Stacy Patterson

Bassam Bamieh, Mihailo R. Jovanović, Partha Mitra et al.

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Timothy Castiglia, Anirban Das, Shiqiang Wang et al.

We propose Compressed Vertical Federated Learning (C-VFL) for communication-efficient training on vertically partitioned data. In C-VFL, a server and multiple parties collaboratively train a model on their respective features utilizing several local iterations and sharing compressed intermediate results periodically. Our work provides the first theoretical analysis of the effect message compression has on distributed training over vertically partitioned data. We prove convergence of non-convex objectives at a rate of $O(\frac{1}{\sqrt{T}})$ when the compression error is bounded over the course of training. We provide specific requirements for convergence with common compression techniques, such as quantization and top-$k$ sparsification. Finally, we experimentally show compression can reduce communication by over $90\%$ without a significant decrease in accuracy over VFL without compression.

Yuhao Yi, Zhongzhi Zhang, Stacy Patterson

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices are subject to white noise. We focus on the coherence of networks characterized in terms of the $H_2$-norm, which quantifies how closely agents track the consensus value. We first provide a lower bound of coherence of a network in terms of its average degree, which is independent of the network order. We then study the coherence of some sparse, scale-free real-world networks, which approaches a constant. We also study numerically the coherence of Barabási-Albert networks and high-dimensional random Apollonian networks, which also converges to a constant when the networks grow. Finally, based on the connection of coherence and the Kirchhoff index, we study analytically the coherence of two deterministically-growing sparse networks and obtain the exact expressions, which tend to small constants. Our results indicate that the effect of noise on the consensus dynamics in power-law networks is negligible. We argue that scale-free topology, together with loopy structure, is responsible for the strong robustness with respect to noisy consensus dynamics in power-law networks.

Stacy Patterson, Neil McGlohon, Kirill Dyagilev

We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the desired trajectory, and (2) convergence rate to a consensus value. The objective is to identify the set of $k$ leaders that optimizes the chosen performance measure. In both cases, an optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the $k$-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the $k$-leader selection problem can be solved in polynomial time (in both $k$ and the network size $n$). We give an $O(n^3)$ solution for optimal $k$-leader selection in path graphs and an $O(kn^3)$ solution for optimal $k$-leader selection in ring graphs.

Erika Mackin, Stacy Patterson

We study the problem of maximizing opinion diversity in a social network that includes opinion leaders with binary opposing opinions. The members of the network who are not leaders form their opinions using the French-DeGroot model of opinion dynamics. To quantify the diversity of such a system, we adapt two diversity measures from ecology to our setting, the Simpson Diversity Index and the Shannon Index. Using these two measures, we formalize the problem of how to place a single leader with opinion 1, given a network with a leader with opinion 0, so as to maximize the opinion diversity. We give analytical solutions to these problems for paths, cycles, and trees, and we highlight our results through a numerical example.

Erika Mackin, Stacy Patterson

We consider the leader selection problem in a network with consensus dynamics where both leader and follower agents are subject to stochastic external disturbances. The performance of the system is quantified by the total steady-state variance of the node states, and the goal is to identify the set of leaders that minimizes this variance. We first show that this performance measure can be expressed as a submodular set function over the nodes in the network. We then use this result to analyze the performance of two greedy, polynomial-time algorithms for leader selection, showing that the leader sets produced by the greedy algorithms are within provable bounds of optimal.

Erika Mackin, Stacy Patterson

We consider how to connect a set of disjoint networks to optimize the performance of the resulting composite network. We quantify this performance by the coherence of the composite network, which is defined by an $H_2$ norm of the system. Two dynamics are considered: noisy consensus dynamics with and without stubborn agents. For noisy consensus dynamics without stubborn agents, we derive analytical expressions for the coherence of composite networks in terms of the coherence of the individual networks and the structure of their interconnections. We also identify optimal interconnection topologies and give bounds on coherence for general composite graphs. For noisy consensus dynamics with stubborn agents, we develop a non-combinatorial algorithm that identifies connecting edges such that the composite network coherence closely approximates the performance of the optimal composite graph.

Neil McGlohon, Stacy Patterson

We consider the problem of regularized regression in a network of communication-constrained devices. Each node has local data and objectives, and the goal is for the nodes to optimize a global objective. We develop a distributed optimization algorithm that is based on recent work on semi-stochastic proximal gradient methods. Our algorithm employs iteratively refined quantization to limit message size. We present theoretical analysis and conditions for the algorithm to achieve a linear convergence rate. Finally, we demonstrate the performance of our algorithm through numerical simulations.

