arXiv subjects

Wenping Cui

Publications and source records attributed to Wenping Cui.

At least 19 recordsLinked to original sources

arXiv2026

Distinct mechanisms underlying in-context learning in transformers

Modern distributed networks, notably transformers, acquire a remarkable ability (termed `in-context learning') to adapt their computation to input statistics, such that a fixed network can be applied to data from a broad range of systems. Here, we provide a complete mechanistic characterization of this behavior in transformers trained on a finite set $S$ of discrete Markov chains. The transformer displays four algorithmic phases, characterized by whether the network memorizes and generalizes, and whether it uses 1-point or 2-point statistics. We show that the four phases are implemented by multi-layer subcircuits that exemplify two qualitatively distinct mechanisms for implementing context-adaptive computations. Minimal models isolate the key features of both motifs. Memorization and generalization phases are delineated by two boundaries that depend on data diversity, $K = |S|$. The first ($K_1^\ast$) is set by a kinetic competition between subcircuits and the second ($K_2^\ast$) is set by a representational bottleneck. A symmetry-constrained theory of a transformer's training dynamics explains the sharp transition from 1-point to 2-point generalization and identifies key features of the loss landscape that allow the network to generalize. Put together, we show that transformers develop distinct subcircuits to implement in-context learning and identify conditions that favor certain mechanisms over others.

cs.LG↗

arXiv2026

Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons

We analyze states of stationary activity in randomly coupled quadratic integrate-and-fire neurons using stochastic mean-field theory. Specifically, we consider the two cases of Gaussian random coupling and Cauchy random coupling, which are representative of systems with light- or with heavy-tailed synaptic strength distributions. For both, Gaussian and Cauchy coupling, bistability between a low activity and a high activity state of self-sustained firing is possible in excitable neurons. In the system with Cauchy coupling we find analytically a directed percolation threshold, i.e., above a critical value of the synaptic strength, activity percolates through the whole network starting from a few spiking units only. The existence of the directed percolation threshold is in agreement with previous numerical results in the literature for integrate-and-fire neurons with heavy-tailed synaptic strength distribution. However, we have found that the transition can be continuous or discontinuous, depending on the excitatory-inhibitory imbalance in the network. Networks with Gaussian coupling and networks with Cauchy coupling and additional additive noise lack the percolation transition in the thermodynamic limit.

cond-mat.dis-nn↗

arXiv2024

Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics

Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and statistical physics. We start by introducing the two classes of mathematical models that have served as the workhorses of community ecology: Consumer Resource Models (CRM) and the generalized Lotka-Volterra models (GLV). We place a special emphasis on graphical methods and general principles. We then review recent works showing a deep and surprising connection between ecological dynamics and constrained optimization. We then shift our focus by analyzing these same models in "high-dimensions" (i.e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.

q-bio.PE↗

arXiv2024

A minimal model of pan-immunity maintenance by horizontal gene transfer in the ecological dynamics of bacteria and phages

Bacteria and phages have been in an ongoing arms race for billions of years. To resist phages bacteria have evolved numerous defense systems, which nevertheless are still overcome by counter-defense mechanisms of specific phages. These defense/counter-defense systems are a major element of microbial genetic diversity and have been demonstrated to propagate between strains by Horizontal Gene Transfer (HGT). It has been proposed that the totality of defense systems found in microbial communities collectively form a distributed "pan-immune" system with individual elements moving between strains via ubiquitous HGT. Here, we formulate a Lotka-Volterra type model of a bacteria/phage community interacting via a combinatorial variety of defense/counter-defense systems and show that HGT enables stable maintenance of diverse defense/counter-defense genes in the microbial pan-genome even when individual microbial strains inevitably undergo extinction. This stability requires the HGT rate to be sufficiently high to ensure that some descendant of a "dying" strain survives, thanks to the immunity acquired through HGT from the community at large, thus establishing a new strain. This mechanism of persistence for the pan-immune gene pool is fundamentally similar to the "island migration" model of ecological diversity, with genes moving between genomes instead of species migrating between islands.

q-bio.PE↗

arXiv2020

The Perturbative Resolvent Method: spectral densities of random matrix ensembles via perturbation theory

We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM). The PRM is based on constructing a linear system of equations and calculating how the solutions to these equation change in response to a small perturbation using the zero-temperature cavity method. We illustrate the power of the method by providing simple analytic derivations of the Wigner Semi-circle Law for symmetric matrices, the Marchenko-Pastur Law for Wishart matrices, the spectral density for a product Wishart matrix composed of two square matrices, and the Circle and elliptic laws for real random matrices.

cond-mat.dis-nn↗

arXiv2019

Effect of resource dynamics on species packing in diverse ecosystems

The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different resource dynamics affect this bound. Here, we analyze a generalized consumer resource model with externally supplied resources and show that -- in contrast to self-renewing resources -- species can occupy only half of all available environmental niches. This motivates us to construct a new schema for classifying ecosystems based on species packing properties.

q-bio.PE↗

arXiv2019

A minimal model for microbial biodiversity can reproduce experimentally observed ecological patterns

