Publications

Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial differential equation itself, one first evaluates a volume integral to account for the source distribution within the domain, followed by solving a boundary integral equation to impose the specified boundary conditions. Here, we present a new fast algorithm which is easy to implement and compatible with virtually any discretization technique, including unstructured domain triangulations, such as those used in standard finite element or finite volume methods. Our approach combines earlier work on potential theory for the heat equation, asymptotic analysis, the nonuniform fast Fourier transform (NUFFT), and the dual-space multilevel kernel-splitting (DMK) framework. It is insensitive to flaws in the triangulation, permitting not just nonconforming elements, but arbitrary aspect ratio triangles, gaps and various other degeneracies. On a single CPU core, the scheme computes the solution at a rate comparable to that of the fast Fourier transform (FFT) in work per gridpoint.

Spatial orientation enables animals to navigate their environment by rapidly mapping the external world and remembering key locations. In mammals, the head-direction (HD) system is an essential component of the navigation system of the brain. Although the tuning of neurons in other areas of this system is unstable—evidenced, for example, by the change in the spatial tuning of hippocampal place cells across days—the
stability of the neuronal code that underlies the sense of direction remains unclear. Here, by longitudinally tracking the activity of the same HD cells in the post-subiculum of freely moving mice, we show stability and plasticity at two levels. Although the population structure remained highly conserved across environments and over time, subtle shifts in population coherence encoded environment identity. In addition, the HD system established a distinct, environment-specific alignment between its internal representation and external landmarks, which persisted for weeks, even
after a single exposure. These findings suggest that the HD system forms long-lasting orientation memories that are anchored to specific environments.

Animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. Several works argue that the brain supports these abilities by forming neural representations from which behaviorally relevant variables can be read out across contexts and tasks. However, it is unclear which features of neural activity facilitate downstream readout. Here we analytically determine the geometric properties of neural activity that govern linear readout generalization on a set of tasks sharing a common latent structure. We show that four statistics summarizing the dimensionality, factorization and correlation structures of neural activity determine generalization. Early in learning, optimal neural representations are lower dimensional and exhibit higher correlations between single units and task variables than late in learning. We support these predictions through biological and artificial neural data analysis. Our results tie the linearly decodable information in neural population activity to its geometry.

Protein denaturation-based assays, such as thermal proximity coaggregation (TPCA) and ion-based proteome-integrated solubility alteration (I-PISA), are powerful tools for characterizing global protein–protein interaction (PPI) networks. These workflows utilize different denaturation methods to probe PPIs, i.e., thermal- or ion-based. How denaturation differences influence PPI network mapping remained to be better understood. Here, we provide an experimental and computational characterization of the effect of the denaturation-based PPI assay on the observed PPI networks. We establish the value of both soluble and insoluble fractions in PPI prediction, determine the ability to minimize sample amount requirement, and assess different relative quantification methods during virus infection. Generating paired TPCA and I-PISA datasets, we define both overlapping sets of proteins and distinct PPI networks specifically captured by these methods. Assessing protein physical properties and subcellar localizations, we show that size, structural complexity, hydrophobicity, and localization influence PPI detection in a workflow-specific manner. We show that the insoluble fractions expand the detectable PPI landscape, underscoring their value in these workflows. Focusing on selected PPI networks (cytoskeletal and DNA repair), we observe the detection of distinct functional populations. Using influenza A infection as a model for cellular perturbation, we demonstrate that the integration of PPI predictions from soluble and insoluble workflows enhances the ability to build biologically informative and interconnected networks. Examining the effects of reducing starting material for TPCA assays, we find that PPI prediction quality remains robust when using a single well of a 96-well plate, a ∼500× reduction in sample input from usual workflows. Introducing simple workflow modifications, we show that label-free data-independent acquisition (DIA) TPCA yields performance comparable to the traditional tandem mass tag (TMT) data-dependent acquisition (DDA) TPCA workflow. This work provides insights into denaturation-based assays, highlights the value of insoluble fractions, and offers practical improvements for enhancing global PPI network mapping.

