arXiv subjects

David Pfau

Publications and source records attributed to David Pfau.

21 records · Page 2Linked to original sources

arXiv2016

Convolution by Evolution: Differentiable Pattern Producing Networks

In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution and learning, produces DPPNs to reconstruct an image. Our main result is that DPPNs can be evolved/trained to compress the weights of a denoising autoencoder from 157684 to roughly 200 parameters, while achieving a reconstruction accuracy comparable to a fully connected network with more than two orders of magnitude more parameters. The regularization ability of the DPPN allows it to rediscover (approximate) convolutional network architectures embedded within a fully connected architecture. Such convolutional architectures are the current state of the art for many computer vision applications, so it is satisfying that DPPNs are capable of discovering this structure rather than having to build it in by design. DPPNs exhibit better generalization when tested on the Omniglot dataset after being trained on MNIST, than directly encoded fully connected autoencoders. DPPNs are therefore a new framework for integrating learning and evolution.

cs.NE↗

arXiv2014

A structured matrix factorization framework for large scale calcium imaging data analysis

We present a structured matrix factorization approach to analyzing calcium imaging recordings of large neuronal ensembles. Our goal is to simultaneously identify the locations of the neurons, demix spatially overlapping components, and denoise and deconvolve the spiking activity of each neuron from the slow dynamics of the calcium indicator. The matrix factorization approach relies on the observation that the spatiotemporal fluorescence activity can be expressed as a product of two matrices: a spatial matrix that encodes the location of each neuron in the optical field and a temporal matrix that characterizes the calcium concentration of each neuron over time. We present a simple approach for estimating the dynamics of the calcium indicator as well as the observation noise statistics from the observed data. These parameters are then used to set up the matrix factorization problem in a constrained form that requires no further parameter tuning. We discuss initialization and post-processing techniques that enhance the performance of our method, along with efficient and largely parallelizable algorithms. We apply our method to {\it in vivo} large scale multi-neuronal imaging data and also demonstrate how similar methods can be used for the analysis of {\it in vivo} dendritic imaging data.

q-bio.NC↗

arXiv2012

Dead leaves and the dirty ground: low-level image statistics in transmissive and occlusive imaging environments

The opacity of typical objects in the world results in occlusion --- an important property of natural scenes that makes inference of the full 3-dimensional structure of the world challenging. The relationship between occlusion and low-level image statistics has been hotly debated in the literature, and extensive simulations have been used to determine whether occlusion is responsible for the ubiquitously observed power-law power spectra of natural images. To deepen our understanding of this problem, we have analytically computed the 2- and 4-point functions of a generalized "dead leaves" model of natural images with parameterized object transparency. Surprisingly, transparency alters these functions only by a multiplicative constant, so long as object diameters follow a power law distribution. For other object size distributions, transparency more substantially affects the low-level image statistics. We propose that the universality of power law power spectra for both natural scenes and radiological medical images -- formed by the transmission of x-rays through partially transparent tissue -- stems from power law object size distributions, independent of object opacity.

cond-mat.stat-mech↗