1,721,264 research outputs found
On the Computational Power of Recurrent Neural Networks for Structures
No full textRecurrent neural networks can simulate any finite state automata as well as any multi-stack Turing machine. When constraining the network architecture, however, this computational power may no longer hold. For example, recurrent cascade-correlation cannot simulate any finite state automata. Thus, it is important to assess the computational power of a given network architecture, since this characterizes the class of functions which, in principle, can be computed by it. We discuss the computational power of neural networks for structures. Elman-style networks, cascade-correlation networks and neural trees for structures are introduced We show that Elman-style networks can simulate any frontier-to-root tree automation while neither cascade-correlation networks nor neural trees can. As a special case of the latter result, we obtain that neural trees for sequences cannot simulate any finite state machine
Labelling Recursive Auto-associative Memory
No full textIn this paper, we propose an extension to the recursive auto-associative memory (RAAM) by Pollack. This extension, the labelling RAAM (LRAAM), can encode labelled graphs with cycles by representing pointers explicitly. Some technical problems encountered in the RAAM, such as the termination problem in the learning and decoding processes, are solved more naturally in the LRAAM framework. The representations developed for the pointers seem to be robust to recurrent decoding along a cycle. Theoretical and experimental results show that the performances of the proposed learning scheme depend on the way the graphs are represented in the training set. Critical features for the representation are cycles and confluent pointers. Data encoded in a LRAAM can be accessed by a pointer as well as by content. Direct access by content can be achieved by transforming the encoder network of the LRAAM into a particular bidirectional associative memory (BAM). Statistics performed on different instances of LRAAM show a strict connection between the associated BAM and a standard BAM. Different access procedures can be defined depending on the access key. The access procedures are not wholly reliable; however, they seem to have a good success rate. The generalization test for the RAAM is no longer complete for the LRAAM. Some suggestions on how to solve this problem are given. Some results on modular LRAAM, stability and application to neural dynamics control are summarized
Equivalence results between feedforward and recurrent neural networks for sequences
No full textIn the context of sequence processing, we study the relationship between single-layer feedforward neural networks,that have simultaneous access to all items composing a sequence, and single-layer recurrent neural networks which access information one step at a time.We treat both linear and nonlinear networks, describing a constructive procedure, based on linear autoencoders for sequences, that given a feedforward neural network shows how to define a recurrent neural network that implements the same function in time. Upper bounds on the required number of hidden units for the recurrent network as a function of some features of the feedforward network are given. By separating the functional from the memory component, the proposed procedure suggests new efficient learning as well as interpretation procedures for recurrent neural networks
An Efficient SMO-like Algorithm for Multiclass SVM
No full textStarting from a reformulation of Cramer & Singer Mul-
ticlass Kernel Machine, we propose a Sequential Minimal Opti-
mization (SMO) like algorithm for incremental and fast optimiza-
tion of the lagrangian. The proposed formulation allowed us to
dene very eective new pattern selection strategies which lead to
better empirical results
The Loading Problem for Recursive Neural Networks
No full textThe present work deals with one of the major and not yet completely understood topics of supervised connectionist models. Namely, it investigates the relationships between the difficulty of a given learning task and the chosen neural network architecture. These relationships have been investigated and nicely established for some interesting problems in the case of neural networks used for processing vectors and sequences, but only a few studies have dealt with loading problems involving graphical inputs. In this paper, we present sufficient conditions which guarantee the absence of local minima of the error function in the case of learning directed acyclic graphs with recursive neural networks. We introduce topological indices which can be directly calculated from the given training set and that allows us to design the neural architecture with local minima free error function. In particular, we conceive a reduction algorithm that involves both the information attached to the nodes and the topology, which enlarges significantly the class of the problems with unimodal error function previously proposed in the literature
- …