This paper introduces quasi-Monte Carlo latent variable models (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard approaches, which rely on a learned encoder and variational lower bounds, QLVMs directly approximate the marginal likelihood by randomized quasi-Monte Carlo integration. While this brute force approach has drawbacks in higher-dimensional spaces, we find that it excels in fitting one, two, and three dimensional deep latent variable models. Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) and importance weighted autoencoders (IWAEs) with matched latent dimensionality. The resulting embeddings enable transparent visualization and post hoc analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial to validate in higher-dimensional spaces. While our approach is compute-intensive and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

The growing scale of deep learning models has rendered exhaustive hyperparameter (HP) optimization prohibitively expensive. A promising solution is the use of scale-aware HPs, which can enable direct transfer of optimal settings from small-scale grid searches to large models with minimal performance loss. Such approaches are useful when the optimal settings converge "fast" enough with scale. While approaches like the Maximal Update Parameterization (μP) have empirically displayed fast transfer when scaling model width, a deeper conceptual understanding of the mechanisms that enable this is still missing. Our work establishes a systematic conceptual framework for analyzing fast HP transfer across different synthetic and practical scenarios. In synthetic settings, we present various quantitative examples where transfer either offers a provable computational advantage or fails even under (μP). We then propose a key property that enables the fast transfer often observed in practice: through a novel decomposition of the optimization trajectory, we identify one component that rapidly converges with model width and determines the optimal HPs, and the other that continues to improve the loss with increased width but has negligible impact on HP choice. We conjecture that this decomposition elucidates the key mechanisms behind fast transfer and empirically validate it in practical settings such as LLM training.

Machine learning interatomic potentials (MLIPs) have become powerful tools to extend molecular simulations beyond the limits of quantum methods, offering near-quantum accuracy at much lower computational cost. Yet, developing reliable MLIPs remains difficult because it requires generating high-quality datasets, preprocessing atomic structures, and carefully training and validating models. In this work, we introduce an Automated Machine Learning Pipeline (AMLP) that unifies the entire workflow from dataset creation to model validation. AMLP employs large-language-model agents to assist with electronic-structure code selection, input preparation, and output conversion, while its analysis suite (AMLP-Analysis), based on ASE supports a range of molecular simulations. The pipeline is built on the MACE architecture and validated on acridine polymorphs, where, with a straightforward fine-tuning of a foundation model, mean absolute errors of 1.7 meV/atom in energies and 7.0 meV/Å in forces are achieved. The fitted MLIP reproduces DFT geometries with sub-Å accuracy and demonstrates stability during molecular dynamics simulations in the microcanonical and canonical ensembles.

We introduce a size-consistent and orbital-invariant formalism for constructing correlation functionals based on the adiabatic connection for density functional theory (DFT). By constructing correlation energy matrices for the weak and strong correlation limits in the space of occupied orbitals, our method, which we call orbital-based size-consistent matrix interpolation (OSMI), avoids previous difficulties in the construction of size-consistent adiabatic connection functionals. We design a simple, nonempirical adiabatic connection and a one-parameter strong-interaction limit functional, and we show that the resulting method reproduces the correlation energy of the uniform electron gas over a wide range of densities. When applied to subsets of the GMTKN55 thermochemistry database, OSMI is more accurate on average than MP2 and nonempirical density functionals. Most notably, OSMI provides excellent predictions of the barrier heights we tested, with average errors of less than 2 kcal mol

The growing availability of biological data resources has transformed research, yet their effective use remains challenging: selecting appropriate sources requires domain knowledge, data are fragmented across databases, and synthesizing results into reliable conclusions is labor-intensive. Although large language models promise to address these barriers, their impact in biomedicine has been limited by unsupported statements, incorrect claims, and lack of provenance. We introduce Alvessa, an evidence-grounded agentic research assistant designed around verifiability. Alvessa integrates entity recognition, orchestration of pre-validated biological tools, and data-constrained answer generation with statement-level verification against retrieved records, explicitly flagging unsupported claims and guiding revision when reliability criteria are not met. We evaluate Alvessa on dbQA from LAB-Bench and GenomeArena, a benchmark of 720 questions spanning gene and variant annotation, pathways, molecular interactions, miRNA targets, drug-target evidence, protein structure, and gene-phenotype associations. Alvessa substantially improves accuracy relative to general-purpose language models and performs comparably to coding-centric agents while producing fully traceable outputs. Using adversarial perturbations, we show that detection of fabricated statements depends critically on access to retrieved evidence. We further demonstrate application to drug discovery, where evidence-grounded synthesis enables identification of candidate targets missed or misattributed by literature-centered reasoning alone. Alvessa and GenomeArena are released to the community to support reproducible, verifiable AI-assisted biological research.

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.