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 1: 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  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 
Context 2: Introduction
Data annotation is a major bottleneck for the application of supervised learning approaches to many problems  As a result, unsupervised methods that learn directly from unlabeled data are increasingly important  For tasks related to unsupervised syntactic analysis, discrete generative models have dominated in recent years – for example, for both part-of-speech (POS) induction BIBREF0 , BIBREF1 and unsupervised dependency parsing BIBREF2 , BIBREF3 , BIBREF4   While similar models have had success on a range of unsupervised tasks, they have mostly ignored the apparent utility of continuous word representations evident from supervised NLP applications BIBREF5 , BIBREF6   In this work, we focus on leveraging and explicitly representing continuous word embeddings within unsupervised models of syntactic structure 
Pre-trained word embeddings from massive unlabeled corpora offer a compact way of injecting a prior notion of word similarity into models that would otherwise treat words as discrete, isolated categories  However, the specific properties of language captured by any particular embedding scheme can be difficult to control, and, further, may not be ideally suited to the task at hand  For example, pre-trained skip-gram embeddings BIBREF7 with small context window size are found to capture the syntactic properties of language well BIBREF8 , BIBREF9   However, if our goal is to separate syntactic categories, this embedding space is not ideal – POS categories correspond to overlapping interspersed regions in the embedding space, evident in Figure SECREF4  
In our approach, we propose to learn a new latent embedding space as a projection of pre-trained embeddings (depicted in Figure SECREF5 ), while jointly learning latent syntactic structure – for example, POS categories or syntactic dependencies  To this end, we introduce a new generative model (shown in Figure FIGREF6 ) that first generates a latent syntactic representation (e g  a dependency parse) from a discrete structured prior (which we also call the “syntax model”), then, conditioned on this representation, generates a sequence of latent embedding random variables corresponding to each word, and finally produces the observed (pre-trained) word embeddings by projecting these latent vectors through a parameterized non-linear function  The latent embeddings can be jointly learned with the structured syntax model in a completely unsupervised fashion 
By choosing an invertible neural network as our non-linear projector, and then parameterizing our model in terms of the projection's inverse, we are able to derive tractable exact inference and marginal likelihood computation procedures so long as inference is tractable in the underlying syntax model  In sec:learn-with-inv we show that this derivation corresponds to an alternate view of our approach whereby we jointly learn a mapping of observed word embeddings to a new embedding space that is more suitable for the syntax model, but include an additional Jacobian regularization term to prevent information loss 
Recent work has sought to take advantage of word embeddings in unsupervised generative models with alternate approaches BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12   BIBREF9 build an HMM with Gaussian emissions on observed word embeddings, but they do not attempt to learn new embeddings  BIBREF10 , BIBREF11 , and BIBREF12 extend HMM or dependency model with valence (DMV) BIBREF2 with multinomials that use word (or tag) embeddings in their parameterization  However, they do not represent the embeddings as latent variables 
In experiments, we instantiate our approach using both a Markov-structured syntax model and a tree-structured syntax model – specifically, the DMV  We evaluate on two tasks: part-of-speech (POS) induction and unsupervised dependency parsing without gold POS tags  Experimental results on the Penn Treebank BIBREF13 demonstrate that our approach improves the basic HMM and DMV by a large margin, leading to the state-of-the-art results on POS induction, and state-of-the-art results on unsupervised dependency parsing in the difficult training scenario where neither gold POS annotation nor punctuation-based constraints are available 
Model
As an illustrative example, we first present a baseline model for Markov syntactic structure (POS induction) that treats a sequence of pre-trained word embeddings as observations  Then, we propose our novel approach, again using Markov structure, that introduces latent word embedding variables and a neural projector  Lastly, we extend our approach to more general syntactic structures 
Example: Gaussian HMM
We start by describing the Gaussian hidden Markov model introduced by BIBREF9 , which is a locally normalized model with multinomial transitions and Gaussian emissions  Given a sentence of length INLINEFORM0 , we denote the latent POS tags as INLINEFORM1 , observed (pre-trained) word embeddings as INLINEFORM2 , transition parameters as INLINEFORM3 , and Gaussian emission parameters as INLINEFORM4   The joint distribution of data and latent variables factors as:
DISPLAYFORM0
where INLINEFORM0 is the multinomial transition probability and INLINEFORM1 is the multivariate Gaussian emission probability 
While the observed word embeddings do inform this model with a notion of word similarity – lacking in the basic multinomial HMM – the Gaussian emissions may not be sufficiently flexible to separate some syntactic categories in the complex pre-trained embedding space – for example the skip-gram embedding space as visualized in Figure SECREF4 where different POS categories overlap  Next we introduce a new approach that adds flexibility to the emission distribution by incorporating new latent embedding variables 
Markov Structure with Neural Projector
To flexibly model observed embeddings and yield a new representation space that is more suitable for the syntax model, we propose to cascade a neural network as a projection function, deterministically transforming the simple space defined by the Gaussian HMM to the observed embedding space  We denote the latent embedding of the INLINEFORM0 word in a sentence as INLINEFORM1 , and the neural projection function as INLINEFORM2 , parameterized by INLINEFORM3   In the case of sequential Markov structure, our new model corresponds to the following generative process:
For each time step INLINEFORM0 ,
[noitemsep, leftmargin=*]
Draw the latent state INLINEFORM0
Draw the latent embedding INLINEFORM0
Deterministically produce embedding
INLINEFORM0
