arXiv subjects

Markus Meister

Publications and source records attributed to Markus Meister.

13 recordsLinked to original sources

arXiv2025

The Standard Model of the Retina

The scientific study of the retina has reached a remarkable state of completion. We can now explain many aspects of early visual processing based on a relatively simple model of neural circuitry in the retina. The same model, with different parameters, produces a great diversity of neural computations. In this article I lay out what that "standard model" is and how it accounts for such a diversity of phenomena. The emergence of such a powerful standard model is unique in systems neuroscience, and I consider what conditions made it possible. The standard model now serves as a baseline from which to organize future retinal research, either by testing the model's assumptions directly, or by identifying phenomena that remain unexplained.

q-bio.NC↗

arXiv2024

The Unbearable Slowness of Being: Why do we live at 10 bits/s?

This article is about the neural conundrum behind the slowness of human behavior. The information throughput of a human being is about 10 bits/s. In comparison, our sensory systems gather data at ~10^9 bits/s. The stark contrast between these numbers remains unexplained and touches on fundamental aspects of brain function: What neural substrate sets this speed limit on the pace of our existence? Why does the brain need billions of neurons to process 10 bits/s? Why can we only think about one thing at a time? The brain seems to operate in two distinct modes: the "outer" brain handles fast high-dimensional sensory and motor signals, whereas the "inner" brain processes the reduced few bits needed to control behavior. Plausible explanations exist for the large neuron numbers in the outer brain, but not for the inner brain, and we propose new research directions to remedy this.

q-bio.NC↗

arXiv2023

A fast algorithm for All-Pairs-Shortest-Paths suitable for neural networks

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given by the adjacency matrix $A_{ij}$ then with a suitably small value of $\gamma$ the shortest path distances are $$ D_{ij} = \operatorname{ceil} \left( \log_{\gamma} {\left[ {\left({\mathbf{I}}-\gamma {\mathbf{A}}\right)^{-1}} \right]}_{ij} \right)$$ We derive several graph-theoretic bounds on the value of $\gamma$, and explore its useful range with numerics on different graph types. Even when the distance function is not globally accurate across the entire graph, it still works locally to instruct pursuit of the shortest path. In this mode, it also extends to weighted graphs with positive edge weights. For a wide range of dense graphs this distance function is computationally faster than the best available alternative. Finally we show that this method leads naturally to a neural network solution of the all-pairs-shortest-path problem.

cs.DS↗

arXiv2022

Efficient population coding of sensory stimuli

The efficient coding theory postulates that single cells in a neuronal population should be optimally configured to efficiently encode information about a stimulus subject to biophysical constraints. This poses the question of how multiple neurons that together represent a common stimulus should optimize their activation functions to provide the optimal stimulus encoding. Previous theoretical approaches have solved this problem with binary neurons that have a step activation function, and have assumed that spike generation is noisy and follows a Poisson process. Here we derive a general theory of optimal population coding with neuronal activation functions of any shape, different types of noise and heterogeneous firing rates of the neurons by maximizing the Shannon mutual information between a stimulus and the neuronal spiking output subject to a constrain on the maximal firing rate. We find that the optimal activation functions are discrete in the biological case of non-negligible noise and demonstrate that the information does not depend on how the population is divided into ON and OFF cells described by monotonically increasing vs. decreasing activation functions, respectively. However, the population with an equal number of ON and OFF cells has the lowest mean firing rate, and hence encodes the highest information per spike. These results are independent of the shape of the activation functions and the nature of the spiking noise. Finally, we derive a relationship for how these activation functions should be distributed in stimulus space as a function of the neurons' firing rates.

q-bio.NC↗

arXiv2022

Learning, fast and slow

Animals can learn efficiently from a single experience and change their future behavior in response. However, in other instances, animals learn very slowly, requiring thousands of experiences. Here I survey tasks involving fast and slow learning and consider some hypotheses for what differentiates the underlying neural mechanisms. It has been proposed that fast learning relies on neural representations that favor efficient Hebbian modification of synapses. These efficient representations may be encoded in the genome, resulting in a repertoire of fast learning that differs across species. Alternatively, the required neural representations may be acquired from experience through a slow process of unsupervised learning from the environment.

q-bio.NC↗

arXiv2021

Curved Micro-Electrode Arrays

Multi-electrode arrays serve to record electrical signals of many neurons in the brain simultaneously. For most of the past century, electrodes that penetrate brain tissue have had exactly one shape: a straight needle. Certainly this was a good starting choice at the time, but there is no reason to think that a straight line would be the optimal shape in all Neuroscience applications. Here I argue that, in fact, a wide variety of curved shapes is equally practical: all possible helices. I discuss the manufacture and manipulation of such devices, and illustrate a few use cases where they will likely outperform conventional needles. With some collective action from the research community, curved arrays could be manufactured and distributed at low cost.

q-bio.NC↗

arXiv2021

Fine-Grained System Identification of Nonlinear Neural Circuits

We study the problem of sparse nonlinear model recovery of high dimensional compositional functions. Our study is motivated by emerging opportunities in neuroscience to recover fine-grained models of biological neural circuits using collected measurement data. Guided by available domain knowledge in neuroscience, we explore conditions under which one can recover the underlying biological circuit that generated the training data. Our results suggest insights of both theoretical and practical interests. Most notably, we find that a sign constraint on the weights is a necessary condition for system recovery, which we establish both theoretically with an identifiability guarantee and empirically on simulated biological circuits. We conclude with a case study on retinal ganglion cell circuits using data collected from mouse retina, showcasing the practical potential of this approach.

q-bio.QM↗

arXiv2021

Learning by Turning: Neural Architecture Aware Optimisation

Descent methods for deep networks are notoriously capricious: they require careful tuning of step size, momentum and weight decay, and which method will work best on a new benchmark is a priori unclear. To address this problem, this paper conducts a combined study of neural architecture and optimisation, leading to a new optimiser called Nero: the neuronal rotator. Nero trains reliably without momentum or weight decay, works in situations where Adam and SGD fail, and requires little to no learning rate tuning. Also, Nero's memory footprint is ~ square root that of Adam or LAMB. Nero combines two ideas: (1) projected gradient descent over the space of balanced networks; (2) neuron-specific updates, where the step size sets the angle through which each neuron's hyperplane turns. The paper concludes by discussing how this geometric connection between architecture and optimisation may impact theories of generalisation in deep learning.

cs.NE↗

arXiv2020

Learning compositional functions via multiplicative weight updates

Compositionality is a basic structural feature of both biological and artificial neural networks. Learning compositional functions via gradient descent incurs well known problems like vanishing and exploding gradients, making careful learning rate tuning essential for real-world applications. This paper proves that multiplicative weight updates satisfy a descent lemma tailored to compositional functions. Based on this lemma, we derive Madam -- a multiplicative version of the Adam optimiser -- and show that it can train state of the art neural network architectures without learning rate tuning. We further show that Madam is easily adapted to train natively compressed neural networks by representing their weights in a logarithmic number system. We conclude by drawing connections between multiplicative weight updates and recent findings about synapses in biology.

cs.NE↗

arXiv2020

PanDA: Panoptic Data Augmentation

The recently proposed panoptic segmentation task presents a significant challenge of image understanding with computer vision by unifying semantic segmentation and instance segmentation tasks. In this paper we present an efficient and novel panoptic data augmentation (PanDA) method which operates exclusively in pixel space, requires no additional data or training, and is computationally cheap to implement. By retraining original state-of-the-art models on PanDA augmented datasets generated with a single frozen set of parameters, we show robust performance gains in panoptic segmentation, instance segmentation, as well as detection across models, backbones, dataset domains, and scales. Finally, the effectiveness of unrealistic-looking training images synthesized by PanDA suggest that one should rethink the need for image realism for efficient data augmentation.

cs.CV↗

arXiv2019

Synthetic Examples Improve Generalization for Rare Classes

The ability to detect and classify rare occurrences in images has important applications - for example, counting rare and endangered species when studying biodiversity, or detecting infrequent traffic scenarios that pose a danger to self-driving cars. Few-shot learning is an open problem: current computer vision systems struggle to categorize objects they have seen only rarely during training, and collecting a sufficient number of training examples of rare events is often challenging and expensive, and sometimes outright impossible. We explore in depth an approach to this problem: complementing the few available training images with ad-hoc simulated data. Our testbed is animal species classification, which has a real-world long-tailed distribution. We analyze the effect of different axes of variation in simulation, such as pose, lighting, model, and simulation method, and we prescribe best practices for efficiently incorporating simulated data for real-world performance gain. Our experiments reveal that synthetic data can considerably reduce error rates for classes that are rare, that as the amount of simulated data is increased, accuracy on the target class improves, and that high variation of simulated data provides maximum performance gain.

cs.CV↗

arXiv2016

Physical limits to magnetogenetics

This is an analysis of how magnetic fields affect biological molecules and cells. It was prompted by a series of prominent reports regarding magnetism in biological systems. The first claims to have identified a protein complex that acts like a compass needle to guide magnetic orientation in animals (Qin et al., 2016). Two other articles report magnetic control of membrane conductance by attaching ferritin to an ion channel protein and then tugging the ferritin or heating it with a magnetic field (Stanley et al., 2015; Wheeler et al., 2016). Here I argue that these claims conflict with basic laws of physics. The discrepancies are large: from 5 to 10 log units. If the reported phenomena do in fact occur, they must have causes entirely different from the ones proposed by the authors. The paramagnetic nature of protein complexes is found to seriously limit their utility for engineering magnetically sensitive cells.

q-bio.NC↗

arXiv2014

Can Humans Really Discriminate 1 Trillion Odors?

A recent paper in a prominent science magazine claims to show that humans can discriminate at least 1 trillion odors. The authors reached that conclusion after performing just 260 comparisons of two smells, of which about half could be discriminated. Furthermore the paper claims that the human ability to discriminate smells vastly exceeds our abilities to discriminate colors or musical tones. Here I show that all these statements are wrong by astronomical factors. A reanalysis of the authors' experiments shows they are also consistent with humans discriminating just 10 odors. The paper's extravagant claims are based on errors of mathematical logic. Further analysis highlights the importance of establishing how many dimensions the perceptual odor space has. I review some arguments on the topic and propose experimental avenues towards an answer.

q-bio.NC↗