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Simulating Weighted Automata with Transformers
核心概念
Transformers can simulate weighted automata efficiently.
要約
Transformers have shown the ability to simulate both weighted finite automata (WFAs) and weighted tree automata (WTAs) with upper bounds on model sizes. The study explores the theoretical foundations and practical implications of using transformers for simulating complex automata models. The results demonstrate that transformers can learn shortcuts to models more complex than deterministic finite automata, providing insights into their sequential reasoning capabilities. Empirical experiments show that gradient-based training can find compact solutions for simulating WFAs. The study also investigates how the number of layers and embedding size impact model performance in simulating synthetic WFAs. Theoretical connections between formal languages, neural networks, and models of computation are discussed, highlighting the potential applications and limitations of using transformers for automata simulation tasks.
Simulating Weighted Automata over Sequences and Trees with Transformers
統計
Recent work has shown that these models can compactly simulate the sequential reasoning abilities of deterministic finite au-tomata (DFAs).
We show that transformers can simulate weighted finite automata (WFAs), a class of models which subsumes DFAs, as well as weighted tree automata (WTA), a generalization of weighted automata to tree structured inputs.
More precisely, we show that, using hard attention and bilinear layers, transformers can exactly simulate all WFAs at length T with O(log T) layers.
For WTAs, the notion of simulation we introduce assumes that the transformer is fed a string representation of a tree and outputs the states of the WTA for each subtree of the input.
Our results extend the ones of Liu et al. (2022) for DFAs in two directions: from boolean to real weights and from sequences to trees.
引用
"Transformers can approximately simulate all WTAs A with n states at length T."
"Empirical experiments show that gradient-based training can find compact solutions for simulating WFAs."
"Transformers have shown impressive empirical successes in recent years."
深掘り質問
Can transformers accurately capture the complexities of weighted finite automata
Transformers have shown the capability to accurately capture the complexities of weighted finite automata (WFAs). The theoretical results presented in the context demonstrate that transformers can simulate WFAs with real weights, a class of models that generalize deterministic and non-deterministic finite automata. By using hard attention and bilinear layers, transformers can exactly simulate all WFAs at length T with a depth of O(log T), embedding dimension proportional to n^2, attention width proportional to n^2, MLP width also proportional to n^2, and O(1) attention heads. Additionally, using soft attention and an MLP for implementation allows transformers to approximately simulate all WFAs at length T up to arbitrary precision ϵ > 0 with similar hyperparameters as before.
What are the practical implications of using transformers for simulating complex automata models beyond theoretical bounds
The practical implications of using transformers for simulating complex automata models beyond theoretical bounds are significant. These findings suggest that transformers can learn shortcuts to more complex models than previously thought possible. By demonstrating the ability of transformers to accurately capture the reasoning capabilities of weighted finite automata within logarithmic depths relative to sequence lengths or tree depths, we open up new possibilities for leveraging transformer architectures in tasks requiring sequential reasoning abilities. This could lead to more efficient and effective solutions in natural language processing tasks involving formal languages recognition or other structured data domains.
How do these findings contribute to our understanding of neural networks' capabilities in handling formal language recognition tasks
These findings contribute significantly to our understanding of neural networks' capabilities in handling formal language recognition tasks by showcasing their capacity for simulating complex automata models such as weighted finite automata (WFAs) and weighted tree automata (WTAs). The ability of transformers to approximate or exactly simulate these advanced computational structures sheds light on their potential for capturing intricate patterns in sequences or trees. This not only expands our knowledge about how neural networks reason but also provides practical insights into designing more powerful models for tasks like code translation, text generation, sentiment analysis, etc., where sequential reasoning plays a crucial role. Ultimately, these results enhance our understanding of the expressive power and computational capabilities of neural networks when dealing with structured data representations commonly found in formal languages contexts.
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