The graphical model is depicted in Figure FIGREF6   The deterministic projection can also be viewed as sampling each observation from a point mass at INLINEFORM0   The joint distribution of our model is: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, and INLINEFORM1 is the Dirac delta function centered at INLINEFORM2 : DISPLAYFORM0
General Structure with Neural Projector
Our approach can be applied to a broad family of structured syntax models  We denote latent embedding variables as INLINEFORM0 , discrete latent variables in the syntax model as INLINEFORM1 ( INLINEFORM2 ), where INLINEFORM3 are conditioned to generate INLINEFORM4   The joint probability of our model factors as:
DISPLAYFORM0
where INLINEFORM0 represents the probability of the syntax model, and can encode any syntactic structure – though, its factorization structure will determine whether inference is tractable in our full model  As shown in Figure FIGREF6 , we focus on two syntax models for syntactic analysis in this paper  The first is Markov-structured, which we use for POS induction, and the second is DMV-structured, which we use to learn dependency parses without supervision 
The marginal data likelihood of our model is: DISPLAYFORM0
While the discrete variables INLINEFORM0 can be marginalized out with dynamic program in many cases, it is generally intractable to marginalize out the latent continuous variables, INLINEFORM1 , for an arbitrary projection INLINEFORM2 in Eq  ( EQREF17 ), which means inference and learning may be difficult  In sec:opt, we address this issue by constraining INLINEFORM3 to be invertible, and show that this constraint enables tractable exact inference and marginal likelihood computation 
Learning & Inference
In this section, we introduce an invertibility condition for our neural projector to tackle the optimization challenge  Specifically, we constrain our neural projector with two requirements: (1) INLINEFORM0 and (2) INLINEFORM1 exists  Invertible transformations have been explored before in independent components analysis BIBREF14 , gaussianization BIBREF15 , and deep density models BIBREF16 , BIBREF17 , BIBREF18 , for unstructured data  Here, we generalize this style of approach to structured learning, and augment it with discrete latent variables ( INLINEFORM2 )  Under the invertibility condition, we derive a learning algorithm and give another view of our approach revealed by the objective function  Then, we present the architecture of a neural projector we use in experiments: a volume-preserving invertible neural network proposed by BIBREF16 for independent components estimation 
Learning with Invertibility
For ease of exposition, we explain the learning algorithm in terms of Markov structure without loss of generality  As shown in Eq  ( EQREF17 ), the optimization challenge in our approach comes from the intractability of the marginalized emission factor INLINEFORM0   If we can marginalize out INLINEFORM1 and compute INLINEFORM2 , then the posterior and marginal likelihood of our Markov-structured model can be computed with the forward-backward algorithm  We can apply Eq  ( EQREF14 ) and obtain : INLINEFORM3
By using the change of variable rule to the integration, which allows the integration variable INLINEFORM0 to be replaced by INLINEFORM1 , the marginal emission factor can be computed in closed-form when the invertibility condition is satisfied: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, INLINEFORM1 is the Jacobian matrix of function INLINEFORM2 at INLINEFORM3 , and INLINEFORM4 represents the absolute value of its determinant  This Jacobian term is nonzero and differentiable if and only if INLINEFORM5 exists 
Eq  ( EQREF19 ) shows that we can directly calculate the marginal emission distribution INLINEFORM0   Denote the marginal data likelihood of Gaussian HMM as INLINEFORM1 , then the log marginal data likelihood of our model can be directly written as: DISPLAYFORM0
where INLINEFORM0 represents the new sequence of embeddings after applying INLINEFORM1 to each INLINEFORM2   Eq  ( EQREF20 ) shows that the training objective of our model is simply the Gaussian HMM log likelihood with an additional Jacobian regularization term  From this view, our approach can be seen as equivalent to reversely projecting the data through INLINEFORM3 to another manifold INLINEFORM4 that is directly modeled by the Gaussian HMM, with a regularization term  Intuitively, we optimize the reverse projection INLINEFORM5 to modify the INLINEFORM6 space, making it more appropriate for the syntax model  The Jacobian regularization term accounts for the volume expansion or contraction behavior of the projection  Maximizing it can be thought of as preventing information loss  In the extreme case, the Jacobian determinant is equal to zero, which means the projection is non-invertible and thus information is being lost through the projection  Such “information preserving” regularization is crucial during optimization, otherwise the trivial solution of always projecting data to the same single point to maximize likelihood is viable 
More generally, for an arbitrary syntax model the data likelihood of our approach is: DISPLAYFORM0
If the syntax model itself allows for tractable inference and marginal likelihood computation, the same dynamic program can be used to marginalize out INLINEFORM0   Therefore, our joint model inherits the tractability of the underlying syntax model 
Invertible Volume-Preserving Neural Net
For the projection we can use an arbitrary invertible function, and given the representational power of neural networks they seem a natural choice  However, calculating the inverse and Jacobian of an arbitrary neural network can be difficult, as it requires that all component functions be invertible and also requires storage of large Jacobian matrices, which is memory intensive  To address this issue, several recent papers propose specially designed invertible networks that are easily trainable yet still powerful BIBREF16 , BIBREF17 , BIBREF19   Inspired by these works, we use the invertible transformation proposed by BIBREF16 , which consists of a series of “coupling layers”  This architecture is specially designed to guarantee a unit Jacobian determinant (and thus the invertibility property) 
From Eq  ( EQREF22 ) we know that only INLINEFORM0 is required for accomplishing learning and inference; we never need to explicitly construct INLINEFORM1   Thus, we directly define the architecture of INLINEFORM2   As shown in Figure FIGREF24 , the nonlinear transformation from the observed embedding INLINEFORM3 to INLINEFORM4 represents the first coupling layer  The input in this layer is partitioned into left and right halves of dimensions, INLINEFORM5 and INLINEFORM6 , respectively  A single coupling layer is defined as: DISPLAYFORM0
where INLINEFORM0 is the coupling function and can be any nonlinear form  This transformation satisfies INLINEFORM1 , and BIBREF16 show that its Jacobian matrix is triangular with all ones on the main diagonal  Thus the Jacobian determinant is always equal to one (i e  volume-preserving) and the invertibility condition is naturally satisfied 
To be sufficiently expressive, we compose multiple coupling layers as suggested in BIBREF16   Specifically, we exchange the role of left and right half vectors at each layer as shown in Figure FIGREF24   For instance, from INLINEFORM0 to INLINEFORM1 the left subset INLINEFORM2 is unchanged, while from INLINEFORM3 to INLINEFORM4 the right subset INLINEFORM5 remains the same  Also note that composing multiple coupling layers does not change the volume-preserving and invertibility properties  Such a sequence of invertible transformations from the data space INLINEFORM6 to INLINEFORM7 is also called normalizing flow BIBREF20  
Experiments
In this section, we first describe our datasets and experimental setup  We then instantiate our approach with Markov and DMV-structured syntax models, and report results on POS tagging and dependency grammar induction respectively  Lastly, we analyze the learned latent embeddings 
Data
For both POS tagging and dependency parsing, we run experiments on the Wall Street Journal (WSJ) portion of the Penn Treebank  To create the observed data embeddings, we train skip-gram word embeddings BIBREF7 that are found to capture syntactic properties well when trained with small context window BIBREF8 , BIBREF9   Following BIBREF9 , the dimensionality INLINEFORM0 is set to 100, and the training context window size is set to 1 to encode more syntactic information  The skip-gram embeddings are trained on the one billion word language modeling benchmark dataset BIBREF21 in addition to the WSJ corpus 
General Experimental Setup
For the neural projector, we employ rectified networks as coupling function INLINEFORM0 following BIBREF16   We use a rectified network with an input layer, one hidden layer, and linear output units, the number of hidden units is set to the same as the number of input units  The number of coupling layers are varied as 4, 8, 16 for both tasks
Context 3: Introduction
Data annotation is a major bottleneck for the application of supervised learning approaches to many problems  As a result, unsupervised methods that learn directly from unlabeled data are increasingly important  For tasks related to unsupervised syntactic analysis, discrete generative models have dominated in recent years – for example, for both part-of-speech (POS) induction BIBREF0 , BIBREF1 and unsupervised dependency parsing BIBREF2 , BIBREF3 , BIBREF4   While similar models have had success on a range of unsupervised tasks, they have mostly ignored the apparent utility of continuous word representations evident from supervised NLP applications BIBREF5 , BIBREF6   In this work, we focus on leveraging and explicitly representing continuous word embeddings within unsupervised models of syntactic structure 
Pre-trained word embeddings from massive unlabeled corpora offer a compact way of injecting a prior notion of word similarity into models that would otherwise treat words as discrete, isolated categories  However, the specific properties of language captured by any particular embedding scheme can be difficult to control, and, further, may not be ideally suited to the task at hand  For example, pre-trained skip-gram embeddings BIBREF7 with small context window size are found to capture the syntactic properties of language well BIBREF8 , BIBREF9   However, if our goal is to separate syntactic categories, this embedding space is not ideal – POS categories correspond to overlapping interspersed regions in the embedding space, evident in Figure SECREF4  
In our approach, we propose to learn a new latent embedding space as a projection of pre-trained embeddings (depicted in Figure SECREF5 ), while jointly learning latent syntactic structure – for example, POS categories or syntactic dependencies  To this end, we introduce a new generative model (shown in Figure FIGREF6 ) that first generates a latent syntactic representation (e g  a dependency parse) from a discrete structured prior (which we also call the “syntax model”), then, conditioned on this representation, generates a sequence of latent embedding random variables corresponding to each word, and finally produces the observed (pre-trained) word embeddings by projecting these latent vectors through a parameterized non-linear function  The latent embeddings can be jointly learned with the structured syntax model in a completely unsupervised fashion 
By choosing an invertible neural network as our non-linear projector, and then parameterizing our model in terms of the projection's inverse, we are able to derive tractable exact inference and marginal likelihood computation procedures so long as inference is tractable in the underlying syntax model  In sec:learn-with-inv we show that this derivation corresponds to an alternate view of our approach whereby we jointly learn a mapping of observed word embeddings to a new embedding space that is more suitable for the syntax model, but include an additional Jacobian regularization term to prevent information loss 
Recent work has sought to take advantage of word embeddings in unsupervised generative models with alternate approaches BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12   BIBREF9 build an HMM with Gaussian emissions on observed word embeddings, but they do not attempt to learn new embeddings  BIBREF10 , BIBREF11 , and BIBREF12 extend HMM or dependency model with valence (DMV) BIBREF2 with multinomials that use word (or tag) embeddings in their parameterization  However, they do not represent the embeddings as latent variables 
In experiments, we instantiate our approach using both a Markov-structured syntax model and a tree-structured syntax model – specifically, the DMV  We evaluate on two tasks: part-of-speech (POS) induction and unsupervised dependency parsing without gold POS tags  Experimental results on the Penn Treebank BIBREF13 demonstrate that our approach improves the basic HMM and DMV by a large margin, leading to the state-of-the-art results on POS induction, and state-of-the-art results on unsupervised dependency parsing in the difficult training scenario where neither gold POS annotation nor punctuation-based constraints are available 
Model
As an illustrative example, we first present a baseline model for Markov syntactic structure (POS induction) that treats a sequence of pre-trained word embeddings as observations  Then, we propose our novel approach, again using Markov structure, that introduces latent word embedding variables and a neural projector  Lastly, we extend our approach to more general syntactic structures 
Example: Gaussian HMM
