."A Hebbian form of synaptic plasticity at inhibitory synapses generates balanced input currents and sparse neuronal responses that stabilize memory traces in neuronal networks" Cortical neurons receive balanced excitatory and inhibitory membrane currents.Here, we show that such a balance can be established and maintained in an experiencedependent manner by synaptic plasticity at inhibitory synapses. The mechanism we put forward provides an explanation for the sparse firing patterns observed in response to natural stimuli and fits well with a recently observed interaction of excitatory and inhibitory receptive field plasticity. We show that the introduction of inhibitory plasticity in suitable recurrent networks provides a homeostatic mechanism that leads to asynchronous irregular network states. Further, it can accommodate synaptic memories with activity patterns that become indiscernible from the background state, but can be re-activated by external stimuli. Our results suggest an essential role of inhibitory plasticity in the formation and maintenance of functional cortical circuitry. 1The balance of excitatory and inhibitory membrane currents a neuron experiences during stimulated and ongoing activity has been the topic of many recent studies (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). This balance, first defined as equal average amounts of de-and hyperpolarizing membrane currents (from hereon referred to as "global balance") is thought to be essential for maintaining stability of cortical networks (1, 2). In the balanced state networks display asynchronous irregular (AI) dynamics that mimic activity patterns observed in cortical neurons. Such asynchronous network states facilitate rapid responses to small changes in the input (2-4), providing an ideal substrate for cortical signal processing (5,15,16). Pathologies that disrupt the balance of excitation and inhibition have often been implicated in neurological diseases such as epilepsy or schizophrenia (17, 18).Moreover, the input currents to a given cortical neuron are not merely globally balanced. Excitatory and inhibitory inputs are coupled also in time (6-8) and co-tuned for different stimulus features (9,10). The tight coupling of excitation and inhibition suggests a more precise, detailed balance, in which each excitatory input arrives at the cell together with an inhibitory counterpart, supposedly supplied through feedforward inhibition (Fig. 1 A). These observations fit well with models of cortical processing in which balanced sensory inputs are left unattended, but can be transiently (11), or persistently turned on by targeted disruptions of the balance (12-14).Although it is widely thought that the excitatory-inhibitory balance plays an important role for stability and information processing in cortical networks, it is still not understood by which mechanisms this balance is established and maintained in the presence of ongoing sensory experiences. Inspired by recent experimental results (9), we investigate the hypothesis that synaptic plastic...

Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.

We present a model for the self-organized formation of place cells, head-direction cells, and spatial-view cells in the hippocampal formation based on unsupervised learning on quasi-natural visual stimuli. The model comprises a hierarchy of Slow Feature Analysis (SFA) nodes, which were recently shown to reproduce many properties of complex cells in the early visual system [1]. The system extracts a distributed grid-like representation of position and orientation, which is transcoded into a localized place-field, head-direction, or view representation, by sparse coding. The type of cells that develops depends solely on the relevant input statistics, i.e., the movement pattern of the simulated animal. The numerical simulations are complemented by a mathematical analysis that allows us to accurately predict the output of the top SFA layer.

Recent experiments have shown that spike-timing-dependent plasticity is influenced by neuromodulation. We derive theoretical conditions for successful learning of reward-related behavior for a large class of learning rules where Hebbian synaptic plasticity is conditioned on a global modulatory factor signaling reward. We show that all learning rules in this class can be separated into a term that captures the covariance of neuronal firing and reward and a second term that presents the influence of unsupervised learning. The unsupervised term, which is, in general, detrimental for reward-based learning, can be suppressed if the neuromodulatory signal encodes the difference between the reward and the expected reward-but only if the expected reward is calculated for each task and stimulus separately. If several tasks are to be learned simultaneously, the nervous system needs an internal critic that is able to predict the expected reward for arbitrary stimuli. We show that, with a critic, reward-modulated spike-timing-dependent plasticity is capable of learning motor trajectories with a temporal resolution of tens of milliseconds. The relation to temporal difference learning, the relevance of block-based learning paradigms, and the limitations of learning with a critic are discussed.

While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical findings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012.

SignificanceUnderstanding the neural code is to attribute proper meaning to temporal sequences of action potentials. We report a simple neural code based on distinguishing single spikes from spikes in close succession, commonly called “bursts.” By separating these two types of responses, we show that ensembles of neurons can communicate rapidly changing and graded information from two sources simultaneously and with minimal cross-talk. Second, we show that this multiplexing can optimize the information transferred per action potential when bursts are relatively rare. Finally, we show that neurons can demultiplex these two streams of information. We propose that this multiplexing may be particularly important in hierarchical communication where bottom–up and top–down information must be distinguished.

Abstract:Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.Mathematical and computational approaches in neuroscience have a long tradition that can be followed back to early mathematical theories of perception [1,2] and of current integration by a neuronal cell membrane [3]. Hodgkin and Huxley combined their experiments with a mathematical description, which they used for simulations on one of the early computers [4]. Hebb's ideas on assembly formation [5] have, already in 1956, inspired simulations on the largest computers available at that time [6]. Since the 1980ies the field of theoretical and computational neuroscience has grown enormously [7].Modern neuroscience methods requiring extensive training have led to a specialization of researchers so that neuroscience today is fragmented into labs working on genes and molecules; on single-cell electrophysiology; on multi-neuron recordings; on cognitive neuroscience and psychophysics, to name just a few. One of the central tasks of computational neuroscience is to bridge these different levels of description by simulation and mathematical theory. The bridge can be built in two different directions. Bottom-up models integrate what is known on a lower level (e.g., properties of ion channels) to explain phenomena observed on a higher level (e.g., generation of action potentials [4,[8][9][10]). Top-down models, on the other hand, start with known cognitive functions of the brain (e.g., working memory), and deduce from these how components (e.g., neurons or groups of neurons) should behave to achieve these functions. Influential examples of the top-down approach are theories of associative memories [11,12], reinforcement learning [13,14], and sparse coding [15,16].Bottom-up and top-down models can either be studied by mathematical theory (theoretical neuroscience) or by computer simulations (computational neuroscience). Theory has the advantage of providing a complete picture of the model behavior for all possible parameter settings, but analytical solutions are restricted to relatively simple models. The aim of theory is therefore to purify biological ideas to the bare minimum, so as to arrive at a 'toy model', which crystallizes a concept in a set of mathematical equations that can be fully understood. Simulations, in contrast, can be applied to all models, simplified as well as complex ones, but they can only sample the model behavior for a...

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.