Aditya Dhodapkar, Avery Smidt, Aaron Verkleeren et al.

Conventional air traffic control divides airspace into specific regions, creating a scaling bottleneck as traffic grows. Choosing how to partition airspace is not straightforward because grid size affects workload, handoff frequency, and the capacity of whatever coordination mechanism operates within each sector. We present a three stage pipeline that automates sectorization and sector coordination while preserving human oversight. First, a two stage XGBoost classifier predicts the optimal 3D grid configuration from 23 location-agnostic traffic features, achieving 91.38% accuracy on a 65,000 sample dataset derived from Federal Aviation Administration System Wide Information Management replays. Second, a leaderless Paxos consensus protocol lets aircraft coordinate sector entries among themselves, maintaining above 96% entry success with low near mid-air collision rates across all tested configurations. Third, Bayesian Optimization with a Gaussian Process surrogate tunes eight protocol parameters per airport in 50 trials, revealing that each traffic environment requires a qualitatively different configuration. The resulting pipeline offers a practical path toward scalable, autonomous airspace management as traffic demand outpaces controller capacity.

Linh Tran, Sanjay Chari, Md. Saikat Islam Khan et al.

We present the Differentially Private Blockchain-Based Vertical Federal Learning (DP-BBVFL) algorithm that provides verifiability and privacy guarantees for decentralized applications. DP-BBVFL uses a smart contract to aggregate the feature representations, i.e., the embeddings, from clients transparently. We apply local differential privacy to provide privacy for embeddings stored on a blockchain, hence protecting the original data. We provide the first prototype application of differential privacy with blockchain for vertical federated learning. Our experiments with medical data show that DP-BBVFL achieves high accuracy with a tradeoff in training time due to on-chain aggregation. This innovative fusion of differential privacy and blockchain technology in DP-BBVFL could herald a new era of collaborative and trustworthy machine learning applications across several decentralized application domains.

Erika Mackin, Stacy Patterson

We investigate the performance of m-th order consensus systems with stochastic external perturbations, where a subset of leader nodes incorporates absolute information into their control laws. The system performance is measured by its coherence, an $H_2$ norm that quantifies the total steady-state variance of the deviation from the desired trajectory. We first give conditions under which such systems are stable, and we derive expressions for coherence in stable second, third, and fourth order systems. We next study the problem of how to identify a set of leaders that optimizes coherence. To address this problem, we define set functions that quantify each system's coherence and prove that these functions are submodular. This allows the use of an efficient greedy algorithm that to find a leader set with which coherence is within a constant bound of optimal. We demonstrate the performance of the greedy algorithm empirically, and further, we show that the optimal leader sets for the different orders of consensus dynamics do not necessarily coincide.

Michael Zuo, Inwon Kang, Stacy Patterson et al.

We explore the privacy-utility tradeoff of synthetic data generation schemes on tabular financial datasets, a domain characterized by high regulatory risk and severe class imbalance. We consider representative tabular data generators, including autoencoders, generative adversarial networks, diffusion, and copula synthesizers. To address the challenges of the financial domain, we provide novel privacy-preserving implementations of GAN and autoencoder synthesizers. We evaluate whether and how well the generators simultaneously achieve data quality, downstream utility, and privacy, with comparison across balanced and imbalanced input datasets. Our results offer insight into the distinct challenges of generating synthetic data from datasets that exhibit severe class imbalance and mixed-type attributes.

Mingzhi Zhu, Michele Merler, Raju Pavuluri et al.

Code agents must both reason over long-horizon repository state and obey strict tool-use protocols. In paired Instruct/Thinking checkpoints, these capabilities are complementary but misaligned. The Instruct model is concise and tool-disciplined, whereas the Thinking model offers stronger planning and recovery behavior but often over-deliberates and degrades agent performance. We present CRANE (Constrained Reasoning Injection for Code Agents via Nullspace Editing), a training-free parameter-editing method that treats the Thinking-Instruct delta as a directional pool of candidate reasoning edits for the Instruct backbone. CRANE combines magnitude thresholding to denoise the delta, a Conservative Taylor Gate to retain edits that are jointly beneficial for reasoning transfer and tool-use preservation, and Graduated Sigmoidal Projection to suppress format-critical update directions. By merging paired Instruct and Thinking checkpoints, CRANE delivers strong gains over either individual model while preserving Instruct-level efficiency: on Roo-Eval it achieves pass1 of 66.2% (+19.5%) for Qwen3-30B-A3B and 81.5% (+8.7%) for Qwen3-Next-80B-A3B; on SWE-bench-Verified it resolves up to 14 additional instances at both scales (122/500 and 180/500); and on Terminal-Bench v2 it improves pass1/pass5 by up to 2.3%/7.8%, reaching 7.6%/17.9% and 14.8%/30.3%, respectively, consistently outperforming alternative merging strategies across all three benchmarks.

