A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback

Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as a candidate for a learning rule that could explain how behaviorally relevant adaptive changes in complex networks of spiking neurons could be achieved in a self-organizing manner through local synaptic plasticity. However, the capabilities and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. Our model for this experiment relies on a combination of reward-modulated STDP with variable spontaneous firing activity. Hence it also provides a possible functional explanation for trial-to-trial variability, which is characteristic for cortical networks of neurons but has no analogue in currently existing artificial computing systems. In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics.     

Big decisions by small networks

The primate brain is able to guide complex decisions that can rapidly be adapted to changing constraints. Unfortunately, the vast numbers of highly interconnected neurons that seem to be needed make it difficult to study the cellular mechanisms that underlie the flexible combination of stored and acute information during a decision. Established simpler networks, particularly with few and identified neurons, would lend themselves more readily to such a dissection. But can simple networks implement complex and flexible decisions similarly? After a brief overview of complex decisions in primates and of decision‐making in simple networks, I argue that simpler systems can combine complexity with accessibility at the cellular level. Indeed, examination of a network in fish may help in dissecting key mechanisms of complex and flexible decision‐making in an established model of synaptic plasticity at the level of identified neurons.     

Pain Facilitation and Activity-Dependent Plasticity in Pain Modulatory Circuitry: Role of BDNF-TrkB Signaling and NMDA Receptors

Pain modulatory circuitry in the brainstem exhibits considerable synaptic plasticity. The increased peripheral neuronal barrage after injury activates spinal projection neurons that then activate multiple chemical mediators including glutamatergic neurons at the brainstem level, leading to an increased synaptic strength and facilitatory output. It is not surprising that a well-established regulator of synaptic plasticity, brain-derived neurotrophic factor (BDNF), contributes to the mechanisms of descending pain facilitation. After tissue injury, BDNF and TrkB signaling in the brainstem circuitry is rapidly activated. Through the intracellular signaling cascade that involves phospholipase C, inositol trisphosphate, protein kinase C, and nonreceptor protein tyrosine kinases; N-methyl-D-aspartate (NMDA) receptors are phosphorylated, descending facilitatory drive is initiated, and behavioral hyperalgesia follows. The synaptic plasticity observed in the pain pathways shares much similarity with more extensively studied forms of synaptic plasticity such as long-term potentiation (LTP) and long-term depression (LTD), which typically express NMDA receptor dependency and regulation by trophic factors. However, LTP and LTD are experimental phenomena whose relationship to functional states of learning and memory has been difficult to prove. Although mechanisms of synaptic plasticity in pain pathways have typically not been related to LTP and LTD, pain pathways have an advantage as a model system for synaptic modifications as there are many well-established models of persistent pain with clear measures of the behavioral phenotype. Further studies will elucidate cellular and molecular mechanisms of pain sensitization and further our understanding of principles of central nervous system plasticity and responsiveness to environmental challenge.     

Models of heterogeneous dopamine signaling in an insect learning and memory center

The Drosophila mushroom body exhibits dopamine dependent synaptic plasticity that underlies the acquisition of associative memories. Recordings of dopamine neurons in this system have identified signals related to external reinforcement such as reward and punishment. However, other factors including locomotion, novelty, reward expectation, and internal state have also recently been shown to modulate dopamine neurons. This heterogeneity is at odds with typical modeling approaches in which these neurons are assumed to encode a global, scalar error signal. How is dopamine dependent plasticity coordinated in the presence of such heterogeneity? We develop a modeling approach that infers a pattern of dopamine activity sufficient to solve defined behavioral tasks, given architectural constraints informed by knowledge of mushroom body circuitry. Model dopamine neurons exhibit diverse tuning to task parameters while nonetheless producing coherent learned behaviors. Notably, reward prediction error emerges as a mode of population activity distributed across these neurons. Our results provide a mechanistic framework that accounts for the heterogeneity of dopamine activity during learning and behavior.     

Bidirectional plasticity gated by hyperpolarization controls the gain of postsynaptic firing responses at central vestibular nerve synapses

Linking synaptic plasticity with behavioral learning requires understanding how synaptic efficacy influences postsynaptic firing in neurons whose role in behavior is understood. Here, we examine plasticity at a candidate site of motor learning: vestibular nerve synapses onto neurons that mediate reflexive movements. Pairing nerve activity with changes in postsynaptic voltage induced bidirectional synaptic plasticity in vestibular nucleus projection neurons: long-term potentiation relied on calcium-permeable AMPA receptors and postsynaptic hyperpolarization, whereas long-term depression relied on NMDA receptors and postsynaptic depolarization. Remarkably, both forms of plasticity uniformly scaled synaptic currents evoked by pulse trains, and these changes in synaptic efficacy were translated into linear increases or decreases in postsynaptic firing responses. Synapses onto local inhibitory neurons were also plastic but expressed only long-term depression. Bidirectional, linear gain control of vestibular nerve synapses onto projection neurons provides a plausible mechanism for motor learning underlying adaptation of vestibular reflexes.     

