Critical neural networks with short and long term plasticity

In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term plasticity, can cause critical neuronal dynamics. Whereas long-term plasticity, such as hebbian or activity dependent plasticity, have a crucial role in shaping the network structure and endowing neural systems with learning abilities. In this work we provide a model which combines both plasticity mechanisms, acting on two different time-scales. The measured avalanche statistics are compatible with experimental results for both the avalanche size and duration distribution with biologically observed percentages of inhibitory neurons. The time-series of neuronal activity exhibits temporal bursts leading to 1/f decay in the power spectrum. The presence of long-term plasticity gives the system the ability to learn binary rules such as XOR, providing the foundation of future research on more complicated tasks such as pattern recognition.Comment: 8 pages, 7 figure

The Neural Particle Filter

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals based on the history of observations, provides a mathematical framework for dynamic perception in real time. Since the general, nonlinear filtering problem is analytically intractable, particle filters are considered among the most powerful approaches to approximating the solution numerically. Yet, these algorithms prevalently rely on importance weights, and thus it remains an unresolved question how the brain could implement such an inference strategy with a neuronal population. Here, we propose the Neural Particle Filter (NPF), a weight-less particle filter that can be interpreted as the neuronal dynamics of a recurrently connected neural network that receives feed-forward input from sensory neurons and represents the posterior probability distribution in terms of samples. Specifically, this algorithm bridges the gap between the computational task of online state estimation and an implementation that allows networks of neurons in the brain to perform nonlinear Bayesian filtering. The model captures not only the properties of temporal and multisensory integration according to Bayesian statistics, but also allows online learning with a maximum likelihood approach. With an example from multisensory integration, we demonstrate that the numerical performance of the model is adequate to account for both filtering and identification problems. Due to the weightless approach, our algorithm alleviates the 'curse of dimensionality' and thus outperforms conventional, weighted particle filters in higher dimensions for a limited number of particles

A novel plasticity rule can explain the development of sensorimotor intelligence

Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, the self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no system specific modifications of the DEP rule but arise rather from the underlying mechanism of spontaneous symmetry breaking due to the tight brain-body-environment coupling. The new synaptic rule is biologically plausible and it would be an interesting target for a neurobiolocal investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution.Comment: 18 pages, 5 figures, 7 video

Branch-specific plasticity enables self-organization of nonlinear computation in single neurons

It has been conjectured that nonlinear processing in dendritic branches endows individual neurons with the capability to perform complex computational operations that are needed in order to solve for example the binding problem. However, it is not clear how single neurons could acquire such functionality in a self-organized manner, since most theoretical studies of synaptic plasticity and learning concentrate on neuron models without nonlinear dendritic properties. In the meantime, a complex picture of information processing with dendritic spikes and a variety of plasticity mechanisms in single neurons has emerged from experiments. In particular, new experimental data on dendritic branch strength potentiation in rat hippocampus have not yet been incorporated into such models. In this article, we investigate how experimentally observed plasticity mechanisms, such as depolarization-dependent STDP and branch-strength potentiation could be integrated to self-organize nonlinear neural computations with dendritic spikes. We provide a mathematical proof that in a simplified setup these plasticity mechanisms induce a competition between dendritic branches, a novel concept in the analysis of single neuron adaptivity. We show via computer simulations that such dendritic competition enables a single neuron to become member of several neuronal ensembles, and to acquire nonlinear computational capabilities, such as for example the capability to bind multiple input features. Hence our results suggest that nonlinear neural computation may self-organize in single neurons through the interaction of local synaptic and dendritic plasticity mechanisms

A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics. Previous numerical works have reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on the neural network evolution. Furthermore, we show that the sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest