Publications by Wulfram Gerstner

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Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model, ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in ...

Synaptic plasticity, the putative basis of learning and memory formation, manifests in various forms and across different timescales. Here we show that the interaction of Hebbian homosynaptic plasticity with rapid non-Hebbian heterosynaptic plasticity is, ...

Lotteries and tickets are often used as a didactical analogy to explain the success of overparameterized neural networks: “larger networks succeed because they more likely contain a well-initialized subnetwork that can learn the task in isolation, much like buying more tickets increases the chances of winning a lottery.” This explanation is intuitive but misleading: it suggests that subnetworks can be treated in isolation from the rest of the network. Following this reasoning leads to interpreting learning

Learning in the brain is poorly understood and learning rules that respect biological constraints, yet yield deep hierarchical representations, are still unknown. Here, we propose a learning rule that takes inspiration from neuroscience and recent advances ...

A description of neuronal activity on the level of ion channels, as in the Hodgkin-Huxley model, leads to a set of coupled nonlinear differential equations which are difficult to analyze. In this paper, we present a conceptual framework for a reduction of the nonlinear spike dynamics to a threshold process. Spikes occur if the membrane potential

u(t)

reaches a threshold

\vartheta

. The voltage response to spike input is described by the postsynaptic potential

\epsilon

. Postsynaptic potentials of severa

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically-detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrate-and-fire models. In the first variant (non-linear integrate-and-fire model), parameters depend on the instantaneous membrane potential whereas in the second variant, they depend on the time elapsed since the last spike (Spike Re

A generalized version of the integrate-and-fire model is presented that qualitatively reproduces firing rates and membrane trajectories of motoneurons. The description is based on the spike-response model and includes 3 different time constants: the passive membrane time constant, a recovery time of the input conductance after each spike, and a time constant of the spike afterpotential. The effect of stochastic background input on the peristimulus time histogram (P STH) response to spike input is calculated

Forming a memory involves linking the different aspects that form an experience. Single-neuron recordings in humans suggest that, in the hippocampus, memories are encoded by partially overlapping engrams, with partial overlaps representing associations. Furthermore, theoretical work with static attractor networks has demonstrated that partial overlaps between engrams can support associative recall within a limited range, beyond which memories remain independent or merge into one. However, how overlaps emerg

Modern reinforcement learning algorithms reach super-human performance on many board and video games, but they are sample inefficient, i.e. they typically require significantly more playing experience than humans to reach an equal performance level. To imp ...

Recent experiments have shown the near possibility to use the brain electrical activity to directly control the movement of robotics or prosthetic devices. In this paper we report results with a portable non-invasive brain-computer interface that makes possible the continuous control of a mobile robot in a house-like environment. The interface uses 8 surface electrodes to measure electroencephalogram (EEG) signals from which a statistical classifier recognizes 3 different mental states. Until now, brain-act

Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. To learn efficient population codes, synaptic plasticity mechanisms must differentiate relevant latent features from spurious input correlations, w ...

Biological information-processing systems, such as populations of sensory and motor neurons, may use correlations between the firings of individual elements to obtain lower noise levels and a systemwide performance improvement in the dynamic range or the signal-to-noise ratio. Here, we implement such correlations in networks of coupled integrate-and-fire neurons using inhibitory coupling and demonstrate that this can improve the system dynamic range and the signal-to-noise ratio in a population rate code. T

Abstract A recurrent neural network fitted to large electrophysiological datasets may help us understand the chain of cortical information transmission. In particular, successful network reconstruction methods should enable a model to predict the response to optogenetic perturbations. We test recurrent neural networks (RNNs) fitted to electrophysiological datasets on unseen optogenetic interventions, and measure that generic RNNs used predominantly in the field generalize poorly on these perturbations. Our

In order to find extrinsic rewards, humans explore their environment even if exploration requires several intermediate, reward-free decisions. It has been hypothesized that intrinsic rewards, such as novelty, surprise, or information gain, guide this reward-free exploration. However, in artificial agents, different intrinsic reward signals induce exploration strategies that respond differently to stochasticity. In particular, some strategies are vulnerable to the “noisy TV problem,” i.e., an attraction to i

What happens in our brain when we make a decision? What triggers a neuron to send out a signal? What is the neural code? This textbook for advanced undergraduate and beginning graduate students provides a thorough and up-to-date introduction to the fields of computational and theoretical neuroscience. It covers classical topics, including the Hodgkin-Huxley equations and Hopfield model, as well as modern developments in the field such as Generalized Linear Models and decision theory. Concepts are introduced

Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved ne

We study how neuronal connections in a population of spiking neurons affect the accuracy of stimulus estimation. Neurons in our model code for a one-dimensional orientation variable

\phi

. Connectivity between two neurons depends on the absolute difference

|\phi-\phi'|

between the preferred orientation of the two neurons. We derive an analytical expression of the activity profile for a population of neurons described by the spike response model with noisy threshold. We estimate the stimulus orientation a

Maximization of information transmission by a spiking-neuron model predicts changes of synaptic connections that depend on timing of pre- and postsynaptic spikes and on the postsynaptic membrane potential. Under the assumption of Poisson firing statistics, the synaptic update rule exhibits all of the features of the Bienenstock-Cooper-Munro rule, in particular, regimes of synaptic potentiation and depression separated by a sliding threshold. Moreover, the learning rule is also applicable to the more realist

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in ...

Wulfram Gerstner

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Theory and Simulation in Neuroscience

Diverse synaptic plasticity mechanisms orchestrated to form and retrieve memories in spiking neural networks

The Puzzling Success of Overparameterization: Lottery Tickets or Escape Dimensions?

Local plasticity rules can learn deep representations using self-supervised contrastive predictions

A framework for spiking neuron models - the spike response model

On the choice of metric in gradient-based theories of brain function

Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy

Noise and the PSTH response to current transients II. Integrate-and-fire model with slow recovery and application to motoneuron data

Emergence of overlapping assemblies in a dynamic attractor model of associative memory

Efficient Model-Based Deep Reinforcement Learning with Variational State Tabulation

Non-Invasive Brain-Actuated Control of a Mobile Robot

Learning what matters: Synaptic plasticity with invariance to second-order input correlations

Noise-shaping in populations of coupled model neurons

Biologically informed cortical models predict optogenetic perturbations

Novelty as a drive of human exploration in complex stochastic environments

Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition

Mesoscopic modeling of hidden spiking neurons

Effect of lateral connections on the accuracy of the population code for a network of spiking neurons

Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission

Improved Similarity Measures for Small Sets of Spike Trains