Barello, G. | Search bioRxiv

bioRxiv2018

Sparse-Coding Variational Auto-Encoders

The sparse coding model posits that the visual system has evolved to efficiently code natural stimuli using a sparse set of features from an overcomplete dictionary. The original sparse coding model suffered from two key limitations, however: (1) computing the neural response to an image patch required minimizing a nonlinear objective function via recurrent dynamics; (2) fitting relied on approximate inference methods that ignored uncertainty. Although subsequent work has developed several methods to overcome these obstacles, we propose a novel solution inspired by the variational auto-encoder (VAE) framework. We introduce the sparse-coding variational auto-encoder (SVAE), which augments the sparse coding model with a probabilistic recognition model parametrized by a deep neural network. This recognition model provides a neurally plausible feedforward implementation for the mapping from image patches to neural activities, and enables a principled method for fitting the sparse coding model to data via maximization of the evidence lower bound (ELBO). The SVAE differs from standard VAEs in three key respects: the latent representation is overcomplete (there are more latent dimensions than image pixels), the prior is sparse or heavy-tailed instead of Gaussian, and the decoder network is a linear projection instead of a deep network. We fit the SVAE to natural image data under different assumed prior distributions, and show that it obtains higher test performance than previous fitting methods. Finally, we examine the response properties of the recognition network and show that it captures important nonlinear properties of neurons in the early visual pathway.

neuroscience↗

bioRxiv2017

Capturing the diversity of biological tuning curves using generative adversarial networks

Tuning curves characterizing the response selectivities of biological neurons often exhibit large degrees of irregularity and diversity across neurons. Theoretical network models that feature heterogeneous cell populations or random connectivity also give rise to diverse tuning curves. However, a general framework for fitting such models to experimentally measured tuning curves is lacking. We address this problem by proposing to view mechanistic network models as generative models whose parameters can be optimized to fit the distribution of experimentally measured tuning curves. A major obstacle for fitting such models is that their likelihood function is not explicitly available or is highly intractable to compute. Recent advances in machine learning provide ways for fitting generative models without the need to evaluate the likelihood and its gradient. Generative Adversarial Networks (GAN) provide one such framework which has been successful in traditional machine learning tasks. We apply this approach in two separate experiments, showing how GANs can be used to fit commonly used mechanistic models in theoretical neuroscience to datasets of measured tuning curves. This fitting procedure avoids the computationally expensive step of inferring latent variables, e.g., the biophysical parameters of individual cells or the particular realization of the full synaptic connectivity matrix, and directly learns model parameters which characterize the statistics of connectivity or of single-cell properties. Another strength of this approach is that it fits the entire, joint distribution of experimental tuning curves, instead of matching a few summary statistics picked a priori by the user. More generally, this framework opens the door to fitting theoretically motivated dynamical network models directly to simultaneously or non-simultaneously recorded neural responses.

neuroscience↗