arXiv subjects

Christian Borgs

Publications and source records attributed to Christian Borgs.

At least 19 recordsLinked to original sources

arXiv2026

Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs

The preferential attachment model (PAM) describes the sequential growth of a network based on the "rich-get-richer" principle. Several versions of it have become established for modeling, e.g., citation networks, capturing a power-law degree distribution. Directed versions of the preferential attachment model where the edges are directed from the new to the old vertices have been the subject of extensive research. They have been shown to exhibit remarkable properties such as heavier tails for the limiting graph-normalized PageRank than for the in-degrees. By contrast, for the undirected version, we recently showed that PageRank has similar tails as the degree. In the present paper, we discuss the PageRank asymptotics for a multi-type version of the undirected PAM (here vertices have different colors), complementing previous results of Antunes, Bhamidi, Banerjee and Pipiras on the asymptotics of PageRank on similar directed multi-type or colored PAMs. Our studies are motivated by the aim to go beyond the rigid rule of edge orientation in directed preferential attachment models. As the main result, for the case of a finite set of colors, we show that the power-law hypothesis for PageRank is fulfilled also for the colored undirected PAM, where, by contrast to the directed case, the power-law exponent is color-dependent for some choices of the initial color distribution and the attractiveness function. For the specific case of a two-type model, we discuss implications of our results on fairness in sampling underrepresented nodes from the network.

math.PR↗

arXiv2026

Auditing the Auditors: Does Community-based Moderation Get It Right?

Online social platforms increasingly rely on crowd-sourced systems to label misleading content at scale, but these systems must both aggregate users' evaluations and decide whose evaluations to trust. To address the latter, many platforms audit users by rewarding agreement with the final aggregate outcome, a design we term consensus-based auditing. We analyze the consequences of this design in X's Community Notes, which in September 2022 adopted consensus-based auditing that ties users' eligibility for participation to agreement with the eventual platform outcome. We find evidence of strategic conformity: minority contributors' evaluations drift toward the majority and their participation share falls on controversial topics, where independent signals matter most. We formalize this mechanism in a behavioral model in which contributors trade off private beliefs against anticipated penalties for disagreement. Motivated by these findings, we propose a two-stage auditing and aggregation algorithm that weights contributors by the stability of their past residuals rather than by agreement with the majority. The method first accounts for differences across content and contributors, and then measures how predictable each contributor's evaluations are relative to the latent-factor model. Contributors whose evaluations are consistently informative receive greater influence in aggregation, even when they disagree with the prevailing consensus. In the Community Notes data, this approach improves out-of-sample predictive performance while avoiding penalization of disagreement.

cs.SI↗

arXiv2025

Travel Bans vs. Other Disease Mitigation Measures: A Mathematical Analysis

As the world grows increasingly connected, infectious disease transmission and outbreaks have become a pressing global concern for public health officials and policymakers. While policy interventions to contain and prevent the spread of disease have been proposed and implemented, there has been little rigorous quantitative analysis of the effectiveness of such interventions. In this paper, we study the susceptible-infected-recovered (SIR) infection process on a dynamic network model that models two communities with travel between them with the infection starting in one of them. In particular, we consider two Erd\H{o}s--R\'enyi graphs where edges are dynamically changing based on node travel between the graphs. We characterize the time evolution of the outbreaks in both communities and pin down the time for when the infection first reaches the second community. Finally, we analyze two types of interventions--travel bans and intra-community interventions in the second community--and prove that travel bans are not effective, while the second type are effective even without travel bans, provided they sufficiently reduce the effective reproduction number. We complement our analytic results by numerical simulations on large networks with realistic degree distributions and disease recovery times, showing that these results are robust, and hold for settings that model actual contact networks and disease spread more closely.

math.PR↗

arXiv2025

A meta-analysis on the performance of machine-learning based language models for sentiment analysis

