109 accepted papers
Multimodal large language models (MLLMs) have markedly expanded the competence of graphical user-interface (GUI) systems, propelling them beyond controlled simulations into complex, real-world environments across diverse platforms. However, practical usefulness is still bounded by the reliability of…
Training LLMs as interactive agents for multi-turn decision-making remains challenging, particularly in long-horizon tasks with sparse and delayed rewards, where agents must execute extended sequences of actions before receiving meaningful feedback. Most existing reinforcement learning (RL) methods …
Unlearning in large language models (LLMs) is critical for regulatory compliance and for building ethical generative AI systems that avoid producing private, toxic, illegal, or copyrighted content. Despite rapid progress, in this work we show that \textit{almost all} existing unlearning methods fail…
Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which introduce extra operations and require significant more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed var…
The Muon optimizer is consistently faster than Adam in training Large Language Models (LLMs), yet the mechanism underlying its success remains unclear. This paper demystifies this mechanism through the lens of associative memory. By ablating the transformer components optimized by Muon, we reveal th…
Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Keller et al., 2024b) combines gradient orthogonalization with first-order momentum and achieves significant improvement in data efficiency over Adam/AdamW for language model…
Modern machine learning (ML) workloads increasingly rely on GPUs, yet achieving high end-to-end performance remains challenging due to dependencies on both GPU kernel efficiency and host-side settings. Although LLM-based methods show promise on automated GPU kernel generation, prior works mainly foc…
Large language models (LLMs) have advanced the automation of data science workflows. Yet it remains unclear whether they can critically leverage external domain knowledge as human data scientists do in practice. To answer this question, we introduce AssistedDS (Assisted Data Science), a benchmark de
Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM reasoning through a novel graphical model incorporating lat…
Differential privacy (DP) offers a robust framework for safeguarding individual data privacy. To utilize DP in training modern machine learning models, differentially private optimizers have been widely used in recent years. A popular approach to privatize an optimizer is to clip the individual gra…
Large Language Models (LLMs) are increasingly deployed as chatbots, yet their ability to personalize responses to user preferences remains limited. We introduce PrefEval, a benchmark for evaluating LLMs' ability to infer, memorize and adhere to user preferences in long-context conversational setting…
This paper introduces \textsc{InfantAgent-Next}, a generalist agent capable of interacting with computers in a multimodal manner, encompassing text, images, audio, and video. Unlike existing approaches that either build intricate workflows around a single large model or only provide workflow modular…
In this work, we focus on the alignment problem of diffusion models with a continuous reward function, which represents specific objectives for downstream tasks, such as increasing darkness or improving the aesthetics of images. The central goal of the alignment problem is to adjust the distribution…
Aligning to human preferences and/or intentions is an important requirement for contemporary foundation models. To ensure alignment, popular approaches such as reinforcement learning with human feedback (RLHF) break down the task into three stages: (i) a model is computed with supervised fine-tuning…
Unlearning aims to remove copyrighted, sensitive, or private content from large language models (LLMs) without a full retraining. In this work, we develop a multi-task unlearning benchmark LUME that features three tasks: (1) unlearn synthetically generated creative short novels, (2) unlearn syntheti
Retrieval-Augmented Generation (RAG) has been empirically shown to enhance the performance of large language models (LLMs) in knowledge-intensive domains such as healthcare, finance, and legal contexts. Given a query, RAG retrieves relevant documents from a corpus and integrates them into the LLMs’…
Supervised fine-tuning is a standard method for adapting pre-trained large language models (LLMs) to downstream tasks. Quantization has been recently studied as a post-training technique for efficient LLM deployment. To obtain quantized fine-tuned LLMs, conventional pipelines would first fine-tune t…
We introduce a zero-shot merging framework for large language models (LLMs) that consolidates specialized domain experts into a single model without any further training. Our core contribution lies in leveraging relative task vectors—difference representations encoding each expert’s unique traits wi
The LLM unlearning technique has recently been introduced to comply with data regulations and address the safety and ethical concerns of LLMs by removing the undesired data-model influence. However, state-of-the-art unlearning methods face a critical vulnerability: they are susceptible to ``relearn…