Learning flexible sensori-motor mappings in a complex network

Given the complex structure of the brain, how can synaptic plasticity explain the learning and forgetting of associations when these are continuously changing? We address this question by studying different reinforcement learning rules in a multilayer network in order to reproduce monkey behavior in a visuomotor association task. Our model can only reproduce the learning performance of the monkey if the synaptic modifications depend on the pre- and postsynaptic activity, and if the intrinsic level of stochasticity is low. This favored learning rule is based on reward modulated Hebbian synaptic plasticity and shows the interesting feature that the learning performance does not substantially degrade when adding layers to the network, even for a complex problem.     

Somato-dendritic Synaptic Plasticity and Error-backpropagation in Active Dendrites

In the last decade dendrites of cortical neurons have been shown to nonlinearly combine synaptic inputs by evoking local dendritic spikes. It has been suggested that these nonlinearities raise the computational power of a single neuron, making it comparable to a 2-layer network of point neurons. But how these nonlinearities can be incorporated into the synaptic plasticity to optimally support learning remains unclear. We present a theoretically derived synaptic plasticity rule for supervised and reinforcement learning that depends on the timing of the presynaptic, the dendritic and the postsynaptic spikes. For supervised learning, the rule can be seen as a biological version of the classical error-backpropagation algorithm applied to the dendritic case. When modulated by a delayed reward signal, the same plasticity is shown to maximize the expected reward in reinforcement learning for various coding scenarios. Our framework makes specific experimental predictions and highlights the unique advantage of active dendrites for implementing powerful synaptic plasticity rules that have access to downstream information via backpropagation of action potentials.     

Spike-based Decision Learning of Nash Equilibria in Two-Player Games

Humans and animals face decision tasks in an uncertain multi-agent environment where an agent''s strategy may change in time due to the co-adaptation of others strategies. The neuronal substrate and the computational algorithms underlying such adaptive decision making, however, is largely unknown. We propose a population coding model of spiking neurons with a policy gradient procedure that successfully acquires optimal strategies for classical game-theoretical tasks. The suggested population reinforcement learning reproduces data from human behavioral experiments for the blackjack and the inspector game. It performs optimally according to a pure (deterministic) and mixed (stochastic) Nash equilibrium, respectively. In contrast, temporal-difference(TD)-learning, covariance-learning, and basic reinforcement learning fail to perform optimally for the stochastic strategy. Spike-based population reinforcement learning, shown to follow the stochastic reward gradient, is therefore a viable candidate to explain automated decision learning of a Nash equilibrium in two-player games.     

Shaping embodied neural networks for adaptive goal-directed behavior

The acts of learning and memory are thought to emerge from the modifications of synaptic connections between neurons, as guided by sensory feedback during behavior. However, much is unknown about how such synaptic processes can sculpt and are sculpted by neuronal population dynamics and an interaction with the environment. Here, we embodied a simulated network, inspired by dissociated cortical neuronal cultures, with an artificial animal (an animat) through a sensory-motor loop consisting of structured stimuli, detailed activity metrics incorporating spatial information, and an adaptive training algorithm that takes advantage of spike timing dependent plasticity. By using our design, we demonstrated that the network was capable of learning associations between multiple sensory inputs and motor outputs, and the animat was able to adapt to a new sensory mapping to restore its goal behavior: move toward and stay within a user-defined area. We further showed that successful learning required proper selections of stimuli to encode sensory inputs and a variety of training stimuli with adaptive selection contingent on the animat's behavior. We also found that an individual network had the flexibility to achieve different multi-task goals, and the same goal behavior could be exhibited with different sets of network synaptic strengths. While lacking the characteristic layered structure of in vivo cortical tissue, the biologically inspired simulated networks could tune their activity in behaviorally relevant manners, demonstrating that leaky integrate-and-fire neural networks have an innate ability to process information. This closed-loop hybrid system is a useful tool to study the network properties intermediating synaptic plasticity and behavioral adaptation. The training algorithm provides a stepping stone towards designing future control systems, whether with artificial neural networks or biological animats themselves.     

