arXiv subjects

Tuan Minh Pham

Publications and source records attributed to Tuan Minh Pham.

15 recordsLinked to original sources

arXiv2026

Entropy Production Rate in Stochastically Time-evolving Asymmetric Networks

Networks that characterise the interactions between units composing complex systems are typically treated as fixed. Yet, such networks often stochastically evolve over time, shaping the collective behavior of complex systems. To date, we lack a general non-equilibrium thermodynamic treatment of such time-dependent networks. In this Letter, to address this problem, we model fluctuating interactions between units of nonlinear network systems as uncorrelated colored noise (i.e., annealed disorder) with a correlation time. This approach enables us to quantify how the entropy production rate (EPR) depends on both the time-scale and the strength of the disorder. Using {\it dynamical mean field theory}, we derive an exact expression for EPR at {\it any} transient time that is validated by simulations of the full dynamics and establish a relation between EPR and autocorrelation at stationarity. We find that annealed disorder shifts the transition from the fixed-point to chaos toward a higher variance of the interactions, thereby suppressing chaos but at the cost of greater dissipation.

cond-mat.stat-mech↗

arXiv2026

Cellular Adaptation to Signal Fluctuations as Learning

Cells represent one of the most fundamental units of life. Underlying their robust performance against environmental variability, such as temporal fluctuations of chemical signals, between different cell types, is a dynamical interrelation between the two components of an intracellular pathway: a gene-regulatory network and its upstream signal transducers. To understand how a single cell utilizes this feedback to self-regulate its gene-expressions, we develop a multiscale model of the pathway's components, in which the adaptive variables responsible for signal interpretation follow a feedback-induced learning process. We then derive a macroscopic theory capturing the covariations between these components - so-called collective modes. Our theory shows how cells can achieve robust output against signal fluctuations via self-regulation rather than simple noise suppression. Such robustness corresponds to a transition from random- to structured collective modes beyond a critical adaptation rate.

q-bio.MN↗

arXiv2026

Symmetric preferences, asymmetric outcomes: Tipping dynamics in an open-city segregation model

Schelling's model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this celebrated model have been proposed by assuming agents tend to increase their satisfaction. Complementary to this traditional, utility-based approach, we model residential moves using satisfaction-independent reaction rates in a spatially extended chemical reaction network. The resulting model exhibits an emergent phenomenon: despite symmetric in-group preferences, the system undergoes a tipping transition at a critical preference level, beyond which one agent type dominates. We characterize this asymmetric phase transition in details using mean-field analysis, numerical simulations and finite size scaling methods. We find that while the transition shares key features with the Ising universality class, such as $\mathbb{Z}_2$ symmetry breaking and similar exponent ratios, the full set of critical exponents does not match any known universality class.

physics.soc-ph↗

arXiv2026

Rethinking Multinomial Logistic Mixture of Experts with Sigmoid Gating Function

The sigmoid gate in mixture-of-experts (MoE) models has been empirically shown to outperform the softmax gate across several tasks, ranging from approximating feed-forward networks to language modeling. Additionally, recent efforts have demonstrated that the sigmoid gate is provably more sample-efficient than its softmax counterpart under regression settings. Nevertheless, there are three notable concerns that have not been addressed in the literature, namely (i) the benefits of the sigmoid gate have not been established under classification settings; (ii) existing sigmoid-gated MoE models may not converge to their ground-truth; and (iii) the effects of a temperature parameter in the sigmoid gate remain theoretically underexplored. To tackle these open problems, we perform a comprehensive analysis of multinomial logistic MoE equipped with a modified sigmoid gate to ensure model convergence. Our results indicate that the sigmoid gate exhibits a lower sample complexity than the softmax gate for both parameter and expert estimation. Furthermore, we find that incorporating a temperature into the sigmoid gate leads to a sample complexity of exponential order due to an intrinsic interaction between the temperature and gating parameters. To overcome this issue, we propose replacing the vanilla inner product score in the gating function with a Euclidean score that effectively removes that interaction, thereby substantially improving the sample complexity to a polynomial order.

stat.ML↗

arXiv2026

A Statistical Theory of Gated Attention through the Lens of Hierarchical Mixture of Experts

