Simultaneous behavioral and electrophysiological recordings call for new methods to reveal the interactions between neural activity and behavior. A milestone would be an interpretable model of the co-variability of spiking activity and behavior across trials. Here, we model a mouse cortical sensory-motor pathway in a tactile detection task reported by licking with a large recurrent spiking neural network (RSNN), fitted to the recordings via gradient-based optimization. We focus specifically on the difficulty to match the trial-to-trial variability in the data. Our solution relies on optimal transport to define a distance between the distributions of generated and recorded trials. The technique is applied to artificial data and neural recordings covering six cortical areas. We find that the resulting RSNN can generate realistic cortical activity and predict jaw movements across the main modes of trial-to-trial variability. Our analysis also identifies an unexpected mode of variability in the data corresponding to task-irrelevant movements of the mouse.

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models.

Eq. (6) suggests that the SDE drift corresponding to the score may be broken down into 3 steps: 1. However, in practice this modification creates a "discontinuity" between the constrained and unconstrained components, leading to erroneous correlations between them in the generated samples. "learning rate" that is determined empirically such that the loss value reduces adequately close to zero Thus it needs to be tuned empirically. The correction in Eq. (16) is equivalent to imposing a Gaussian likelihood on Remark 2. The post-processing presented in this section is similar to [ In this section, we present the most relevant components for completeness and better reproducibility. B.2 Sampling The reverse SDE in Eq. (5) used for sampling may be rewritten in terms of denoiser D As stated in 4.1 of the main text, for this The energy-based metrics are already defined in Eq. (12) and Eq.

In the following, we respond to all the reviewers' questions that will be addressed in the paper's final version together W e would also like to point out t hat the bounds' tightness is shown not only in Fig.1 but However, as the Reviewer ment ions, the paper offers new insights for feature mappings' Those with large number of samples were used for co mparison with performance bounds in Fig.1 over one Theorem 1. Infinite instance spaces would require to use heav ier tools from variational analysis in such proof, but the