Echo State Condition at the Critical Point

Recurrent networks with transfer functions that fulfill the Lipschitz continuity with K=1 may be echo state networks if certain limitations on the recurrent connectivity are applied. It has been shown that it is sufficient if the largest singular value of the recurrent connectivity is smaller than 1. The main achievement of this paper is a proof under which conditions the network is an echo state network even if the largest singular value is one. It turns out that in this critical case the exact shape of the transfer function plays a decisive role in determining whether the network still fulfills the echo state condition. In addition, several examples with one neuron networks are outlined to illustrate effects of critical connectivity. Moreover, within the manuscript a mathematical definition for a critical echo state network is suggested

Multiplex visibility graphs to investigate recurrent neural network dynamics

Source at https://doi.org/10.1038/srep44037 .A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning them properly may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize internal dynamics of a class of RNNs called echo state networks (ESNs). We design principled unsupervised methods to derive hyperparameters configurations yielding maximal ESN performance, expressed in terms of prediction error and memory capacity. In particular, we propose to model time series generated by each neuron activations with a horizontal visibility graph, whose topological properties have been shown to be related to the underlying system dynamics. Successively, horizontal visibility graphs associated with all neurons become layers of a larger structure called a multiplex. We show that topological properties of such a multiplex reflect important features of ESN dynamics that can be used to guide the tuning of its hyperparamers. Results obtained on several benchmarks and a real-world dataset of telephone call data records show the effectiveness of the proposed methods

A Review of Findings from Neuroscience and Cognitive Psychology as Possible Inspiration for the Path to Artificial General Intelligence

This review aims to contribute to the quest for artificial general intelligence by examining neuroscience and cognitive psychology methods for potential inspiration. Despite the impressive advancements achieved by deep learning models in various domains, they still have shortcomings in abstract reasoning and causal understanding. Such capabilities should be ultimately integrated into artificial intelligence systems in order to surpass data-driven limitations and support decision making in a way more similar to human intelligence. This work is a vertical review that attempts a wide-ranging exploration of brain function, spanning from lower-level biological neurons, spiking neural networks, and neuronal ensembles to higher-level concepts such as brain anatomy, vector symbolic architectures, cognitive and categorization models, and cognitive architectures. The hope is that these concepts may offer insights for solutions in artificial general intelligence.Comment: 143 pages, 49 figures, 244 reference

Salience Coding in the Basal Forebrain and the Heterogeneous Underpinnings Underlying Novelty Computations

Humans and animals are consistently learning from the environment by interacting with it and getting feedback from their actions. In the environment, some objects are more important than others, because they are associated with reward, uncertainty, surprise, or novelty etc. These objects are salient to the animal. Salient objects attract attention and orientation, increase arousal, facilitate learning and memory, and affect reinforcement learning and credit assignment. However, the neural basis to support these effects is still not fully understood.We first studied how the basal forebrain, one of the principal sources of modulation of the neocortex, encodes salience events. We found two types of neurons that process salient events in distinct manners: one with phasic burst activity to cues predicting salient events and one with ramping activity anticipating such events. Bursting neurons respond to reward itself and cues that predict the magnitude, probability, and timing of reward. However, they do not have a selective response to reward omission. Thus, bursting neurons signal surprise associated with external events, which is different from the reward prediction error signaled by the midbrain dopamine neurons. Furthermore, they discriminate fully expected novel visual objects from familiar objects and respond to object-sequence violations. In contrast, ramping neurons predict the timing of many salient, novel, and surprising events. Their ramping activity is highly sensitive to the subjects\u27 confidence in event timing and on average encodes the subjects\u27 surprise after unexpected events occur. These data suggest that the primate BF contains mechanisms to anticipate the timing of a diverse set of salient external events (via tonic ramping activity) and to rapidly deploy cognitive resources when these events occur (via phasic bursting activity). Then we sailed out to study one special salience signal – Novelty. The basal forebrain responds to novelty, but the neuronal mechanisms of novelty detection remain unclear. Prominent theories propose that novelty is either derived from the computation of recency or is a form of sensory surprise. Here, we used high-channel electrophysiology in primates to show that, in many prefrontal, temporal, and subcortical brain areas, object novelty sensitivity is related to both computations of recency (the sensitivity to how long ago a stimulus was experienced) and sensory surprise (violation of predictions about incoming sensory information). Also, we studied neuronal novelty-to-familiarity transformations during learning across many days and found a diversity of timescales in neurons\u27 learning rates and between-session forgetting rates within and across brain regions that is well suited to support flexible behavior and learning in response to novelty. These findings show that novelty sensitivity arises on multiple timescales across single neurons due to diverse related computations of sensory surprise and recency, and shed light on the logic and computational underpinnings of novelty detection in the primate brain

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project

Persistence in complex systems

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423)

Persistence in complex systems

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems’ persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423)