The goal of the Inverse reinforcement learning (IRL) task is to identify the underlying reward function and the corresponding optimal policy from a set of expert demonstrations. While most IRL algorithms’ theoretical guarantees rely on a linear reward structure, we aim to extend the theoretical unde…
Machine unlearning has been used to remove unwanted knowledge acquired by large language models (LLMs). In this paper, we examine machine unlearning from an optimization perspective, framing it as a regularized multi-task optimization problem, where one task optimizes a forgetting objective and anot…
Decentralized computation has received considerable research interest lately, due to its wide applications in information processing systems. However, one key requirement to establish convergence for almost all decentralized algorithms, for convex and non-convex problems alike, is that the loss func…
Privacy is a growing concern in modern deep-learning systems and applications. Differentially private (DP) training prevents the leakage of sensitive information in the collected training data from the trained machine learning models. DP optimizers, including DP stochastic gradient descent (DPSGD) a…
Diffusion models (DMs) have achieved remarkable success in text-to-image generation, but they also pose safety risks, such as the potential generation of harmful content and copyright violations. The techniques of machine unlearning, also known as concept erasing, have been developed to address thes…
Backdoor attacks pose a significant security risk to machine learning applications due to their stealthy nature and potentially serious consequences. Such attacks involve embedding triggers within a learning model with the intention of causing malicious behavior when an active trigger is present whi…
Differentially Private Stochastic Gradient Descent with Gradient Clipping (DPSGD-GC) is a powerful tool for training deep learning models using sensitive data, providing both a solid theoretical privacy guarantee and high efficiency. However, existing research has shown that DPSGD-GC only converges…
A key challenge in contrastive learning is to generate negative samples from a large sample set to contrast with positive samples, for learning better encoding of the data. These negative samples often follow a softmax distribution which are dynamically updated during the training process. However,…
Aligning human preference and value is an important requirement for contemporary foundation models. State-of-the-art techniques such as Reinforcement Learning from Human Feedback (RLHF) often consist of two stages: 1) supervised fine-tuning (SFT), where the model is fine-tuned by learning from human…
Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and computational costs. One promising approach is to execute seco…
Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce Meta-Adaptive Optimizers (MADA), a unified optimizer framework…
The superior performance of large foundation models can be attributed to the use of massive amounts of high-quality data. However, such datasets often contain sensitive, private and copyrighted material that requires formal protection. While differential privacy (DP) is a prominent method used to ga…
Safeguarding intellectual property and preventing potential misuse of AI-generated images are of paramount importance. This paper introduces a robust and agile plug-and-play watermark detection framework, referred to as RAW. As a departure from existing encoder-decoder methods, which incorporate fix…
In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard. Yet, as LLMs grow in size, the substantial memory overhead from back-propagation (BP) for FO gradient computati…
Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of paramete…
While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Wh…
We consider a Bayesian approach to offline model-based inverse reinforcement learning (IRL). The proposed framework differs from existing offline model-based IRL approaches by performing simultaneous estimation of the expert's reward function and subjective model of environment dynamics. We make use…
Backdoor attacks involve inserting poisoned samples during training, resulting in a model containing a hidden backdoor that can trigger specific behaviors without impacting performance on normal samples. These attacks are challenging to detect, as the backdoored model appears normal until activated…
In this work, we propose algorithms for solving a class of Bilevel Optimization (BLO) problems, with applications in areas such as signal processing, networking and machine learning. Specifically, we develop a novel barrier-based gradient approximation algorithm that transforms the constrained BLO p…
Federated Learning (FL) is a distributed learning paradigm that allows multiple clients to learn a joint model by utilizing privately held data at each client. Significant research efforts have been devoted to develop advanced algorithms that deal with the situation where the data at individual clie…
This work develops analysis and algorithms for solving a class of bilevel optimization problems where the lower-level (LL) problems have linear constraints. Most of the existing approaches for constrained bilevel problems rely on value function-based approximate reformulations, which suffer from iss…
Massive data is often considered essential for deep learning applications, but it also incurs significant computational and infrastructural costs. Therefore, dataset pruning (DP) has emerged as an effective way to improve data efficiency by identifying and removing redundant training samples without…
