Visualisation and 'diagnostic classifiers' reveal how recurrent and recursive neural networks process hierarchical structure (1711.10203v2)

Abstract: We investigate how neural networks can learn and process languages with hierarchical, compositional semantics. To this end, we define the artificial task of processing nested arithmetic expressions, and study whether different types of neural networks can learn to compute their meaning. We find that recursive neural networks can find a generalising solution to this problem, and we visualise this solution by breaking it up in three steps: project, sum and squash. As a next step, we investigate recurrent neural networks, and show that a gated recurrent unit, that processes its input incrementally, also performs very well on this task. To develop an understanding of what the recurrent network encodes, visualisation techniques alone do not suffice. Therefore, we develop an approach where we formulate and test multiple hypotheses on the information encoded and processed by the network. For each hypothesis, we derive predictions about features of the hidden state representations at each time step, and train 'diagnostic classifiers' to test those predictions. Our results indicate that the networks follow a strategy similar to our hypothesised 'cumulative strategy', which explains the high accuracy of the network on novel expressions, the generalisation to longer expressions than seen in training, and the mild deterioration with increasing length. This is turn shows that diagnostic classifiers can be a useful technique for opening up the black box of neural networks. We argue that diagnostic classification, unlike most visualisation techniques, does scale up from small networks in a toy domain, to larger and deeper recurrent networks dealing with real-life data, and may therefore contribute to a better understanding of the internal dynamics of current state-of-the-art models in natural language processing.

• The paper demonstrates that TreeRNNs generalize well on nested arithmetic through a precise three-step composition function.
• It reveals that GRUs employ a cumulative strategy to incrementally interpret lengthy expressions with high accuracy.
• The study introduces diagnostic classification as a novel method to probe and interpret internal network representations.

Analysis of Neural Networks in Processing Hierarchical Structures

This paper explores the capability of neural networks to process hierarchical, compositional structures, specifically focusing on nested arithmetic expressions as a proxy for more complex structures such as natural language. The authors systematically investigate the dynamics of both recursive and recurrent neural networks, presenting a detailed examination of their internal workings.

Summary of Key Findings

Recursive Neural Networks

The authors first consider Recursive Neural Networks (TreeRNNs) and examine their capacity to learn the meanings of nested arithmetic expressions. The TreeRNNs demonstrate robust generalization to expressions longer than those seen during training. This is attributed to a carefully structured composition function composed of three steps: project, sum, and squash. This recursive strategy capitalizes on a geometric arrangement of word embeddings and their subsequent projections to compute compositional semantics accurately within a low-dimensional space. In effect, the TreeRNN efficiently leverages a recursive symbolic strategy to solve the task, approximating a principled solution in the network's architecture.

Recurrent Neural Networks

Subsequently, the paper shifts focus to Recurrent Neural Networks (RNNs), particularly evaluating Simple Recurrent Networks (SRNs) and Gated Recurrent Units (GRUs). GRUs outperform SRNs, demonstrating a solid ability to generalize, with only a slight degradation in accuracy as the length of expressions increases. However, the internal dynamics of GRUs pose a significant challenge due to their complexity, including recurrent connections and gating mechanisms.

To overcome this complexity, authors develop a novel approach, termed `diagnostic classification', for probing the network's strategy. Diagnostic classifiers are employed to predict internal states aligned with two hypothesized processing strategies—cumulative and recursive. The results reveal that GRUs favor a cumulative strategy, progressively interpreting the meaning of expressions. This implies GRUs employ strategies beyond simple memorization, integrating inputs incrementally with high accuracy.

Implications and Future Directions

The findings underscore the potential of GRUs to handle sequences with deep hierarchical dependencies, an essential ability for natural language processing tasks. This capacity to model deep hierarchical structures suggests applicability beyond arithmetic to more complex linguistic and cognitive tasks.

Moreover, the introduction of diagnostic classification represents a significant methodological contribution. This technique allows for a deeper analysis of neural networks, offering insights into what information is encoded in hidden representations. Future research can build upon this work by applying diagnostic classifiers to more complex and higher-dimensional networks, facilitating understanding of advanced models in real-world language processing applications.

The paper not only provides a rigorous analysis of compositional semantics in neural networks but also offers methods that can be adapted to analyze the latent operations within other deep learning architectures. Consequently, it enhances our ability to interpret neural network models, easing the often-cited issue of their 'black-box' nature. Moving forward, this line of inquiry promises to provide substantial theoretical and practical contributions to artificial intelligence development, especially in domains requiring nuanced understanding of hierarchical structures such as language and cognitive modeling.