Publications by Wulfram Gerstner

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Continuous attractor models of working-memory store continuous-valued information in continuous state-spaces, but are sensitive to noise processes that degrade memory retention. Short-term synaptic plasticity of recurrent synapses has previously been shown ...

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current—is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) r

In many daily tasks, we make multiple decisions before reaching a goal. In order to learn such sequences of decisions, a mechanism to link earlier actions to later reward is necessary. Reinforcement learning (RL) theory suggests two classes of algorithms s ...

Opinions strongly diverge on what constitutes a good model of a neuron. Two lines of thought on this have coexisted for a long time: detailed biophysical models (of the style proposed in 1952 by the physiologists Alan Hodgkin and Andrew Huxley) that describe ion channels on the tree-like spatial structure of the neuronal cell, and simple "integrate-and-fire" models based on the much older insight that pulsatile electrical activity (known as an action potential or spike) is a threshold process. Electrophysio

Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning r ...

We derive a plausible learning rule updating the synaptic efficacies for feedforward, feedback and lateral connections between observed and latent neurons. Operating in the context of a generative model for distributions of spike sequences, the learning me ...

Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs potentials, it is natural to correlate presynaptic

We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For N units, these sequences have length T = 2^N; that is, they cover the full state space. We present a mathe ...

Memory consolidation involves a process of engram reorganization and stabilization that is thought to occur primarily during sleep through a combination of neural replay, homeostatic plasticity, synaptic maturation, and pruning. From a computational perspective, however, this process remains puzzling, as it is unclear how the underlying mechanisms can be incorporated into a common mathematical model of learning and memory. Here, we propose a solution by deriving a consolidation model that uses replay and tw

Classical experiments on spike timing-dependent plasticity (STDP) use a protocol based on pairs of presynaptic and postsynaptic spikes repeated at a given frequency to induce synaptic potentiation or depression. Therefore, standard STDP models have expressed the weight change as a function of pairs of presynaptic and postsynaptic spike. Unfortunately, those paired-based STDP models cannot account for the dependence on the repetition frequency of the pairs of spike. Moreover, those STDP models cannot reprodu

Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show that the incoming weight vector of each neuron is identifiable up to sign or scaling, depending on the activation function. Our novel method ’Expand-and-Cluster’ can identify layer sizes and weights of a target network for all commonly used activation functions. Expand-and-

The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the presynaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cel ...

Novelty signals in the brain modulate learning and drive exploratory behaviors in humans and animals. While the perceived novelty of a stimulus is known to depend on previous experience, the effect of stimulus representations on novelty computation remains elusive. In particular, existing models of novelty computation fail to account for the effects of stimulus similarities that are abundant in naturalistic environments and tasks. Here, we present a unifying, biologically plausible model that captures how s

The firing activities of place cells in the rat hippocampus exhibit strong correlations to the animal's location. External (e.g. visual) as well as internal (proprioceptive and vestibular) sensory information take part in controlling hippocampal place fiel ...

Brain activity recorded non-invasively is sufficient to control a moblie robot if advanced robotics is used in combination with asynchronous EEG analysis and machine learning techniques. Until now brain-actuated control has mainly relied on implanted electrodes, since EEG based systems have bben considered tto slow for controlling rapid and complex sequences of movements. We show that two human subjects successfully moved a robot between several rooms by mental control only using an EEG based brain-machine

In randomly connected networks of pulse-coupled elements a time-dependent input signal can be buffered over a short time. We studied the signal buffering properties in simulated networks as a function of the networks' state, characterized by both the Lyapu ...

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacti ...

Different neural systems are involved in animal navigation depending on the type of task. Experimental studies support the idea that the hippocampus is necessary to learn a spatial representation required to navigate toward hidden goals (place response), w ...

A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on a large corpus o ...

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an ...

Wulfram Gerstner

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Stability of working memory in continuous attractor networks under the control of short-term plasticity

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

One-shot learning and behavioral eligibility traces in sequential decision making

How Good are Neuron Models?

Code-specific policy gradient rules for spiking neurons

Variational Learning for Recurrent Spiking Networks

Mathematical Formulations of Hebbian Learning

Exponentially long orbits in Hopfield neural networks

Two-factor synaptic consolidation reconciles robust memory with pruning and homeostatic scaling

Triplets of Spikes in a Model of Spike Timing-Dependent Plasticity

Expand-and-Cluster: Parameter Recovery of Neural Networks

Short-term-plasticity orchestrates the response of pyramidal cells and interneurons to population bursts

Representational similarity modulates neural and behavioral signatures of novelty

Modelling Path Integrator Recalibration Using Hippocampal Place cells

Non-invasive Brain actuated control of a mobile robot by Human EEG

Signal buffering in random networks of spiking neurons: microscopic vs. macroscopic phenomena

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

Competition between cue response and place response: A model of rat navigation behaviour

Algorithmic Composition of Melodies with Deep Recurrent Neural Networks

An exact mapping from ReLU networks to spiking neural networks