arXiv subjects

Michael G. Müller

Publications and source records attributed to Michael G. Müller.

4 recordsLinked to original sources

arXiv2022

Simplex Closing Probabilities in Directed Graphs

Recent work in mathematical neuroscience has calculated the directed graph homology of the directed simplicial complex given by the brains sparse adjacency graph, the so called connectome. These biological connectomes show an abundance of both high-dimensional directed simplices and Betti-numbers in all viable dimensions - in contrast to Erdős-Rényi-graphs of comparable size and density. An analysis of synthetically trained connectomes reveals similar findings, raising questions about the graphs comparability and the nature of origin of the simplices. We present a new method capable of delivering insight into the emergence of simplices and thus simplicial abundance. Our approach allows to easily distinguish simplex-rich connectomes of different origin. The method relies on the novel concept of an almost-d-simplex, that is, a simplex missing exactly one edge, and consequently the almost-d-simplex closing probability by dimension. We also describe a fast algorithm to identify almost-d-simplices in a given graph. Applying this method to biological and artificial data allows us to identify a mechanism responsible for simplex emergence, and suggests this mechanism is responsible for the simplex signature of the excitatory subnetwork of a statistical reconstruction of the mouse primary visual cortex. Our highly optimised code for this new method is publicly available.

math.CO↗

arXiv2022

Cortical oscillations implement a backbone for sampling-based computation in spiking neural networks

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.

q-bio.NC↗

arXiv2019

A model for structured information representation in neural networks

Humans possess the capability to reason at an abstract level and to structure information into abstract categories, but the underlying neural processes have remained unknown. Experimental evidence has recently emerged for the organization of an important aspect of abstract reasoning: for assigning words to semantic roles in a sentence, such as agent (or subject) and patient (or object). Using minimal assumptions, we show how such a binding of words to semantic roles emerges in a generic spiking neural network through Hebbian plasticity. The resulting model is consistent with the experimental data and enables new computational functionalities such as structured information retrieval, copying data, and comparisons. It thus provides a basis for the implementation of more demanding cognitive computations by networks of spiking neurons.

q-bio.NC↗

arXiv2018

Camera-based vehicle velocity estimation from monocular video

This paper documents the winning entry at the CVPR2017 vehicle velocity estimation challenge. Velocity estimation is an emerging task in autonomous driving which has not yet been thoroughly explored. The goal is to estimate the relative velocity of a specific vehicle from a sequence of images. In this paper, we present a light-weight approach for directly regressing vehicle velocities from their trajectories using a multilayer perceptron. Another contribution is an explorative study of features for monocular vehicle velocity estimation. We find that light-weight trajectory based features outperform depth and motion cues extracted from deep ConvNets, especially for far-distance predictions where current disparity and optical flow estimators are challenged significantly. Our light-weight approach is real-time capable on a single CPU and outperforms all competing entries in the velocity estimation challenge. On the test set, we report an average error of 1.12 m/s which is comparable to a (ground-truth) system that combines LiDAR and radar techniques to achieve an error of around 0.71 m/s.

cs.CV↗