This paper presents a meta-analysis evaluating ML performance in sentiment analysis for Twitter data. The study aims to estimate the average performance, assess heterogeneity between and within studies, and analyze how study characteristics influence model performance. Using PRISMA guidelines, we searched academic databases and selected 195 trials from 20 studies with 12 study features. Overall accuracy, the most reported performance metric, was analyzed using double arcsine transformation and a three-level random effects model. The average overall accuracy of the AIC-optimized model was 0.80 [0.76, 0.84]. This paper provides two key insights: 1) Overall accuracy is widely used but often misleading due to its sensitivity to class imbalance and the number of sentiment classes, highlighting the need for normalization. 2) Standardized reporting of model performance, including reporting confusion matrices for independent test sets, is essential for reliable comparisons of ML classifiers across studies, which seems far from common practice.

cs.CL↗

arXiv2025

System of Agentic AI for the Discovery of Metal-Organic Frameworks

Generative models and machine learning promise accelerated material discovery in MOFs for CO2 capture and water harvesting but face significant challenges navigating vast chemical spaces while ensuring synthetizability. Here, we present MOFGen, a system of Agentic AI comprising interconnected agents: a large language model that proposes novel MOF compositions, a diffusion model that generates crystal structures, quantum mechanical agents that optimize and filter candidates, and synthetic-feasibility agents guided by expert rules and machine learning. Trained on all experimentally reported MOFs and computational databases, MOFGen generated hundreds of thousands of novel MOF structures and synthesizable organic linkers. Our methodology was validated through high-throughput experiments and the successful synthesis of five "AI-dreamt" MOFs, representing a major step toward automated synthesizable material discovery.

cond-mat.mtrl-sci↗

arXiv2024

A Law of Large Numbers for SIR on the Stochastic Block Model: A Proof via Herd Immunity

In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where infected vertices infect susceptible neighbors at some rate $\eta$ and recover at rate $\gamma$, and the SBM is a random graph model where vertices are partitioned into a finite number of communities. The connection probability between two vertices depends on their community affiliation, here scaled so that the average degrees have a finite limit as the network grows. We prove laws of large numbers (LLN) for the epidemic's trajectory to a system of ordinary differential equations over any time horizon (finite or infinite), including in particular a LLN for the final size of the infection. Our proofs rely on two main ingredients: (i) a new coupling of the SIR epidemic and the randomness of the SBM, revealing a vector-valued random variable that drives the epidemic (related to what is usually called the ``force of the infection'' via a linear transformation), and (ii) a novel technique for analyzing the limiting behavior of the infinite time horizon for the infection, using the fact that once the infection passes the herd immunity threshold it dies out quickly and has a negligible impact on the overall size of the infection.

math.PR↗

arXiv2024

Manifold-Constrained Nucleus-Level Denoising Diffusion Model for Structure-Based Drug Design

Artificial intelligence models have shown great potential in structure-based drug design, generating ligands with high binding affinities. However, existing models have often overlooked a crucial physical constraint: atoms must maintain a minimum pairwise distance to avoid separation violation, a phenomenon governed by the balance of attractive and repulsive forces. To mitigate such separation violations, we propose NucleusDiff. It models the interactions between atomic nuclei and their surrounding electron clouds by enforcing the distance constraint between the nuclei and manifolds. We quantitatively evaluate NucleusDiff using the CrossDocked2020 dataset and a COVID-19 therapeutic target, demonstrating that NucleusDiff reduces violation rate by up to 100.00% and enhances binding affinity by up to 22.16%, surpassing state-of-the-art models for structure-based drug design. We also provide qualitative analysis through manifold sampling, visually confirming the effectiveness of NucleusDiff in reducing separation violations and improving binding affinities.

q-bio.QM↗

arXiv2024

Single and Multi-Hop Question-Answering Datasets for Reticular Chemistry with GPT-4-Turbo

The rapid advancement in artificial intelligence and natural language processing has led to the development of large-scale datasets aimed at benchmarking the performance of machine learning models. Herein, we introduce 'RetChemQA,' a comprehensive benchmark dataset designed to evaluate the capabilities of such models in the domain of reticular chemistry. This dataset includes both single-hop and multi-hop question-answer pairs, encompassing approximately 45,000 Q&As for each type. The questions have been extracted from an extensive corpus of literature containing about 2,530 research papers from publishers including NAS, ACS, RSC, Elsevier, and Nature Publishing Group, among others. The dataset has been generated using OpenAI's GPT-4 Turbo, a cutting-edge model known for its exceptional language understanding and generation capabilities. In addition to the Q&A dataset, we also release a dataset of synthesis conditions extracted from the corpus of literature used in this study. The aim of RetChemQA is to provide a robust platform for the development and evaluation of advanced machine learning algorithms, particularly for the reticular chemistry community. The dataset is structured to reflect the complexities and nuances of real-world scientific discourse, thereby enabling nuanced performance assessments across a variety of tasks. The dataset is available at the following link: https://github.com/nakulrampal/RetChemQA

