Tensor decompositions of higher-order correlations by nonlinear Hebbian learning

Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. These nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher-order input correlations. The particular input correlation decomposed and the form of the decomposition depend on the location of nonlinearities in the plasticity rule. For simple, biologically motivated parameters, the neuron learns eigenvectors of higher-order input correlation tensors. We prove that tensor eigenvectors are attractors and determine their basins of attraction. We calculate the volume of those basins, showing that the dominant eigenvector has the largest basin of attraction. We then study arbitrary learning rules and find that any learning rule that admits a finite Taylor expansion into the neural input and output also has stable equilibria at generalized eigenvectors of higher-order input correlation tensors. Nonlinearities in synaptic plasticity thus allow a neuron to encode higher-order input correlations in a simple fashion.https://proceedings.neurips.cc/paper/2021/hash/5e34a2b4c23f4de585fb09a7f546f527-Abstract.htm

Correlations, fluctuations and stability of a finite-size network of coupled oscillators

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.Comment: 25 pages (2 column), 12 figures, modifications for resubmissio

Reconciling functional differences in populations of neurons recorded with two-photon imaging and electrophysiology

Extracellular electrophysiology and two-photon calcium imaging are widely used methods for measuring physiological activity with single cell resolution across large populations of neurons in the brain. While these two modalities have distinct advantages and disadvantages, neither provides complete, unbiased information about the underlying neural population. Here, we compare evoked responses in visual cortex recorded in awake mice under highly standardized conditions using either imaging or electrophysiology. Across all stimulus conditions tested, we observe a larger fraction of responsive neurons in electrophysiology and higher stimulus selectivity in calcium imaging. This work explores which data transformations are most useful for explaining these modality specific discrepancies. We show that the higher selectivity in imaging can be partially reconciled by applying a spikes-to-calcium forward model to the electrophysiology data. However, the forward model could not reconcile differences in responsiveness without sub selecting neurons based on event rate or level of signal contamination. This suggests that differences in responsiveness more likely reflect neuronal sampling bias or cluster merging artifacts during spike sorting of electrophysiological recordings, rather than flaws in event detection from fluorescence time series. This work establishes the dominant impacts of the two modalities9 respective biases on a set of functional metrics that are fundamental for characterizing sensory-evoked responses.R01 EB026908 - NIBIB NIH HHShttps://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC8285106&blobtype=pdfPublished versio

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong