Variational inference via radial transport

In variational inference (VI), the practitioner approximates a high-dimensional distribution $π$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions might not capture the correct radial profile of $π$, resulting in poor coverage. In this work, we approach the VI problem from the perspective of optimizing over these radial profiles. Our algorithm radVI is a cheap, effective add-on to many existing VI schemes, such as Gaussian (mean-field) VI and Laplace approximation. We provide theoretical convergence guarantees for our algorithm, owing to recent developments in optimization over the Wasserstein space--the space of probability distributions endowed with the Wasserstein distance--and new regularity properties of radial transport maps in the style of Caffarelli (2000).

NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models

Characterizing the diverse computational properties of human neurons via multimodal electrophysiological, transcriptomic, and morphological data provides the foundation for constructing and validating bio-realistic neuron models that can advance our understanding of fundamental mechanisms underlying brain function. However, current modeling approaches remain constrained by the limited availability and intrinsic variability of experimental neuronal data. To capture variability, ensembles of deterministic models are often used, but are difficult to scale as model generation requires repeating computationally expensive optimization for each neuron. While deep learning is becoming increasingly relevant in this space, it fails to capture the full biophysical complexity of neurons, their nonlinear voltage dynamics, and variability. To address these shortcomings, we introduce NOBLE, a neural operator framework that learns a mapping from a continuous frequency-modulated embedding of interpretable neuron features to the somatic voltage response induced by current injection. Trained on data generated from biophysically realistic neuron models, NOBLE predicts distributions of neural dynamics accounting for the intrinsic experimental variability. Unlike conventional bio-realistic neuron models, interpolating within the embedding space offers models whose dynamics are consistent with experimentally observed responses. NOBLE is the first scaled-up deep learning framework validated on real experimental data, enabling efficient generation of synthetic neurons that exhibit trial-to-trial variability and achieve a $4200\times$ speedup over numerical solvers. To this end, NOBLE captures fundamental neural properties, opening the door to a better understanding of cellular composition and computations, neuromorphic architectures, large-scale brain circuits, and general neuroAI applications.