Objective Functions

To subserve learning, synaptic plasticity must change how neurons respond to inputs. By contrast, mainstream research on synaptic plasticity is looking in the opposite direction and studies how postsynaptic activity takes part in shaping synaptic plasticity. These studies have been very successful in dissecting the mechanistic underpinnings of synaptic changes (Martin et al., 2000). In addition, they have been highly productive in generating a plethora of phenomenological synaptic learning rules, mostly one (in unfortunate cases also more than one) rule per induction protocol (Korte & Schmitz, 2016). However, these approaches are ill-posed to answer what it is about its postsynaptic response that a neuron is trying to change when engaging synaptic plasticity. To address this fundamental question, we disconnect from the established lines of research and align ourselves with the perspective of the brain when required to change its function. Specifically, we will measure the objective functions that govern synaptic plasticity. The nonlinear spike generating mechanisms that map postsynaptic voltage traces to discrete spike trains has prevented such measurements in the past. Here, we embrace a recently developed measure of postsynaptic responses, the spike-threshold-surface, that provides the basis for continuous objective functions for learning of discrete spiking responses (Gütig, 2016). Given a pattern of presynaptic activity, the spike-threshold-surface quantifies how far a neuron is away from generating different numbers of output spikes. Our goal is to measure how synaptic plasticity changes these distances (Fig. 1).

Fig. 1
(A) Multicompartmental neuron model (Armatrudo et al., 2012); (B) progression of voltage traces from cool to warm colors during operation of spike-timing dependent plasticity. (C) Although the number of spikes remains constant (4 spikes), the spike-threshold-surfaces before (blue) and after (red) plasticity reveal an increased plateau width, i.e. margin, around 4 spikes (dashed vertical line). Large margin classification is crucial for generalization and belongs to the most important breakthroughs in machine learning. Solid lines: synaptic stimulation, dotted lines: dynamic clamp.