Synaptic Plasticity in Correlated Balanced Networks

Akil, Alan Eric; Rosenbaum, R. A.; Josić, Krešimir

doi:10.48550/arxiv.2004.12453

Cited by 2 publications

(2 citation statements)

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“…We now investigate a simulation study which is based upon neuroscience applications. Here, we simulate data from the balanced network model of (Akil, Rosenbaum, and Josić, 2020), which utilizes a neuronal spiking model in order to create data which emulates the physical processes which comprise functional neuronal connectivity. In particular, the balanced network generates correlated spiking patterns between variables over time, mimicking the behavior of neurons as observed during calcium imaging experiments.…”

Section: Artificial Neuronal Networkmentioning

confidence: 99%

Extreme Graphical Models with Applications to Functional Neuronal Connectivity

Chang¹,

Allen²

2021

Preprint

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With modern calcium imaging technology, the activities of thousands of neurons can be recorded simultaneously in vivo. These experiments can potentially provide new insights into functional connectivity, defined as the statistical relationships between the spiking activity of neurons in the brain. As a commonly used tool for estimating conditional dependencies in high-dimensional settings, graphical models are a natural choice for analyzing calcium imaging data. However, raw neuronal activity recording data presents a unique challenge: the important information lies in the rare extreme value observations that indicate neuronal firing, as opposed to the non-extreme observations associated with inactivity. To address this issue, we develop a novel class of graphical models, called the extreme graphical model, which focuses on finding relationships between features with respect to the extreme values. Our model assumes the conditional distributions a subclass of the generalized normal or Subbotin distribution, and yields a form of a curved exponential family graphical model. We first derive the form of the joint multivariate distribution of the extreme graphical model and show the conditions under which it is normalizable. We then demonstrate the model selection consistency of our estimation method. Lastly, we study the empirical performance of the extreme graphical model through several simulation studies as well as through a real data example, in which we apply our method to a real-world calcium imaging data set.

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Section: Artificial Neuronal Networkmentioning

confidence: 99%

Extreme Graphical Models with Applications to Functional Neuronal Connectivity

Chang¹,

Allen²

2021

Preprint

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“…An important line of mathematical analysis focusses on understanding how the learning algorithms impact the long-term weight evolution; see for example (Kempter et al 1999;Markram et al 2012;Oja 1982). A common approach to this is to assume that learning is deterministic (Gerstner and Kistler 2002;Akil et al 2020Akil et al , 2021. This means that the evolution of weights is not materially impacted by random fluctuations in the input data, which simplifies the mathematics.…”

Section: Introductionmentioning

confidence: 99%

Information theoretical properties of a spiking neuron trained with Hebbian and STDP learning rules

Chu

2023

Nat Comput

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Using formal methods complemented by large-scale simulations we investigate information theoretical properties of spiking neurons trained using Hebbian and STDP learning rules. It is shown that weight space contains meta-stable states, which are points where the average weight change under the learning rule vanishes. These points may capture the random walker transiently. The dwell time in the vicinity of the meta-stable state is either quasi-infinite or very short and depends on the level of noise in the system. Moreover, important information theoretic quantities, such as the amount of information the neuron transmits are determined by the meta-stable state. While the Hebbian learning rule reliably leads to meta-stable states, the STDP rule tends to be unstable in the sense that for most choices of hyper-parameters the weights are not captured by meta-stable states, except for a restricted set of choices. It emerges that stochastic fluctuations play an important role in determining which meta-stable state the neuron takes. To understand this, we model the trajectory of the neuron through weight space as an inhomogeneous Markovian random walk, where the transition probabilities between states are determined by the statistics of the input signal.

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Synaptic Plasticity in Correlated Balanced Networks

Cited by 2 publications

References 0 publications

Extreme Graphical Models with Applications to Functional Neuronal Connectivity

Extreme Graphical Models with Applications to Functional Neuronal Connectivity

Information theoretical properties of a spiking neuron trained with Hebbian and STDP learning rules

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