Self-attention has greatly contributed to the success of the widely used Transformer architecture by enabling learning from data with long-range dependencies. In an effort to improve performance, a gated attention model that leverages a gating mechanism within the multi-head self-attention has recently been proposed as a promising alternative. Gated attention has been empirically demonstrated to increase the expressiveness of low-rank mapping in standard attention and even to eliminate the attention sink phenomenon. Despite its efficacy, a clear theoretical understanding of gated attention's benefits remains lacking in the literature. To close this gap, we rigorously show that each entry in a gated attention matrix or a multi-head self-attention matrix can be written as a hierarchical mixture of experts. By recasting learning as an expert estimation problem, we demonstrate that gated attention is more sample-efficient than multi-head self-attention. In particular, while the former needs only a polynomial number of data points to estimate an expert, the latter requires exponentially many data points to achieve the same estimation error. Furthermore, our analysis also provides a theoretical justification for why gated attention yields higher performance when a gate is placed at the output of the scaled dot product attention or the value map rather than at other positions in the multi-head self-attention architecture.

cs.LG↗

arXiv2025

Xenophobia based on a few attributes can impede society's cohesiveness

Xenophobic interactions play a role as important as homophilic ones in shaping many dynamical processes on social networks, such as opinion formation, social balance, or epidemic spreading. In this paper, we use belief propagation and Monte Carlo simulations on tree-like signed graphs to predict that a sufficient propensity to xenophobia can impede a consensus that would otherwise emerge via a phase transition. As the strength of xenophobic interactions and the rationality of individuals with respect to social stress decrease, this transition changes from continuous to discontinuous, with a strong dependence on the initial conditions. The size of the parameter region where consensus can be reached from any initial condition decays as a power-law function of the number of discussed topics.

physics.soc-ph↗

arXiv2025

Effects of clustering heterogeneity on the spectral density of sparse networks

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the spectral properties of the network adjacency matrix. In the case of heterogeneous networks, we demonstrate that the spectral density becomes more symmetric as the fluctuations in the triangle-degree sequence increase. This phenomenon is explained by the small clustering coefficient of networks with a large variance of the triangle-degree distribution. In the homogeneous case of regular clustered networks, we find that both perturbative and non-perturbative approximations fail to predict the spectral density in the high-connectivity limit. This suggests that traditional large-degree approximations may be ineffective in studying the spectral properties of networks with more complex motifs. Our theoretical results are fully confirmed by numerical diagonalizations of finite adjacency matrices.

cond-mat.dis-nn↗

arXiv2024

Dynamical Theory for Adaptive Systems

The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) to analyse nonequilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness.

q-bio.PE↗

arXiv2023

Simulation of Hadronic Interactions with Deep Generative Models

Accurate simulation of detector responses to hadrons is paramount for all physics programs at the Large Hadron Collider (LHC). Central to this simulation is the modeling of hadronic interactions. Unfortunately, the absence of first-principle theoretical guidance has made this a formidable challenge. The state-of-the-art simulation tool, \textsc{Geant4}, currently relies on phenomenology-inspired parametric models. Each model is designed to simulate hadronic interactions within specific energy ranges and for particular types of hadrons. Despite dedicated tuning efforts, these models sometimes fail to describe the data in certain physics processes accurately. Furthermore, fine-tuning these models with new measurements is laborious. Our research endeavors to leverage generative models to simulate hadronic interactions. While our ultimate goal is to train a generative model using experimental data, we have taken a crucial step by training conditional normalizing flow models with \textsc{Geant4} simulation data. Our work marks a significant stride toward developing a fully differentiable and data-driven model for hadronic interactions in High Energy and Nuclear Physics.

hep-ph↗

arXiv2023

Hierarchical Graph Neural Networks for Particle Track Reconstruction

We introduce a novel variant of GNN for particle tracking called Hierarchical Graph Neural Network (HGNN). The architecture creates a set of higher-level representations which correspond to tracks and assigns spacepoints to these tracks, allowing disconnected spacepoints to be assigned to the same track, as well as multiple tracks to share the same spacepoint. We propose a novel learnable pooling algorithm called GMPool to generate these higher-level representations called "super-nodes", as well as a new loss function designed for tracking problems and HGNN specifically. On a standard tracking problem, we show that, compared with previous ML-based tracking algorithms, the HGNN has better tracking efficiency performance, better robustness against inefficient input graphs, and better convergence compared with traditional GNNs.