Brayden Hollis, Stacy Patterson, Jinda Cui et al.

We present BubbleTouch, an open source quasi-static simulator for robotic tactile skins. BubbleTouch can be used to simulate contact with a robot's tactile skin patches as it interacts with humans and objects. The simulator creates detailed traces of contact forces that can be used in experiments in tactile contact activities. We summarize the design of BubbleTouch and highlight our recent work that uses BubbleTouch for experiments with tactile object recognition.

Linh Tran, Ana Milanova, Stacy Patterson

Federated Learning (FL) with parameter-efficient fine-tuning, such as Low-Rank Adaptation (LoRA), enables scalable model training on distributed data. However, when combined with Differential Privacy (DP), LoRA often introduces errors during global aggregation and amplifies the negative effect of DP noise. Existing cross-silo FL approaches mitigate the aggregation error by freezing one LoRA module and applying output perturbation. However, in a restricted low-rank subspaces, this additive noise frequently overwhelms the signals of the weight matrices, leading to suboptimal accuracy. To address this vulnerability, we propose FedPower, a differentially private cross-silo FL framework that reshapes server-side aggregation. Instead of perturbing mismatched low-rank factors, FedPower explicitly reconstructs and clips full-rank client updates to bound the sensitivity. The server then projects the exact aggregated update back into a secure low-rank space using PowerDP, a novel differentially private low-rank factorization mechanism. Based on simultaneous subspace iteration, PowerDP injects calibrated DP noise prior to the final orthonormalization step, effectively mitigates the negative effect of DP noise by preserving matrix orthogonality. We provide rigorous theoretical analyses establishing sensitivity bounds for subspace projections, proving that FedPower achieves both sample-level and client-level DP. Extensive experiments on various language understanding tasks in cross-silo FL settings show that FedPower is robust against tight privacy budgets while adding negligible computational overheads. Additional empirical study on different DP noise injection schemes validates the effectiveness of PowerDP in improving the tradeoff in accuracy and privacy. Evaluation on three different membership inference attacks validates the robustness and privacy-preserving capability of the proposed framework.

Lei Yu, Meng Han, Yiming Li et al.

Vertical Federated Learning (VFL) is a federated learning paradigm where multiple participants, who share the same set of samples but hold different features, jointly train machine learning models. Although VFL enables collaborative machine learning without sharing raw data, it is still susceptible to various privacy threats. In this paper, we conduct the first comprehensive survey of the state-of-the-art in privacy attacks and defenses in VFL. We provide taxonomies for both attacks and defenses, based on their characterizations, and discuss open challenges and future research directions. Specifically, our discussion is structured around the model's life cycle, by delving into the privacy threats encountered during different stages of machine learning and their corresponding countermeasures. This survey not only serves as a resource for the research community but also offers clear guidance and actionable insights for practitioners to safeguard data privacy throughout the model's life cycle.

Linh Tran, Wei Sun, Stacy Patterson et al.

Multimodal Large Language Models (LLMs) are pivotal in revolutionizing customer support and operations by integrating multiple modalities such as text, images, and audio. Federated Prompt Learning (FPL) is a recently proposed approach that combines pre-trained multimodal LLMs such as vision-language models with federated learning to create personalized, privacy-preserving AI systems. However, balancing the competing goals of personalization, generalization, and privacy remains a significant challenge. Over-personalization can lead to overfitting, reducing generalizability, while stringent privacy measures, such as differential privacy, can hinder both personalization and generalization. In this paper, we propose a Differentially Private Federated Prompt Learning (DP-FPL) approach to tackle this challenge by leveraging a low-rank factorization scheme to capture generalization while maintaining a residual term that preserves expressiveness for personalization. To ensure privacy, we introduce a novel method where we apply local differential privacy to the two low-rank components of the local prompt, and global differential privacy to the global prompt. Our approach mitigates the impact of privacy noise on the model performance while balancing the tradeoff between personalization and generalization. Extensive experiments demonstrate the effectiveness of our approach over other benchmarks.

Mingzhi Zhu, Boris Sobolev, Rahul Krishna et al.

