longer be a big problem in getting access to published research 
Context 3: Introduction and Background
Many reinforcement learning algorithms are designed for relatively small discrete or continuous action spaces and so have trouble scaling  Text-adventure games—or interaction fictions—are simulations in which both an agents' state and action spaces are in textual natural language  An example of a one turn agent interaction in the popular text-game Zork1 can be seen in Fig  FIGREF1  Text-adventure games provide us with multiple challenges in the form of partial observability, commonsense reasoning, and a combinatorially-sized state-action space  Text-adventure games are structured as long puzzles or quests, interspersed with bottlenecks  The quests can usually be completed through multiple branching paths  However, games can also feature one or more bottlenecks  Bottlenecks are areas that an agent must pass through in order to progress to the next section of the game regardless of what path the agent has taken to complete that section of the quest BIBREF0  In this work, we focus on more effectively exploring this space and surpassing these bottlenecks—building on prior work that focuses on tackling the other problems 
Formally, we use the definition of text-adventure games as seen in BIBREF1 and BIBREF2  These games are partially observable Markov decision processes (POMDPs), represented as a 7-tuple of $\langle S,T,A,\Omega , O,R, \gamma \rangle $ representing the set of environment states, mostly deterministic conditional transition probabilities between states, the vocabulary or words used to compose text commands, observations returned by the game, observation conditional probabilities, reward function, and the discount factor respectively  For our purposes, understanding the exact state and action spaces we use in this work is critical and so we define each of these in relative depth 
Action-Space  To solve Zork1, the cannonical text-adventure games, requires the generation of actions consisting of up to five-words from a relatively modest vocabulary of 697 words recognized by the game’s parser  This results in $\mathcal {O}(697^5)={1 64e14}$ possible actions at every step  To facilitate text-adventure game playing, BIBREF2 introduce Jericho, a framework for interacting with text-games  They propose a template-based action space in which the agent first selects a template, consisting of an action verb and preposition, and then filling that in with relevant entities $($e g  $[get]$ $ [from] $ $)$  Zork1 has 237 templates, each with up to two blanks, yielding a template-action space of size $\mathcal {O}(237 \times 697^2)={1 15e8}$  This space is still far larger than most used by previous approaches applying reinforcement learning to text-based games 
State-Representation  Prior work has shown that knowledge graphs are effective in terms of dealing with the challenges of partial observability $($BIBREF3 BIBREF3; BIBREF4$)$  A knowledge graph is a set of 3-tuples of the form $\langle subject, relation, object \rangle $  These triples are extracted from the observations using Stanford's Open Information Extraction (OpenIE) BIBREF5  Human-made text-adventure games often contain relatively complex semi-structured information that OpenIE is not designed to parse and so they add additional rules to ensure that the correct information is parsed  The graph itself is more or less a map of the world, with information about objects' affordances and attributes linked to the rooms that they are place in a map  The graph also makes a distinction with respect to items that are in the agent's possession or in their immediate surrounding environment  An example of what the knowledge graph looks like and specific implementation details can be found in Appendix SECREF14 
BIBREF6 introduce the KG-A2C, which uses a knowledge graph based state-representation to aid in the section of actions in a combinatorially-sized action-space—specifically they use the knowledge graph to constrain the kinds of entities that can be filled in the blanks in the template action-space  They test their approach on Zork1, showing the combination of the knowledge graph and template action selection resulted in improvements over existing methods  They note that their approach reaches a score of 40 which corresponds to a bottleneck in Zork1 where the player is eaten by a “grue” (resulting in negative reward) if the player has not first lit a lamp  The lamp must be lit many steps after first being encountered, in a different section of the game; this action is necessary to continue exploring but doesn’t immediately produce any positive reward  That is, there is a long term dependency between actions that is not immediately rewarded, as seen in Figure FIGREF1  Others using artificially constrained action spaces also report an inability to pass through this bottleneck BIBREF7, BIBREF8  They pose a significant challenge for these methods because the agent does not see the correct action sequence to pass the bottleneck enough times  This is in part due to the fact that for that sequence to be reinforced, the agent needs to reach the next possible reward beyond the bottleneck 