This work revisits the joint transmit beamforming and antenna selection problem. Existing approaches find approximate solutions to this NP-hard problem via various heuristics, e.g., convex/nonconvex relaxation, greedy method, and (deep) supervised learning. However, optimality (or even feasibility)…
A poisoning backdoor attack is a rising security concern for deep learning. This type of attack can result in the backdoored model functioning normally most of the time but exhibiting abnormal behavior when presented with inputs containing the backdoor trigger, making it difficult to detect and prev…
Transformers are central in modern natural language processing and computer vision applications. Despite recent works devoted to reducing the quadratic cost of such models with respect to sequence length, dealing with ultra long sequences (e.g., $>$16K tokens) remains challenging. Applications such…
Invariant risk minimization (IRM) has received increasing attention as a way to acquire environment-agnostic data representations and predictions, and also a principled solution for preventing spurious correlations from being learned and improving models’ out-of-distribution generalization. Yet, rec…
Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive a…
Bilevel optimization has been shown to be a powerful framework for formulating multi-task machine learning problems, e.g., reinforcement learning (RL) and meta-learning, where the decision variables are coupled in both levels of the minimization problems. In practice, the learning tasks would be loc…
In modern machine learning systems, distributed algorithms are deployed across applications to ensure data privacy and optimal utilization of computational resources. This work offers a fresh perspective to model, analyze, and design distributed optimization algorithms through the lens of stochastic…
The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH…
In this work, we develop an implicit gradient-type (IG-AL) algorithm for bilevel optimization with strongly convex linear inequality constrained lower-level problems. Many learning problems of interest, including problems in distributed optimization, machine learning, economics, and transport resear…
This work develops a novel framework for communication-efficient distributed learning where the models to be learned are overparameterized. We focus on a class of kernel learning problems (which includes the popular neural tangent kernel (NTK) learning as a special case) and propose a novel {\it mul…
Decentralized optimization are playing an important role in applications such as training large machine learning models, among others. Despite its superior practical performance, there has been some lack of fundamental understanding about its theoretical properties. In this work, we address the foll…
Current deep neural networks (DNNs) are vulnerable to adversarial attacks, where adversarial perturbations to the inputs can change or manipulate classification. To defend against such attacks, an effective and popular approach, known as adversarial training (AT), has been shown to mitigate the nega…
The lack of adversarial robustness has been recognized as an important issue for state-of-the-art machine learning (ML) models, e.g., deep neural networks (DNNs). Thereby, robustifying ML models against adversarial attacks is now a major focus of research. However, nearly all existing defense method…
To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the payoffs of the agents with incentives while anticipating the…
Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherent nested structure: the inner loop finds the optimal policy given parame…
Supervised learning scenarios, where labels and features are possibly mismatched, have been an emerging concern in machine learning applications. For example, researchers often need to align heterogeneous data from multiple resources to the same entities without a unique identifier in the socioecono…
Adversarial training (AT) is a widely recognized defense mechanism to gain the robustness of deep neural networks against adversarial attacks. It is built on min-max optimization (MMO), where the minimizer (i.e., defender) seeks a robust model to minimize the worst-case training loss in the presence…
Providing privacy protection has been one of the primary motivations of Federated Learning (FL). Recently, there has been a line of work on incorporating the formal privacy notion of differential privacy with FL. To guarantee the client-level differential privacy in FL algorithms, the clients’ trans…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel optimization problems. We focus on bilevel problems where the lower…
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with…
Spectrum cartography (SC) aims at estimating the multi-aspect (e.g., space, frequency, and time) interference level caused by multiple emitters from limited measurements. Early SC approaches rely on model assumptions about the radio map, e.g., sparsity and smoothness, which may be grossly violated u…
Canonical polyadic decomposition (CPD) has been a workhorse for multimodal data analytics. This work puts forth a stochastic algorithmic framework for CPD under β-divergence, which is well-motivated in statistical learning—where the Euclidean distance is typically not preferred. Despite the existenc…
