1. @ NeurIPS 2016
Tim Dunn, May

2. ~10,000 recorded neurons
How can we deconstruct this complex network activity to shed light on brain mechanisms?

3. Hypothesis: Neural firing rates can be explained as linear transformations, followed by exponentiation, of low-dimensional temporal factors. These factors evolve with non-linear dynamics that depend on unobserved external input.
Let v=W(u) denote v=Wu+b
Values of low-D factors at time t
keeps rates positive
firing rates for all neurons at time t
Binned spike # for all neurons at time t
f 𝑡 =𝐅( f 𝑡−1 , u 𝑡 )
Some unobserved input
(e.g. input from another brain area)
non-linear function

4. F is modeled with a GRU, and f as a linear transformation of the GRU state. From some initial state, this model can be run forward in time to generate neural spiking data
Gaussian Priors

5. F is modeled with a GRU, and f as a linear transformation of the GRU state. From some initial state, this model can be run forward in time to generate neural spiking data

6. But what we would like to do is infer g 0 and u 𝑡 (and thus g 𝑡 ) for all time points, given the observed spiking patterns in the neural population. To do this, the authors use a VAE strategy to find approximate posteriors,
Additional extrinsic information that can affect firing patterns, like a visual stimulus

7. Encoder network for Mean and variance given by:
With E obtained running a GRU forward and backward in time over all data
With the initial RNN states as additional learnable parameters

8. Encoder network for
A bidirectional GRU is used again, this time to generate a time-dependent variable
Which, rather than being fed into a Gaussian, is fed into another GRU (the “controller”)
The dependence on f introduces the conditioning on g 0 and u 1:𝑡−1

9. Encoder network for
Finally,
with

10. Full LFADS
With initial state sampled from

11. Full LFADS loss function
Maximize the lower bound on the marginal data log-likelihood

12. Full LFADS

13. Experiments

14. Experiments