More efficient exploration strategies are required to pass bottlenecks  Our contributions are two-fold  We first introduce a method that detects bottlenecks in text-games using the overall reward gained and the knowledge graph state  This method freezes the policy used to reach the bottleneck and restarts the training from there on out, additionally conducting a backtracking search to ensure that a sub-optimal policy has not been frozen  The second contribution explore how to leverage knowledge graphs to improve existing exploration algorithms for dealing with combinatorial action-spaces such as Go-Explore BIBREF9  We additionally present a comparative ablation study analyzing the performance of these methods on the popular text-game Zork1 
Exploration Methods
In this section, we describe methods to explore combinatorially sized action spaces such as text-games—focusing especially on methods that can deal with their inherent bottleneck structure  We first describe our method that explicitly attempts to detect bottlenecks and then describe how an exploration algorithm such as Go Explore BIBREF9 can leverage knowledge graphs 
KG-A2C-chained An example of a bottleneck can be seen in Figure FIGREF1  We extend the KG-A2C algorithm as follows  First, we detect bottlenecks as states where the agent is unable to progress any further  We set a patience parameter and if the agent has not seen a higher score in patience steps, the agent assumes it has been limited by a bottleneck  Second, when a bottleneck is found, we freeze the policy that gets the agent to the state with the highest score  The agent then begins training a new policy from that particular state 
Simply freezing the policy that led to the bottleneck, however, can potentially result in a policy one that is globally sub-optimal  We therefore employ a backtracking strategy that restarts exploration from each of the $n$ previous steps—searching for a more optimal policy that reaches that bottleneck

ground_truth: the attention heads in the proposed adaptively sparse Transformer can specialize more and with higher confidence

We introduce sparse attention into the Transformer architecture

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. Which languages are similar to each other?
Context 4: Introduction
Knowledge Base Question Answering (KBQA) systems answer questions by obtaining information from KB tuples BIBREF0 , BIBREF1 , BIBREF2 , BIBREF3 , BIBREF4 , BIBREF5   For an input question, these systems typically generate a KB query, which can be executed to retrieve the answers from a KB  Figure 1 illustrates the process used to parse two sample questions in a KBQA system: (a) a single-relation question, which can be answered with a single $<$ head-entity, relation, tail-entity $>$ KB tuple BIBREF6 , BIBREF7 , BIBREF2 ; and (b) a more complex case, where some constraints need to be handled for multiple entities in the question  The KBQA system in the figure performs two key tasks: (1) entity linking, which links $n$ -grams in questions to KB entities, and (2) relation detection, which identifies the KB relation(s) a question refers to 
The main focus of this work is to improve the relation detection subtask and further explore how it can contribute to the KBQA system  Although general relation detection methods are well studied in the NLP community, such studies usually do not take the end task of KBQA into consideration  As a result, there is a significant gap between general relation detection studies and KB-specific relation detection  First, in most general relation detection tasks, the number of target relations is limited, normally smaller than 100  In contrast, in KBQA even a small KB, like Freebase2M BIBREF2 , contains more than 6,000 relation types  Second, relation detection for KBQA often becomes a zero-shot learning task, since some test instances may have unseen relations in the training data  For example, the SimpleQuestions BIBREF2 data set has 14% of the golden test relations not observed in golden training tuples  Third, as shown in Figure 1 (b), for some KBQA tasks like WebQuestions BIBREF0 , we need to predict a chain of relations instead of a single relation  This increases the number of target relation types and the sizes of candidate relation pools, further increasing the difficulty of KB relation detection  Owing to these reasons, KB relation detection is significantly more challenging compared to general relation detection tasks 
