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Title: Discovering the compositional structure of vector representations with Role Learning Networks

Paper content:
Neural networks (NNs) are able to perform tasks that rely on compositional structure even though they lack obvious mechanisms for representing this structure.
To analyze the internal representations that enable such success, we propose ROLE, a technique that detects whether these representations implicitly encode symbolic structure.
ROLE learns to approximate the representations of a target encoder E by learning a symbolic constituent structure and an embedding of that structure into E’s representational vector space.
The constituents of the approximating symbol structure are defined by structural positions — roles — that can be filled by symbols.
We show that when E is constructed to explicitly embed a particular type of structure (e.g., string or tree), ROLE successfully extracts the ground-truth roles defining that structure.
We then analyze a seq2seq network trained to perform a more complex compositional task (SCAN), where there is no ground truth role scheme available.
For this model, ROLE successfully discovers an interpretable symbolic structure that the model implicitly uses to perform the SCAN task, providing a comprehensive account of the link between the representations and the behavior of a notoriously hard-to-interpret type of model.
We verify the causal importance of the discovered symbolic structure by showing that, when we systematically manipulate hidden embeddings based on this symbolic structure, the model’s output is also changed in the way predicted by our analysis.
Finally, we use ROLE to explore whether popular sentence embedding models are capturing compositional structure and find evidence that they are not; we conclude by discussing how insights from ROLE can be used to impart new inductive biases that will improve the compositional abilities of such models.
We have introduced ROLE, a neural network that learns to approximate the representations of an existing target neural network E using an explicit symbolic structure.
ROLE successfully discovers symbolic structure both in models that explicitly define this structure and in an RNN without explicit structure trained on the fully-compositional SCAN task.
When applied to sentence embedding models trained on partially-compositional tasks, ROLE performs better than hand-specified role schemes but still provides little evidence that the sentence encodings represent compositional structure.
Uncovering the latent symbolic structure of NN representations on fully-compositional tasks is a significant step towards explaining how they can achieve the level of compositional generalization that they do, and suggests types of inductive bias to improve such generalization for partially-compositional tasks.
We offer several observations about this algorithm.
1. This algorithm may seem convoluted, but a few observations can illuminate how the roles assigned by such an algorithm support success on the SCAN task.
First, a sequence will contain role 30 if and only if it contains and, and it will contain role 17 if and only if it contains after.
Thus, by implicitly checking for the presence of these two roles (regardless of the fillers bound to them), the decoder can tell whether the output involves one or two basic commands, where the presence of and or after leads to two basic commands and the absence of both leads to one basic command.
Moreover, if there are two basic commands, whether it is role 17 or role 30 that is present can tell the decoder whether the input order of these commands also corresponds to their output order (when it is and in play, i.e., role 30), or if the input order is reversed (when it is after in play, i.e., role 17).
With these basic structural facts established, the decoder can begin to decode the specific commands.
For example, if the input is a sequence with after, it can begin with the command after after, which it can decode by checking which fillers are bound to the relevant roles for that type of command.
It may seem odd that so many of the roles are based on position (e.g., "first word" and "second-to-last word"), rather than more functionally-relevant categories such as "direction word."
However, this approach may actually be more efficient: Each command consists of a single mandatory element (namely, an action word such as walk or jump) followed by several optional modifiers (namely, rotation words, direction words, and cardinalities).
Because most of the word categories are optional, it might be inefficient to check for the presence of, e.g., a cardinality, since many sequences will not have one.
By contrast, every sequence will have a last word, and checking the identity of the last word provides much functionally-relevant information: if that word is not a cardinality, then the decoder knows that there is no cardinality present in the command (because if there were, it would be the last word); and if it is a cardinality, then that is important to know, because the presence of twice or thrice can dramatically affect the shape of the output sequence.
In this light, it is unsurprising that the SCAN encoder has implicitly learned several different roles that essentially mean the last element of a particular subcommand.
2. The algorithm does not constitute a simple, transparent role scheme.
But its job is to describe the representations that the original network produces, and we have no a priori expectation about how complex that process may be.
The role-assignment algorithm implicitly learned by ROLE is interpretable locally (each line is readily expressible in simple English), but not intuitively transparent globally.
We see this as a positive result, in two respects.
First, it shows why ROLE is crucial: no human-generated role scheme would provide a good approximation to this algorithm.
Such an algorithm can only be identified because ROLE is able to use gradient descent to find role schemes far more complex than any we would hypothesize intuitively.
This enables us to analyze networks far more complex than we could analyze previously, being necessarily limited to hand-designed role schemes based on human intuitions about how to perform the task.
Second, when future work illuminates the computation in the original SCAN GRU seq2seq decoder, the baroqueness of the role-assignment algorithm that ROLE has shown to be implicit in the seq2seq encoder can potentially explain certain limitations in the original model, which is known to suffer from severe failures of systematic generalization outside the training distribution (Lake and Baroni, 2018).
It is reasonable to hypothesize that systematic generalization requires that the encoder learn an implicit role scheme that is relatively simple and highly compositional.
Future proposals for improving the systematic generalization of models on SCAN can be examined using ROLE to test the hypothesis that greater systematicity requires greater compositional simplicity in the role scheme implicitly learned by the encoder.
3. While the role-assignment algorithm of A.8.1 may not be simple, from a certain perspective, it is quite surprising that it is not far more complex.
Although ROLE is provided 50 roles to learn to deploy as it likes, it only chooses to use 16 of them (only 16 are ever selected as the arg max(a t ); see Sec. 6.1).
Furthermore, the SCAN grammar generates 20,910 input sequences, containing a total of 151,688 words (an average of 7.25 words per input).
This means that, if one were to generate a series of conditional statements to determine which role is assigned to each word in every context, this could in theory require up to 151,688 conditionals (e.g., "if the filler is 'jump' in the context 'walk thrice after opposite left', then assign role 17").
However, our algorithm involves just 47 conditionals.
This reduction helps explain how the model performs so well on the test set: If it used many more of the 151,688 possible conditional rules, it would completely overfit the training examples in a way that would be unlikely to generalize.
The 47-conditional algorithm we found is more likely to generalize by abstracting over many details of the context.
4. Were it not for ROLE's ability to characterize the representations generated by the original encoder in terms of implicit roles, providing an equally complete and accurate interpretation of those representations would necessarily require identifying the conditions determining the activation level of each of the 100 neurons hosting those representations.
It seems to us grossly overly optimistic to estimate that each neuron's activation level in the representation of a given input could be characterized by a property of the input statable in, say, two lines of roughly 20 words/symbols; yet even then, the algorithm would require 200 lines, whereas the algorithm in A.8.1 requires 47 lines of that scale.
Thus, by even such a crude estimate of the degree of complexity expected for an algorithm describing the representations in terms of neuron activities, the algorithm we find, stated over roles, is 4 times simpler.

assistant: text: We introduce a new analysis technique that discovers interpretable compositional structure in notoriously hard-to-interpret recurrent neural networks.