We start by describing the Gaussian hidden Markov model introduced by BIBREF9 , which is a locally normalized model with multinomial transitions and Gaussian emissions  Given a sentence of length INLINEFORM0 , we denote the latent POS tags as INLINEFORM1 , observed (pre-trained) word embeddings as INLINEFORM2 , transition parameters as INLINEFORM3 , and Gaussian emission parameters as INLINEFORM4   The joint distribution of data and latent variables factors as:
DISPLAYFORM0
where INLINEFORM0 is the multinomial transition probability and INLINEFORM1 is the multivariate Gaussian emission probability 
While the observed word embeddings do inform this model with a notion of word similarity – lacking in the basic multinomial HMM – the Gaussian emissions may not be sufficiently flexible to separate some syntactic categories in the complex pre-trained embedding space – for example the skip-gram embedding space as visualized in Figure SECREF4 where different POS categories overlap  Next we introduce a new approach that adds flexibility to the emission distribution by incorporating new latent embedding variables 
Markov Structure with Neural Projector
To flexibly model observed embeddings and yield a new representation space that is more suitable for the syntax model, we propose to cascade a neural network as a projection function, deterministically transforming the simple space defined by the Gaussian HMM to the observed embedding space  We denote the latent embedding of the INLINEFORM0 word in a sentence as INLINEFORM1 , and the neural projection function as INLINEFORM2 , parameterized by INLINEFORM3   In the case of sequential Markov structure, our new model corresponds to the following generative process:
For each time step INLINEFORM0 ,
[noitemsep, leftmargin=*]
Draw the latent state INLINEFORM0
Draw the latent embedding INLINEFORM0
Deterministically produce embedding
INLINEFORM0
The graphical model is depicted in Figure FIGREF6   The deterministic projection can also be viewed as sampling each observation from a point mass at INLINEFORM0   The joint distribution of our model is: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, and INLINEFORM1 is the Dirac delta function centered at INLINEFORM2 : DISPLAYFORM0
General Structure with Neural Projector
Our approach can be applied to a broad family of structured syntax models  We denote latent embedding variables as INLINEFORM0 , discrete latent variables in the syntax model as INLINEFORM1 ( INLINEFORM2 ), where INLINEFORM3 are conditioned to generate INLINEFORM4   The joint probability of our model factors as:
DISPLAYFORM0
where INLINEFORM0 represents the probability of the syntax model, and can encode any syntactic structure – though, its factorization structure will determine whether inference is tractable in our full model  As shown in Figure FIGREF6 , we focus on two syntax models for syntactic analysis in this paper  The first is Markov-structured, which we use for POS induction, and the second is DMV-structured, which we use to learn dependency parses without supervision 
The marginal data likelihood of our model is: DISPLAYFORM0
While the discrete variables INLINEFORM0 can be marginalized out with dynamic program in many cases, it is generally intractable to marginalize out the latent continuous variables, INLINEFORM1 , for an arbitrary projection INLINEFORM2 in Eq  ( EQREF17 ), which means inference and learning may be difficult  In sec:opt, we address this issue by constraining INLINEFORM3 to be invertible, and show that this constraint enables tractable exact inference and marginal likelihood computation 
Learning & Inference
In this section, we introduce an invertibility condition for our neural projector to tackle the optimization challenge  Specifically, we constrain our neural projector with two requirements: (1) INLINEFORM0 and (2) INLINEFORM1 exists  Invertible transformations have been explored before in independent components analysis BIBREF14 , gaussianization BIBREF15 , and deep density models BIBREF16 , BIBREF17 , BIBREF18 , for unstructured data  Here, we generalize this style of approach to structured learning, and augment it with discrete latent variables ( INLINEFORM2 )  Under the invertibility condition, we derive a learning algorithm and give another view of our approach revealed by the objective function  Then, we present the architecture of a neural projector we use in experiments: a volume-preserving invertible neural network proposed by BIBREF16 for independent components estimation 
Learning with Invertibility
For ease of exposition, we explain the learning algorithm in terms of Markov structure without loss of generality  As shown in Eq  ( EQREF17 ), the optimization challenge in our approach comes from the intractability of the marginalized emission factor INLINEFORM0   If we can marginalize out INLINEFORM1 and compute INLINEFORM2 , then the posterior and marginal likelihood of our Markov-structured model can be computed with the forward-backward algorithm  We can apply Eq  ( EQREF14 ) and obtain : INLINEFORM3
By using the change of variable rule to the integration, which allows the integration variable INLINEFORM0 to be replaced by INLINEFORM1 , the marginal emission factor can be computed in closed-form when the invertibility condition is satisfied: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, INLINEFORM1 is the Jacobian matrix of function INLINEFORM2 at INLINEFORM3 , and INLINEFORM4 represents the absolute value of its determinant  This Jacobian term is nonzero and differentiable if and only if INLINEFORM5 exists 
Eq  ( EQREF19 ) shows that we can directly calculate the marginal emission distribution INLINEFORM0   Denote the marginal data likelihood of Gaussian HMM as INLINEFORM1 , then the log marginal data likelihood of our model can be directly written as: DISPLAYFORM0
where INLINEFORM0 represents the new sequence of embeddings after applying INLINEFORM1 to each INLINEFORM2   Eq  ( EQREF20 ) shows that the training objective of our model is simply the Gaussian HMM log likelihood with an additional Jacobian regularization term  From this view, our approach can be seen as equivalent to reversely projecting the data through INLINEFORM3 to another manifold INLINEFORM4 that is directly modeled by the Gaussian HMM, with a regularization term  Intuitively, we optimize the reverse projection INLINEFORM5 to modify the INLINEFORM6 space, making it more appropriate for the syntax model  The Jacobian regularization term accounts for the volume expansion or contraction behavior of the projection  Maximizing it can be thought of as preventing information loss  In the extreme case, the Jacobian determinant is equal to zero, which means the projection is non-invertible and thus information is being lost through the projection

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

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 datasets do they evaluate on?
Context 2:  We optimize marginal data likelihood directly using Adam BIBREF22   For both tasks in the fully unsupervised setting, we do not tune the hyper-parameters using supervised data 
Unsupervised POS tagging
For unsupervised POS tagging, we use a Markov-structured syntax model in our approach, which is a popular structure for unsupervised tagging tasks BIBREF9 , BIBREF10  
Following existing literature, we train and test on the entire WSJ corpus (49208 sentences, 1M tokens)  We use 45 tag clusters, the number of POS tags that appear in WSJ corpus  We train the discrete HMM and the Gaussian HMM BIBREF9 as baselines  For the Gaussian HMM, mean vectors of Gaussian emissions are initialized with the empirical mean of all word vectors with an additive noise  We assume diagonal covariance matrix for INLINEFORM0 and initialize it with the empirical variance of the word vectors  Following BIBREF9 , the covariance matrix is fixed during training  The multinomial probabilities are initialized as INLINEFORM1 , where INLINEFORM2   For our approach, we initialize the syntax model and Gaussian parameters with the pre-trained Gaussian HMM  The weights of layers in the rectified network are initialized from a uniform distribution with mean zero and a standard deviation of INLINEFORM3 , where INLINEFORM4 is the input dimension  We evaluate the performance of POS tagging with both Many-to-One (M-1) accuracy BIBREF23 and V-Measure (VM) BIBREF24   Given a model we found that the tagging performance is well-correlated with the training data likelihood, thus we use training data likelihood as a unsupervised criterion to select the trained model over 10 random restarts after training 50 epochs  We repeat this process 5 times and report the mean and standard deviation of performance 
We compare our approach with basic HMM, Gaussian HMM, and several state-of-the-art systems, including sophisticated HMM variants and clustering techniques with hand-engineered features  The results are presented in Table TABREF32   Through the introduced latent embeddings and additional neural projection, our approach improves over the Gaussian HMM by 5 4 points in M-1 and 5 6 points in VM  Neural HMM (NHMM) BIBREF10 is a baseline that also learns word representation jointly  Both their basic model and extended Conv version does not outperform the Gaussian HMM  Their best model incorporates another LSTM to model long distance dependency and breaks the Markov assumption, yet our approach still achieves substantial improvement over it without considering more context information  Moreover, our method outperforms the best published result that benefits from hand-engineered features BIBREF27 by 2 0 points on VM 
We found that most tagging errors happen in noun subcategories  Therefore, we do the one-to-one mapping between gold POS tags and induced clusters and plot the normalized confusion matrix of noun subcategories in Figure FIGREF35   The Gaussian HMM fails to identify “NN” and “NNS” correctly for most cases, and it often recognizes “NNPS” as “NNP”  In contrast, our approach corrects these errors well 
Unsupervised Dependency Parsing without gold POS tags
For the task of unsupervised dependency parse induction, we employ the Dependency Model with Valence (DMV) BIBREF2 as the syntax model in our approach  DMV is a generative model that defines a probability distribution over dependency parse trees and syntactic categories, generating tokens and dependencies in a head-outward fashion  While, traditionally, DMV is trained using gold POS tags as observed syntactic categories, in our approach, we treat each tag as a latent variable, as described in sec:general-neural 
Most existing approaches to this task are not fully unsupervised since they rely on gold POS tags following the original experimental setup for DMV  This is partially because automatically parsing from words is difficult even when using unsupervised syntactic categories BIBREF29   However, inducing dependencies from words alone represents a more realistic experimental condition since gold POS tags are often unavailable in practice  Previous work that has trained from words alone often requires additional linguistic constraints (like sentence internal boundaries) BIBREF29 , BIBREF30 , BIBREF31 , BIBREF32 , acoustic cues BIBREF33 , additional training data BIBREF4 , or annotated data from related languages BIBREF34   Our approach is naturally designed to train on word embeddings directly, thus we attempt to induce dependencies without using gold POS tags or other extra linguistic information 
Like previous work we use sections 02-21 of WSJ corpus as training data and evaluate on section 23, we remove punctuations and train the models on sentences of length INLINEFORM0 , “head-percolation” rules BIBREF39 are applied to obtain gold dependencies for evaluation  We train basic DMV, extended DMV (E-DMV) BIBREF35 and Gaussian DMV (which treats POS tag as unknown latent variables and generates observed word embeddings directly conditioned on them following Gaussian distribution) as baselines  Basic DMV and E-DMV are trained with Viterbi EM BIBREF40 on unsupervised POS tags induced from our Markov-structured model described in sec:pos  Multinomial parameters of the syntax model in both Gaussian DMV and our model are initialized with the pre-trained DMV baseline  Other parameters are initialized in the same way as in the POS tagging experiment  The directed dependency accuracy (DDA) is used for evaluation and we report accuracy on sentences of length INLINEFORM1 and all lengths  We train the parser until training data likelihood converges, and report the mean and standard deviation over 20 random restarts 
Our model directly observes word embeddings and does not require gold POS tags during training  Thus, results from related work trained on gold tags are not directly comparable  However, to measure how these systems might perform without gold tags, we run three recent state-of-the-art systems in our experimental setting: UR-A E-DMV BIBREF36 , Neural E-DMV BIBREF11 , and CRF Autoencoder (CRFAE) BIBREF37   We use unsupervised POS tags (induced from our Markov-structured model) in place of gold tags  We also train basic DMV on gold tags and include several state-of-the-art results on gold tags as reference points 
As shown in Table TABREF39 , our approach is able to improve over the Gaussian DMV by 4 8 points on length INLINEFORM0 and 4 8 points on all lengths, which suggests the additional latent embedding layer and neural projector are helpful  The proposed approach yields, to the best of our knowledge, state-of-the-art performance without gold POS annotation and without sentence-internal boundary information  DMV, UR-A E-DMV, Neural E-DMV, and CRFAE suffer a large decrease in performance when trained on unsupervised tags – an effect also seen in previous work BIBREF29 , BIBREF34   Since our approach induces latent POS tags jointly with dependency trees, it may be able to learn POS clusters that are more amenable to grammar induction than the unsupervised tags  We observe that CRFAE underperforms its gold-tag counterpart substantially  This may largely be a result of the model's reliance on prior linguistic rules that become unavailable when gold POS tag types are unknown  Many extensions to DMV can be considered orthogonal to our approach – they essentially focus on improving the syntax model  It is possible that incorporating these more sophisticated syntax models into our approach may lead to further improvements 