cs.CL↗

arXiv2024

A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics

In drug discovery, molecular dynamics (MD) simulation for protein-ligand binding provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. There has been a long history of improving the efficiency of MD simulations through better numerical methods and, more recently, by utilizing machine learning (ML) methods. Yet, challenges remain, such as accurate modeling of extended-timescale simulations. To address this issue, we propose NeuralMD, the first ML surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding dynamics. We propose a principled approach that incorporates a novel physics-informed multi-grained group symmetric framework. Specifically, we propose (1) the BindingNet model that satisfies group symmetry using vector frames and captures the multi-level protein-ligand interactions, and (2) an augmented neural differential equation solver that learns the trajectory under Newtonian mechanics. For the experiment, we design ten single-trajectory and three multi-trajectory binding simulation tasks. We demonstrate the efficiency and effectiveness of NeuralMD, achieving over 1K$\times$ speedup compared to standard numerical MD simulations. NeuralMD also outperforms all other ML approaches, achieving up to 15$\times$ reduction in reconstruction error and 70% increase in validity. Additionally, we qualitatively illustrate that the oscillations in the predicted trajectories align more closely with ground-truth dynamics than those of other machine-learning methods. We believe NeuralMD paves the foundation for a new research paradigm in simulating protein-ligand dynamics.

cs.LG↗

arXiv2023

Image and Data Mining in Reticular Chemistry Using GPT-4V

The integration of artificial intelligence into scientific research has reached a new pinnacle with GPT-4V, a large language model featuring enhanced vision capabilities, accessible through ChatGPT or an API. This study demonstrates the remarkable ability of GPT-4V to navigate and obtain complex data for metal-organic frameworks, especially from graphical sources. Our approach involved an automated process of converting 346 scholarly articles into 6240 images, which represents a benchmark dataset in this task, followed by deploying GPT-4V to categorize and analyze these images using natural language prompts. This methodology enabled GPT-4V to accurately identify and interpret key plots integral to MOF characterization, such as nitrogen isotherms, PXRD patterns, and TGA curves, among others, with accuracy and recall above 93%. The model's proficiency in extracting critical information from these plots not only underscores its capability in data mining but also highlights its potential in aiding the creation of comprehensive digital databases for reticular chemistry. In addition, the extracted nitrogen isotherm data from the selected literature allowed for a comparison between theoretical and experimental porosity values for over 200 compounds, highlighting certain discrepancies and underscoring the importance of integrating computational and experimental data. This work highlights the potential of AI in accelerating scientific discovery and innovation, bridging the gap between computational tools and experimental research, and paving the way for more efficient, inclusive, and comprehensive scientific inquiry.

cs.AI↗

arXiv2023

A GPT-4 Reticular Chemist for Guiding MOF Discovery

We present a new framework integrating the AI model GPT-4 into the iterative process of reticular chemistry experimentation, leveraging a cooperative workflow of interaction between AI and a human researcher. This GPT-4 Reticular Chemist is an integrated system composed of three phases. Each of these utilizes GPT-4 in various capacities, wherein GPT-4 provides detailed instructions for chemical experimentation and the human provides feedback on the experimental outcomes, including both success and failures, for the in-context learning of AI in the next iteration. This iterative human-AI interaction enabled GPT-4 to learn from the outcomes, much like an experienced chemist, by a prompt-learning strategy. Importantly, the system is based on natural language for both development and operation, eliminating the need for coding skills, and thus, make it accessible to all chemists. Our collaboration with GPT-4 Reticular Chemist guided the discovery of an isoreticular series of MOFs, with each synthesis fine-tuned through iterative feedback and expert suggestions. This workflow presents a potential for broader applications in scientific research by harnessing the capability of large language models like GPT-4 to enhance the feasibility and efficiency of research activities.

