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Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period. [ABSTRACT FROM AUTHOR]

Memory storage in the brain relies on mechanisms acting on time scales from minutes, for long-term synaptic potentiation, to days, for memory consolidation. During such processes, neural circuits distinguish synapses relevant for forming a long-term storage, which are consolidated, from synapses of short-term storage, which fade. How time scale integration and synaptic differentiation is simultaneously achieved remains unclear. Here we show that synaptic scaling – a slow process usually associated with the maintenance of activity homeostasis – combined with synaptic plasticity may simultaneously achieve both, thereby providing a natural separation of short- from long-term storage. The interaction between plasticity and scaling provides also an explanation for an established paradox where memory consolidation critically depends on the exact order of learning and recall. These results indicate that scaling may be fundamental for stabilizing memories, providing a dynamic link between early and late memory formation processes. [ABSTRACT FROM AUTHOR]

Classical conditioning (conventionally modeled as correlation-based learning) and operant conditioning (conventionally modeled as reinforcement learning or reward-based learning) have been found in biological systems. Evidence shows that these two mechanisms strongly involve learning about associations. Based on these biological findings, we propose a new learning model to achieve successful control policies for artificial systems. This model combines correlation-based learning using input correlation learning (ICO learning) and reward-based learning using continuous actor-critic reinforcement learning (RL), thereby working as a dual learner system. The model performance is evaluated by simulations of a cart-pole system as a dynamic motion control problem and a mobile robot system as a goal-directed behavior control problem. Results show that the model can strongly improve pole balancing control policy, i.e., it allows the controller to learn stabilizing the pole in the largest domain of initial conditions compared to the results obtained when using a single learning mechanism. This model can also find a successful control policy for goal-directed behavior, i.e., the robot can effectively learn to approach a given goal compared to its individual components. Thus, the study pursued here sharpens our understanding of how two different learning mechanisms can be combined and complement each other for solving complex tasks. [ABSTRACT FROM AUTHOR]

Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter online to yield optimal asymptotic convergence speed. We study the adaptive control map both analytically and numerically and prove that it converges at least linearly to a value determined by the spectral radius of the control map at the periodic orbit to be stabilized. The method is easy to implement algorithmically and may ?nd applications for adaptive online control of biological and engineering systems. [ABSTRACT FROM AUTHOR]

Conventional synaptic plasticity in combination with synaptic scaling is a biologically plausible plasticity rule that guides the development of synapses towards stability. Here we analyze the development of synaptic connections and the resulting activity patterns in different feed-forward and recurrent neural networks, with plasticity and scaling. We show under which constraints an external input given to a feed-forward network forms an input trace similar to a cell assembly (Hebb, 1949) by enhancing synaptic weights to larger stable values as compared to the rest of the network. For instance, a weak input creates a less strong representation in the network than a strong input which produces a trace along large parts of the network. These processes are strongly influenced by the underlying connectivity. For example, when embedding recurrent structures (excitatory rings, etc.) into a feed-forward network, the input trace is extended into more distant layers, while inhibition shortens it. These findings provide a better understanding of the dynamics of generic network structures where plasticity is combined with scaling. This makes it also possible to use this rule for constructing an artificial network with certain desired storage properties. [ABSTRACT FROM AUTHOR]

In this theoretical contribution, we provide mathematical proof that two of the most important classes of network learning—correlation-based differential Hebbian learning and reward-based temporal difference learning—are asymptotically equivalent when timing the learning with a modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning framework from a correlation-based perspective more closely related to the biophysics of neurons. [ABSTRACT FROM AUTHOR]

An abstract of the research paper "Synaptic Scaling Generically Stabilizes Circuit Connectivity," by Christian Tetzlaff and colleagues, presented at the Twentieth Annual Computational Neuroscience Meeting, held in Stockholm, Sweden, from July 23-28, 2011.

Fruit flies (Drosophila melanogaster) rely on their olfactory system to process environmental information. This information has to be transmitted without system-relevant loss by the olfactory system to deeper brain areas for learning. Here we study the role of several parameters of the fly's olfactory system and the environment and how they influence olfactory information transmission. We have designed an abstract model of the antennal lobe, the mushroom body and the inhibitory circuitry. Mutual information between the olfactory environment, simulated in terms of different odor concentrations, and a sub-population of intrinsic mushroom body neurons (Kenyon cells) was calculated to quantify the efficiency of information transmission. With this method we study, on the one hand, the effect of different connectivity rates between olfactory projection neurons and firing thresholds of Kenyon cells. On the other hand, we analyze the influence of inhibition on mutual information between environment and mushroom body. Our simulations show an expected linear relation between the connectivity rate between the antennal lobe and the mushroom body and firing threshold of the Kenyon cells to obtain maximum mutual information for both low and high odor concentrations. However, contradicting all-day experiences, high odor concentrations cause a drastic, and unrealistic, decrease in mutual information for all connectivity rates compared to low concentration. But when inhibition on the mushroom body is included, mutual information remains at high levels independent of other system parameters. This finding points to a pivotal role of inhibition in fly information processing without which the system efficiency will be substantially reduced.

Conventional synaptic plasticity in combination with synaptic scaling is a biologically plausible plasticity rule that guides the development of synapses toward stability. Here we analyze the development of synaptic connections and the resulting activity patterns in different feed-forward and recurrent neural networks, with plasticity and scaling. We show under which constraints an external input given to a feed-forward network forms an input trace similar to a cell assembly (Hebb, 1949) by enhancing synaptic weights to larger stable values as compared to the rest of the network. For instance, a weak input creates a less strong representation in the network than a strong input which produces a trace along large parts of the network. These processes are strongly influenced by the underlying connectivity. For example, when embedding recurrent structures (excitatory rings, etc.) into a feed-forward network, the input trace is extended into more distant layers, while inhibition shortens it. These findings provide a better understanding of the dynamics of generic network structures where plasticity is combined with scaling. This makes it also possible to use this rule for constructing an artificial network with certain desired storage properties.

Synaptic scaling is a slow process that modifies synapses, keeping the firing rate of neural circuits in specific regimes. Together with other processes, such as conventional synaptic plasticity in the form of long term depression and potentiation, synaptic scaling changes the synaptic patterns in a network, ensuring diverse, functionally relevant, stable, and input-dependent connectivity. How synaptic patterns are generated and stabilized, however, is largely unknown. Here we formally describe and analyze synaptic scaling based on results from experimental studies and demonstrate that the combination of different conventional plasticity mechanisms and synaptic scaling provides a powerful general framework for regulating network connectivity. In addition, we design several simple models that reproduce experimentally observed synaptic distributions as well as the observed synaptic modifications during sustained activity changes. These models predict that the combination of plasticity with scaling generates globally stable, input-controlled synaptic patterns, also in recurrent networks. Thus, in combination with other forms of plasticity, synaptic scaling can robustly yield neuronal circuits with high synaptic diversity, which potentially enables robust dynamic storage of complex activation patterns. This mechanism is even more pronounced when considering networks with a realistic degree of inhibition. Synaptic scaling combined with plasticity could thus be the basis for learning structured behavior even in initially random networks.

Network activity and network connectivity mutually influence each other. Especially for fast processes, like spike-timing-dependent plasticity (STDP), which depends on the interaction of few (two) signals, the question arises how these interactions are continuously altering the behavior and structure of the network. To address this question a time-continuous treatment of plasticity is required. However, this is - even in simple recurrent network structures - currently not possible. Thus, here we develop for a linear differential Hebbian learning system a method by which we can analytically investigate the dynamics and stability of the connections in recurrent networks. We use noisy periodic external input signals, which through the recurrent connections lead to complex actual ongoing inputs and observe that large stable ranges emerge in these networks without boundaries or weight-normalization. Somewhat counter-intuitively, we find that about 40% of these cases are obtained with a long-term potentiation-dominated STDP curve. Noise can reduce stability in some cases, but generally this does not occur. Instead stable domains are often enlarged. This study is a first step toward a better understanding of the ongoing interactions between activity and plasticity in recurrent networks using STDP. The results suggest that stability of (sub-)networks should generically be present also in larger structures.