Sensitivity Analysis
In the above experiments we initialize the structured syntax components with the pre-trained Gaussian or discrete baseline, which is shown as a useful technique to help train our deep models  We further study the results with fully random initialization  In the POS tagging experiment, we report the results in Table TABREF48   While the performance with 4 layers is comparable to the pre-trained Gaussian initialization, deeper projections (8 or 16 layers) result in a dramatic drop in performance  This suggests that the structured syntax model with very deep projections is difficult to train from scratch, and a simpler projection might be a good compromise in the random initialization setting 
Different from the Markov prior in POS tagging experiments, our parsing model seems to be quite sensitive to the initialization  For example, directed accuracy of our approach on sentences of length INLINEFORM0 is below 40 0 with random initialization  This is consistent with previous work that has noted the importance of careful initialization for DMV-based models such as the commonly used harmonic initializer BIBREF2   However, it is not straightforward to apply the harmonic initializer for DMV directly in our model without using some kind of pre-training since we do not observe gold POS 
We investigate the effect of the choice of pre-trained embedding on performance while using our approach  To this end, we additionally include results using fastText embeddings BIBREF41 – which, in contrast with skip-gram embeddings, include character-level information  We set the context windows size to 1 and the dimension size to 100 as in the skip-gram training, while keeping other parameters set to their defaults  These results are summarized in Table TABREF50 and Table TABREF51   While fastText embeddings lead to reduced performance with our model, our approach still yields an improvement over the Gaussian baseline with the new observed embeddings space 
Qualitative Analysis of Embeddings
We perform qualitative analysis to understand how the latent embeddings help induce syntactic structures  First we filter out low-frequency words and punctuations in WSJ, and visualize the rest words (10k) with t-SNE BIBREF42 under different embeddings  We assign each word with its most likely gold POS tags in WSJ and color them according to the gold POS tags 
For our Markov-structured model, we have displayed the embedding space in Figure SECREF5 , where the gold POS clusters are well-formed  Further, we present five example target words and their five nearest neighbors in terms of cosine similarity  As shown in Table TABREF53 , the skip-gram embedding captures both semantic and syntactic aspects to some degree, yet our embeddings are able to focus especially on the syntactic aspects of words, in an unsupervised fashion without using any extra morphological information 
In Figure FIGREF54 we depict the learned latent embeddings with the DMV-structured syntax model  Unlike the Markov structure, the DMV structure maps a large subset of singular and plural nouns to the same overlapping region  However, two clusters of singular and plural nouns are actually separated  We inspect the two clusters and the overlapping region in Figure FIGREF54 , it turns out that the nouns in the separated clusters are words that can appear as subjects and, therefore, for which verb agreement is important to model  In contrast, the nouns in the overlapping region are typically objects  This demonstrates that the latent embeddings are focusing on aspects of language that are specifically important for modeling dependency without ever having seen examples of dependency parses  Some previous work has deliberately created embeddings to capture different notions of similarity BIBREF43 , BIBREF44 , while they use extra morphology or dependency annotations to guide the embedding learning, our approach provides a potential alternative to create new embeddings that are guided by structured syntax model, only using unlabeled text corpora 
Related Work
Our approach is related to flow-based generative models, which are first described in NICE BIBREF16 and have recently received more attention BIBREF17 , BIBREF19 , BIBREF18   This relevant work mostly adopts simple (e g  Gaussian) and fixed priors and does not attempt to learn interpretable latent structures  Another related generative model class is variational auto-encoders (VAEs) BIBREF45 that optimize a lower bound on the marginal data likelihood, and can be extended to learn latent structures BIBREF46 , BIBREF47   Against the flow-based models, VAEs remove the invertibility constraint but sacrifice the merits of exact inference and exact log likelihood computation, which potentially results in optimization challenges BIBREF48   Our approach can also be viewed in connection with generative adversarial networks (GANs) BIBREF49 that is a likelihood-free framework to learn implicit generative models  However, it is non-trivial for a gradient-based method like GANs to propagate gradients through discrete structures 
Conclusion
In this work, we define a novel generative approach to leverage continuous word representations for unsupervised learning of syntactic structure  Experiments on both POS induction and unsupervised dependency parsing tasks demonstrate the effectiveness of our proposed approach  Future work might explore more sophisticated invertible projections, or recurrent projections that jointly transform the entire input sequence 
Context 3:  Such “information preserving” regularization is crucial during optimization, otherwise the trivial solution of always projecting data to the same single point to maximize likelihood is viable 
More generally, for an arbitrary syntax model the data likelihood of our approach is: DISPLAYFORM0
If the syntax model itself allows for tractable inference and marginal likelihood computation, the same dynamic program can be used to marginalize out INLINEFORM0   Therefore, our joint model inherits the tractability of the underlying syntax model 
Invertible Volume-Preserving Neural Net
For the projection we can use an arbitrary invertible function, and given the representational power of neural networks they seem a natural choice  However, calculating the inverse and Jacobian of an arbitrary neural network can be difficult, as it requires that all component functions be invertible and also requires storage of large Jacobian matrices, which is memory intensive  To address this issue, several recent papers propose specially designed invertible networks that are easily trainable yet still powerful BIBREF16 , BIBREF17 , BIBREF19   Inspired by these works, we use the invertible transformation proposed by BIBREF16 , which consists of a series of “coupling layers”  This architecture is specially designed to guarantee a unit Jacobian determinant (and thus the invertibility property) 
From Eq  ( EQREF22 ) we know that only INLINEFORM0 is required for accomplishing learning and inference; we never need to explicitly construct INLINEFORM1   Thus, we directly define the architecture of INLINEFORM2   As shown in Figure FIGREF24 , the nonlinear transformation from the observed embedding INLINEFORM3 to INLINEFORM4 represents the first coupling layer  The input in this layer is partitioned into left and right halves of dimensions, INLINEFORM5 and INLINEFORM6 , respectively  A single coupling layer is defined as: DISPLAYFORM0
where INLINEFORM0 is the coupling function and can be any nonlinear form  This transformation satisfies INLINEFORM1 , and BIBREF16 show that its Jacobian matrix is triangular with all ones on the main diagonal  Thus the Jacobian determinant is always equal to one (i e  volume-preserving) and the invertibility condition is naturally satisfied 
To be sufficiently expressive, we compose multiple coupling layers as suggested in BIBREF16   Specifically, we exchange the role of left and right half vectors at each layer as shown in Figure FIGREF24   For instance, from INLINEFORM0 to INLINEFORM1 the left subset INLINEFORM2 is unchanged, while from INLINEFORM3 to INLINEFORM4 the right subset INLINEFORM5 remains the same  Also note that composing multiple coupling layers does not change the volume-preserving and invertibility properties  Such a sequence of invertible transformations from the data space INLINEFORM6 to INLINEFORM7 is also called normalizing flow BIBREF20  
Experiments
In this section, we first describe our datasets and experimental setup  We then instantiate our approach with Markov and DMV-structured syntax models, and report results on POS tagging and dependency grammar induction respectively  Lastly, we analyze the learned latent embeddings 
Data
For both POS tagging and dependency parsing, we run experiments on the Wall Street Journal (WSJ) portion of the Penn Treebank  To create the observed data embeddings, we train skip-gram word embeddings BIBREF7 that are found to capture syntactic properties well when trained with small context window BIBREF8 , BIBREF9   Following BIBREF9 , the dimensionality INLINEFORM0 is set to 100, and the training context window size is set to 1 to encode more syntactic information  The skip-gram embeddings are trained on the one billion word language modeling benchmark dataset BIBREF21 in addition to the WSJ corpus 
General Experimental Setup
For the neural projector, we employ rectified networks as coupling function INLINEFORM0 following BIBREF16   We use a rectified network with an input layer, one hidden layer, and linear output units, the number of hidden units is set to the same as the number of input units  The number of coupling layers are varied as 4, 8, 16 for both tasks  We optimize marginal data likelihood directly using Adam BIBREF22   For both tasks in the fully unsupervised setting, we do not tune the hyper-parameters using supervised data 
Unsupervised POS tagging
For unsupervised POS tagging, we use a Markov-structured syntax model in our approach, which is a popular structure for unsupervised tagging tasks BIBREF9 , BIBREF10  
Following existing literature, we train and test on the entire WSJ corpus (49208 sentences, 1M tokens)  We use 45 tag clusters, the number of POS tags that appear in WSJ corpus  We train the discrete HMM and the Gaussian HMM BIBREF9 as baselines  For the Gaussian HMM, mean vectors of Gaussian emissions are initialized with the empirical mean of all word vectors with an additive noise  We assume diagonal covariance matrix for INLINEFORM0 and initialize it with the empirical variance of the word vectors  Following BIBREF9 , the covariance matrix is fixed during training  The multinomial probabilities are initialized as INLINEFORM1 , where INLINEFORM2   For our approach, we initialize the syntax model and Gaussian parameters with the pre-trained Gaussian HMM  The weights of layers in the rectified network are initialized from a uniform distribution with mean zero and a standard deviation of INLINEFORM3 , where INLINEFORM4 is the input dimension  We evaluate the performance of POS tagging with both Many-to-One (M-1) accuracy BIBREF23 and V-Measure (VM) BIBREF24   Given a model we found that the tagging performance is well-correlated with the training data likelihood, thus we use training data likelihood as a unsupervised criterion to select the trained model over 10 random restarts after training 50 epochs  We repeat this process 5 times and report the mean and standard deviation of performance 
We compare our approach with basic HMM, Gaussian HMM, and several state-of-the-art systems, including sophisticated HMM variants and clustering techniques with hand-engineered features  The results are presented in Table TABREF32   Through the introduced latent embeddings and additional neural projection, our approach improves over the Gaussian HMM by 5 4 points in M-1 and 5 6 points in VM  Neural HMM (NHMM) BIBREF10 is a baseline that also learns word representation jointly  Both their basic model and extended Conv version does not outperform the Gaussian HMM  Their best model incorporates another LSTM to model long distance dependency and breaks the Markov assumption, yet our approach still achieves substantial improvement over it without considering more context information  Moreover, our method outperforms the best published result that benefits from hand-engineered features BIBREF27 by 2 0 points on VM 
We found that most tagging errors happen in noun subcategories  Therefore, we do the one-to-one mapping between gold POS tags and induced clusters and plot the normalized confusion matrix of noun subcategories in Figure FIGREF35   The Gaussian HMM fails to identify “NN” and “NNS” correctly for most cases, and it often recognizes “NNPS” as “NNP”  In contrast, our approach corrects these errors well 
Unsupervised Dependency Parsing without gold POS tags
For the task of unsupervised dependency parse induction, we employ the Dependency Model with Valence (DMV) BIBREF2 as the syntax model in our approach  DMV is a generative model that defines a probability distribution over dependency parse trees and syntactic categories, generating tokens and dependencies in a head-outward fashion  While, traditionally, DMV is trained using gold POS tags as observed syntactic categories, in our approach, we treat each tag as a latent variable, as described in sec:general-neural 
Most existing approaches to this task are not fully unsupervised since they rely on gold POS tags following the original experimental setup for DMV

ground_truth:  Wall Street Journal (WSJ) portion of the Penn Treebank

Unanswerable

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 is the invertibility condition?
