Uygar Sümbül

Yeganeh Marghi, Kelly Jin, Uygar Sümbül

Optimal transport (OT) provides a principled framework for mapping between probability distributions. Despite extensive progress, applying OT to large-scale data remains computationally demanding, and the resulting pointwise transport plans are often difficult to interpret. We introduce Optimal Mixture Transport (OMT), a scalable framework that shifts the transport paradigm from individual samples to mixtures of subpopulations, reformulating the transport problem as a strictly biconvex optimization with a unique global minimizer. We further establish theoretical guarantees on the stability of the OMT map, showing that bounded perturbations of the underlying distributions lead to bounded changes in the transport plan. By formulating subpopulations as exponential-family distributions, OMT decouples computational complexity from the sample size, scaling solely with the number of mixture components. We demonstrate the effectiveness and practicality of OMT on a wide range of synthetic benchmarks and real-world datasets, including image data and large-scale single-cell RNA sequencing measurements.

Lu Mi, Trung Le, Tianxing He et al.

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal activity is a combination of its time-invariant identity and the inputs the neuron receives from the rest of the circuit. Here, we propose a self-supervised learning based method to assign time-invariant representations to individual neurons based on permutation-, and population size-invariant summary of population recordings. We fit dynamical models to neuronal activity to learn a representation by considering the activity of both the individual and the neighboring population. Our self-supervised approach and use of implicit representations enable robust inference against imperfections such as partial overlap of neurons across sessions, trial-to-trial variability, and limited availability of molecular (transcriptomic) labels for downstream supervised tasks. We demonstrate our method on a public multimodal dataset of mouse cortical neuronal activity and transcriptomic labels. We report > 35% improvement in predicting the transcriptomic subclass identity and > 20% improvement in predicting class identity with respect to the state-of-the-art.

Yiliu Wang, Timothy Doyeon Kim, Eric Shea-Brown et al.

Switching dynamical systems can model complicated time series data while maintaining interpretability by inferring a finite set of dynamics primitives and explaining different portions of the observed time series with one of these primitives. However, due to the discrete nature of this set, such models struggle to capture smooth, variable-speed transitions, as well as stochastic mixtures of overlapping states, and the inferred dynamics often display spurious rapid switching on real-world datasets. Here, we propose the Gumbel Dynamical Model (GDM). First, by introducing a continuous relaxation of discrete states and a different noise model defined on the relaxed-discrete state space via the Gumbel distribution, GDM expands the set of available state dynamics, allowing the model to approximate smoother and non-stationary ground-truth dynamics more faithfully. Second, the relaxation makes the model fully differentiable, enabling fast and scalable training with standard gradient descent methods. We validate our approach on standard simulation datasets and highlight its ability to model soft, sticky states and transitions in a stochastic setting. Furthermore, we apply our model to two real-world datasets, demonstrating its ability to infer interpretable states in stochastic time series with multiple dynamics, a setting where traditional methods often fail.

Trung Le, Hao Fang, Jingyuan Li et al.

Intracortical Brain-Computer Interfaces (iBCI) aim to decode behavior from neural population activity, enabling individuals with motor impairments to regain motor functions and communication abilities. A key challenge in long-term iBCI is the nonstationarity of neural recordings, where the composition and tuning profiles of the recorded populations are unstable across recording sessions. Existing methods attempt to address this issue by explicit alignment techniques; however, they rely on fixed neural identities and require test-time labels or parameter updates, limiting their generalization across sessions and imposing additional computational burden during deployment. In this work, we introduce SPINT - a Spatial Permutation-Invariant Neural Transformer framework for behavioral decoding that operates directly on unordered sets of neural units. Central to our approach is a novel context-dependent positional embedding scheme that dynamically infers unit-specific identities, enabling flexible generalization across recording sessions. SPINT supports inference on variable-size populations and allows few-shot, gradient-free adaptation using a small amount of unlabeled data from the test session. To further promote model robustness to population variability, we introduce dynamic channel dropout, a regularization method for iBCI that simulates shifts in population composition during training. We evaluate SPINT on three multi-session datasets from the FALCON Benchmark, covering continuous motor decoding tasks in human and non-human primates. SPINT demonstrates robust cross-session generalization, outperforming existing zero-shot and few-shot unsupervised baselines while eliminating the need for test-time alignment and fine-tuning. Our work contributes an initial step toward a robust and scalable neural decoding framework for long-term iBCI applications.

Yeganeh M. Marghi, Rohan Gala, Uygar Sümbül

Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture representations. However, posterior approximation in high-dimensional latent spaces, particularly for discrete factors remains challenging. Here, we propose an unsupervised variational framework using multiple interacting networks called cpl-mixVAE that scales well to high-dimensional discrete settings. In this framework, the mixture representation of each network is regularized by imposing a consensus constraint on the discrete factor. We justify the use of this framework by providing both theoretical and experimental results. Finally, we use the proposed method to jointly uncover discrete and continuous factors of variability describing gene expression in a single-cell transcriptomic dataset profiling more than a hundred cortical neuron types.

Rohan Gala, Nathan Gouwens, Zizhen Yao et al.

Recent developments in high throughput profiling of individual neurons have spurred data driven exploration of the idea that there exist natural groupings of neurons referred to as cell types. The promise of this idea is that the immense complexity of brain circuits can be reduced, and effectively studied by means of interactions between cell types. While clustering of neuron populations based on a particular data modality can be used to define cell types, such definitions are often inconsistent across different characterization modalities. We pose this issue of cross-modal alignment as an optimization problem and develop an approach based on coupled training of autoencoders as a framework for such analyses. We apply this framework to a Patch-seq dataset consisting of transcriptomic and electrophysiological profiles for the same set of neurons to study consistency of representations across modalities, and evaluate cross-modal data prediction ability. We explore the problem where only a subset of neurons is characterized with more than one modality, and demonstrate that representations learned by coupled autoencoders can be used to identify types sampled only by a single modality.

James Gornet, Kannan Umadevi Venkataraju, Arun Narasimhan et al.

Reconstructing multiple molecularly defined neurons from individual brains and across multiple brain regions can reveal organizational principles of the nervous system. However, high resolution imaging of the whole brain is a technically challenging and slow process. Recently, oblique light sheet microscopy has emerged as a rapid imaging method that can provide whole brain fluorescence microscopy at a voxel size of 0.4 by 0.4 by 2.5 cubic microns. On the other hand, complex image artifacts due to whole-brain coverage produce apparent discontinuities in neuronal arbors. Here, we present connectivity-preserving methods and data augmentation strategies for supervised learning of neuroanatomy from light microscopy using neural networks. We quantify the merit of our approach by implementing an end-to-end automated tracing pipeline. Lastly, we demonstrate a scalable, distributed implementation that can reconstruct the large datasets that sub-micron whole-brain images produce.