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We review a body of theoretical and experimental research on Hebbian and homeostatic plasticity, starting from a puzzling observation: while homeostasis of synapses found in experiments is a slow compensatory process, most mathematical models of synaptic plasticity use rapid compensatory processes (RCPs). Even worse, with the slow homeostatic plasticity reported in experiments, simulations of existing plasticity models cannot maintain network stability unless further control mechanisms are implemented. To solve this paradox, we suggest that in addition to slow forms of homeostatic plasticity there are RCPs which stabilize synaptic plasticity on short timescales. These rapid processes may include heterosynaptic depression triggered by episodes of high postsynaptic firing rate. While slower forms of homeostatic plasticity are not sufficient to stabilize Hebbian plasticity, they are important for fine-tuning neural circuits. Taken together we suggest that learning and memory rely on an intricate interplay of diverse plasticity mechanisms on different timescales which jointly ensure stability and plasticity of neural circuits. This article is part of the themed issue ‘Integrating Hebbian and homeostatic plasticity’.

The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Synaptic plasticity, the putative basis of learning and memory formation, manifests in various forms and across different timescales. Here we show that the interaction of Hebbian homosynaptic plasticity with rapid non-Hebbian heterosynaptic plasticity is, when complemented with slower homeostatic changes and consolidation, sufficient for assembly formation and memory recall in a spiking recurrent network model of excitatory and inhibitory neurons. In the model, assemblies were formed during repeated sensory stimulation and characterized by strong recurrent excitatory connections. Even days after formation, and despite ongoing network activity and synaptic plasticity, memories could be recalled through selective delay activity following the brief stimulation of a subset of assembly neurons. Blocking any component of plasticity prevented stable functioning as a memory network. Our modelling results suggest that the diversity of plasticity phenomena in the brain is orchestrated towards achieving common functional goals. The brain exhibits a diversity of plasticity mechanisms across different timecales that constitute the putative basis for learning and memory. Here, the authors demonstrate how these different plasticity mechanisms are orchestrated to support the formation of robust and stable neural cell assemblies.

Most elementary behaviors such as moving the arm to grasp an object or walking into the next room to explore a museum evolve on the time scale of seconds; in contrast, neuronal action potentials occur on the time scale of a few milliseconds. Learning rules of the brain must therefore bridge the gap between these two different time scales. Modern theories of synaptic plasticity have postulated that the co-activation of pre- and postsynaptic neurons sets a flag at the synapse, called an eligibility trace, that leads to a weight change only if an additional factor is present while the flag is set. This third factor, signaling reward, punishment, surprise, or novelty, could be implemented by the phasic activity of neuromodulators or specific neuronal inputs signaling special events. While the theoretical framework has been developed over the last decades, experimental evidence in support of eligibility traces on the time scale of seconds has been collected only during the last few years. Here we review, in the context of three-factor rules of synaptic plasticity, four key experiments that support the role of synaptic eligibility traces in combination with a third factor as a biological implementation of neoHebbian three-factor learning rules.

A recent competition encouraged modelers to predict neuronal activity. Which neuron model performed the best? Opinions strongly diverge on what constitutes a good model of a neuron ( 1 – 3 ). Two lines of thought on this have coexisted for a long time: detailed biophysical models (of the style proposed in 1952 by the physiologists Alan Hodgkin and Andrew Huxley) that describe ion channels on the tree-like spatial structure of the neuronal cell ( 4 ), and simple “integrate-and-fire” models based on the much older insight that pulsatile electrical activity (known as an action potential or spike) is a threshold process. Electrophysiologists generally prefer the biophysical models, familiar with the notion of ion channels that open and close (and hence, alter neuronal activity) depending on environmental conditions. Theoreticians, by contrast, typically prefer simple neuron models with few parameters that are amenable to mathematical analysis. Earlier this year, following previous attempts at model comparison on a smaller scale ( 5 ), the International Neuroinformatics Coordinating Facility (INCF) launched an international competition ( 6 ) that allowed a quantitative comparison of neuron models.

Using a combination of computational modeling and electrophysiological recordings, the authors show that the dynamics of spike-frequency adaptation have the effect of temporally decorrelating incoming signals. This decorrelation makes for more energy-efficient information transfer in the CNS. Spike-frequency adaptation (SFA) is widespread in the CNS, but its function remains unclear. In neocortical pyramidal neurons, adaptation manifests itself by an increase in the firing threshold and by adaptation currents triggered after each spike. Combining electrophysiological recordings in mice with modeling, we found that these adaptation processes lasted for more than 20 s and decayed over multiple timescales according to a power law. The power-law decay associated with adaptation mirrored and canceled the temporal correlations of input current received in vivo at the somata of layer 2/3 somatosensory pyramidal neurons. These findings suggest that, in the cortex, SFA causes temporal decorrelation of output spikes (temporal whitening), an energy-efficient coding procedure that, at high signal-to-noise ratio, improves the information transfer.

Communication by rare, binary spikes is a key factor for the energy efficiency of biological brains. However, it is harder to train biologically-inspired spiking neural networks than artificial neural networks. This is puzzling given that theoretical results provide exact mapping algorithms from artificial to spiking neural networks with time-to-first-spike coding. In this paper we analyze in theory and simulation the learning dynamics of time-to-first-spike-networks and identify a specific instance of the vanishing-or-exploding gradient problem. While two choices of spiking neural network mappings solve this problem at initialization, only the one with a constant slope of the neuron membrane potential at threshold guarantees the equivalence of the training trajectory between spiking and artificial neural networks with rectified linear units. For specific image classification architectures comprising feed-forward dense or convolutional layers, we demonstrate that deep spiking neural network models can be effectively trained from scratch on MNIST and Fashion-MNIST datasets, or fine-tuned on large-scale datasets, such as CIFAR10, CIFAR100 and PLACES365, to achieve the exact same performance as that of artificial neural networks, surpassing previous spiking neural networks. Our approach accomplishes high-performance classification with less than 0.3 spikes per neuron, lending itself for an energy-efficient implementation. We also show that fine-tuning spiking neural networks with our robust gradient descent algorithm enables their optimization for hardware implementations with low latency and resilience to noise and quantization. To address challenges of training spiking neural networks (SNNs) at scale, the authors propose a scalable, approximation-free training method for deep SNNs using time-to-first-spike coding. They demonstrate enhanced performance and energy efficiency for neuromorphic hardware.

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.

Continuous attractor models of working-memory store continuous-valued information in continuous state-spaces, but are sensitive to noise processes that degrade memory retention. Short-term synaptic plasticity of recurrent synapses has previously been shown to affect continuous attractor systems: short-term facilitation can stabilize memory retention, while short-term depression possibly increases continuous attractor volatility. Here, we present a comprehensive description of the combined effect of both short-term facilitation and depression on noise-induced memory degradation in one-dimensional continuous attractor models. Our theoretical description, applicable to rate models as well as spiking networks close to a stationary state, accurately describes the slow dynamics of stored memory positions as a combination of two processes: (i) diffusion due to variability caused by spikes; and (ii) drift due to random connectivity and neuronal heterogeneity. We find that facilitation decreases both diffusion and directed drifts, while short-term depression tends to increase both. Using mutual information, we evaluate the combined impact of short-term facilitation and depression on the ability of networks to retain stable working memory. Finally, our theory predicts the sensitivity of continuous working memory to distractor inputs and provides conditions for stability of memory.