This paper improves KB relation detection to cope with the problems mentioned above  First, in order to deal with the unseen relations, we propose to break the relation names into word sequences for question-relation matching  Second, noticing that original relation names can sometimes help to match longer question contexts, we propose to build both relation-level and word-level relation representations  Third, we use deep bidirectional LSTMs (BiLSTMs) to learn different levels of question representations in order to match the different levels of relation information  Finally, we propose a residual learning method for sequence matching, which makes the model training easier and results in more abstract (deeper) question representations, thus improves hierarchical matching 
In order to assess how the proposed improved relation detection could benefit the KBQA end task, we also propose a simple KBQA implementation composed of two-step relation detection  Given an input question and a set of candidate entities retrieved by an entity linker based on the question, our proposed relation detection model plays a key role in the KBQA process: (1) Re-ranking the entity candidates according to whether they connect to high confident relations detected from the raw question text by the relation detection model  This step is important to deal with the ambiguities normally present in entity linking results  (2) Finding the core relation (chains) for each topic entity selection from a much smaller candidate entity set after re-ranking  The above steps are followed by an optional constraint detection step, when the question cannot be answered by single relations (e g , multiple entities in the question)  Finally the highest scored query from the above steps is used to query the KB for answers 
Our main contributions include: (i) An improved relation detection model by hierarchical matching between questions and relations with residual learning; (ii) We demonstrate that the improved relation detector enables our simple KBQA system to achieve state-of-the-art results on both single-relation and multi-relation KBQA tasks 
Background: Different Granularity in KB Relations
Previous research BIBREF4 , BIBREF20 formulates KB relation detection as a sequence matching problem  However, while the questions are natural word sequences, how to represent relations as sequences remains a challenging problem  Here we give an overview of two types of relation sequence representations commonly used in previous work 
(1) Relation Name as a Single Token (relation-level)  In this case, each relation name is treated as a unique token  The problem with this approach is that it suffers from the low relation coverage due to limited amount of training data, thus cannot generalize well to large number of open-domain relations  For example, in Figure 1 , when treating relation names as single tokens, it will be difficult to match the questions to relation names “episodes_written” and “starring_roles” if these names do not appear in training data – their relation embeddings $\mathbf {h}^r$ s will be random vectors thus are not comparable to question embeddings $\mathbf {h}^q$ s 
(2) Relation as Word Sequence (word-level)  In this case, the relation is treated as a sequence of words from the tokenized relation name  It has better generalization, but suffers from the lack of global information from the original relation names  For example in Figure 1 (b), when doing only word-level matching, it is difficult to rank the target relation “starring_roles” higher compared to the incorrect relation “plays_produced”  This is because the incorrect relation contains word “plays”, which is more similar to the question (containing word “play”) in the embedding space  On the other hand, if the target relation co-occurs with questions related to “tv appearance” in training, by treating the whole relation as a token (i e  relation id), we could better learn the correspondence between this token and phrases like “tv show” and “play on” 
The two types of relation representation contain different levels of abstraction  As shown in Table 1 , the word-level focuses more on local information (words and short phrases), and the relation-level focus more on global information (long phrases and skip-grams) but suffer from data sparsity  Since both these levels of granularity have their own pros and cons, we propose a hierarchical matching approach for KB relation detection: for a candidate relation, our approach matches the input question to both word-level and relation-level representations to get the final ranking score  Section "Improved KB Relation Detection" gives the details of our proposed approach 
Improved KB Relation Detection
This section describes our hierarchical sequence matching with residual learning approach for relation detection  In order to match the question to different aspects of a relation (with different abstraction levels), we deal with three problems as follows on learning question/relation representations 
Relation Representations from Different Granularity