Recent research advocates deploying smaller, specialized code LLMs in agentic frameworks alongside frontier models, sparking interest in efficient strategies for multi-task learning that balance performance, constraints, and costs. We compare two approaches for creating small, multi-task code LLMs: data mixing versus model merging. We conduct extensive experiments across two model families (Qwen Coder and DeepSeek Coder) at two scales (2B and 7B parameters), fine-tuning them for code generation and code summarization tasks. Our evaluation on HumanEval, MBPP, and CodeXGlue benchmarks reveals that model merging achieves the best overall performance at larger scale across model families, retaining 96% of specialized model performance on code generation tasks while maintaining summarization capabilities. Notably, merged models can even surpass individually fine-tuned models, with our best configuration of Qwen Coder 2.5 7B model achieving 92.7% Pass@1 on HumanEval compared to 90.9% for its task-specific fine-tuned equivalent. At a smaller scale we find instead data mixing to be a preferred strategy. We further introduce a weight analysis technique to understand how different tasks affect model parameters and their implications for merging strategies. The results suggest that careful merging and mixing strategies can effectively combine task-specific capabilities without significant performance degradation, making them ideal for resource-constrained deployment scenarios.

Linh Tran, Timothy Castiglia, Stacy Patterson et al.

We present Poisson Binomial Mechanism Vertical Federated Learning (PBM-VFL), a communication-efficient Vertical Federated Learning algorithm with Differential Privacy guarantees. PBM-VFL combines Secure Multi-Party Computation with the recently introduced Poisson Binomial Mechanism to protect parties' private datasets during model training. We define the novel concept of feature privacy and analyze end-to-end feature and sample privacy of our algorithm. We compare sample privacy loss in VFL with privacy loss in HFL. We also provide the first theoretical characterization of the relationship between privacy budget, convergence error, and communication cost in differentially-private VFL. Finally, we empirically show that our model performs well with high levels of privacy.

Timothy Castiglia, Yi Zhou, Shiqiang Wang et al.

We propose LESS-VFL, a communication-efficient feature selection method for distributed systems with vertically partitioned data. We consider a system of a server and several parties with local datasets that share a sample ID space but have different feature sets. The parties wish to collaboratively train a model for a prediction task. As part of the training, the parties wish to remove unimportant features in the system to improve generalization, efficiency, and explainability. In LESS-VFL, after a short pre-training period, the server optimizes its part of the global model to determine the relevant outputs from party models. This information is shared with the parties to then allow local feature selection without communication. We analytically prove that LESS-VFL removes spurious features from model training. We provide extensive empirical evidence that LESS-VFL can achieve high accuracy and remove spurious features at a fraction of the communication cost of other feature selection approaches.

Saswata Paul, Stacy Patterson, Carlos Varela

Autonomous air traffic management (ATM) operations for urban air mobility (UAM) will necessitate the use of distributed protocols for decentralized coordination between aircraft. As UAM operations are time-critical, it will be imperative to have formal guarantees of progress for the distributed protocols used in ATM. Under asynchronous settings, message transmission and processing delays are unbounded, making it impossible to provide deterministic bounds on the time required to make progress. We present an approach for formally guaranteeing timely progress in a Two-Phase Acknowledge distributed knowledge propagation protocol by probabilistically modeling the delays using theories of the Multicopy Two-Hop Relay protocol and the M/M/1 queue system. The guarantee states a probabilistic upper bound to the time for progress as a function of the probabilities of the total transmission and processing delays being less than two given values. We also showcase the development of a library of formal theories, that is tailored towards reasoning about timely progress in distributed protocols deployed in airborne networks, in the Athena proof assistant.

Anirban Das, Timothy Castiglia, Shiqiang Wang et al.

We consider federated learning in tiered communication networks. Our network model consists of a set of silos, each holding a vertical partition of the data. Each silo contains a hub and a set of clients, with the silo's vertical data shard partitioned horizontally across its clients. We propose Tiered Decentralized Coordinate Descent (TDCD), a communication-efficient decentralized training algorithm for such two-tiered networks. The clients in each silo perform multiple local gradient steps before sharing updates with their hub to reduce communication overhead. Each hub adjusts its coordinates by averaging its workers' updates, and then hubs exchange intermediate updates with one another. We present a theoretical analysis of our algorithm and show the dependence of the convergence rate on the number of vertical partitions and the number of local updates. We further validate our approach empirically via simulation-based experiments using a variety of datasets and objectives.

Anirban Das, Stacy Patterson

We consider decentralized model training in tiered communication networks. Our network model consists of a set of silos, each holding a vertical partition of the data. Each silo contains a hub and a set of clients, with the silo's vertical data shard partitioned horizontally across its clients. We propose Tiered Decentralized Coordinate Descent (TDCD), a communication-efficient decentralized training algorithm for such two-tiered networks. To reduce communication overhead, the clients in each silo perform multiple local gradient steps before sharing updates with their hub. Each hub adjusts its coordinates by averaging its workers' updates, and then hubs exchange intermediate updates with one another. We present a theoretical analysis of our algorithm and show the dependence of the convergence rate on the number of vertical partitions, the number of local updates, and the number of clients in each hub. We further validate our approach empirically via simulation-based experiments using a variety of datasets and both convex and non-convex objectives.