Role of delayed nonsynaptic neuronal plasticity in long-term associative memory

BACKGROUND: It is now well established that persistent nonsynaptic neuronal plasticity occurs after learning and, like synaptic plasticity, it can be the substrate for long-term memory. What still remains unclear, though, is how nonsynaptic plasticity contributes to the altered neural network properties on which memory depends. Understanding how nonsynaptic plasticity is translated into modified network and behavioral output therefore represents an important objective of current learning and memory research. RESULTS: By using behavioral single-trial classical conditioning together with electrophysiological analysis and calcium imaging, we have explored the cellular mechanisms by which experience-induced nonsynaptic electrical changes in a neuronal soma remote from the synaptic region are translated into synaptic and circuit level effects. We show that after single-trial food-reward conditioning in the snail Lymnaea stagnalis, identified modulatory neurons that are extrinsic to the feeding network become persistently depolarized between 16 and 24 hr after training. This is delayed with respect to early memory formation but concomitant with the establishment and duration of long-term memory. The persistent nonsynaptic change is extrinsic to and maintained independently of synaptic effects occurring within the network directly responsible for the generation of feeding. Artificial membrane potential manipulation and calcium-imaging experiments suggest a novel mechanism whereby the somal depolarization of an extrinsic neuron recruits command-like intrinsic neurons of the circuit underlying the learned behavior. CONCLUSIONS: We show that nonsynaptic plasticity in an extrinsic modulatory neuron encodes information that enables the expression of long-term associative memory, and we describe how this information can be translated into modified network and behavioral output.     

What can neurons do for their brain? Communicate selectivity with bursts

Neurons deep in cortex interact with the environment extremely indirectly; the spikes they receive and produce are pre- and post-processed by millions of other neurons. This paper proposes two information-theoretic constraints guiding the production of spikes, that help ensure bursting activity deep in cortex relates meaningfully to events in the environment. First, neurons should emphasize selective responses with bursts. Second, neurons should propagate selective inputs by burst-firing in response to them. We show the constraints are necessary for bursts to dominate information-transfer within cortex, thereby providing a substrate allowing neurons to distribute credit amongst themselves. Finally, since synaptic plasticity degrades the ability of neurons to burst selectively, we argue that homeostatic regulation of synaptic weights is necessary, and that it is best performed offline during sleep.     

Neuromodulation of STDP through short-term changes in firing causality

Spike timing dependent plasticity (STDP) likely plays an important role in forming and changing connectivity patterns between neurons in our brain. In a unidirectional synaptic connection between two neurons, it uses the causal relation between spiking activity of a presynaptic input neuron and a postsynaptic output neuron to change the strength of this connection. While the nature of STDP benefits unsupervised learning of correlated inputs, any incorporation of value into the learning process needs some form of reinforcement. Chemical neuromodulators such as Dopamine or Acetylcholine are thought to signal changes between external reward and internal expectation to many brain regions, including the basal ganglia. This effect is often modelled through a direct inclusion of the level of Dopamine as a third factor into the STDP rule. While this gives the benefit of direct control over synaptic modification, it does not account for observed instantaneous effects in neuronal activity on application of Dopamine agonists. Specifically, an instant facilitation of neuronal excitability in the striatum can not be explained by the only indirect effect that dopamine-modulated STDP has on a neuron’s firing pattern. We therefore propose a model for synaptic transmission where the level of neuromodulator does not directly influence synaptic plasticity, but instead alters the relative firing causality between pre- and postsynaptic neurons. Through the direct effect on postsynaptic activity, our rule allows indirect modulation of the learning outcome even with unmodulated, two-factor STDP. However, it also does not prohibit joint operation together with three-factor STDP rules.     

Towards a general theory of neural computation based on prediction by single neurons

Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise"). A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of undifferentiated neurons, each implementing similar learning algorithms.     

A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales

Volitional behavior relies on the brain's ability to remap sensory flow to motor programs whenever demanded by a changed behavioral context. To investigate the circuit basis of such flexible behavior, we have developed a biophysically based decision-making network model of spiking neurons for arbitrary sensorimotor mapping. The model quantitatively reproduces behavioral and prefrontal single-cell data from an experiment in which monkeys learn visuomotor associations that are reversed unpredictably from time to time. We show that when synaptic modifications occur on multiple timescales, the model behavior becomes flexible only when needed: slow components of learning usually dominate the decision process. However, if behavioral contexts change frequently enough, fast components of plasticity take over, and the behavior exhibits a quick forget-and-learn pattern. This model prediction is confirmed by monkey data. Therefore, our work reveals a scenario for conditional associative learning that is distinct from instant switching between sets of well-established sensorimotor associations.     

Cellular bases of behavioral plasticity: establishing and modifying synaptic circuits in the Drosophila genetic system

Genetic malleability and amenability to behavioral assays make Drosophila an attractive model for dissecting the molecular mechanisms of complex behaviors, such as learning and memory. At a cellular level, Drosophila has contributed a wealth of information on the mechanisms regulating membrane excitability and synapse formation, function, and plasticity. Until recently, however, these studies have relied almost exclusively on analyses of the peripheral neuromuscular junction, with a smaller body of work on neurons grown in primary culture. These experimental systems are, by themselves, clearly inadequate for assessing neuronal function at the many levels necessary for an understanding of behavioral regulation. The pressing need is for access to physiologically relevant neuronal circuits as they develop and are modified throughout life. In the past few years, progress has been made in developing experimental approaches to examine functional properties of identified populations of Drosophila central neurons, both in cell culture and in vivo. This review focuses on these exciting developments, which promise to rapidly expand the frontiers of functional cellular neurobiology studies in Drosophila. We discuss here the technical advances that have begun to reveal the excitability and synaptic transmission properties of central neurons in flies, and discuss how these studies promise to substantially increase our understanding of neuronal mechanisms underlying behavioral plasticity.     

