# Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli

## TL;DR

This paper presents a novel sparse functional identification method for complex cells that efficiently decodes visual stimuli from spike data, outperforming existing models and algorithms.

## Contribution

It introduces a rank minimization framework for decoding and identifying complex cell responses, establishing a duality that enhances evaluation and performance.

## Key findings

- Significantly reduces sampling measurements needed for decoding
- Outperforms generalized quadratic and spike-triggered covariance models
- Provides efficient algorithms for low-rank dendritic stimulus identification

## Abstract

We investigate the sparse functional identification of complex cells and the decoding of visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm of both temporal and spatio-temporal stimuli is formulated as a rank minimization problem that significantly reduces the number of sampling measurements (spikes) required for decoding. We also establish the duality between sparse decoding and functional identification, and provide algorithms for identification of low-rank dendritic stimulus processors. The duality enables us to efficiently evaluate our functional identification algorithms by reconstructing novel stimuli in the input space. Finally, we demonstrate that our identification algorithms substantially outperform the generalized quadratic model, the non-linear input model and the widely used spike-triggered covariance algorithm.