Publications

The male fruit fly produces ~1.8 mm long sperm, thousands of which can be stored until mating in a ~200 micron sac, the seminal vesicle. While the evolutionary pressures driving such extreme sperm (flagellar) lengths have long been investigated, the physical consequences of their gigantism are unstudied. Through high-resolution three-dimensional reconstructions of in vivo sperm morphologies and rapid live imaging, we discovered that stored sperm are organized into a dense and highly aligned state. The packed flagella exhibit system-wide collective 'material' flows, with persistent and slow-moving topological defects; individual sperm, despite their extraordinary lengths, propagate rapidly through the flagellar material, moving in either direction along material director lines. To understand how these collective behaviors arise from the constituents' nonequilibrium dynamics, we conceptualize the motion of individual sperm as topologically confined to a reptation-like tube formed by its neighbors. Therein, sperm propagate through observed amplitude-constrained and internally driven flagellar bending waves, pushing off counter-propagating neighbors. From this conception, we derive a continuum theory that produces an extensile material stress that can sustain an aligned flagellar material. Experimental perturbations and simulations of active elastic filaments verify our theoretical predictions. Our findings suggest that active stresses in the flagellar material maintain the sperm in an unentangled, hence functional state, in both sexes, and establish giant sperm in their native habitat as a novel and physiologically relevant active matter system

Recent breakthroughs in protein structure prediction have led to a surge in high-quality 3D models, highlighting the need for efficient computational solutions. In our work, we examine the structural clusters from the AlphaFold Protein Structure Database (AFDB), a high-quality subset of ESMAtlas, and the Microbiome Immunity Project (MIP). We create a single cohesive low-dimensional representation of the resulting protein space. We show that, while each database occupies distinct regions, they collectively exhibit significant overlap in their functional profiles. High-level biological functions tend to cluster in particular regions, revealing a shared functional landscape despite the diverse sources of data. By creating a representation of protein structure space, localizing functional annotations within this space, and providing an open-access web-server for exploration, this work offers insights for future research concerning protein sequence-structure-function relationships, enabling biological questions to be asked about taxonomic assignments, environmental factors, or functional specificity. This approach is generalizable, thus enabling further discovery beyond findings presented here.

We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-vector product (matvec) queries of the form $x \rightarrow Ax$ and $x \rightarrow A^Tx$. This problem is of central importance to algorithms across scientific computing and machine learning, with applications to fast multiplication and inversion for structured matrices, building preconditioners for first-order optimization, and as a model for differential operator learning. Prior work focuses on obtaining query complexity upper and lower bounds for learning specific structured matrix families that commonly arise in applications.
We initiate the study of the problem in greater generality, aiming to understand the query complexity of learning approximations from general matrix families. Our main result focuses on finding a near-optimal approximation to $A$ from any finite-sized family of matrices, $\mathcal{F}$. Standard results from matrix sketching show that $O(\log|\mathcal{F}|)$ matvec queries suffice in this setting. This bound can also be achieved, and is optimal, for vector-matrix-vector queries of the form $x,y\rightarrow x^TAy$, which have been widely studied in work on rank-$1$ matrix sensing.
Surprisingly, we show that, in the matvec model, it is possible to obtain a nearly quadratic improvement in complexity, to $\tilde{O}(\sqrt{\log|\mathcal{F}|})$. Further, we prove that this bound is tight up to log-log this http URL covering number arguments, our result extends to well-studied infinite families. As an example, we establish that a near-optimal approximation from any \emph{linear matrix family} of dimension $q$ can be learned with $\tilde{O}(\sqrt{q})$ matvec queries, improving on an $O(q)$ bound achievable via sketching techniques and vector-matrix-vector queries.

