Sequential Neural Networks as Automata (1906.01615v3)

Abstract: This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network memory follows from this definition. We then characterize the classes of languages acceptable by various recurrent networks, attention, and convolutional networks. We find that LSTMs function like counter machines and relate convolutional networks to the subregular hierarchy. Overall, this work attempts to increase our understanding and ability to interpret neural networks through the lens of theory. These theoretical insights help explain neural computation, as well as the relationship between neural networks and natural language grammar.

• The paper introduces a framework linking sequential neural networks to automata theory, clarifying the networks' computational and language acceptance capabilities.
• The analysis categorizes recurrent architectures like LSTMs and GRUs by their state complexity and expressiveness, differentiating them from simple RNNs.
• The study highlights how attention and convolutional layers influence computational power, with attention boosting state complexity beyond traditional bounds.

Overview of "Sequential Neural Networks as Automata"

William Merrill's paper, "Sequential Neural Networks as Automata," provides a dense theoretical exploration of neural networks, particularly sequential models, through the lens of formal language theory and automata. By establishing a framework to relate different types of neural networks to well-studied automata, the paper paves the way to decipher the computations these networks are capable of executing. The primary focus is on improving interpretability and providing a deeper understanding of how neural networks simulate these computations, aligning them with formal language constructs.

Key Contributions

The paper explores the following significant aspects:

1. Network Acceptance of Languages: Merrill introduces the notion of what it means for a neural network to "accept" a language, borrowing concepts from traditional automata. This foundation is pivotal in assessing the computational capabilities of neural networks.
2. Characterization of Recurrent Networks: The work categorizes recurrent architectures like LSTMs, GRUs, and simple RNNs by the types of languages they can accept. For example, LSTMs are shown to function akin to counter machines wielding more computational power than simple recurrent networks (SRNs) which align with finite-state automata.
3. Impact of Attention and Convolutional Layers: Attention mechanisms, particularly significant in transformers, are highlighted for their potential in expanding state complexity beyond what is typically feasible with traditional recurrent models. Convolutional architectures are located within the subregular hierarchy, suggesting limitations in expressiveness relative to recurrent networks.
4. Asymptotic Analysis: By employing an asymptotic view to analyze neural network behavior, Merrill asserts bounds on network memory (state complexity) and the expressive power of architectures, extending insights beyond empirical results.

Detailed Insights

• RNN and LSTM Analysis: RNNs are generally characterized as finite-state, with state complexity constrained to $O(1)$. Alternatively, LSTMs possess $O(n^k)$ state complexity, allowing them to implement more intricate computations, like counter operations, due to their cell state—but they do not reach Turing-complete power under realistic constraints.
• Empirical and Asymptotic Congruence: Although theoretical characterizations are powerful, Merrill notes discrepancies between asymptotic predictions and empirical observations. For instance, even GRUs and SRNs learned to solve counting tasks beyond regular capabilities, suggesting models can form behaviors that deviate from purely asymptotic expectations.
• Attention and Memory: Attention mechanisms create potential for $2^{\Theta(n)}$ state complexity, distinct from the bounded complexity of LSTMs, and present a unique mechanism for facilitating sub-tasks like copying or aligning long sequences, which aligns with real-world applications in NLP, such as machine translation.
• Convolutional Networks' Place: Positioned within the space of strictly local languages, convolutional networks are shown to be inherently limited in sequence-based tasks, aligning more with phonological pattern modeling rather than broader syntax or semantic modeling.

Implications and Future Directions

This theoretical framework bolstered by empirical validation sets a foundation for future work to explore the interface between neural networks and formal grammars. Understanding these computability limits can guide the development of more effective architectures or hybrid models that combine strengths from various network types to transcend current boundaries. Additionally, regularization methods, like noise during training, could steer real-world applications toward strategies that align with theoretical insights while enhancing generalization.

In summary, Merrill's exploration into "Sequential Neural Networks as Automata" equips researchers with a profound toolset for analyzing neural networks' computational essence through formal automata frameworks, providing clarity and direction for both theoretical and practical advancements in AI and computational linguistics.