**accepting state**,**activation function**,**activation function****differentiable**

**activation function**- ,

**activation function****properties**

**activation function**- ,
**radial basis functions**

**activation function****rational****threshold|seethreshold linear unit**

**activation****function****derivative**

**Adali@Adali, T.****Alon, N.**, , , , ,**Alopex****alphabet**,**Alquezar@Alquézar, R.**, ,**asynchronous DTRNN****asynchronous transduction****attractor****attractor****limit cycle**

**Aussem, A.****automata****deterministic finite-state**, , , , , , , , , , , , ,**finite-state**, , , ,**neural nets and finite-state automata****pushdown**

**backpropagation**, ,**backpropagation****focused****through time**, , , ,

**Baltersee, J.****batch learning**, , , ,**Bengio, Y.**,**Bengio. Y.****bias****as a learnable parameter**,**notation**

**Blair, A.**, , , , ,**blank symbol****in Turing Machines**,

**bounds to number of units**,**Box, G.E.****BPS****BPTT|seebackpropagation through time****Bradley, M.J.****Bridle, J.S.****Bulsari, A.B.**,**Carrasco, R.C.**, , , , , , , , , ,**Casey, M.**,**Cauwenberghs, G.**,**Chalmers, D.J.****Chambers, J.****channel equalization****Chen, W.-Y.**,**Cheng, Y.****Chiu, C.-C.****Chomsky's hierarchy**,**Chomsky, N.****Chovan, T.****Chrisman, L.****Cid-Sueiro, J.**,**Cleeremans, A.**, , , , ,**clock****external**

**Clouse, D.S.**,**clustering****hierarchical**,**of DTRNN state vectors**, , , ,

**compression of signals****compressor****in RAAM**

**computability of natural functions****Connor, J.T.****construction of FSM in DTRNN**, , , , , ,**context-free****grammar**, , , , ,**language**

**context-sensitive grammar**, ,**continuous-time recurrent neural networks****control****countable set****cycles in neural networks**, , ,**Das, R.**,**Das, S.**, , , , ,**decision function****decoder****in RAAM**,**in RAAM networks|seerecursive auto-associative memory**

**definite-memory machines****denumerable set****derivatives****of error**, , ,

**deterministic finite-state automata**, , , , , , , , , , , , , , ,**DFA|seedeterministic finite-state automata****discrete-time recurrent neural network**, , , , , , , , , , , , , , , , , , , , , , , , , , ,**discrete-time recurrent neural network****first-order**

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,
,
**second-order**

**discrete-time recurrent neural network**- ,
,

**discrete-time recurrent neural network**- ,
,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,
,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,
,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,
,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network**- ,

**discrete-time recurrent neural network****Turing computability**

**discrete-time recurrent neural network**- ,

**discretization****of DTRNN state space****of neuron outputs**

**Draye, J.P.****Dreider, J.F.**,**DTRNN|seediscrete-time recurrent neural network****dynamical system****dynamics****atractor****continuous-state****next state****of a DTRNN**, , , , , ,

**Dzielinski, A.****EKF****Elman net**, , , ,**Elman, J.L.**, , , , , , , , , , , ,**empty string****encoder****in RAAM**, ,

**encoding****of FSM in DTRNN**, , ,**of input symbols****of Turing machines in DTRNN**

**equivalence****of BPTT and RTRL****of DFA and Moore machines****of FSM and DTRNN**, ,**of Moore and Mealy machines****of sequence classification and transduction****of TLU and McCulloch-Pitts units**

**error function**,**error function****differentiable**,

**error function****gradient of**

**error function**- ,
,

**error function****in batch learning**

**error function**- ,
,
**in online learning****in pattern learning**

**error function**- ,

**error function****local minima**,

**error function****minima****minima****multiple**

**error function****quadratic****special**

**excitation threshold****excitatory connection**,**exclusive encoding****of symbols**,

**exclusive-or function**, , ,**expression****regular**,**regular****equivalence with DTRNN****equivalence with finite-state machines**

**temporal propositional**

**extended Kalman filter****extraction****of FSM from DTRNN**, , ,**of FSM from DTRNN****through partition of state space**, ,

**of FSM from DTRNN****trivial**

**of FSM from DTRNN****using clustering**

**of FSM from DTRNN**- ,

**of FSM from DTRNN**- ,

**of FSM from DTRNN****using self-organizing maps**

**of FSM from DTRNN**- ,

**Fahlman, S.E.**, , , ,**Fallside, F.**, , , , ,**fan-in**,**fan-out****Fanelli, R.**, ,**feedback****in DTRNN**,**in DTRNN****local**