Timothy Castiglia, Anirban Das, Stacy Patterson

We propose Multi-Level Local SGD, a distributed gradient method for learning a smooth, non-convex objective in a heterogeneous multi-level network. Our network model consists of a set of disjoint sub-networks, with a single hub and multiple worker nodes; further, worker nodes may have different operating rates. The hubs exchange information with one another via a connected, but not necessarily complete communication network. In our algorithm, sub-networks execute a distributed SGD algorithm, using a hub-and-spoke paradigm, and the hubs periodically average their models with neighboring hubs. We first provide a unified mathematical framework that describes the Multi-Level Local SGD algorithm. We then present a theoretical analysis of the algorithm; our analysis shows the dependence of the convergence error on the worker node heterogeneity, hub network topology, and the number of local, sub-network, and global iterations. We back up our theoretical results via simulation-based experiments using both convex and non-convex objectives.

Matthew Obetz, Stacy Patterson, Ana Milanova

We present new operational semantics for serverless computing that model the event-driven relationships between serverless functions, as well as their interaction with platforms services such as databases and object stores. These semantics precisely encapsulate how control transfers between functions, both directly and through reads and writes to platform services. We use these semantics to define the notion of the service call graph for serverless applications that captures program flows through functions and services. Finally, we construct service call graphs for twelve serverless JavaScript applications, using a prototype of our call graph construction algorithm, and we evaluate their accuracy.

Stacy Patterson, Yuhao Yi, Zhongzhi Zhang

We study the performance of leader-follower noisy consensus networks, and in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered (1) noise-free leaders, in which leaders dictate the trajectory exactly and followers are subject to external disturbances, and (2) noise-corrupted leaders, in which both leaders and followers are subject to external perturbations. We measure the performance of a network by its coherence, an $H_2$ norm that quantifies how closely the followers track the leaders' trajectory. For both dynamics, we show a relationship between the coherence and resistance distances in an a electrical network. Using this relationship, we derive closed-form expressions for coherence as a function of the locations of the leaders. Further, we give analytical solutions to the optimal leader selection problem for several special classes of graphs.

Brayden Hollis, Stacy Patterson, Jeff Trinkle

The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable human-level dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, data acquisition, and data processing. To help address these challenges, we develop a tactile sensing technique based on compressed sensing. Compressed sensing simultaneously performs data sampling and compression with recovery guarantees and has been successfully applied in computer vision. We use compressed sensing techniques for tactile data acquisition to reduce hardware complexity and data transmission, while allowing fast, accurate reconstruction of the full-resolution signal. For our simulated test array of 4096 taxels, we achieve reconstruction quality equivalent to measuring all taxel signals independently (the full signal) from just 1024 measurements (the compressed signal) at a rate over 100Hz. We then apply tactile compressed sensing to the problem of object classification. Specifically, we perform object classification on the compressed tactile data based on a method called compressed learning. We obtain up to 98% classification accuracy, even with a compression ratio of 64:1.

Brayden Hollis, Stacy Patterson, Jeff Trinkle

The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable human-level dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, power consumption, and data processing. To help address these challenges, we previously developed a tactile sensing technique based compressed sensing that reduces hardware complexity and data transmission, while allowing accurate reconstruction of the full-resolution signal. In this paper, we apply tactile compressed sensing to the problem of object classification. Specifically, we perform object classification on the compressed tactile data. We evaluate our method using BubbleTouch, our tactile array simulator. Our results show our approach achieves high classification accuracy, even with compression factors up to 64.

Brayden Hollis, Stacy Patterson, Jeff Trinkle

Whole body tactile perception via tactile skins offers large benefits for robots in unstructured environments. To fully realize this benefit, tactile systems must support real-time data acquisition over a massive number of tactile sensor elements. We present a novel approach for scalable tactile data acquisition using compressed sensing. We first demonstrate that the tactile data is amenable to compressed sensing techniques. We then develop a solution for fast data sampling, compression, and reconstruction that is suited for tactile system hardware and has potential for reducing the wiring complexity. Finally, we evaluate the performance of our technique on simulated tactile sensor networks. Our evaluations show that compressed sensing, with a compression ratio of 3 to 1, can achieve higher signal acquisition accuracy than full data acquisition of noisy sensor data.