cs.AI↗

arXiv2023

ChatGPT Chemistry Assistant for Text Mining and Prediction of MOF Synthesis

We use prompt engineering to guide ChatGPT in the automation of text mining of metal-organic frameworks (MOFs) synthesis conditions from diverse formats and styles of the scientific literature. This effectively mitigates ChatGPT's tendency to hallucinate information -- an issue that previously made the use of Large Language Models (LLMs) in scientific fields challenging. Our approach involves the development of a workflow implementing three different processes for text mining, programmed by ChatGPT itself. All of them enable parsing, searching, filtering, classification, summarization, and data unification with different tradeoffs between labor, speed, and accuracy. We deploy this system to extract 26,257 distinct synthesis parameters pertaining to approximately 800 MOFs sourced from peer-reviewed research articles. This process incorporates our ChemPrompt Engineering strategy to instruct ChatGPT in text mining, resulting in impressive precision, recall, and F1 scores of 90-99%. Furthermore, with the dataset built by text mining, we constructed a machine-learning model with over 86% accuracy in predicting MOF experimental crystallization outcomes and preliminarily identifying important factors in MOF crystallization. We also developed a reliable data-grounded MOF chatbot to answer questions on chemical reactions and synthesis procedures. Given that the process of using ChatGPT reliably mines and tabulates diverse MOF synthesis information in a unified format, while using only narrative language requiring no coding expertise, we anticipate that our ChatGPT Chemistry Assistant will be very useful across various other chemistry sub-disciplines.

cs.IR↗

arXiv2023

Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materials

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these scientific problems, molecules serve as the fundamental building blocks, and machine learning has emerged as a highly effective and powerful tool for modeling their geometric structures. Nevertheless, due to the rapidly evolving process of the field and the knowledge gap between science (e.g., physics, chemistry, & biology) and machine learning communities, a benchmarking study on geometrical representation for such data has not been conducted. To address such an issue, in this paper, we first provide a unified view of the current symmetry-informed geometric methods, classifying them into three main categories: invariance, equivariance with spherical frame basis, and equivariance with vector frame basis. Then we propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies. Geom3D contains 16 advanced symmetry-informed geometric representation models and 14 geometric pretraining methods over 46 diverse datasets, including small molecules, proteins, and crystalline materials. We hope that Geom3D can, on the one hand, eliminate barriers for machine learning researchers interested in exploring scientific problems; and, on the other hand, provide valuable guidance for researchers in computational chemistry, structural biology, and materials science, aiding in the informed selection of representation techniques for specific applications.

cs.LG↗

arXiv2023

Disincentivizing Polarization in Social Networks

On social networks, algorithmic personalization drives users into filter bubbles where they rarely see content that deviates from their interests. We present a model for content curation and personalization that avoids filter bubbles, along with algorithmic guarantees and nearly matching lower bounds. In our model, the platform interacts with $n$ users over $T$ timesteps, choosing content for each user from $k$ categories. The platform receives stochastic rewards as in a multi-arm bandit. To avoid filter bubbles, we draw on the intuition that if some users are shown some category of content, then all users should see at least a small amount of that content. We first analyze a naive formalization of this intuition and show it has unintended consequences: it leads to ``tyranny of the majority'' with the burden of diversification borne disproportionately by those with minority interests. This leads us to our model which distributes this burden more equitably. We require that the probability any user is shown a particular type of content is at least $\gamma$ times the average probability all users are shown that type of content. Full personalization corresponds to $\gamma = 0$ and complete homogenization corresponds to $\gamma = 1$; hence, $\gamma$ encodes a hard cap on the level of personalization. We also analyze additional formulations where the platform can exceed its cap but pays a penalty proportional to its constraint violation. We provide algorithmic guarantees for optimizing recommendations subject to these constraints. These include nearly matching upper and lower bounds for the entire range of $\gamma \in [0,1]$ showing that the reward of a multi-agent variant of UCB is nearly optimal. Using real-world preference data, we empirically verify that under our model, users share the burden of diversification with only minor utility loss under our constraints.