Surveys of microbial biodiversity such as the Earth Microbiome Project (EMP) and the Human Microbiome Project (HMP) have revealed robust ecological patterns across different environments. A major goal in ecology is to leverage these patterns to identify the ecological processes shaping microbial ecosystems. One promising approach is to use minimal models that can relate mechanistic assumptions at the microbe scale to community-level patterns. Here, we demonstrate the utility of this approach by showing that the Microbial Consumer Resource Model (MiCRM) -- a minimal model for microbial communities with resource competition, metabolic crossfeeding and stochastic colonization -- can qualitatively reproduce patterns found in survey data including compositional gradients, dissimilarity/overlap correlations, richness/harshness correlations, and nestedness of community composition. By using the MiCRM to generate synthetic data with different environmental and taxonomical structure, we show that large scale patterns in the EMP can be reproduced by considering the energetic cost of surviving in harsh environments and HMP patterns may reflect the importance of environmental filtering in shaping competition. We also show that recently discovered dissimilarity-overlap correlations in the HMP likely arise from communities that share similar environments rather than reflecting universal dynamics. We identify ecologically meaningful changes in parameters that alter or destroy each one of these patterns, suggesting new mechanistic hypotheses for further investigation. These findings highlight the promise of minimal models for microbial ecology.

q-bio.PE↗

arXiv2019

The Community Simulator: A Python package for microbial ecology

Natural microbial communities contain hundreds to thousands of interacting species. For this reason, computational simulations are playing an increasingly important role in microbial ecology. In this manuscript, we present a new open-source, freely available Python package called Community Simulator for simulating microbial population dynamics in a reproducible, transparent and scalable way. The Community Simulator includes five major elements: tools for preparing the initial states and environmental conditions for a set of samples, automatic generation of dynamical equations based on a dictionary of modeling assumptions, random parameter sampling with tunable levels of metabolic and taxonomic structure, parallel integration of the dynamical equations, and support for metacommunity dynamics with migration between samples. To significantly speed up simulations using Community Simulator, our Python package implements a new Expectation-Maximization (EM) algorithm for finding equilibrium states of community dynamics that exploits a recently discovered duality between ecological dynamics and convex optimization. We present data showing that this EM algorithm improves performance by between one and two orders compared to direct numerical integration of the corresponding ordinary differential equations. We conclude by listing several recent applications of the Community Simulator to problems in microbial ecology, and discussing possible extensions of the package for directly analyzing microbiome compositional data.

q-bio.PE↗

arXiv2019

Diverse communities behave like typical random ecosystems

In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here, we draw on recent progress in random matrix theory and statistical physics to extend May's approach to generalized consumer-resource models. We show that in diverse ecosystems adding even modest amounts of noise to consumer preferences results in a transition to "typicality" where macroscopic ecological properties of communities are indistinguishable from those of random ecosystems, even when resource preferences have prominent designed structures. We test these ideas using numerical simulations on a wide variety of ecological models. Our work offers an explanation for the success of random consumer-resource models in reproducing experimentally observed ecological patterns in microbial communities and highlights the difficulty of scaling up bottom-up approaches in synthetic ecology to diverse communities.

q-bio.PE↗

arXiv2019

The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory

Fifty years ago, Robert MacArthur showed that stable equilibria optimize quadratic functions of the population sizes in several important ecological models. Here, we generalize this finding to a broader class of systems within the framework of contemporary niche theory, and precisely state the conditions under which an optimization principle (not necessarily quadratic) can be obtained. We show that conducting the optimization in the space of environmental states instead of population sizes leads to a universal and transparent physical interpretation of the objective function. Specifically, the equilibrium state minimizes the perturbation of the environment induced by the presence of the competing species, subject to the constraint that no species has a positive net growth rate. We use this "minimum environmental perturbation principle" to make new predictions for eco-evolution and community assembly, and describe a simple experimental setting where its conditions of validity have been empirically tested.

q-bio.PE↗

arXiv2019

The Thermodynamic Uncertainty Relation in Biochemical Oscillations

Living systems regulate many aspects of their behavior through periodic oscillations of molecular concentrations, which function as `biochemical clocks.' These clocks are intrinsically subject to thermal fluctuations, so that the duration of a full oscillation cycle is random. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered `thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule, and confirm that it approaches the optimal precision as this number increases.

physics.bio-ph↗

arXiv2018

Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer resource models describing ecological dynamics. Combining this duality with a recent `cavity solution', we analyze high-dimensional, random QP where the optimization function and constraints are drawn randomly. Our theory shows remarkable agreement with numerics and points to a deep connection between optimization, dynamical systems, and ecology.

cond-mat.stat-mech↗

arXiv2018

Available energy fluxes drive a transition in the diversity, stability, and functional structure of microbial communities

