Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with ANNs. We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience. Details of these optimization processes are largely unknown. But their functional contribution can be approximated through powerful optimization methods, such as backpropagation through time (BPTT). A second major mismatch between RSNNs in the brain and models is that the latter only show a small fraction of the dynamics of neurons and synapses in the brain. We include neurons in our RSNN model that reproduce one prominent dynamical process of biological neurons that takes place at the behaviourally relevant time scale of seconds: neuronal adaptation. We denote these networks as LSNNs because of their Long short-term memory. The inclusion of adapting neurons drastically increases the computing and learning capability of RSNNs if they are trained and configured by deep learning (BPTT combined with a rewiring algorithm that optimizes the network architecture). In fact, the computational performance of these RSNNs approaches for the first time that of LSTM networks. In addition RSNNs with adapting neurons can acquire abstract knowledge from prior learning in a Learning-to-Learn (L2L) scheme, and transfer that knowledge in order to learn new but related tasks from very few examples. We demonstrate this for supervised learning and reinforcement learning.
Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with ANNs. We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience.
We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transform the inputs into rich high-dimensional representations based on past context. The random input representations can be efficiently interpreted by an output (or readout) layer with trainable parameters. Systematic initialization of the random connections and training of the readout layer using Q-learning algorithm enable such small random spiking networks to learn optimally and achieve the same learning efficiency as humans on complex reinforcement learning tasks like Atari games. The spike-based approach using small random recurrent networks provides a computationally efficient alternative to state-of-the-art deep reinforcement learning networks with several layers of trainable parameters. The low-complexity spiking networks can lead to improved energy efficiency in event-driven neuromorphic hardware for complex reinforcement learning tasks.
An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated weights are not essential for learning deep representations. Random BP replaces feedback weights with random ones and encourages the network to adjust its feed-forward weights to learn pseudo-inverses of the (random) feedback weights. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware. The rule requires only one addition and two comparisons for each synaptic weight using a two-compartment leaky Integrate & Fire (I&F) neuron, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving nearly identical classification accuracies compared to artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.
Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (~millisecond) spike-based interactions for efficient encoding of information, and a delayed memory XOR task over extended duration (~second). The results show that our method indeed optimizes the spiking network dynamics on the time scale of individual spikes as well as behavioral time scales. In conclusion, our result offers a general purpose supervised learning algorithm for spiking neural networks, thus advancing further investigations on spike-based computation.