cs.CY↗

arXiv2023

Locality via Global Ties: Stability of the 2-Core Against Misspecification

For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the $k$-core, the size and probability of an epidemic outbreak, etc. In this paper, we study the question of when these algorithms are robust against misspecification of the graph model, for the special case of the 2-core. We show that, for locally converging graphs with bounded average degrees, under a weak notion of expansion, a local sampling algorithm provides robust estimates for the size of both the 2-core and its largest component. Our weak notion of expansion generalizes the classical definition of expansion, while holding for many well-studied random graph models. Our method involves a two-step sprinkling argument. In the first step, we use sprinkling to establish the existence of a non-empty $2$-core inside the giant, while in the second, we use this non-empty $2$-core as seed for a second sprinkling argument to establish that the giant contains a linear sized $2$-core. The second step is based on a novel coloring scheme for the vertices in the tree-part. Our algorithmic results follow from the structural properties for the $2$-core established in the course of our sprinkling arguments. The run-time of our local algorithm is constant independent of the graph size, with the value of the constant depending on the desired asymptotic accuracy $\epsilon$. But given the existential nature of local limits, our arguments do not give any bound on the functional dependence of this constant on $\epsilon$, nor do they give a bound on how large the graph has to be for the asymptotic additive error bound $\epsilon$ to hold.

cs.DS↗

arXiv2022

Estimating Total Treatment Effect in Randomized Experiments with Unknown Network Structure

Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, to public policy and to the technology industry at large. Here, we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact their neighbors' outcomes, an issue referred to as network interference or as non-individualized treatment response. A key challenge in these situations, is that the network is often unknown, and difficult, or costly, to measure. In this paper, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference, assuming a potential outcomes model with heterogeneous additive network effects. This model encompasses a broad class of network interference sources, including spillover, peer effects, and contagion. Within this framework, we show that, surprisingly, given access to average historical baseline measurements prior to the experiment, we can develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. We believe our results are poised to impact current randomized experimentation strategies due to its ease of interpretation and implementation, alongside its provable theoretical insights under heterogeneous network effects.

stat.ME↗

arXiv2022

Locality of Random Digraphs on Expanders

We study random digraphs on sequences of expanders with bounded average degree {which converge locally in probability}. We prove that the threshold for the existence of a giant strongly connected component, as well as the asymptotic fraction of nodes with giant fan-in or nodes with giant fan-out are local, in the sense that they are the same for two sequences with the same local limit. The digraph has a bow-tie structure, with all but a vanishing fraction of nodes lying either in the unique strongly connected giant and its fan-in and fan-out, or in sets with small fan-in and small fan-out. All local quantities are expressed in terms of percolation on the limiting rooted graph, without any structural assumptions on the limit, allowing, in particular, for non tree-like graphs. {In the course of establishing these results, we generalize previous results on the locality of the size of the giant to expanders of bounded average degree with possibly non-tree like limits. We also show that regardless of the local convergence of a sequence, the uniqueness of the giant and convergence of its relative size for unoriented percolation imply the bow-tie structure for directed percolation.} An application of our methods shows that the critical threshold for bond percolation and random digraphs on preferential attachment graphs is $p_c=0$, with an infinite order phase transition at $p_c$.

math.PR↗

arXiv2022

Efficient sampling and counting algorithms for the Potts model on $\mathbb Z^d$ at all temperatures

For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature $β\geq 0$. This shows that the physical phase transition of the Potts model presents no algorithmic barrier to efficient sampling, and stands in contrast to Markov chain mixing time results: the Glauber dynamics mix slowly at and below the critical temperature, and the Swendsen--Wang dynamics mix slowly at the critical temperature. We also provide an efficient algorithm (an FPRAS) for approximating the partition functions of these models at all temperatures. Our algorithms are based on representing the random cluster model as a contour model using Pirogov--Sinai theory, and then computing an accurate approximation of the logarithm of the partition function by inductively truncating the resulting cluster expansion. The main innovation of our approach is an algorithmic treatment of unstable ground states, which is essential for our algorithms to apply to all inverse temperatures $β$. By treating unstable ground states our work gives a general template for converting probabilistic applications of Pirogov-Sinai theory to efficient algorithms.

math.PR↗