Computation in Recurrent Neural Networks: From Counters to Iterated Function Systems

By Yvonne Kalinke, Helko Lehmann. 1998

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Citations in the corpus

Deep learning in neural networks: An overview (2014, neutral): “…that require learning the rules of regular languages describable by deterministic Finite State Automata (FSAs) (Blair & Pollack, 1997; Casey, 1996; Kalinke & Lehmann, 1998; Manolios & Fanelli, 1994; Omlin & Giles, 1996; Siegelmann, 1992; Vahed & Omlin, 2004; Watrous & Kuhn, 1992; Zeng, Goodman, &…”
Approximating the Semantics of Logic Programs by Recurrent Neural Networks (1999, background): “Other approaches relate recursive neural networks to deterministic finite state machines (for first order networks see [26–28]; for second order networks see [29–31]; for radial basis function networks see [32]; for iterated function systems see [33, 34]).”
LSTM recurrent networks learn simple context-free and context-sensitive languages (2001, background): “RNN algorithms on numerous tasks involving real-valued or discrete inputs and targets [5], [7], including tasks that require to learn the rules of regular languages (RLs) describable by deterministic finite-state automata (DFA) [1], [2], [ 8 ], [21], [31].”
Theoretical Limitations of Self-Attention in Neural Sequence Models (2019, unknown): “e models of recursion and hierarchical structure as found in natural language. A range of studies has experimentally examined the ability of recurrent networks to model counter languages such as anbn Kalinke and Lehmann, 1998 ;Gers and Schmidhuber ,2001 Cartling 2008 ;Weiss et al. ,2018 Suzgun et al”
Dimensions of Neural-symbolic Integration - A Structured Survey (2005, methodology): “[H¨olldobler et al. , 1997, Kalinke and Lehmann, 1998] study the representation of counters using recurrent networks, and connectionist uniﬁcation algorithms as studied in [H¨olldobler, 1990, H¨olldobler and Kurfess, 1992, H¨olldobler, 1993] are designed for manipulating terms, but already in a…”