The spectral radius remains a valid indicator of the echo state property for large reservoirs

In the field of Reservoir Computing, scaling the spectral radius of the weight matrix of a random recurrent neural network to below unity is a commonly used method to ensure the Echo State Property. Recently it has been shown that this condition is too weak. To overcome this problem, other more involved - sufficient conditions for the Echo State Property have been proposed. In this paper we provide a large-scale experimental verification of the Echo State Property for large recurrent neural networks with zero input and zero bias. Our main conclusion is that the spectral radius method remains a valid indicator of the Echo State Property; the probability that the Echo State Property does not hold, drops for larger networks with spectral radius below unity, which are the ones of practical interest

Terrain classification for a quadruped robot

Using data retrieved from the Puppy II robot at the University of Zurich (UZH), we show that machine learning techniques with non-linearities and fading memory are effective for terrain classification, both supervised and unsupervised, even with a limited selection of input sensors. The results indicate that most information for terrain classification is found in the combination of tactile sensors and proprioceptive joint angle sensors. The classification error is small enough to have a robot adapt the gait to the terrain and hence move more robustly

Input-to-State Representation in linear reservoirs dynamics

Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them appealing for analytical studies by a large community of researchers with backgrounds spanning from dynamical systems to neuroscience. However, even in the simple linear case, the working principle of these networks is not fully understood and their design is usually driven by heuristics. A novel analysis of the dynamics of such networks is proposed, which allows the investigator to express the state evolution using the controllability matrix. Such a matrix encodes salient characteristics of the network dynamics; in particular, its rank represents an input-indepedent measure of the memory capacity of the network. Using the proposed approach, it is possible to compare different reservoir architectures and explain why a cyclic topology achieves favourable results as verified by practitioners

Calibrated reservoir computers

We observe the presence of infinitely fine-scaled alternations within the performance landscape of reservoir computers aimed for chaotic data forecasting. We investigate the emergence of the observed structures by means of variations of the transversal stability of the synchronization manifold relating the observational and internal dynamical states. Finally, we deduce a simple calibration method in order to attenuate the thus evidenced performance uncertainty

Echo state network‐based feature extraction for efficient color image segmentation

Image segmentation plays a crucial role in many image processing and understanding applications. Despite the huge number of proposed image segmentation techniques, accurate segmentation remains a significant challenge in image analysis. This article investigates the viability of using echo state network (ESN), a biologically inspired recurrent neural network, as features extractor for efficient color image segmentation. First, an ensemble of initial pixel features is extracted from the original images and injected into the ESN reservoir. Second, the internal activations of the reservoir neurons are used as new pixel features. Third, the new features are classified using a feed forward neural network as a readout layer for the ESN. The quality of the pixel features produced by the ESN is evaluated through extensive series of experiments conducted on real world image datasets. The optimal operating range of different ESN setup parameters for producing competitive quality features is identified. The performance of the proposed ESN‐based framework is also evaluated on a domain‐specific application, namely, blood vessel segmentation in retinal images where experiments are conducted on the widely used digital retinal images for vessel extraction (DRIVE) dataset. The obtained results demonstrate that the proposed method outperforms state‐of‐the‐art general segmentation techniques in terms of performance with an F‐score of 0.92 ± 0.003 on the segmentation evaluation dataset. In addition, the proposed method achieves a comparable segmentation accuracy (0.9470) comparing with reported techniques of segmentation of blood vessels in images of retina and outperform them in terms of processing time. The average time required by our technique to segment one retinal image from DRIVE dataset is 8 seconds. Furthermore, empirically derived guidelines are proposed for adequately setting the ESN parameters for effective color image segmentation