We provide our model with both types of relation representation: word-level and relation-level  Therefore, the input relation becomes $\mathbf {r}=\lbrace r^{word}_1,\cdots ,r^{word}_{M_1}\rbrace  \cup \lbrace r^{rel}_1,\cdots ,r^{rel}_{M_2}\rbrace $ , where the first $M_1$ tokens are words (e g  {episode, written}), and the last $M_2$ tokens are relation names, e g , {episode_written} or {starring_roles, series} (when the target is a chain like in Figure 1 (b))  We transform each token above to its word embedding then use two BiLSTMs (with shared parameters) to get their hidden representations $[\mathbf {B}^{word}_{1:M_1}:\mathbf {B}^{rel}_{1:M_2}]$ (each row vector $\mathbf {\beta }_i$ is the concatenation between forward/backward representations at $i$ )  We initialize the relation sequence LSTMs with the final state representations of the word sequence, as a back-off for unseen relations  We apply one max-pooling on these two sets of vectors and get the final relation representation $\mathbf {h}^r$  
Different Abstractions of Questions Representations
From Table 1 , we can see that different parts of a relation could match different contexts of question texts  Usually relation names could match longer phrases in the question and relation words could match short phrases  Yet different words might match phrases of different lengths 
As a result, we hope the question representations could also comprise vectors that summarize various lengths of phrase information (different levels of abstraction), in order to match relation representations of different granularity  We deal with this problem by applying deep BiLSTMs on questions  The first-layer of BiLSTM works on the word embeddings of question words $\mathbf {q}=\lbrace q_1,\cdots ,q_N\rbrace $ and gets hidden representations $\mathbf {\Gamma }^{(1)}_{1:N}=[\mathbf {\gamma }^{(1)}_1;\cdots ;\mathbf {\gamma }^{(1)}_N]$   The second-layer BiLSTM works on $\mathbf {\Gamma }^{(1)}_{1:N}$ to get the second set of hidden representations $\mathbf {\Gamma }^{(2)}_{1:N}$   Since the second BiLSTM starts with the hidden vectors from the first layer, intuitively it could learn more general and abstract information compared to the first layer 
Note that the first(second)-layer of question representations does not necessarily correspond to the word(relation)-level relation representations, instead either layer of question representations could potentially match to either level of relation representations  This raises the difficulty of matching between different levels of relation/question representations; the following section gives our proposal to deal with such problem 
Hierarchical Matching between Relation and Question
Now we have question contexts of different lengths encoded in $\mathbf {\Gamma }^{(1)}_{1:N}$ and $\mathbf {\Gamma }^{(2)}_{1:N}$   Unlike the standard usage of deep BiLSTMs that employs the representations in the final layer for prediction, here we expect that two layers of question representations can be complementary to each other and both should be compared to the relation representation space (Hierarchical Matching)  This is important for our task since each relation token can correspond to phrases of different lengths, mainly because of syntactic variations  For example in Table 1 , the relation word written could be matched to either the same single word in the question or a much longer phrase be the writer of 
We could perform the above hierarchical matching by computing the similarity between each layer of $\mathbf {\Gamma }$ and $\mathbf {h}^r$ separately and doing the (weighted) sum between the two scores  However this does not give significant improvement (see Table 2 )  Our analysis in Section "Relation Detection Results" shows that this naive method suffers from the training difficulty, evidenced by that the converged training loss of this model is much higher than that of a single-layer baseline model  This is mainly because (1) Deep BiLSTMs do not guarantee that the two-levels of question hidden representations are comparable, the training usually falls to local optima where one layer has good matching scores and the other always has weight close to 0  (2) The training of deeper architectures itself is more difficult 
To overcome the above difficulties, we adopt the idea from Residual Networks BIBREF23 for hierarchical matching by adding shortcut connections between two BiLSTM layers  We proposed two ways of such Hierarchical Residual Matching: (1) Connecting each $\mathbf {\gamma }^{(1)}_i$ and $\mathbf {\gamma }^{(2)}_i$ , resulting in a $\mathbf {\gamma }^{^{\prime }}_i=\mathbf {\gamma }^{(1)}_i + \mathbf {\gamma }^{(2)}_i$ for each position $i$   Then the final question representation $\mathbf {h}^q$ becomes a max-pooling over all $\mathbf {\gamma }^{^{\prime }}_i$ s, 1 $\le $ i $\le $ $N$   (2) Applying max-pooling on $\mathbf {\Gamma }^{(1)}_{1:N}$ and $\mathbf {\gamma }^{(2)}_i$0 to get $\mathbf {\gamma }^{(2)}_i$1 and $\mathbf {\gamma }^{(2)}_i$2 , respectively, then setting $\mathbf {\gamma }^{(2)}_i$3   Finally we compute the matching score of $\mathbf {\gamma }^{(2)}_i$4 given $\mathbf {\gamma }^{(2)}_i$5 as $\mathbf {\gamma }^{(2)}_i$6  
