Mathematical Modeling ePosters

Imagine predicting the precise responses to arbitrary sensory stimuli for a neuron probed deeply within a brain. We developed a robust characterization technique called spike-triggered descent (STD) which optimally recovers n-order kernels for the very general cumulative spike response model (CSRM). This works by…

The critical brain hypothesis proposes that neural networks operate near criticality to reap the computational benefits of accessing a wide range of timescales [1]. Proponents of this viewpoint highlight the presence of heavy-tailed (power-law) spatiotemporal correlations as markers of criticality in the brain [2].…

Cognitive flexibility is characterized by the ability to adapt behavior in response to changing environments. When the environment changes, previously appropriate behavior can lead to negative feedback. Surprising negative feedback – failure to receive a reward when strongly expected – may signal a change in the…

Mounting evidence suggests that traveling waves are a key dynamical motif in biological neural information processing systems [Muller et al., 2018], yet their precise computational role remains under investigation. While the Transformer architecture [Vaswani et al., 2023] has achieved state-of-the-art performance…

A line or a ring attractor stores active memory of an analog quantity that outlasts a transient stimulus. Such continuous attractor states can be realized by a recurrent neural network, when the connection weights are finely tuned. However, a continuum of attractor states is vulnerable to parameter variations,…

Reinstating details of previously seen stimuli given a recall cue is a common cognitive function. Studies suggest that such recollection involves hippocampus-mediated top-down reactivation of neural ensembles active during encoding, yet the neural mechanisms of such generative retrieval remain unknown. We formulate a…

The internal compass of the brain, also known as the head-direction (HD) system, forms a crucial component of the neural circuit necessary for effective spatial orientation, and includes regions such as the anterodorsal thalamic nucleus (ADN). It maintains a sense of orientation by integrating self-motion with local…

Because the world is dynamic and only imperfectly observable, many of the decisions we make are necessarily uncertain. How do we navigate such uncertainty? From the perspective of cognitive neuroscience, the classic answer would be that we evaluate the benefits of each potential choice and then lean towards the one…

Targeted photostimulation optogenetics offers unprecedented precision in perturbing neural circuits in action. However, due to the complexity of neural responses, perturbing neurons chosen randomly or based on their task selectivity often produces weak or counter-intuitive effects. Recurrent neural networks (RNNs)…

A large part of mammalian brains is dedicated to sensory processing. Sensory receptors extract distinct but partly correlated features of the environment that vary at different timescales, and then transmit them through subcortical structures and a succession of recurrently connected cortical areas. A general theory…

Normalization mechanism has often been used to describe neurons' sublinear responses to multiple stimuli in visual cortex. Neurons in the visual cortex exhibit highly heterogeneous degrees of normalization. Past work has proposed several hypotheses of the functions of normalization in both biological and artificial…

Continuous attractors offer a unique class of dynamical systems solutions for storing continuous-valued variables in recurrent neural states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes…

Animals constantly decide how to allocate mental resources to thrive in their environments. Managing learning is a key challenge, and recent experiments show that animals often incur attentional costs for the potential of greater future rewards, or disengage when a task appears unlearnable, exhibiting nuanced…

Odor naming is considered as a particularly challenging task. In free odor naming scenarios people often fail to respond with any linguistic label to certain odors they smell, resulting in what is called an omission (i.e., a lack of response). The cognitive demands and the nature of interactions between olfaction and…

In modern deep neural networks, the intricate learning dynamics of individual neurons often remain obscured due to global optimization methods. This contrasts with biological neural networks, which achieve robustness and efficiency through self-organized, local learning processes using limited global information. To…

Activity-dependent structural plasticity plays a pivotal role in the self-organization of neuronal networks. Emerging activity continuously feeds back into the growth process, regulating connectivity and activity homeostatically towards an optimal functional dynamic range. Transferred into cell culture, neurons follow…

Spiking Neural Networks (SNNs) promise energy efficiency and offer a more brain-like alternative to artificial neural networks. A major challenge to unleashing their potential, however, is to make them trainable on challenging tasks that require credit assignment across long time horizons. Gradient-based learning,…

Neural events are characteristic transient, coordinated neural activities observable in the brain’s aggregate signals, such as local field potentials (LFPs). It was shown that certain neural events, like sharp wave-ripples (SWR) [1], play a crucial role in various cognitive functions, including memory consolidation…

Exploring the origins of animal and human behavior within cortical circuits remains a puzzle awaiting resolution. It is established that when animals and humans compare two stimuli (d1 and d2) separated by a delay interval (Fig. 1a), their perception is influenced by a perceptual bias, characterized by a contraction…

It is appealing to disclose the state of an animal as well as the functional connectivity of its neuronal circuit by calculating pairwise and higher-order interactions (HOI) among neuronal activity. Here, we present a systematic approach to achieve these goals by analysing the spiking activity of simultaneously…

AMPA receptors (AMPARs) mediate fast excitatory neurotransmission and participate in memory formation. Synaptic strength is proportional to the number of AMPARs in the postsynaptic membrane. Previous models of AMPA receptor trafficking can explain their fast, brief incorporation in dendritic spines after LTP induction…

Most mammalian species present topological maps of preference for the ori- entation of edges in their early visual cortex. However, despite the evidence that evolution has favoured topological map organisation in most species, a clear explanation for the functional role of such maps is lacking. Traditional approaches…

Advancements in machine learning have drastically improved our ability to fit biophysical models of neural systems. We present here a fully-differentiable, biophysical model of the mouse retina that is primed for gradient-based optimization. Our model is based on the Jaxley software library (Deistler et al. 2024,…

Interactions between spiking units grouped in distinct excitatory (E) and inhibitory (I) populations can result in a complex dynamical landscape. Part of this complexity, namely dynamics that depend on undelayed connectivities and external inputs, is retained by a simplified model, the threshold-linear network (TLN),…