**in DTRNN**- ,
,

**feedforward neural net****as next-state function****as output function**

**feedforward neural net**- ,

**feedforward neural net**- ,
,

**feedforward neural net****in BPTT training**

**feedforward neural net****in RAAM****layered****lower-triangular**,**training**

**feedforward neural net****two-layer**

**feedforward neural net**- ,

**feedforward neural net**- ,
,

**Feldkamp, L.A****FFNN|seefeedforward neural net****Figueiras-Vidal, A.R.****filtering of discrete-time signals****final state****of a Turing machine**

**final state**- ,

**finite-memory machines****finite-state automata****deterministic**

**finite-state automata**- ,

**finite-state machine****finite-state machines****finite-state machines****and neural nets**

**finite-state machines****approximate**

**finite-state machines****as transducers****classes**

**finite-state machines****compatible with learning set**

**finite-state machines****definite-memory machines****deterministic****DTRNN behaving as**, , ,

**finite-state machines**- ,
**earliest DTRNN as****emulation by DTRNN**

**finite-state machines**- ,
,
,
,

**finite-state machines**- ,

**finite-state machines****encoding in DTRNN**

**finite-state machines**- ,

**finite-state machines**- ,
**encoding in threshold DTRNN**, , ,**equivalence to DTRNN**,**extraction****extraction from DTRNN**, ,

**finite-state machines****finite-memory machines**

**finite-state machines****inference**

**finite-state machines**- ,
,
,

**finite-state machines****learning by DTRNN**

**finite-state machines**- ,
,
**learning in sigmoid DTRNN****next-state function****probabilistic****pushdown automata as****states****as clusters in state space**, , , , ,

**transition**

**finite-state machines**- ,
**with stack**

**finite-state****automata****automata****deterministic**, , , , , , , , , , , , ,

**behavior****behavior****of DTRNN****of DTRNN**, , , , , , , , , , , , ,

**computation**, ,

**fixed points**,**Forcada, M.L.**, , , , , , ,**fractal dimension****Frasconi, P.**,**FSM|seefinite-state machines****functions****computable by TLU****recursively computable**

**generalization**, ,**Gershenfeld, N.A.****Giles, C.L.**, , , , , , , , , , , , , , , , , , ,**Gori, M.**,**Goudreau, M.****Goudreau, M.W.**, , , ,**gradient****descent**, , , , ,**learning algorithm**, , , ,

**Gradient**- ,

**gradient**- ,
,
,
,
,
**pseudo-gradient learning****vanishing**

**grammar**, , ,**grammar****as generator****Chomsky's hierarchy**,**context-free**, , , ,**context-sensitive**,**inference**, , , , , ,**language generated by****regular**,**rules in DTRNN**,**Tomita's****unrestricted**,

**grammatical inference**, , , , ,**grammatical inference****using DTRNN**

**grammatical inference**- ,

**grammatical inference**- ,
,
,
,
,
,

**Haykin, S.**, , , , ,**hidden****layer**, , , ,**state**, ,**state****neural architectures without**,

**unit**, , , ,**unit****activation patterns**

**units**

**hierarchy****Chomsky's**,

**Hopfield, J.J.****Horne, B.G.**, , ,**Hush, D.R.**, , ,**Ifeachor, E.C.****implementation****of FSM in DTRNN**, , , , , ,

**inductive bias**,**inhibitory connection**,**initial state****as a learnable parameter****as a learnable parameter****of a DTRNN**,**of a DTRNN****derivatives**

**of a DTRNN****learning**

**of a FSM****of a pushdown automaton****of a Turing machine**

**input****alphabet**, , , ,**layer****neurons**, ,**sequence**, ,**sequence****length**

**string****symbol****symbol****representation**,

**symbols****representation**

**to a DTRNN**, , , ,**to a TLU**, , ,**window****window****in a NARX**,**in a TDNN**,

**instability****internal representation**, ,**interpretation****of DTRNN output****as symbols**

**of DTRNN outputs****of DTRNN outputs****as probabilities**, ,

**of DTRNN outputs****as symbols**

**Janacek, G.****Jordan, M.I.**,**Kaiser, J.F.****Kalman filter****extended**

**Kalman, B.L.****Kechriotis, G.****Kleene's theorem****Kleene, S.C.**, , , , , , , ,**Kohavi, Z.****Kohonen, T.**, , ,**Kolen, J.F.**, ,**Kremer, S.C**, , , , , ,**Kremer, S.C.**, , ,**Kuhn, G.M.**, , ,**Kwasny, S.C.****language****recognizer****accepted by DTRNN****accepted by Turing machines****acceptor**, ,**acceptor****neural**,**Turing machine as**

