This webinar on learning and memory features three experts—Nicolas Brunel, Ashok Litwin-Kumar, and Julijana Gjorgieva—who present theoretical and computational approaches to understanding how neural circuits acquire and store information across different scales. Brunel discusses calcium-based plasticity and how standard “Hebbian-like” plasticity rules inferred from in vitro or in vivo datasets constrain synaptic dynamics, aligning with classical observations (e.g., STDP) and explaining how synaptic connectivity shapes memory. Litwin-Kumar explores insights from the fruit fly connectome, emphasizing how the mushroom body—a key site for associative learning—implements a high-dimensional, random representation of sensory features. Convergent dopaminergic inputs gate plasticity, reflecting a high-dimensional “critic” that refines behavior. Feedback loops within the mushroom body further reveal sophisticated interactions between learning signals and action selection. Gjorgieva examines how activity-dependent plasticity rules shape circuitry from the subcellular (e.g., synaptic clustering on dendrites) to the cortical network level. She demonstrates how spontaneous activity during development, Hebbian competition, and inhibitory-excitatory balance collectively establish connectivity motifs responsible for key computations such as response normalization.

Learning in neural networks requires assigning the right values to thousands to trillions or more of individual connections, so that the network as a whole produces the desired behavior. Neuroscientists have gained insights into this “credit assignment” problem through decades of experimental, modeling, and theoretical studies. This has suggested key roles for synaptic eligibility traces and top-down feedback signals, among other factors. Here we study the potential contribution of another type of signaling that is being revealed in greater and greater fidelity by ongoing molecular and genomics studies. This is the set of modulatory pathways local to a given circuit, which form an intriguing second type of connectome overlayed on top of synaptic connectivity. We will share ongoing modeling and theoretical work that explores the possible roles of this local modulatory connectome in network learning.

Precise synaptic connectivity is a prerequisite for the function of neural circuits, yet individual neurons, taken out of their developmental context, readily form unspecific synapses. How does genetically encoded brain wiring deal with this apparent contradiction? Brain wiring is a developmental growth process that is not only characterized by precision, but also flexibility and robustness. As in any other growth process, cellular interactions are restricted in space and time. Correspondingly, molecular and cellular interactions are restricted to those that 'get to see' each other during development. This seminar will explore the question how neurons decide when and where to make synapses using the Drosophila visual system as a model. New findings reveal that pattern formation during growth and the kinetics of live neuronal interactions restrict synapse formation and partner choice for neurons that are not otherwise prevented from making incorrect synapses in this system. For example, cell biological mechanisms like autophagy as well as developmental temperature restrict inappropriate partner choice through a process of kinetic exclusion that critically contributes to wiring specificity. The seminar will explore these and other neuronal strategies when and where to make synapses during developmental growth that contribute to precise, flexible and robust outcomes in brain wiring.

Microglia are the immune cells of the brain, and play increasingly appreciated roles in synapse formation, brain plasticity, and cognition. A growing appreciation that the immune system involved in diseases like schizophrenia, epilepsy, and neurodegenerative diseases has led to renewed interest in how microglia regulate synaptic connectivity. Our group previously identified the IL-1 family cytokine Interleukin-33 (IL-33) as a novel regulator of microglial activation and function. I will discuss a mechanism by which microglia regulate synaptic plasticity and long-term memories by engulfing brain extracellular matrix (ECM) proteins. These studies raise the question of how these pathways may be altered or could be modified in the context of disease.

We study the dynamics of (inhibitory) balanced networks at varying (i) the level of symmetry in the synaptic connectivity; and (ii) the ariance of the synaptic efficacies (synaptic gain). We find three regimes of activity. For suitably low synaptic gain, regardless of the level of symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits chaotic activity for zero or negative levels of symmetry (i.e., random or antisymmetric). Instead, for positive levels of symmetry, there is multi-stability among a large number of marginally stable fixed points. In this regime, ergodicity is broken and the network exhibits non-exponential relaxational dynamics. We discuss the potential relevance of such a “glassy” phase to explain some features of cortical activity.

The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function. However, quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of rectified-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. We then use this analytical characterization to rigorously analyze the solution space geometry and derive certainty conditions guaranteeing a non-zero synapse between neurons.