Context 3:  This is partially because automatically parsing from words is difficult even when using unsupervised syntactic categories BIBREF29   However, inducing dependencies from words alone represents a more realistic experimental condition since gold POS tags are often unavailable in practice  Previous work that has trained from words alone often requires additional linguistic constraints (like sentence internal boundaries) BIBREF29 , BIBREF30 , BIBREF31 , BIBREF32 , acoustic cues BIBREF33 , additional training data BIBREF4 , or annotated data from related languages BIBREF34   Our approach is naturally designed to train on word embeddings directly, thus we attempt to induce dependencies without using gold POS tags or other extra linguistic information 
Like previous work we use sections 02-21 of WSJ corpus as training data and evaluate on section 23, we remove punctuations and train the models on sentences of length INLINEFORM0 , “head-percolation” rules BIBREF39 are applied to obtain gold dependencies for evaluation  We train basic DMV, extended DMV (E-DMV) BIBREF35 and Gaussian DMV (which treats POS tag as unknown latent variables and generates observed word embeddings directly conditioned on them following Gaussian distribution) as baselines  Basic DMV and E-DMV are trained with Viterbi EM BIBREF40 on unsupervised POS tags induced from our Markov-structured model described in sec:pos  Multinomial parameters of the syntax model in both Gaussian DMV and our model are initialized with the pre-trained DMV baseline  Other parameters are initialized in the same way as in the POS tagging experiment  The directed dependency accuracy (DDA) is used for evaluation and we report accuracy on sentences of length INLINEFORM1 and all lengths  We train the parser until training data likelihood converges, and report the mean and standard deviation over 20 random restarts 
Our model directly observes word embeddings and does not require gold POS tags during training  Thus, results from related work trained on gold tags are not directly comparable  However, to measure how these systems might perform without gold tags, we run three recent state-of-the-art systems in our experimental setting: UR-A E-DMV BIBREF36 , Neural E-DMV BIBREF11 , and CRF Autoencoder (CRFAE) BIBREF37   We use unsupervised POS tags (induced from our Markov-structured model) in place of gold tags  We also train basic DMV on gold tags and include several state-of-the-art results on gold tags as reference points 
As shown in Table TABREF39 , our approach is able to improve over the Gaussian DMV by 4 8 points on length INLINEFORM0 and 4 8 points on all lengths, which suggests the additional latent embedding layer and neural projector are helpful  The proposed approach yields, to the best of our knowledge, state-of-the-art performance without gold POS annotation and without sentence-internal boundary information  DMV, UR-A E-DMV, Neural E-DMV, and CRFAE suffer a large decrease in performance when trained on unsupervised tags – an effect also seen in previous work BIBREF29 , BIBREF34   Since our approach induces latent POS tags jointly with dependency trees, it may be able to learn POS clusters that are more amenable to grammar induction than the unsupervised tags  We observe that CRFAE underperforms its gold-tag counterpart substantially  This may largely be a result of the model's reliance on prior linguistic rules that become unavailable when gold POS tag types are unknown  Many extensions to DMV can be considered orthogonal to our approach – they essentially focus on improving the syntax model  It is possible that incorporating these more sophisticated syntax models into our approach may lead to further improvements 
Sensitivity Analysis
In the above experiments we initialize the structured syntax components with the pre-trained Gaussian or discrete baseline, which is shown as a useful technique to help train our deep models  We further study the results with fully random initialization  In the POS tagging experiment, we report the results in Table TABREF48   While the performance with 4 layers is comparable to the pre-trained Gaussian initialization, deeper projections (8 or 16 layers) result in a dramatic drop in performance  This suggests that the structured syntax model with very deep projections is difficult to train from scratch, and a simpler projection might be a good compromise in the random initialization setting 
Different from the Markov prior in POS tagging experiments, our parsing model seems to be quite sensitive to the initialization  For example, directed accuracy of our approach on sentences of length INLINEFORM0 is below 40 0 with random initialization  This is consistent with previous work that has noted the importance of careful initialization for DMV-based models such as the commonly used harmonic initializer BIBREF2   However, it is not straightforward to apply the harmonic initializer for DMV directly in our model without using some kind of pre-training since we do not observe gold POS 
We investigate the effect of the choice of pre-trained embedding on performance while using our approach  To this end, we additionally include results using fastText embeddings BIBREF41 – which, in contrast with skip-gram embeddings, include character-level information  We set the context windows size to 1 and the dimension size to 100 as in the skip-gram training, while keeping other parameters set to their defaults  These results are summarized in Table TABREF50 and Table TABREF51   While fastText embeddings lead to reduced performance with our model, our approach still yields an improvement over the Gaussian baseline with the new observed embeddings space 
Qualitative Analysis of Embeddings
We perform qualitative analysis to understand how the latent embeddings help induce syntactic structures  First we filter out low-frequency words and punctuations in WSJ, and visualize the rest words (10k) with t-SNE BIBREF42 under different embeddings  We assign each word with its most likely gold POS tags in WSJ and color them according to the gold POS tags 
For our Markov-structured model, we have displayed the embedding space in Figure SECREF5 , where the gold POS clusters are well-formed  Further, we present five example target words and their five nearest neighbors in terms of cosine similarity  As shown in Table TABREF53 , the skip-gram embedding captures both semantic and syntactic aspects to some degree, yet our embeddings are able to focus especially on the syntactic aspects of words, in an unsupervised fashion without using any extra morphological information 
In Figure FIGREF54 we depict the learned latent embeddings with the DMV-structured syntax model  Unlike the Markov structure, the DMV structure maps a large subset of singular and plural nouns to the same overlapping region  However, two clusters of singular and plural nouns are actually separated  We inspect the two clusters and the overlapping region in Figure FIGREF54 , it turns out that the nouns in the separated clusters are words that can appear as subjects and, therefore, for which verb agreement is important to model  In contrast, the nouns in the overlapping region are typically objects  This demonstrates that the latent embeddings are focusing on aspects of language that are specifically important for modeling dependency without ever having seen examples of dependency parses  Some previous work has deliberately created embeddings to capture different notions of similarity BIBREF43 , BIBREF44 , while they use extra morphology or dependency annotations to guide the embedding learning, our approach provides a potential alternative to create new embeddings that are guided by structured syntax model, only using unlabeled text corpora 
Related Work
Our approach is related to flow-based generative models, which are first described in NICE BIBREF16 and have recently received more attention BIBREF17 , BIBREF19 , BIBREF18   This relevant work mostly adopts simple (e g  Gaussian) and fixed priors and does not attempt to learn interpretable latent structures  Another related generative model class is variational auto-encoders (VAEs) BIBREF45 that optimize a lower bound on the marginal data likelihood, and can be extended to learn latent structures BIBREF46 , BIBREF47   Against the flow-based models, VAEs remove the invertibility constraint but sacrifice the merits of exact inference and exact log likelihood computation, which potentially results in optimization challenges BIBREF48   Our approach can also be viewed in connection with generative adversarial networks (GANs) BIBREF49 that is a likelihood-free framework to learn implicit generative models  However, it is non-trivial for a gradient-based method like GANs to propagate gradients through discrete structures 
Conclusion
In this work, we define a novel generative approach to leverage continuous word representations for unsupervised learning of syntactic structure  Experiments on both POS induction and unsupervised dependency parsing tasks demonstrate the effectiveness of our proposed approach  Future work might explore more sophisticated invertible projections, or recurrent projections that jointly transform the entire input sequence 

ground_truth: The neural projector must be invertible.

we constrain our neural projector with two requirements: (1) INLINEFORM0 and (2) INLINEFORM1 exists