**concatenation****context-free****defined by grammar****finite-state****generated by a grammar****generator****generator****probabilistic**

**learning by DTRNN****natural****recognition by DTRNN****recognizer**, ,**regular**, , , ,**regular****acceptor****recognition by DTRNN**

**transducer**

**Lawrence, S.C.****layers****hidden**, , , ,**in BPTT**,**in feedforward neural net**,**output**, ,

**LBA****learnable parameters**, , , , , , , , , , ,**learnable parameters****updating****batch**

**learnable parameters****updating****gradient**

**learnable parameters****updating****in BPTT****in perturbative methods****in RTRL**

**learnable parameters****updating****online**

**learnable parameters****updating**- ,

**learnable parameters****updating**- ,
**pattern**,

**learnable parameters****updating****random**

**learning algorithm**, ,**learning algorithm****backpropagation****for DTRNN**,**generalization test**

**learning algorithm****gradient-based**

**learning algorithm**- ,
,
,
,
,

**learning algorithm**- ,

**learning algorithm**- ,
**gradient-descent****inductive bias**

**learning algorithm****long-term dependencies**

**learning algorithm****non-gradient-based**

**learning algorithm**- ,

**learning algorithm**- ,
,

**learning algorithm****pseudo-gradient-based**

**learning algorithm****recurrent cascade correlation**

**learning set**, , , , , , , , , , ,**learning set****noisy****of trees**

**learning set****partition**

**Li, C.J.****Li, L.****Lin, T.****linearly-bounded automata****local minima**, ,**local-feedback DTRNN**, ,**logical functions**, ,**logical functions****computability**

**logistic function**, ,**long-term dependencies**, , , , ,**lower-triangular feedforward neural net**,**Manolios, P.**, ,**Mars, P.****Martin, R.D.****McClelland, J.L.****McCulloch, W.S.**, , , , , ,**McCulloch-Pitts net****Mealy machines**, , , , , , , ,**Mealy machines****as sequence procesors****binary****neural**

**Mealy machines**- ,

**Mealy machines**- ,

**Mealy machines**- ,

**Mealy machines**- ,

**minimization****of error function****of FSM**,

**Minsky, M.L.**, , , , , , , , ,**Mitra, S.K.****Moore machines**, , , ,**Moore machines****neural**

**Moore machines**- ,

**Moore machines**- ,
,
,
,
,
,

**Moore machines**- ,

**Mozer, M.C.**, , , , , ,**multilayer perceptron**,**Narendra, K.S.**,**NARX (nonlinear auto-regressive with exogenous inputs)****natural language****natural numbers****natural numbers****functions of**,

**Neco@Ñeco, R.P.**,**Nerrand, O.****neural****Mealy machines****Moore machine****state machine**, , , , , , , , , , , ,

**neurocontrol****neuron field**,**next move function****next-state function**, , , , , , , , , , , , , , ,**next-state function****of a TDNN**

**node****of a tree**, ,

**non-gradient-based****learning algorithms**, ,

**nonterminal symbols**,**NSM|seeneural state machine****observability of state**,**Omlin, C.W.**, ,**one-hot encoding****of symbols**, ,

**online learning**, ,**online learning****using RTRL**

**online learning**- ,

**Oppenheim, A.V.****Ortiz-Fuentes, J.D.****output****alphabet**, ,**desired**, ,**function**, , , , , , , , , , , , , , , , , , ,**of a DTRNN****of a TLU**, , ,**of DTRNN****as projection of state vector**, , ,

**of sigmoid units****sequence**, , ,**sequence****length**

**space**,**space****of a DTRNN**

**symbols****representation**

**unit**, ,**window****window****in a NARX**,

**P/Poly****computational class**

**Parberry, I.****Parisi, R.****parsing****parsing****shift-reduce**

**Parthasarathy, K.**,**partition****of learning sets****of state space**, , , , , , ,

**pattern learning**, ,**PDA**,**Pearlmutter, B.****perceptron****multilayer****two-layer**

**Perrin, D.****Pineda, F.J.****Pitts, W.H.**, , , , , ,**Pollack, J.B.**, , , , , , , , , , , , , , , , , , , , ,**prediction****by DTRNN****of a sequence**,**of next symbol****of next symbol****using DTRNN**, ,

**time-series**,**time-series****using DTRNN**

**predictive coding**,**probabilistic****finite-state machine****language generator**

**probabilities****in DTRNN outputs**, , ,

**probability distribution**, , ,**processing****element****of natural language****of sequences**, , ,**of sequences****adaptive****classification**

