Probability Theory ePosters

The synaptic connection strengths in the brain largely follow a heavy-tailed distribution, whereas most theoretical frameworks assume a Gaussian distribution due to the mathematical complexity involved. Understanding how these heavy-tailed distributions influence neural dynamics is crucial for developing more…

Recent evidence suggests the brain performs sampling-based Bayesian inference to solve various cognitive tasks [1–6]. Neural sampling requires neural circuits to exhibit statistically stable variability to draw posterior samples. While ad-hoc frameworks simply inject randomness into spike emission, it remains unknown…

To date, most studies of neural representation have focused on how a single stimulus is encoded in the spiking activity of neurons. Consequently, little is known about how sensory neurons can preserve information from multiple stimuli – a problem given that many sensory neurons have relatively broad receptive fields.…

Mean-field models of neuronal populations in the brain have proven extremely useful to understand network dynamics and response to stimuli, but these models generally lack a faithful description of the fluctuations in the biologically relevant case of finite network size and connection probabilities $p<1$ (non-full…

Uncertainty is a fundamental aspect of the natural environment. Computing with uncertain information is important not only for encoding and decoding stimuli in early sensory areas, but also for more complex downstream inference and integration. The head-direction (HD) system is a prominent example of this, where…

From the periodic spiking of single neurons to brain rhythms, oscillations are a ubiquitous neural phenomenon. Phase reduction is a powerful way of analysing deterministic systems exhibiting such oscillatory behavior: the N-dimensional state of the system is encoded into a one dimensional phase variable via projection…

Biological neural network models with synaptic plasticity pose challenges for both theoretical and numerical analyses. The numerical bottleneck arises from the $N^2$ scaling of synapses. Additionally, the intricate coupling between neuron and synapse dynamics, along with plasticity-induced heterogeneity, hinders the…

Animals possess complex innate computational capabilities essential for their survival, such as recognizing poisonous food or walking right after birth. However, specifying the precise wiring diagram for neuronal circuits to achieve these behaviors is too complex to be compressed through the "genomic bottleneck" [3].…

Continual learning involves a network adapting to new data while retaining previously learned information. In Artificial Neural Networks , this process faces the challenge of catastrophic forgetting, where updating parameters with new data causes an exponential decline in accuracy over time for previously learned…

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a…

We consider two spiking neurons, with one neuron driving the other. From a statistical point of view, the relationship between the two neurons can be quantified by (i) the cross-correlation $C(t,t^{\prime})$ of the two spike trains, a measure of similarity of spontaneous fluctuations, and (ii) the linear response…

In order to analyse complex networks in the cerebral cortex, different approaches are used in computational neuroscience: microscopic network models that consider every single neuron in simulations aiming for a realistic biological description as well as heuristic firing rate or neural-mass models which deliver a…

Pyramidal neurons in mammalian cortical layer 5 (L5) send long-range projections to other cortical areas and subcortical structures. Understanding the outputs of the cortex thus requires understanding the activity of these neurons. Thick-tufted L5 pyramidal neurons generate two types of action potentials: 1) the…

Unsupervised segmentation of behavior and neural activity into simpler alternating states is providing unprecedented insights onto the neural underpinnings of decision-making. Recurrent Switching Linear Dynamical Systems (rSLDS) models use observations or continuous latent activity to guide the switching in states,…

Decision making is essential to cognition, often requiring the integration of sequences of observations over time. Choice rules trigger decisions once sufficient evidence is acquired for a choice. Models often describe single accumulation-to-bound processes, but organisms often decide in groups or accumulate multiple…

A common approach to model local neural circuits is to assume random connectivity. But how is our choice of randomness informed by known network properties? And how does it affect the network's behavior? Previous approaches have focused on prescribing increasingly sophisticated statistics of synaptic strengths and…

We study randomly connected neural networks to understand the effects of network architectures on network dynamics. Specifically, we examine the impact of sparse connectivity combined with Dale’s law on network stability by analysing the eigenspectrum of the networked Jacobian. Previous work has examined the effects…

The spiking activity of neurons is highly variable and is often described as a Poisson process. This variability comes from random fluctuations within the membrane potential (V) that leads to random spike times. Prior analysis has shown that the variability of V, in response to stimuli, became quenched, where the…

The idea of estimating synaptic connectivity and strength from parallel spike trains has been entertained since the late 1960s, but the last few years have seen a resurgence in proposed methods. A majority of model-free techniques estimate synaptic coupling via a “separation of timescales” (SOT) principle applied to…

The $k$-cap (or $k$-winners-take-all) process is a simple model of firing activity and inhibition in the brain. The process models the formation of neural assemblies, a longstanding proposal for the representation of abstract concepts in the brain. It is applied to a directed graph as follows: in each iteration, a…

For animals to navigate an uncertain world, their brains need to estimate uncertainty at the timescales of sensations and actions. Sampling-based algorithms afford a theoretically-grounded framework for probabilistic inference in neural circuits, but it remains unknown how one can implement fast sampling algorithms in…

Quantification of information content and its temporal variation in intracellular calcium spike trains in neurons helps one understand functions such as memory, learning, and cognition. Such quantification could also reveal pathological signaling perturbation that potentially leads to devastating neurodegenerative…

In a standard model, associative memories are represented by assemblies of strongly interconnected neurons. It has recently been proposed that these assemblies are not static but drift freely in neural circuits. This explains experimental findings of changing memory representations. On the level of single neurons,…

Neural circuits encode and transmit information to support a diversity of tasks. Such neural coding is corrupted by noise and uncertainty, which in turn results in different magnitudes of error in the signals that are received by downstream regions. Therefore, even in the same task and given a fixed distribution of…