hep-ex↗

arXiv2022

Double-replica theory for evolution of genotype-phenotype interrelationship

The relationship between genotype and phenotype plays a crucial role in determining the function and robustness of biological systems. Here the evolution progresses through the change in genotype, whereas the selection is based on the phenotype, and genotype-phenotype relation also evolves. Theory for such phenotypic evolution remains poorly-developed, in contrast to evolution under the fitness landscape determined by genotypes. Here we provide statistical-physics formulation of this problem by introducing replicas for genotype and phenotype. We apply it to an evolution model, in which phenotypes are given by spin configurations; genotypes are interaction matrix for spins to give the Hamiltonian, and the fitness depends only on the configuration of a subset of spins called target. We describe the interplay between the genetic variations and phenotypic variances by noise in this model by our new approach that extends the replica theory for spin-glasses to include spin-replica for phenotypes and coupling-replica for genotypes. Within this framework we obtain a phase diagram of the evolved phenotypes against the noise and selection pressure, where each phase is distinguished by the fitness and overlaps for genotypes and phenotypes. Among the phases, robust fitted phase, relevant to biological evolution, is achieved under the intermediate level of noise (temperature), where robustness to noise and to genetic mutation are correlated, as a result of replica symmetry. We also find a trade-off between maintaining a high fitness level of phenotype and acquiring a robust pattern of genes as well as the dependence of this trade-off on the ratio between the size of the functional (target) part to that of the remaining non-functional (non-target) one. The selection pressure needed to achieve high fitness increases with the fraction of target spins.

q-bio.PE↗

arXiv2022

Homophily-based social group formation in a spin-glass self-assembly framework

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intra-group homophily), and opinions between individuals belonging to different groups tend to be different (inter-group heterophily). We compute the associated non-trivial phase diagram by solving a self-consistency equation for 'magnetization' (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with non-zero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.

cond-mat.stat-mech↗

arXiv2020

Balanced and fragmented phases in societies with homophily and social balance

Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations -- and social balance -- the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode multiple (binary) opinions of individuals and social interactions between individuals can be positive or negative. Recent work suggests that large systems of N >> 1 individuals never reach a balanced state (where unbalanced triads with one or three hostile links remain), provided the number of attributes for each agent is less than O(N^2) [Phys. Rev. Lett. 125, 078302]. Here we show that this statement is overly restrictive. Within a Hamiltonian framework that minimizes individuals' social stress, we demonstrate that stationary, balanced, but fragmented states can be reached for any number of attributes, if, in addition to homophily, individuals take into account a significant fraction, q, of their triadic relations. Above a critical value q_c, balanced states result. This result also holds for sparse realistic social networks. Finally, in the limit of small q, our result agrees with that of [Phys. Rev. Lett. 125, 078302].

physics.soc-ph↗

arXiv2020

The effect of social balance on social fragmentation

With the availability of cell phones, internet, social media etc. the interconnectedness of people within most societies has increased drastically over the past three decades. Across the same timespan, we are observing the phenomenon of increasing levels of fragmentation in society into relatively small and isolated groups that have been termed filter bubbles, or echo chambers. These pose a number of threats to open societies, in particular, a radicalisation in political, social or cultural issues, and a limited access to facts. In this paper we show that these two phenomena might be tightly related. We study a simple stochastic co-evolutionary model of a society of interacting people. People are not only able to update their opinions within their social context, but can also update their social links from collaborative to hostile, and vice versa. The latter is implemented such that social balance is realised. We find that there exists a critical level of interconnectedness, above which society fragments into small sub-communities that are positively linked within and hostile towards other groups. We argue that the existence of a critical communication density is a universal phenomenon in all societies that exhibit social balance. The necessity arises from the underlying mathematical structure of a phase transition phenomenon that is known from the theory of a kind of disordered magnets called spin glasses. We discuss the consequences of this phase transition for social fragmentation in society.

physics.soc-ph↗

arXiv2016

Fractional kinetics emerging from ergodicity breaking in random media

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, p-variation and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from non-fractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

cond-mat.stat-mech↗