Publications

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that allows some neurons to remain unmatched, yielding rotation-sensitive but robust correspondences. This partial soft-matching distance provides theoretical advantages -- relaxing strict mass conservation while maintaining interpretable transport costs -- and practical benefits through efficient neuron ranking in terms of cross-network alignment without costly iterative recomputation. In simulations, it preserves correct matches under outliers and reliably selects the correct model in noise-corrupted identification tasks. On fMRI data, it automatically excludes low-reliability voxels and produces voxel rankings by alignment quality that closely match computationally expensive brute-force approaches. It achieves higher alignment precision across homologous brain areas than standard soft-matching, which is forced to match all units regardless of quality. In deep networks, highly matched units exhibit similar maximally exciting images, while unmatched units show divergent patterns. This ability to partition by match quality enables focused analyses, e.g., testing whether networks have privileged axes even within their most aligned subpopulations. Overall, partial soft-matching provides a principled and practical method for representational comparison under partial correspondence.

We present a new computational tool for the simulation of aligned assemblies of thin, bendable, but inextensible fibers immersed in a linear Stokes fluid. Such systems are of great importance in cellular mechanics because they arise in many intracellular (e.g., cytoskeleton-cytoplasm interactions) and extracellular (e.g., ciliary locomotion) microscale biological processes. The fiber bed is represented as an anisotropic poroelastic medium that obeys the Euler-Bernoulli beam theory and is hydrodynamically coupled to the viscous fluid through local-slender body theory. We develop two methodologies to solve the resulting fluid-structure interaction problem: (1) a classical approach where the solid is solved in the Lagrangian frame, and the fluid is solved using an Arbitrary-Lagrangian-Eulerian (ALE) method, and (2) a novel approach where the solid equations are expressed in the Eulerian frame and the fiber-fluid system is solved together using an ALE method. In both cases, the resulting set of equations is approximated using a Petrov-Galerkin stabilized finite element method specifically designed for the fiber-fluid interaction problem. Equal-order continuous finite elements are used for the spatial discretization of the deforming physical domain, and finite differences are used for temporal discretization. Both approaches are shown to be numerically stable and convergent at the expected order; and additionally, the pure ALE method can resolve extreme fiber deformations without the need for mesh reconstruction. Finally, our methods are validated by direct comparisons to discrete fiber simulations in two benchmark tests: (a) the shearing of an anchored fiber bed and (b) the emergence and evolution of cell-spanning vortices in cellular geometries.

Solid-phase peptide synthesis enables the study of countless peptides, but aggregation during synthesis hinders production of many sequences of interest. Now, machine learning models enable prior identification of aggregation-prone sequences, and highlight amino acid composition, rather than specific sequence, as the major determinant of aggregation.

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these approximate posteriors so that they appropriately capture uncertainty. vWe introduce two methods that extend simulation-based calibration checking (SBC) to widen approximate posterior uncertainty intervals to aim for marginal calibration. We demonstrate these methods in several experimental settings, and we discuss the challenge of calibration using posterior inferences and the potential for posterior recalibration of hierarchical models.

We introduce a biologically inspired, multilayer neural architecture composed of Rectified Spectral Units (ReSUs). Each ReSU projects a recent window of its input history onto a canonical direction obtained via canonical correlation analysis (CCA) of previously observed past-future input pairs, and then rectifies either its positive or negative component. By encoding canonical directions in synaptic weights and temporal filters, ReSUs implement a local, self-supervised algorithm for progressively constructing increasingly complex features.
To evaluate both computational power and biological fidelity, we trained a two-layer ReSU network in a self-supervised regime on translating natural scenes. First-layer units, each driven by a single pixel, developed temporal filters resembling those of Drosophila post-photoreceptor neurons (L1/L2 and L3), including their empirically observed adaptation to signal-to-noise ratio (SNR). Second-layer units, which pooled spatially over the first layer, became direction-selective -- analogous to T4 motion-detecting cells -- with learned synaptic weight patterns approximating those derived from connectomic reconstructions.
Together, these results suggest that ReSUs offer (i) a principled framework for modeling sensory circuits and (ii) a biologically grounded, backpropagation-free paradigm for constructing deep self-supervised neural networks.

Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to task performance. We develop a statistical-mechanical theory of regression capacity that relates linear decoding efficiency of continuous variables to geometric properties of neural manifolds. Our theory handles complex neural variability and applies to real data, revealing increasing capacity for decoding object position and size along the monkey visual stream.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

While cryo-electron microscopy (cryo-EM) has come to prominence in the last decade due to its ability to resolve biomolecular complexes at atomic resolution, advancements in experimental and computational methods have made cryo-EM promising for investigating intracellular organization and heterogeneous molecular states. A primary challenge for these alternative applications is the development of techniques for cryo-EM data analysis, which are very computationally demanding. To this end, it is advantageous to leverage advanced scientific computing frameworks for statistical analysis. One such framework is JAX, an emerging array-oriented Python numerical computing package for automatic differentiation and vectorization with a growing ecosystem for statistical inference and machine learning. We have developed cryoJAX, a cryo-EM image-simulation library for building computational data-analysis applications in JAX. CryoJAX is a flexible modeling language for cryo-EM image formation and therefore can support a wide range of data analysis downstream. By integrating with the JAX ecosystem, cryoJAX enables the development and deployment of algorithms for the growing breadth of scientific applications for cryo-EM.

This article, gathered and elaborated from a lecture by Eero Simoncelli at the 2024 Analytical Connectionism Summer School, reviews several approaches for modeling the probabilistic distribution of natural images and their interaction with the problem of image denoising. The lecture starts with the Gaussian spectral model of the 1950s as a conceptual foundation and quantitative baseline, followed by sparse coding models which took hold in the 1990s. These statistical models of natural images can be used as prior probability distributions for solving inverse problems such as denoising, using a Bayesian framework. Finally, the lecture describes recent work in machine learning in which the process of constructing a denoiser is reversed: a neural network is trained to solve the denoising problem without first specifying a prior distribution, and this trained network is subsequently used as an implicit model of the distribution of natural images. Images can be drawn from this implicit model through a reverse diffusion process, and the model can also be used to solve inference problems. This allows researchers to investigate the extent to which these DNNs are generalizing beyond their training data (as necessary for accurately modeling the distribution of natural images) as opposed to memorizing the images they were trained on.

We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green’s function for the scalar wave equation). With M points in the spatial discretization and Nt time steps of size Δt, a naive implementation would require O(M2Nt2) work in dimensions where the weak Huygens’ principle applies. We avoid this all-to-all interaction using a smoothly windowed decomposition into a local part, treated directly, plus a history part, approximated by a NF-term Fourier series. In one dimension, our method requires O((M+NFlogNF)Nt) work, with NF=O(1/Δt), by exploiting the non-uniform fast Fourier transform. We demonstrate the method’s performance for time-domain scattering problems involving a large number M of springs (point scatterers) attached to a vibrating string at arbitrary locations, with either periodic or free-space boundary conditions. We typically achieve 10-digit accuracy, and include tests for M up to a million.