Robustness of learning that is based on covariance-driven synaptic plasticity

It is widely believed that learning is due, at least in part, to long-lasting modifications of the strengths of synapses in the brain. Theoretical studies have shown that a family of synaptic plasticity rules, in which synaptic changes are driven by covariance, is particularly useful for many forms of learning, including associative memory, gradient estimation, and operant conditioning. Covariance-based plasticity is inherently sensitive. Even a slight mistuning of the parameters of a covariance-based plasticity rule is likely to result in substantial changes in synaptic efficacies. Therefore, the biological relevance of covariance-based plasticity models is questionable. Here, we study the effects of mistuning parameters of the plasticity rule in a decision making model in which synaptic plasticity is driven by the covariance of reward and neural activity. An exact covariance plasticity rule yields Herrnstein's matching law. We show that although the effect of slight mistuning of the plasticity rule on the synaptic efficacies is large, the behavioral effect is small. Thus, matching behavior is robust to mistuning of the parameters of the covariance-based plasticity rule. Furthermore, the mistuned covariance rule results in undermatching, which is consistent with experimentally observed behavior. These results substantiate the hypothesis that approximate covariance-based synaptic plasticity underlies operant conditioning. However, we show that the mistuning of the mean subtraction makes behavior sensitive to the mistuning of the properties of the decision making network. Thus, there is a tradeoff between the robustness of matching behavior to changes in the plasticity rule and its robustness to changes in the properties of the decision making network.     

Network, cellular and molecular mechanisms of plasticity in simple nervous systems

In the present study we will try to single out several principles of the nervous system functioning essential for describing mechanisms of learning and memory basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data: main changes in functioning due to learning occur in effectivity of synaptic inputs and in the intrinsic properties of postsynaptic neurons; due to learning some synaptic inputs of neurons selectively change its effectivity due to pre- and postsynaptic changes, but the induction of plasticity always starts in postsynapse, maintaining of long-term memory in postsynapse is also shown; reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; activity of modulatory neurons is necessary for development of plastic modifications of behavior (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; changes due to learning occur at least in two independent loci in the nervous system. A possibility for erasure of memory with participation of nitroxide is experimentally and theoretically based.     

Modulation of hippocampal plasticity in learning and memory

Synaptic plasticity plays a central role in the study of neural mechanisms of learning and memory. Plasticity rules are not invariant over time but are under neuromodulatory control, enabling behavioral states to influence memory formation. Neuromodulation controls synaptic plasticity at network level by directing information flow, at circuit level through changes in excitation/inhibition balance, and at synaptic level through modulation of intracellular signaling cascades. Although most research has focused on modulation of principal neurons, recent progress has uncovered important roles for interneurons in not only routing information, but also setting conditions for synaptic plasticity. Moreover, astrocytes have been shown to both gate and mediate plasticity. These additional mechanisms must be considered for a comprehensive mechanistic understanding of learning and memory.     

Coexistence of Reward and Unsupervised Learning During the Operant Conditioning of Neural Firing Rates

A fundamental goal of neuroscience is to understand how cognitive processes, such as operant conditioning, are performed by the brain. Typical and well studied examples of operant conditioning, in which the firing rates of individual cortical neurons in monkeys are increased using rewards, provide an opportunity for insight into this. Studies of reward-modulated spike-timing-dependent plasticity (RSTDP), and of other models such as R-max, have reproduced this learning behavior, but they have assumed that no unsupervised learning is present (i.e., no learning occurs without, or independent of, rewards). We show that these models cannot elicit firing rate reinforcement while exhibiting both reward learning and ongoing, stable unsupervised learning. To fix this issue, we propose a new RSTDP model of synaptic plasticity based upon the observed effects that dopamine has on long-term potentiation and depression (LTP and LTD). We show, both analytically and through simulations, that our new model can exhibit unsupervised learning and lead to firing rate reinforcement. This requires that the strengthening of LTP by the reward signal is greater than the strengthening of LTD and that the reinforced neuron exhibits irregular firing. We show the robustness of our findings to spike-timing correlations, to the synaptic weight dependence that is assumed, and to changes in the mean reward. We also consider our model in the differential reinforcement of two nearby neurons. Our model aligns more strongly with experimental studies than previous models and makes testable predictions for future experiments.