Intuitively, the proposed method should benefit from hierarchical training since the second layer is fitting the residues from the first layer of matching, so the two layers of representations are more likely to be complementary to each other  This also ensures the vector spaces of two layers are comparable and makes the second-layer training easier 
During training we adopt a ranking loss to maximizing the margin between the gold relation $\mathbf {r}^+$ and other relations $\mathbf {r}^-$ in the candidate pool $R$  
$$l_{\mathrm {rel}} = \max \lbrace 0, \gamma - s_{\mathrm {rel}}(\mathbf {r}^+; \mathbf {q}) + s_{\mathrm {rel}}(\mathbf {r}^-; \mathbf {q})\rbrace  \nonumber $$   (Eq  12)
where $\gamma $ is a constant parameter  Fig 2 summarizes the above Hierarchical Residual BiLSTM (HR-BiLSTM) model 
Another way of hierarchical matching consists in relying on attention mechanism, e g  BIBREF24 , to find the correspondence between different levels of representations  This performs below the HR-BiLSTM (see Table 2 ) 
KBQA Enhanced by Relation Detection
This section describes our KBQA pipeline system  We make minimal efforts beyond the training of the relation detection model, making the whole system easy to build 
Following previous work BIBREF4 , BIBREF5 , our KBQA system takes an existing entity linker to produce the top- $K$ linked entities, $EL_K(q)$ , for a question $q$ (“initial entity linking”)  Then we generate the KB queries for $q$ following the four steps illustrated in Algorithm "KBQA Enhanced by Relation Detection"  
[htbp] InputInput OutputOutput Top query tuple $(\hat{e},\hat{r}, \lbrace (c, r_c)\rbrace )$ Entity Re-Ranking (first-step relation detection): Use the raw question text as input for a relation detector to score all relations in the KB that are associated to the entities in $EL_K(q)$ ; use the relation scores to re-rank $EL_K(q)$ and generate a shorter list $EL^{\prime }_{K^{\prime }}(q)$ containing the top- $K^{\prime }$ entity candidates (Section "Entity Re-Ranking" ) Relation Detection: Detect relation(s) using the reformatted question text in which the topic entity is replaced by a special token $<$ e $>$ (Section "Relation Detection" ) Query Generation: Combine the scores from step 1 and 2, and select the top pair $(\hat{e},\hat{r})$ (Section "Query Generation" ) Constraint Detection (optional): Compute similarity between $q$ and any neighbor entity $c$ of the entities along $EL_K(q)$0 (connecting by a relation $EL_K(q)$1 ) , add the high scoring $EL_K(q)$2 and $EL_K(q)$3 to the query (Section "Constraint Detection" )  KBQA with two-step relation detection
Compared to previous approaches, the main difference is that we have an additional entity re-ranking step after the initial entity linking  We have this step because we have observed that entity linking sometimes becomes a bottleneck in KBQA systems  For example, on SimpleQuestions the best reported linker could only get 72 7% top-1 accuracy on identifying topic entities  This is usually due to the ambiguities of entity names, e g  in Fig 1 (a), there are TV writer and baseball player “Mike Kelley”, which is impossible to distinguish with only entity name matching 
Having observed that different entity candidates usually connect to different relations, here we propose to help entity disambiguation in the initial entity linking with relations detected in questions 
Sections "Entity Re-Ranking" and "Relation Detection" elaborate how our relation detection help to re-rank entities in the initial entity linking, and then those re-ranked entities enable more accurate relation detection  The KBQA end task, as a result, benefits from this process 
Entity Re-Ranking
In this step, we use the raw question text as input for a relation detector to score all relations in the KB with connections to at least one of the entity candidates in $EL_K(q)$   We call this step relation detection on entity set since it does not work on a single topic entity as the usual settings  We use the HR-BiLSTM as described in Sec  "Improved KB Relation Detection"   For each question $q$ , after generating a score $s_{rel}(r;q)$ for each relation using HR-BiLSTM, we use the top $l$ best scoring relations ( $R^{l}_q$ ) to re-rank the original entity candidates  Concretely, for each entity $e$ and its associated relations $R_e$ , given the original entity linker score $s_{linker}$ , and the score of the most confident relation $r\in R_q^{l} \cap R_e$ , we sum these two scores to re-rank the entities:
$$s_{\mathrm {rerank}}(e;q) =& \alpha \cdot s_{\mathrm {linker}}(e;q) \nonumber \\ + & (1-\alpha ) \cdot \max _{r \in R_q^{l} \cap R_e} s_{\mathrm {rel}}(r;q) \nonumber $$   (Eq

ground_truth: Nguni languages (zul, xho, nbl, ssw), Sotho languages (nso, sot, tsn)

The Nguni languages are similar to each other, The same is true of the Sotho languages

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. What are the results from these proposed strategies?
