Is a 4-bit synaptic weight resolution enough? - constraints on enabling spike-timing dependent plasticity in neuromorphic hardware.

Large-scale neuromorphic hardware systems typically bear the trade-off between detail level and required chip resources. Especially when implementing spike-timing dependent plasticity, reduction in resources leads to limitations as compared to floating point precision. By design, a natural modification that saves resources would be reducing synaptic weight resolution. In this study, we give an estimate for the impact of synaptic weight discretization on different levels, ranging from random walks of individual weights to computer simulations of spiking neural networks. The FACETS wafer-scale hardware system offers a 4-bit resolution of synaptic weights, which is shown to be sufficient within the scope of our network benchmark. Our findings indicate that increasing the resolution may not even be useful in light of further restrictions of customized mixed-signal synapses. In addition, variations due to production imperfections are investigated and shown to be uncritical in the context of the presented study. Our results represent a general framework for setting up and configuring hardware-constrained synapses. We suggest how weight discretization could be considered for other backends dedicated to large-scale simulations. Thus, our proposition of a good hardware verification practice may rise synergy effects between hardware developers and neuroscientists.

An imperfect dopaminergic error signal can drive temporal-difference learning.

An open problem in the field of computational neuroscience is how to link synaptic plasticity to system-level learning. A promising framework in this context is temporal-difference (TD) learning. Experimental evidence that supports the hypothesis that the mammalian brain performs temporal-difference learning includes the resemblance of the phasic activity of the midbrain dopaminergic neurons to the TD error and the discovery that cortico-striatal synaptic plasticity is modulated by dopamine. However, as the phasic dopaminergic signal does not reproduce all the properties of the theoretical TD error, it is unclear whether it is capable of driving behavior adaptation in complex tasks. Here, we present a spiking temporal-difference learning model based on the actor-critic architecture. The model dynamically generates a dopaminergic signal with realistic firing rates and exploits this signal to modulate the plasticity of synapses as a third factor. The predictions of our proposed plasticity dynamics are in good agreement with experimental results with respect to dopamine, pre- and post-synaptic activity. An analytical mapping from the parameters of our proposed plasticity dynamics to those of the classical discrete-time TD algorithm reveals that the biological constraints of the dopaminergic signal entail a modified TD algorithm with self-adapting learning parameters and an adapting offset. We show that the neuronal network is able to learn a task with sparse positive rewards as fast as the corresponding classical discrete-time TD algorithm. However, the performance of the neuronal network is impaired with respect to the traditional algorithm on a task with both positive and negative rewards and breaks down entirely on a task with purely negative rewards. Our model demonstrates that the asymmetry of a realistic dopaminergic signal enables TD learning when learning is driven by positive rewards but not when driven by negative rewards.

Enabling functional neural circuit simulations with distributed computing of neuromodulated plasticity.

A major puzzle in the field of computational neuroscience is how to relate system-level learning in higher organisms to synaptic plasticity. Recently, plasticity rules depending not only on pre- and post-synaptic activity but also on a third, non-local neuromodulatory signal have emerged as key candidates to bridge the gap between the macroscopic and the microscopic level of learning. Crucial insights into this topic are expected to be gained from simulations of neural systems, as these allow the simultaneous study of the multiple spatial and temporal scales that are involved in the problem. In particular, synaptic plasticity can be studied during the whole learning process, i.e., on a time scale of minutes to hours and across multiple brain areas. Implementing neuromodulated plasticity in large-scale network simulations where the neuromodulatory signal is dynamically generated by the network itself is challenging, because the network structure is commonly defined purely by the connectivity graph without explicit reference to the embedding of the nodes in physical space. Furthermore, the simulation of networks with realistic connectivity entails the use of distributed computing. A neuromodulated synapse must therefore be informed in an efficient way about the neuromodulatory signal, which is typically generated by a population of neurons located on different machines than either the pre- or post-synaptic neuron. Here, we develop a general framework to solve the problem of implementing neuromodulated plasticity in a time-driven distributed simulation, without reference to a particular implementation language, neuromodulator, or neuromodulated plasticity mechanism. We implement our framework in the simulator NEST and demonstrate excellent scaling up to 1024 processors for simulations of a recurrent network incorporating neuromodulated spike-timing dependent plasticity.

A spiking neural network model of an actor-critic learning agent.

The ability to adapt behavior to maximize reward as a result of interactions with the environment is crucial for the survival of any higher organism. In the framework of reinforcement learning, temporal-difference learning algorithms provide an effective strategy for such goal-directed adaptation, but it is unclear to what extent these algorithms are compatible with neural computation. In this article, we present a spiking neural network model that implements actor-critic temporal-difference learning by combining local plasticity rules with a global reward signal. The network is capable of solving a nontrivial gridworld task with sparse rewards. We derive a quantitative mapping of plasticity parameters and synaptic weights to the corresponding variables in the standard algorithmic formulation and demonstrate that the network learns with a similar speed to its discrete time counterpart and attains the same equilibrium performance.