Order Matters: Sequence to sequence for sets (1511.06391v4)

Abstract: Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark LLMing and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

• The paper empirically demonstrates that the ordering of inputs and outputs critically impacts seq2seq performance, with reversals notably improving BLEU and F1 scores.
• The paper proposes novel extensions for unordered sets, employing attention-based encoding for inputs and a dynamic order search for outputs.
• The paper validates these methods on tasks like sorting and parsing, achieving significant gains in accuracy and efficiency over traditional approaches.

Order Matters: Sequence to Sequence for Sets

This paper by Vinyals et al. addresses the challenge of applying the sequence-to-sequence (seq2seq) framework to problems where the input and/or output is a set rather than a sequence. Traditionally, seq2seq models have demonstrated efficacy across a broad range of tasks in natural language processing, such as machine translation and image captioning. However, these tasks inherently assume a fixed order in the input and output sequences. Vinyals et al. argue that for tasks involving sets, the lack of a natural order necessitates reconsideration of the seq2seq framework.

Main Contributions

1. Empirical Analysis of Ordering: The paper provides compelling empirical evidence that the order in which input and/or output data is presented to a model significantly affects its performance. They demonstrate this by reordering data in machine translation and parsing tasks, observing notable differences in performance metrics.
2. Extension of Seq2seq for Input Sets: The authors propose a novel extension to handle unordered input sets. This approach employs attention mechanisms to ensure permutation invariance and avoids the inefficiency of fixed-dimensional representations like bag-of-words models.
3. Extension for Output Sets: To handle unordered output sets, the paper introduces a method incorporating a search over possible output orders during training. This approach maximizes the conditional probability over the optimal ordering, identified dynamically.
4. Experimental Validation: The modifications to the seq2seq framework are validated on benchmark datasets and artificial tasks, including sorting numbers and estimating the joint probability of unknown graphical models. The results underscore the significance of order and demonstrate the effectiveness of the proposed methods.

Key Findings

1. Impact of Input Order: The authors highlight scenarios in which the order of inputs considerably impacts model performance. For instance, reversing the input sequence improved BLEU scores in machine translation by 5.0 points and F1 scores in parsing by 0.5%.
2. Read-Process-Write Architecture: They implement a Read-Process-Write model, utilizing attention mechanisms for encoding input sets. This architecture outperforms traditional seq2seq models on sorting tasks when the process includes attention-induced processing steps.
3. Output Order Matters: Experiments reveal that the choice of output order affects LLMing and parsing tasks. For example, different linearizations of parse trees yielded substantial variations in F1 scores, indicating the influence of output ordering on model performance.
4. Search Over Orders: The paper outlines a strategy of searching over possible orders during training using a sampling-based approach. This method maintains computational feasibility while enabling the model to learn the optimal order dynamically.

Numerical Results

Table 1 in the paper shows that for sorting numbers, the proposed model with process steps outperforms the vanilla seq2seq approach. For instance, with 10 process steps, the accuracy for sorting 10 items improves from 8% to 50%. These results validate the effectiveness of the Read-Process-Write architecture. Furthermore, the LLMing experiment reports perplexities of 225 with natural order versus 280 with a random ordering, underscoring the importance of order.

Practical and Theoretical Implications

The findings have profound implications for both theoretical and practical applications of seq2seq models:

• Theoretical: This work provokes a reevaluation of the assumptions underlying sequence modeling. It bridges the understanding of how RNNs handle dependency structures in unordered data and suggests potential directions for future models that can dynamically determine optimal data orderings.
• Practical: From a practical standpoint, the proposed methods can enhance the performance of models in applications where data lacks a natural order. This advancement opens pathways for more efficient handling of tasks like object detection, where detected objects do not follow a predefined sequence.

Future Directions

The paper suggests multiple avenues for future research:

1. Dynamic Ordering in Practical Tasks: Extended exploration of dynamic ordering methods in diverse real-world applications, such as recommender systems and question answering, could provide deeper insights.
2. Scaling Techniques: Developing more scalable techniques for searching over orders efficiently, including integrating these methods into larger, more complex models.
3. Model Interpretability: Investigating how dynamic order selection impacts the interpretability of model decisions, particularly in critical applications like healthcare and finance.

Conclusion

Vinyals et al. provide an essential extension to the seq2seq framework, facilitating its application to sets by addressing the critical issue of ordering. Their solutions, validated by extensive empirical evidence, underscore the significance of order in model performance and pave the way for more adept handling of non-sequential data in machine learning. The proposed methodologies form a foundation for future research in making seq2seq models more adaptable and robust across a wider array of tasks.