Context 3:  At each step, we keep track of a buffer of $n$ states and admissible actions that led up to that locally optimal state  We force the agent to explore from this state to attempt to drive it out of the local optima  If it is further unable to find itself out of this local optima, we refresh the training process again, but starting at the state immediately before the agent reaches the local optima  If this continues to fail, we continue to iterate through this buffer of seen states states up to that local optima until we either find a more optimal state or we run out of states to refresh from, in which we terminate the training algorithm 
KG-A2C-Explore Go-Explore BIBREF9 is an algorithm that is designed to keep track of sub-optimal and under-explored states in order to allow the agent to explore upon more optimal states that may be a result of sparse rewards  The Go-Explore algorithm consists of two phases, the first to continuously explore until a set of promising states and corresponding trajectories are found on the basis of total score, and the second to robustify this found policy against potential stochasticity in the game  Promising states are defined as those states when explored from will likely result in higher reward trajectories  Since the text games we are dealing with are mostly deterministic, with the exception of Zork in later stages, we only focus on using Phase 1 of the Go-Explore algorithm to find an optimal policy  BIBREF10 look at applying Go-Explore to text-games on a set of simpler games generated using the game generation framework TextWorld BIBREF1  Instead of training a policy network in parallel to generate actions used for exploration, they use a small set of “admissible actions”—actions guaranteed to change the world state at any given step during Phase 1—to explore and find high reward trajectories  This space of actions is relatively small (of the order of $10^2$ per step) and so finding high reward trajectories in larger action-spaces such as in Zork would be infeasible
Go-Explore maintains an archive of cells—defined as a set of states that map to a single representation—to keep track of promising states  BIBREF9 simply encodes each cell by keeping track of the agent's position and BIBREF10 use the textual observations encoded by recurrent neural network as a cell representation  We improve on this implementation by training the KG-A2C network in parallel, using the snapshot of the knowledge graph in conjunction with the game state to further encode the current state and use this as a cell representation  At each step, Go-Explore chooses a cell to explore at random (weighted by score to prefer more advanced cells)  The KG-A2C will run for a number of steps, starting with the knowledge graph state and the last seen state of the game from the cell  This will generate a trajectory for the agent while further training the KG-A2C at each iteration, creating a new representation for the knowledge graph as well as a new game state for the cell  After expanding a cell, Go-Explore will continue to sample cells by weight to continue expanding its known states  At the same time, KG-A2C will benefit from the heuristics of selecting preferred cells and be trained on promising states more often 
Evaluation
We compare our two exploration strategies to the following baselines and ablations:
KG-A2C This is the exact same method presented in BIBREF6 with no modifications 
A2C Represents the same approach as KG-A2C but with all the knowledge graph components removed  The state representation is text only encoded using recurrent networks 
A2C-chained Is a variation on KG-A2C-chained where we use our policy chaining approach with the A2C method to train the agent instead of KG-A2C 
A2C-Explore Uses A2C in addition to the exploration strategy seen in KG-A2C-Explore  The cell representations here are defined in terms of the recurrent network based encoding of the textual observation 
Figure FIGREF10 shows that agents utilizing knowledge-graphs in addition to either enhanced exploration method far outperform the baseline A2C and KG-A2C  KG-A2C-chained and KG-A2C-Explore both pass the bottleneck of a score of 40, whereas A2C-Explore gets to the bottleneck but cannot surpass it 