Efficiently finding First-order Nash Equilibria (FNE) in zero-sum games can be challenging, even in a two-player setting. This work proposes an algorithm for finding the FNEs of a two-player zero-sum game, in which the local cost functions can be non-convex, and the players only have access to local…
This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly convex-strongly concave objective functions, we establish an $O\left(1/n\right)$ generalization bound by using a probab…
There has been a growing interest in developing data-driven, in particular deep neural network (DNN) based methods for modern communication tasks. For a few popular tasks such as power control, beamforming, and MIMO detection, these methods achieve state-of-the-art performance while requiring less c…
Despite the existence of divergence examples, RMSprop remains one of the most popular algorithms in machine learning. Towards closing the gap between theory and practice, we prove that RMSprop converges with proper choice of hyper-parameters under certain conditions. More specifically, we prove tha…
Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local up…
Modern neural networks are often quite wide, causing large memory and computation costs. It is thus of great interest to train a narrower network. However, training narrow neural nets remains a challenging task. We ask two theoretical questions: Can narrow networks have as strong expressivity as wid…
This paper discusses formulations and algorithms which allow a number of agents to collectively solve problems involving both (non-convex) minimization and (concave) maximization operations. These problems have a number of interesting applications in information processing and machine learning, and…
Recently, there is a growing interest in the study of median-based algorithms for distributed non-convex optimization. Two prominent examples include signSGD with majority vote, an effective approach for communication reduction via 1-bit compression on the local gradients, and medianSGD, an algorith…
This paper proposes two efficient algorithms for computing approximate second-order stationary points (SOSPs) of problems with generic smooth non-convex objective functions and generic linear constraints. While finding (approximate) SOSPs for the class of smooth non-convex linearly constrained probl…
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform state-of-the-art centralized algorithms, in applications involving high…
In this paper, we study the problem of constrained min-max optimization in a black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimat…
This paper studies a gradient temporal difference (GTD) algorithm using neural network (NN) function approximators to minimize the mean squared Bellman error (MSBE). For off-policy learning, we show that the minimum MSBE problem can be recast into a min-max optimization involving a pair of over-para…
Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate differential privacy by training their models with (differentially) p…
The min-max problem, also known as the saddle point problem, can be used to formulate a wide range of applications in signal processing and wireless communications. However, existing optimization theory and methods, which mostly deal with problems with certain convex-concave structure, are not appli…
In this paper, we use the perturbed gradient based alternating minimization for solving a class of low-rank matrix factorization problems. Alternating minimization is a simple but popular approach which has been applied to problems in optimization, machine learning, data mining, and signal processin…
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these “sacrifices” do not always require more computational efforts. To shed light on such a “free-lunch” phen…
This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the ''``Adam-type'', includes the popular algorithms such as Adam, AMSGrad, AdaGrad. Despite their pop…
Alternating gradient descent (A-GD) is a simple but popular algorithm in machine learning, which updates two blocks of variables in an alternating manner using gradient descent steps. In this paper, we consider a smooth unconstrained nonconvex optimization problem, and propose a perturbed A-GD (PA-G…
In this paper, a gradient-based method for bound constrained non-convex problems is proposed. By leveraging both projected gradient descent and perturbed gradient descent, the proposed algorithm, named perturbed projected gradient descent (PP-GD), converges to some approximate second-order stationar…
Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of acto…
Policy evaluation with smooth and nonlinear function approximation has shown great potential for reinforcement learning. Compared to linear function approxi- mation, it allows for using a richer class of approximation functions such as the neural networks. Traditional algorithms are based on two tim…
The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems. However, AdaMM is not suited for solving black-box optimization…
In this paper, we design and analyze a new zeroth-order (ZO) stochastic optimization algorithm, ZO-signSGD, which enjoys dual advantages of gradient-free operations and signSGD. The latter requires only the sign information of gradient estimates but is able to achieve a comparable or even better c…
In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization o…