A fundamental goal of microbial ecology is to understand what determines the diversity, stability, and structure of microbial ecosystems. The microbial context poses special conceptual challenges because of the strong mutual influences between the microbes and their chemical environment through the consumption and production of metabolites. By analyzing a generalized consumer resource model that explicitly includes cross-feeding, stochastic colonization, and thermodynamics, we show that complex microbial communities generically exhibit a transition as a function of available energy fluxes from a "resource-limited" regime where community structure and stability is shaped by energetic and metabolic considerations to a diverse regime where the dominant force shaping microbial communities is the overlap between species' consumption preferences. These two regimes have distinct species abundance patterns, different functional profiles, and respond differently to environmental perturbations. Our model reproduces large-scale ecological patterns observed across multiple experimental settings such as nestedness and differential beta diversity patterns along energy gradients. We discuss the experimental implications of our results and possible connections with disorder-induced phase transitions in statistical physics.

physics.bio-ph↗

arXiv2017

Identifying feasible operating regimes for early T-cell recognition: The speed, energy, accuracy trade-off in kinetic proofreading and adaptive sorting

In the immune system, T cells can quickly discriminate between foreign and self ligands with high accuracy. There is evidence that T-cells achieve this remarkable performance utilizing a network architecture based on a generalization of kinetic proofreading (KPR). KPR-based mechanisms actively consume energy to increase the specificity beyond what is possible in equilibrium.An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) in KPR and its generalization. Here, we revisit this question through numerical simulations where we simultaneously measure the speed, accuracy, and energy consumption of the KPR and adaptive sorting networks for different parameter choices. Our simulations highlight the existence of a 'feasible operating regime' in the speed-energy-accuracy plane where T-cells can quickly differentiate between foreign and self ligands at reasonable energy expenditure. We give general arguments for why we expect this feasible operating regime to be a generic property of all KPR-based biochemical networks and discuss implications for our understanding of the T cell receptor circuit.

q-bio.MN↗

arXiv2015

Canonical Quantization of Crystal Dislocation and Electron-Dislocation Scattering in an Isotropic Medium

Crystal dislocations govern the plastic mechanical properties of materials but also affect the electrical and optical properties. However, a fundamental and quantitative quantum-mechanical theory of dislocation remains undiscovered for decades. Here we present an exactly solvable quantum field theory of dislocation, for both edge and screw dislocations in an isotropic medium by introducing a new quasiparticle "dislon". With this approach, the electron-dislocation relaxation time is studied from electron self-energy which can be reduced to classical results. Moreover, a fundamentally new type of electron energy Friedel oscillation near dislocation core is predicted, which can occur even with single electron at present. For the first time, the effect of dislocations on materials' non-mechanical properties can be studied at a full quantum field theoretical level.

cond-mat.mtrl-sci↗

arXiv2015

Proximity Driven Enhanced Magnetic Order at Ferromagnetic Insulator / Magnetic Topological Insulator Interface

Magnetic exchange driven proximity effect at a magnetic insulator / topological insulator (MI/TI) interface provides a rich playground for novel phenomena as well as a way to realize low energy dissipation quantum devices. Here we report a dramatic enhancement of proximity exchange coupling in the MI / magnetic-TI EuS / Sb$_{2-x}$V$_x$Te$_3$ hybrid heterostructure, where V doping is used to drive the TI (Sb$_{2}$Te$_3$) magnetic. We observe an artificial antiferromagnetic-like structure near the MI/TI interface, which may account for the enhanced proximity coupling. The interplay between the proximity effect and doping provides insights into controllable engineering of magnetic order using a hybrid heterostructure.

cond-mat.mes-hall↗

arXiv2014

Magnetic Proximity Effect and Interlayer Exchange Coupling of Ferromagnetic/Topological Insulator/Ferromagnetic Trilayer

Magnetic proximity effect between topological insulator (TI) and ferromagnetic insulator (FMI) is considered to have great potential in spintronics. However, a complete determination of interfacial magnetic structure has been highly challenging. We theoretically investigate the interlayer exchange coupling of two FMIs separated by a TI thin film, and show that the particular electronic states of the TI contributing to the proximity effect can be directly identified through the coupling behavior between two FMIs, together with a tunability of coupling constant. Such FMI/TI/FMI structure not only serves as a platform to clarify the magnetic structure of FMI/TI interface, but also provides insights into designing the magnetic storage devices with ultrafast response.

cond-mat.mes-hall↗

arXiv2014

Tunable THz Surface Plasmon Polariton based on Topological Insulator-Layered Superconductor Hybrid Structure

We theoretically investigate the surface plasmon polariton (SPP) at the interface between 3D strong topological insulator (TI) and layered superconductor-magnetic insulator structure. The tunability of SPP through electronic doping can be enhanced when the magnetic permeability of the layered structure becomes higher. When the interface is gapped by superconductivity or perpendicular magnetism, SPP dispersion is further distorted, accompanied by a shift of group velocity and penetration depth. Such a shift of SPP reaches maximum when the magnitude of Fermi level approaches the gap value, and may lead to observable effects. The tunable SPP at the interface between layered superconductor and magnetism materials in proximity to TI surface may provide new insight in the detection of Majorana Fermions.

cond-mat.mes-hall↗