Henning Sprekeler

Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks.

Plasticity at inhibitory synapses maintains balanced excitatory and inhibitory synaptic inputs at cortical neurons. Cortical neurons receive balanced excitatory and inhibitory synaptic currents. Such a balance could be established and maintained in an experience-dependent manner by synaptic plasticity at inhibitory synapses. We show that this mechanism provides an explanation for the sparse firing patterns observed in response to natural stimuli and fits well with a recently observed interaction of excitatory and inhibitory receptive field plasticity. The introduction of inhibitory plasticity in suitable recurrent networks provides a homeostatic mechanism that leads to asynchronous irregular network states. Further, it can accommodate synaptic memories with activity patterns that become indiscernible from the background state but can be reactivated by external stimuli. Our results suggest an essential role of inhibitory plasticity in the formation and maintenance of functional cortical circuitry.

Slowness and Sparseness Lead to Place, Head-Direction, and Spatial-View Cells

We present a model for the self-organized formation of place cells, head-direction cells, and spatial-view cells in the hippocampal formation based on unsupervised learning on quasi-natural visual stimuli. The model comprises a hierarchy of Slow Feature Analysis (SFA) nodes, which were recently shown to reproduce many properties of complex cells in the early visual system [1]. The system extracts a distributed grid-like representation of position and orientation, which is transcoded into a localized place-field, head-direction, or view representation, by sparse coding. The type of cells that develops depends solely on the relevant input statistics, i.e., the movement pattern of the simulated animal. The numerical simulations are complemented by a mathematical analysis that allows us to accurately predict the output of the top SFA layer.

Functional Requirements for Reward-Modulated Spike-Timing-Dependent Plasticity

Recent experiments have shown that spike-timing-dependent plasticity is influenced by neuromodulation. We derive theoretical conditions for successful learning of reward-related behavior for a large class of learning rules where Hebbian synaptic plasticity is conditioned on a global modulatory factor signaling reward. We show that all learning rules in this class can be separated into a term that captures the covariance of neuronal firing and reward and a second term that presents the influence of unsupervised learning. The unsupervised term, which is, in general, detrimental for reward-based learning, can be suppressed if the neuromodulatory signal encodes the difference between the reward and the expected reward—but only if the expected reward is calculated for each task and stimulus separately. If several tasks are to be learned simultaneously, the nervous system needs an internal critic that is able to predict the expected reward for arbitrary stimuli. We show that, with a critic, reward-modulated spike-timing-dependent plasticity is capable of learning motor trajectories with a temporal resolution of tens of milliseconds. The relation to temporal difference learning, the relevance of block-based learning paradigms, and the limitations of learning with a critic are discussed.

Theory and Simulation in Neuroscience

Theory Drives Understanding The role of theory and simulation in neuroscience has been hotly debated over the past few years, in particular in the context of the recent launch of several big projects aimed at creating artificial or virtual brains. Gerstner et al. (p. 60) review how theory and simulations have interacted over the years and how they have contributed to our present view of how the brain works. 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 order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.

Reinforcement Learning Using a Continuous Time Actor-Critic Framework with Spiking Neurons

Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.

Inhibitory synaptic plasticity: spike timing-dependence and putative network function

While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical findings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012.

Slow Feature Analysis

© 2008, 2009, 2016 Laurenz Wiskott (ORCID http://orcid.org/0000-0001-6237-740X, homepage https://www.ini.rub. de/PEOPLE/wiskott/). This work (except for all figures from other sources, if present) is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License, see http://creativecommons.org/licenses/by-sa/4.0/. If figures are not included for copyright reasons, they are uni colored, but the word ’Figure’, ’Image’, or the like in the reference is often linked to a freely available copy. Core text and formulas are set in dark red, one can repeat the lecture notes quickly by just reading these; marks important formulas or items worth remembering and learning for an exam; ♦ marks less important formulas or items that I would usually also present in a lecture; + marks sections that I would usually skip in a lecture. More teaching material is available at https://www.ini.rub.de/PEOPLE/wiskott/Teaching/Material/.

Slowness: An Objective for Spike-Timing-Dependent Plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.

On the relation of slow feature analysis and laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs.

Predictive coding and the slowness principle: An information-theoretic approach

Understanding the guiding principles of sensory coding strategies is a main goal in computational neuroscience. Among others, the principles of predictive coding and slowness appear to capture aspects of sensory processing. Predictive coding postulates that sensory systems are adapted to the structure of their input signals such that information about future inputs is encoded. Slow feature analysis (SFA) is a method for extracting slowly varying components from quickly varying input signals, thereby learning temporally invariant features. Here, we use the information bottleneck method to state an information-theoretic objective function for temporally local predictive coding. We then show that the linear case of SFA can be interpreted as a variant of predictive coding that maximizes the mutual information between the current output of the system and the input signal in the next time step. This demonstrates that the slowness principle and predictive coding are intimately related.