**of sequences****using DTRNN**, , ,

**of sequences**- ,

**of sequences**- ,
,

**of strings**,**sequential****synchronous**

**production****of a grammar**,

**pseudo-gradient****learning algorithm**

**pushdown automaton**, , , ,**pushdown automaton****as Turing machine simulator**

**Puskorius, G.V****Qian, N.****RAAM|seerecursive auto-associative memory****radial basis functions****rational activation function**, ,**real-time recurrent learning**, , , , , ,**real-time recurrent learning****relation to extended Kalman filter**

**recognition****of languages****by DTRNN**

**of sequences**,**of speech**

**recognizer****dynamical**, ,**finite-state**,**for context-free languages****language**, ,**neural**

**reconstructor****in RAAM**

**recurrent cascade correlation**,**recurrent neural network****discrete-time**,

**recurrent neural network**- ,
,
,
,

**recurrent neural network**- ,

**recurrent neural network**- ,

**recurrent neural network**- ,

**recurrent neural network**- ,

**recurrent neural network**- ,
,

**recurrent neural network**- ,

**recurrent neural network**- ,

**recurrent neural network**- ,

**recurrent neural network**- ,
,
,

**recurrent neural network**- ,
,
,

**recurrent neural network**- ,

**recurrent neural network**- ,
,
,
,
,

**recurrent neural network**- ,

**recurrent neural network**- ,
,

**recurrent neural network**- ,

**recurrent neural network**- ,
,
,

**recurrent neural network**- ,

**recurrent neural network**- ,
,
,

**recursive auto-associative memory**, , ,**recursive auto-associative memory****labeling**

**recursive hetero-associative memory****recursivity****in grammars**

**region****of output space****in DTRNN**

**of output space**- ,
**in RAAM**

**of state space****in DTRNN**

**of state space**- ,
**in RAAM**

**regular****events****expression****grammar**,**language**, , ,**language****acceptor****recognition by DTRNN**

**representation****learned by DTRNN**, , ,**of FSM in DTRNN****of FSM****in DTRNN**

**of inputs in DTRNN**, , ,**of outputs in DTRNN****of parse trees in RAAM****of sequences in RAAM**,**of terminals in RAAM**

**rewrite rules****in a grammar****recursive**

**Robinson, A.J.**, , , , ,**Robinson-Fallside network****augmented**

**Rosenberg, C.R.****RTRL|seereal-time recurrent learning****rule****extraction from DTRNN****representation in DTRNN**

**Rumelhart, D.E.**, ,**Sajda, J.**, ,**sampling****discrete-time**,

**Sanfeliu, A.**, ,**Saxen@Saxén, H.**,**Schafer, R.W.****second-order DTRNN**, , , , , , , , , , , , , , , ,**Sejnowski, T.J.**,**self-organizing feature maps**,**sequence****classification****continuation****generation**,**input**, ,**output**, , ,**prediction**, ,**prediction****for speech coding**

**processing**, ,**processing****adaptive****as language recognition****long-term dependencies**,**sequential****synchronous****using DTRNN**, , , , , , ,

**processor****discrete-time****state-based**

**recognition**,**representation****in RAAM**

**transduction****transduction****synchronous**,

**sequential****processing****processing****in Mealy and Moore machines**

**transduction****by DTRNN**

**Shanblatt, M.A.****Siegelmann, H.T.**, ,**sigmoid****function****function****logistic**, ,

**units****DTRNN using**

**signal****compression****discrete-time**,**filtering****processing**

**Sima@Šíma, J.**,**single-layer****DTRNN**,**feedforward neural net****feedforward neural net****as output function**

**feedforward neural net**- ,

**Siu, K.Y.****Sluijter, R.J.**,**SOFM**,**Sontag, E.D.**,**space complexity of learning****speech****coding****through sequence prediction****using DTRNN**

