Imagine predicting the precise responses to arbitrary sensory stimuli for a neuron probed deeply within a brain. We developed a robust characterization technique called spike-triggered descent (STD) which optimally recovers n-order kernels for the very general cumulative spike response model (CSRM). This works by simulating a model neuron that learns to reproduce the observed spike train. Learning is achieved via parameter optimization that relies on a metric induced on the space of spike trains modeled as a novel inner product space. This technique can precisely learn kernels on extremely limited simulated datasets consisting of only a few dozen spikes. To demonstrate the strength of this approach beyond cross model comparisons, we extracted kernels from Rokem’s Locusta migratoria tympanal nerve and Stevenink’s H1 Blowfly datasets. While STD can work in a variety of scenarios, other techniques can produce better results on the models for which they were designed. A foundational technique called spike-triggered average (STA), after which ours is named, does particularly well characterizing linear-nonlinear-Poisson (LNP) model neurons. The STA kernel is the pseudoinverse interpreted as the signal's autocorrelation times the correlation of the signal with the membrane potential. In practice, the spike rate is used which is allowed by Bussgang’s theorem. Fortunately, STA is easy to understand, implement, and can be used as a way to initialize kernel parameters for STD. Another important technique is the maximum likelihood estimation (MLE) approach (developed by Paninski et al.) designed for the linear-noisey leaky-integrate-and-fire (L-NLIF) model. It works by maximizing the probability of firing at spikes and not firing between. In our cross model analysis, we have shown that the CSRM model can exactly replicate L-NLIF spikes. STD currently performs better than MLE in zero to low noise settings and we’re actively improving its results.