The sum-of-correlations (SUMCOR) generalized canonical correlation analysis (GCCA) aims at producing low-dimensional representations of multiview data via enforcing pairwise similarity of the reduced-dimension views. SUMCOR has been applied to a large variety of applications including blind separati…
Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm robotics, and power grids, we study policy evaluation in MARL,…
To support multiple on-demand services over several fixed communication networks, the network operators must allow flexible customization and fast provision of their network resources. One effective approach is network virtualization, whereby each service is mapped to a virtual subnetwork providing…
Symmetric nonnegative matrix factorization (SymNMF) plays an important role in applications of many data analytics problems such as community detection, document clustering and image segmentation. In this paper, we consider a stochastic SymNMF problem in which the observation matrix is generated in…
Symmetric non-negative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. Different from the existing wo…
Many problems of recent interest in signal processing, machine learning and wireless communications can be posed as nonconvex nonsmooth optimization problems. These problems are generally difficult to solve especially when the optimization variables are nonlinearly coupled in some nonconvex constrai…
In this paper we consider nonconvex optimization and learning over a network of distributed nodes. We develop a Proximal Primal-Dual Algorithm (Prox-PDA), which enables the network nodes to distributedly and collectively compute the set of first-order stationary solutions in a global sublinear manne…
Unlike dimensionality reduction (DR) tools for single-view data, e.g., principal component analysis (PCA), canonical correlation analysis (CCA) and generalized CCA (GCCA) are able to integrate information from multiple feature spaces of data. This is critical in multi-modal data fusion and analytics…
Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtaine…
Traffic engineering (TE) problem is a central component of the next generation cloud-based wireless networks. In this paper, we study a new resource allocation scheme for effective traffic engineering under practical constraints such as the finite buffer size at each node. To reduce the computationa…
This paper studies joint source transmit beamforming and relay amplification matrix design to achieve rate maximization for full-duplex (FD) MIMO amplify-and-forward (AF) relay systems with consideration of relay processing delay (RPD). The problem is difficult to solve due mainly to the self-interf…
The cyclic block coordinate descent-type (CBCD-type) methods have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical machine learning methods such as elastic-net regression, ridge penalized logistic regr…
Alternating direction method of multipliers (ADMM) has been recognized as an efficient approach for solving many large-scale learning problems over a computer cluster. However, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by…
We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmen…
The nonnegative matrix factorization (NMF) has been a popular model for a wide range of signal processing and machine learning problems. It is usually formulated as a nonconvex cost minimization problem. This work settles the convergence issue of a popular algorithm based on the alternating directio…
This paper considers multi-agent distributed optimization with quantized communication which is needed when inter-agent communications are subject to finite capacity and other practical constraints. To minimize the global objective formed by a sum of local convex functions, we develop a quantized di…
We consider solving a convex, nonsmooth and stochastic optimization problem over a multi-agent network. Each agent has access to a local objective function and can communicate with its immediate neighbors only. We develop a dynamic stochastic proximal-gradient consensus (DySPGC) algorithm, featuring…
In this work, we consider enhancing a target speech from a single-channel noisy observation corrupted by non-stationary noises at low signal-to-noise ratios (SNRs). We take a classification-based approach, where the objective is to estimate an Ideal Binary Mask (IBM) that classifies each time-freque…
In this paper, we analyze the behavior of the alternating direction method of multipliers (ADMM), for solving a family of nonconvex problems. Our focus is given to the well-known consensus and sharing problems, both of which have wide applications in signal processing. We show that in the presence o…
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an O(1/r) complexity (r is the number of passes of all blocks).…
In this paper, we propose a beamforming algorithm for binaural hearing aids with enhanced noise suppression capability. The enhancement is based on incorporating a priori spatial information into the conventional multichannel Wiener filtering (MWF) approach for noise suppression. We develop a low co…
We consider the distributed network routing problem in a large-scale hierarchical network whereby the nodes are partitioned into subnetworks, each managed by a network controller (NC), and there is a central NC to coordinate the operation of the distributed NCs. We propose a semi-asynchronous routin…