**modelling of coarticulatory features****recognition**

**Sperduti, A.**,**stability of DTRNN as language recognizers****stability****of DTRNN as language recognizers**

**stack****empty****external**, , , , ,**in pushdown automata**,**simulating Turing machines****unary**

**Starita, A.****start symbol of a grammar****start symbol****of a grammar**,

**state space****of DTRNN**, ,**of DTRNN****clustering**

**state space****of DTRNN**- ,
,

**state space****of DTRNN**- ,

**state space****of DTRNN**- ,

**of DTRNN**- ,
**partition**

**state space****of DTRNN**- ,
,

**of DTRNN**- ,

**of DTRNN**- ,

**state space****of DTRNN**- ,

**state space****of DTRNN****regions****topological mapping**

**of RAAM**

**state space****of RAAM****regions**

**state space****partition****to extract FSM**,

**state****accepting****accepting****of a pushdown automaton**

**final****of a Turing machine**,

**initial****of a DTRNN**,**of a DTRNN****learning**,

**of a DTRNN**- ,

**of a pushdown automaton****of a Turing machine**

**initial|seealsoinitial state****of a FSM**

**observable**,**of a FSM****of a pushdown automaton****of a Turing machine****of DFA****representation in DTRNN**

**transition**,**transition****in a FSM**, , , ,**in a Turing machine**

**unit****units**, , , , , ,**units****hidden**, ,**in DTRNN**,

**vector**, , , ,**vector****clustering**, ,**in a NARX**

**state-based sequence processor****step function****string**,**string****acceptance****by a DFA****by a DTRNN****by a pushdown automaton****by a Turing machine**

**continuation****by DTRNN**,

**empty****generation****by a grammar****by DTRNN**

**input**,**output****processing****by DTRNN**,**by FSM**

**recognition****by automata**

**rejection****by DFA****by DTRNN**

**transduction****translation****translation****by DTRNN**

**valid****as defined by grammar**

**super-Turing****computation****by DTRNN****subclass P/Poly**

**Swift, L.****symbol****blank****in Turing machine**,

**encoding****one-hot, local, or exclusive**

**end-of-string**,**in stack of pushdown automaton****in tape of Turing machine****input symbol**,**input symbol****representation in DTRNN**, ,

**next symbol****prediction**

**next symbol**- ,

**next symbol**- ,

**nonterminal**,**one-hot encoding**,**output**, , ,**output****by DTRNN**,**representation in DTRNN**

**stack**,**start symbol****of a grammar**

**start symbol**- ,
,

**string**,**terminal**, ,**useless****variable**

**synapse**,**synapse****excitatory**,**inhibitory**,

**synchronous****processing****sequence transduction****transduction**,**transduction****by DTRNN**

**system identification****tape****alphabet, in a Turing machine****in linearly bounded automata****of a nonuniform Turing machine****of a Turing machine**, , , ,

**target**, , ,**target`don't care'' targets****TDNN****teacher forcing****temporal propositional expression**,**terminal symbol**, , ,**test set****threshold linear unit**, , , , , , , , , , ,**threshold unit****time complexity****of learning**,

**time-delay neural network****time-series prediction**,**time-series prediction****using DTRNN**

**Tino@Tino, P.**, ,**TLU|seethreshold linear unit****TM|seeTuring machine****Tomita, M.**,**TPE|seetemporal propositional expression****training algorithm|seelearning algorithm****transducer****finite-state****of strings**

**transduction****of sequences****of sequences****asynchronous**

**of sequences****sequential**

**of sequences****synchronous**,**using DTRNN**

**of trees**

**transition****function|seenext-state function****in a FSM**, , , , , ,**in a pushdown automaton**,**in a Turing machine**

**translation|seetransduction****tree****learning set****node**, ,**storing in RAAM**, ,**transduction**

**Turing machine**, , , , , , , , , , , , ,**Turing machine****deterministic**

**Turing machine****nondeterministic**

**Turing machine****nonuniform**,**universal**,

**Turing, A.M.****two-layer feedforward neural net**, , ,**type 0 grammar****type 1 grammar****type 2 grammar****type 3 grammar****unfolding****in BPTT**

**unit****demon****threshold****threshold linear**, ,

**universal Turing machine**,**Unnikrishnan, K.P.****unrestricted grammar**,**updating of learnable parameters****batch****in BPTT****in perturbative methods****in RTRL****online**,**pattern**,**random****using gradient**

**valence****of a tree**

**vanishing gradient****variable****in a grammar**, , ,

**vector****input vector****input vector****to a DTRNN****to a TLU**

**of weights****space****of inputs****of outputs**

**state vector**, ,**state vector****clustering**

**state vector**- ,

**state vector**- ,
,
**in a NARX**

**Venugopal, K.P.****Waibel, A.****Wang, J.****Watrous, R.L.**, , ,**Weigend, A.S.****weights****as learnable parameters**,**derivatives of error with respect to****derivatives of state with respect to****equivalence in BPTT****feedback****in DTRNN****in TDNN****organized in blocks**

**notation****perturbation****perturbation****learning algorithm**,

**space****vector**

**Werbos, P.J.**, , ,**Williams, R.J.**, , , , , , ,**window****of inputs****of inputs****in a NARX**, ,

**of inputs****in a TDNN**

**of outputs****of outputs****in a NARX**,

**Wu, G.****Wu, L.****Zbikowski, R.****Zeng, Z.**, , ,**Zipser, D.**, , , , , ,

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Debian User 2002-01-21