Physiological experiments have highlighted how the dendrites of biological neurons can nonlinearly process distributed synaptic inputs. However, it is unclear how qualitative aspects of a dendritic tree, such as its branched morphology, its repetition of presynaptic inputs, voltage-gated ion channels, electrical properties and complex synapses, determine neural computation beyond this apparent nonlinearity. While it has been speculated that the dendritic tree of a neuron can be seen as a multi-layer neural network and it has been shown that such an architecture could be computationally strong, we do not know if that computational strength is preserved under these qualitative biological constraints. Here we simulate multi-layer neural network models of dendritic computation with and without these constraints. We find that dendritic model performance on interesting machine learning tasks is not hurt by most of these constraints and may synergistically benefit from all of them combined. Our results suggest that single real dendritic trees may be able to learn a surprisingly broad range of tasks through the emergent capabilities afforded by their properties.

The spike-threshold nonlinearity is a fundamental, yet enigmatic, component of biological computation — despite its role in many theories, it has evaded definitive characterisation. Indeed, much classic work has attempted to limit the focus on spiking by smoothing over the spike threshold or by approximating spiking dynamics with firing-rate dynamics. Here, we take a novel perspective that captures the full potential of spike-based computation. Based on previous studies of the geometry of efficient spike-coding networks, we consider a population of neurons with low-rank connectivity, allowing us to cast each neuron’s threshold as a boundary in a space of population modes, or latent variables. Each neuron divides this latent space into subthreshold and suprathreshold areas. We then demonstrate how a network of inhibitory (I) neurons forms a convex, attracting boundary in the latent coding space, and a network of excitatory (E) neurons forms a concave, repellant boundary. Finally, we show how the combination of the two yields stable dynamics at the crossing of the E and I boundaries, and can be mapped onto a constrained optimization problem. The resultant EI networks are balanced, inhibition-stabilized, and exhibit asynchronous irregular activity, thereby closely resembling cortical networks of the brain. Moreover, we demonstrate how such networks can be tuned to either suppress or amplify noise, and how the composition of inhibitory convex and excitatory concave boundaries can result in universal function approximation. Our work puts forth a new theory of biologically-plausible computation in balanced spiking networks, and could serve as a novel framework for scalable and interpretable computation with spikes.

Vision begins in the eye, and what the “retina tells the brain” is a major interest in visual neuroscience. To deduce what the retina encodes (“tells”), computational models are essential. The most important models in the retina currently aim to understand the responses of the retinal output neurons – the ganglion cells. Typically, these models make simplifying assumptions about the neurons in the retinal network upstream of ganglion cells. One important assumption is linear spatial integration. In this talk, I first define what it means for a neuron to be spatially linear or nonlinear and how we can experimentally measure these phenomena. Next, I introduce the neurons upstream to retinal ganglion cells, with focus on bipolar cells, which are the connecting elements between the photoreceptors (input to the retinal network) and the ganglion cells (output). This pivotal position makes bipolar cells an interesting target to study the assumption of linear spatial integration, yet due to their location buried in the middle of the retina it is challenging to measure their neural activity. Here, I present bipolar cell data where I ask whether the spatial linearity holds under artificial and natural visual stimuli. Through diverse analyses and computational models, I show that bipolar cells are more complex than previously thought and that they can already act as nonlinear processing elements at the level of their somatic membrane potential. Furthermore, through pharmacology and current measurements, I illustrate that the observed spatial nonlinearity arises at the excitatory inputs to bipolar cells. In the final part of my talk, I address the functional relevance of the nonlinearities in bipolar cells through combined recordings of bipolar and ganglion cells and I show that the nonlinearities in bipolar cells provide high spatial sensitivity to downstream ganglion cells. Overall, I demonstrate that simple linear assumptions do not always apply and more complex models are needed to describe what the retina “tells” the brain.

Neuronal dendritic trees display a wide range of nonlinear input integrations due to their voltage-dependent active calcium channels. We reveal that in vivo-like fluctuating input enhances nonlinearity substantially in a single dendritic compartment and shifts the input-output relation to exhibiting nonmonotonous or bistable dynamics. In particular, with the slow activation of calcium dynamics, we analyze noise-induced bistability and its timescales. We show bistability induces long-timescale fluctuation that can account for observed dendritic plateau potentials in vivo conditions. In a multicompartmental model neuron with realistic synaptic input, we show that noise-induced bistability persists in a wide range of parameters. Using Fredholm's theory to calculate the spiking rate of multivariable neurons, we discuss how dendritic bistability shifts the spiking dynamics of single neurons and its implications for network phenomena in the processing of in vivo–like fluctuating input.