Integrating task-relevant information into neural representations is a fundamental ability of both biological and artificial intelligence systems. Recent theories have categorized learning into two regimes: the rich regime, where neural networks actively learn task-relevant features, and the lazy regime, where networks behave like random feature models. Yet this simple lazy-rich dichotomy overlooks a diverse underlying taxonomy of feature learning, shaped by differences in learning algorithms, network architectures, and data properties. To address this gap, we introduce an analysis framework to study feature learning via the geometry of neural representations. Rather than inspecting individual learned features, we characterize how task-relevant representational manifolds evolve throughout the learning process. We show, in both theoretical and empirical settings, that as networks learn features, task-relevant manifolds untangle, with changes in manifold geometry revealing distinct learning stages and strategies beyond the lazy-rich dichotomy. This framework provides novel insights into feature learning across neuroscience and machine learning, shedding light on structural inductive biases in neural circuits and the mechanisms underlying out-of-distribution generalization.

Synchronization among a group of active agents is ubiquitous in nature. Although synchronization based on direct interactions between agents described by the Kuramoto model is well understood, the other general mechanism based on indirect interactions among agents sharing limited resources are less known. Here, we propose a minimal thermodynamically consistent model for the altruistic resource-sharing (ARS) mechanism wherein resources are needed for an individual agent to advance but a more advanced agent has a lower competence to obtain resources. We show that while differential competence in ARS mechanism provides a negative feedback leading to synchronization it also breaks detailed balance and thus requires additional energy dissipation besides the cost of driving individual agents. By solving the model analytically, our study reveals a general trade-off relation between the total energy dissipation rate and the two key performance measures of the system: average speed and synchronization accuracy. For a fixed dissipation rate, there is a distinct speed-accuracy Pareto front traversed by the scarcity of resources: scarcer resources lead to slower speed but more accurate synchronization. Increasing energy dissipation eases this trade-off by pushing the speed-accuracy Pareto front outward. The connections of our work to realistic biological systems such as the KaiABC system in cyanobacterial circadian clock and other theoretical results based on thermodynamic uncertainty relation are also discussed.

Convergence analysis can characterize genetic elements underlying morphological adaptations. However, its performance on regulatory elements is limited due to their modular composition of transcription factor motifs, which have rapid turnover and experience different evolutionary pressures.

We introduce phyloConverge, a phylogenetic method that performs scalable, fine-grained local convergence analysis of genomic elements at flexible length scales. Using a benchmarking case of convergent subterranean mammal adaptation, phyloConverge identifies rate-accelerated conserved noncoding elements (CNEs) with high specificity and statistical robustness relative to competing methods. From CNE-level scoring, we detect the convergent regression of entire CNE units and highlight the contrast that subterranean-associated coding region regression is highly specific to ocular functions, whereas regulatory element regression is enriched for accompanying neuronal phenotypes and other developmental processes. From transcription factor motif-level scoring, we dissect elements into subregions with uneven convergence signals and demonstrate the modular adaptation of CNEs with high functional specificity. Finally, we demonstrate phyloConverge’s scalability to perform high-resolution convergence analysis genome-wide.

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projection and an arbitrary unknown, low-dimensional link function. As such, they constitute a natural template for feature learning in neural networks. We consider a two-timescale algorithm, whereby the low-dimensional link function is learnt with a non-parametric model infinitely faster than the subspace parametrizing the low-rank projection. By appropriately exploiting the matrix semigroup structure arising over the subspace correlation matrices, we establish global convergence of the resulting Grassmannian gradient flow dynamics, and provide a quantitative description of its associated “saddle-to-saddle” dynamics. Notably, the timescales associated with each saddle can be explicitly characterized in terms of an appropriate Hermite decomposition of the target link function.

We address the problem of predicting the next states of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural blackbox solution to this task, the presence of a wellstructured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next states through time integration. Our framework decouples dynamics estimation — i.e., DISCovering an evolution Operator from a short trajectory — from state prediction — i.e., evolving this operator. Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well to unseen initial conditions and remains competitive when fine-tuned on downstream tasks. The code will be made publicly available upon publication at https: //github.com/RudyMorel/DISCO.