Roger Labahn

Design strategies for weight matrices of echo state networks

This article develops approaches to generate dynamical reservoirs of echo state networks with desired properties reducing the amount of randomness. It is possible to create weight matrices with a predefined singular value spectrum. The procedure guarantees stability (echo state property). We prove the minimization of the impact of noise on the training process. The resulting reservoir types are strongly related to reservoirs already known in the literature. Our experiments show that well-chosen input weights can improve performance.

Quick gossiping by telegraphs

Abstract We consider gossiping in the complete doubly directed graph, i.e. telegrams arranged in rounds are used to exchange information between n points, each having one initial item. It is proved that at least 1.44·log 2 n rounds are needed to inform everybody about those n distinct items of information.

Kernels of minimum size gossip schemes

Abstract The main part of gossip schemes are the kernels of their minimal orders. We give a complete characterization of all kernels that may appear in gossip schemes on simple graphs with a minimum number of calls. As consequences we prove several results on gossip schemes, e.g. the minimum number of rounds of a gossip scheme with a minimum number of calls is computed. Moreover, in the new context we give proofs of known results, e.g. the well-known four-cycle theorem. In the last part, we deal with order theoretic questions for such kernel posets. After describing all p -grid-kernels in terms of permutations and subsets, isomorphism is investigated and they are enumerated. Then we compute the order dimension and the jump number of all possible kernels, and finally, we show how to determine the numbers of their linear extensions.

Information flows on hypergraphs

Abstract We consider a generalization of the well-known gossip problem for hypergraphs: In a given set V of points, let each point of a subset X ⊆ V know a unit of information which is not known by any other point. The points of V communicate by a sequence of k -party conference calls during which the k points exchange all the information known to them, and none of which are redundant. This exchange of information stops when every point of a subset Y ⊆ V knows all the initial units of information. We give both lower and upper bounds on the number of calls in such a sequence, and we present a structural description of such processes.

Regular expressions for decoding of neural network outputs

This article proposes a convenient tool for decoding the output of neural networks trained by Connectionist Temporal Classification (CTC) for handwritten text recognition. We use regular expressions to describe the complex structures expected in the writing. The corresponding finite automata are employed to build a decoder. We analyze theoretically which calculations are relevant and which can be avoided. A great speed-up results from an approximation. We conclude that the approximation most likely fails if the regular expression does not match the ground truth which is not harmful for many applications since the low probability will be even underestimated. The proposed decoder is very efficient compared to other decoding methods. The variety of applications reaches from information retrieval to full text recognition. We refer to applications where we integrated the proposed decoder successfully.