comment on recent paper by Maas and Orponen

[C Omlin]

In their recent paper "On the Effect of Analog Noise in
Discrete-Time Analog Computations" Wolfgang Maas and Pekka Orponen
discuss the stable encoding of deterministic finite-state automata in recurrent
neural networks with sigmoidal discriminant functions. This problem
has previously been discussed in the literature:

	P. Frasconi, M. Gori, M. Maggini, G. Soda,
        "A Unified Approach for Integrating Explicit Knowledge
        and Learning by Example in Recurrent Networks",
        IJCNN'91 Proceedings, Vol. 1, p. 811, 1991.

   	P. Frasconi, M. Gori, M. Maggini, G. Soda,
   	"Unified Integration of Explicit Rules and Learning
        by Example in Recurrent Networks", IEEE Transactions
	on Knowledge and Data Engineering, Vol. 6, No, 6, 1994.

	P. Frasconi, M. Gori, G. Soda,
	"Injecting Nondeterministic Finite State Automata
	into Recurrent Networks", Technical Report, Dipartimento di
	Sistemi e Informatica, Universita di Firenze, Italy,
        1993.

    	P. Frasconi, M. Gori, M. Maggini, G. Soda,
        "Representation of Finite State Automata in Recurrent Radial
 	Basis Function Networks", Machine Learning, Vol. 23, No. 1.
        p. 5-32, 1996.

	C.W. Omlin, C.L. Giles,
	"Stable Encoding of Large Finite-State Automata in 
	Recurrent Neural Networks with Sigmoid Discriminants" 
        Neural Computation, Vol. 8, No. 7, p. 675-696, 1996.
        (This paper discusses scaling issues for neural DFA
	encodings.)
      
	C.W. Omlin, C.L. Giles, 
        "Constructing Deterministic Finite-State Automata
        in Recurrent Neural Networks", Journal of the ACM, 
        Vol. 43, No. 6, p. 937-972, 1996.
 	(This paper discusses the theoretical foundations for
	encoding DFAs in second-order recurrent neural networks,
        and also shows that encodings can be made stable in the
        presence of noise. It also contains a table summarizing
        various encoding methods and the required resources
        (neurons/weights), and restrictions on weight values and
	fan-in/out.)

Best regards,

Christian Omlin


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