  An open question in systems and computational neuroscience is how neural
circuits accumulate evidence towards a decision. Fitting models of
decision-making theory to neural activity helps answer this question, but
current approaches limit the number of these models that we can fit to neural
data. Here we propose a unifying framework for modeling neural activity during
decision-making tasks. The framework includes the canonical drift-diffusion
model and enables extensions such as multi-dimensional accumulators, variable
and collapsing boundaries, and discrete jumps. Our framework is based on
constraining the parameters of recurrent state-space models, for which we
introduce a scalable variational Laplace-EM inference algorithm. We applied the
modeling approach to spiking responses recorded from monkey parietal cortex
during two decision-making tasks. We found that a two-dimensional accumulator
better captured the trial-averaged responses of a set of parietal neurons than
a single accumulator model. Next, we identified a variable lower boundary in
the responses of an LIP neuron during a random dot motion task.