There are a couple of key insights that can be drawn from these results The first is that the knowledge graph appears to be critical; it is theorized to help with partial observability  However the knowledge graph representation isn't sufficient in that the knowledge graph representation without enhanced exploration methods cannot surpass the bottleneck  A2C-chained—which explores without a knowledge graph—fails to even outperform the baseline A2C  We hypothesize that this is due to the knowledge graph aiding implicitly in the sample efficiency of bottleneck detection and subsequent exploration  That is, exploring after backtracking from a potentially detected bottleneck is much more efficient in the knowledge graph based agent 
The Go-Explore based exploration algorithm sees less of a difference between agents  A2C-Explore converges more quickly, but to a lower reward trajectory that fails to pass the bottleneck, whereas KG-A2C-Explore takes longer to reach a similar reward but consistently makes it through the bottleneck  The knowledge graph cell representation appears to thus be a better indication of what a promising state is as opposed to just the textual observation 
Comparing the advanced exploration methods when using the knowledge graph, we see that both agents successfully pass the bottleneck corresponding to entering the cellar and lighting the lamp and reach comparable scores within a margin of error  KG-A2C-chained is significantly more sample efficient and converges faster  We can infer that chaining policies by explicitly detecting bottlenecks lets us pass it more quickly than attempting to find promising cell representations with Go-Explore  This form of chained exploration with backtracking is particularly suited to sequential decision making problems that can be represented as acyclic directed graphs as in Figure FIGREF1 
Appendix ::: Zork1
Zork1 is one of the first text-adventure games and heavily influences games released later in terms of narrative style and game structure  It is a dungeon crawler where the player must explore a vast world and collect a series of treasures  It was identified by BIBREF2 as a moonshot game and has been the subject of much work in leaning agents BIBREF12, BIBREF7, BIBREF11, BIBREF8  Rewards are given to the player when they collect treasures as well as when important intermediate milestones needed to further explore the world are passed  Figure FIGREF15 and Figure FIGREF1 show us a map of the world of Zork1 and the corresponding quest structure 
The bottleneck seen at a score of around 40 is when the player first enters the cellar on the right side of the map  The cellar is dark and you need to immediately light the lamp to see anything  Attempting to explore the cellar in the dark results in you being instantly killed by a monster known as a “grue” 
Appendix ::: Knowledge Graph Rules
We make no changes from the graph update rules used by BIBREF6  Candidate interactive objects are identified by performing part-of-speech tagging on the current observation, identifying singular and proper nouns as well as adjectives, and are then filtered by checking if they can be examined using the command $examine$ $OBJ$  Only the interactive objects not found in the inventory are linked to the node corresponding to the current room and the inventory items are linked to the “you” node  The only other rule applied uses the navigational actions performed by the agent to infer the relative positions of rooms, e g  $\langle kitchen,down,cellar \rangle $ when the agent performs $go$ $down$ when in the kitchen to move to the cellar 
Appendix ::: Hyperparameters
Hyperparameters used for our agents are given below  Patience and buffer size are used for the policy chaining method as described in Section SECREF2  Cell step size is a parameter used for Go-Explore and describes how many steps are taken when exploring in a given cell state  Base hyperparameters for KG-A2C are taken from BIBREF6 and the same parameters are used for A2C 

ground_truth: Reward of 11.8 for the A2C-chained model, 41.8 for the KG-A2C-chained model, 40 for A2C-Explore and 44 for KG-A2C-Explore.

KG-A2C-chained and KG-A2C-Explore both pass the bottleneck of a score of 40