An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has been introduced by Carnevale and Hines. However, the integration scheme imposes nonphysiological constraints on the time constants of the synaptic currents, which hamper its general applicability. This letter addresses this problem in two ways. First, we provide physical arguments demonstrating why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. As part of our formal proof, we introduce the generalized Carnevale-Hines lemma, a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems, including receptor-neurotransmitter dissociation followed by channel closing. Through repeated application of the generalized lemma, we lift most of the original constraints on the time constants. Thus, we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse types than was previously thought.

Animal learning is associated with changes in the efficacy of connections between neurons. The rules that govern this plasticity can be tested in neural networks. Rules that train neural networks to map stimuli onto outputs are given by supervised learning and reinforcement learning theories. Supervised learning is efficient but biologically implausible. In contrast, reinforcement learning is biologically plausible but comparatively inefficient. It lacks a mechanism that can identify units at early processing levels that play a decisive role in the stimulus-response mapping. Here we show that this so-called credit assignment problem can be solved by a new role for attention in learning. There are two factors in our new learning scheme that determine synaptic plasticity: (1) a reinforcement signal that is homogeneous across the network and depends on the amount of reward obtained after a trial, and (2) an attentional feedback signal from the output layer that limits plasticity to those units at earlier processing levels that are crucial for the stimulus-response mapping. The new scheme is called attention-gated reinforcement learning (AGREL). We show that it is as efficient as supervised learning in classification tasks. AGREL is biologically realistic and integrates the role of feedback connections, attention effects, synaptic plasticity, and reinforcement learning signals into a coherent framework.