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Foundation models are now a major focus of leading technology organizations due to their ability to generalize across diverse tasks. Existing approaches for adapting foundation models to new applications often rely on Federated Learning (FL) and disclose the foundation model weights to clients when using it to initialize the global model. While these methods ensure client data privacy, they compromise model and information security. In this paper, we introduce Federated Learning Aggregation Biased by a Foundation Model (FedBaF), a novel method for dynamically integrating pre-trained foundation model weights during the FL aggregation phase. Unlike conventional methods, FedBaF preserves the confidentiality of the foundation model while still leveraging its power to train more accurate models, especially in non-IID and adversarial scenarios. Our comprehensive experiments use Pre-ResNet and foundation models like Vision Transformer to demonstrate that FedBaF not only matches, but often surpasses the test accuracy of traditional weight initialization methods by up to 11.4\% in IID and up to 15.8\% in non-IID settings. Additionally, FedBaF applied to a Transformer-based language model significantly reduced perplexity by up to 39.2\%.

Calculus of Variations is the mathematics of functional optimization, i.e., when the solutions are functions over a time interval. This is particularly important when the time interval is unknown like in minimum-time control problems, so that forward in time solutions are not possible. Calculus of Variations offers a robust framework for learning optimal control and inference. How can this framework be leveraged to design neural networks to solve challenges in control and inference? We propose the Pontryagin's Maximum Principle Neural Network (PMP-net) that is tailored to estimate control and inference solutions, in accordance with the necessary conditions outlined by Pontryagin's Maximum Principle. We assess PMP-net on two classic optimal control and inference problems: optimal linear filtering and minimum-time control. Our findings indicate that PMP-net can be effectively trained in an unsupervised manner to solve these problems without the need for ground-truth data, successfully deriving the classical "Kalman filter" and "bang-bang" control solution. This establishes a new approach for addressing general, possibly yet unsolved, optimal control problems., Comment: 16 pages, 5 figures, under review at ICLR 2025

Peer-to-peer learning is an increasingly popular framework that enables beyond-5G distributed edge devices to collaboratively train deep neural networks in a privacy-preserving manner without the aid of a central server. Neural network training algorithms for emerging environments, e.g., smart cities, have many design considerations that are difficult to tune in deployment settings -- such as neural network architectures and hyperparameters. This presents a critical need for characterizing the training dynamics of distributed optimization algorithms used to train highly nonconvex neural networks in peer-to-peer learning environments. In this work, we provide an explicit, non-asymptotic characterization of the learning dynamics of wide neural networks trained using popular distributed gradient descent (DGD) algorithms. Our results leverage both recent advancements in neural tangent kernel (NTK) theory and extensive previous work on distributed learning and consensus. We validate our analytical results by accurately predicting the parameter and error dynamics of wide neural networks trained for classification tasks.

Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in optimization, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel neural network architectures that parameterize gradients of various function classes. GradNets exhibit specialized architectural constraints that ensure correspondence to gradient functions. We provide a comprehensive GradNet design framework that includes methods for transforming GradNets into monotone gradient networks (mGradNets), which are guaranteed to represent gradients of convex functions. We establish the approximation capabilities of the proposed GradNet and mGradNet. Our results demonstrate that these networks universally approximate the gradients of (convex) functions. Furthermore, these networks can be customized to correspond to specific spaces of (monotone) gradient functions, including gradients of transformed sums of (convex) ridge functions. Our analysis leads to two distinct GradNet architectures, GradNet-C and GradNet-M, and we describe the corresponding monotone versions, mGradNet-C and mGradNet-M. Our empirical results show that these architectures offer efficient parameterizations and outperform popular methods in gradient field learning tasks.

Uncertainty quantification of neural networks is critical to measuring the reliability and robustness of deep learning systems. However, this often involves costly or inaccurate sampling methods and approximations. This paper presents a sample-free moment propagation technique that propagates mean vectors and covariance matrices across a network to accurately characterize the input-output distributions of neural networks. A key enabler of our technique is an analytic solution for the covariance of random variables passed through nonlinear activation functions, such as Heaviside, ReLU, and GELU. The wide applicability and merits of the proposed technique are shown in experiments analyzing the input-output distributions of trained neural networks and training Bayesian neural networks., Comment: Accepted to AISTATS 2024

Peer-to-peer deep learning algorithms are enabling distributed edge devices to collaboratively train deep neural networks without exchanging raw training data or relying on a central server. Peer-to-Peer Learning (P2PL) and other algorithms based on Distributed Local-Update Stochastic/mini-batch Gradient Descent (local DSGD) rely on interleaving epochs of training with distributed consensus steps. This process leads to model parameter drift/divergence amongst participating devices in both IID and non-IID settings. We observe that model drift results in significant oscillations in test performance evaluated after local training and consensus phases. We then identify factors that amplify performance oscillations and demonstrate that our novel approach, P2PL with Affinity, dampens test performance oscillations in non-IID settings without incurring any additional communication cost., Comment: Asilomar Conference on Signals, Systems, and Computers 2023 Camera-Ready Version

In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) Partial observability -- time series data is only available over a subset of the nodes; ii) Input noise -- it is correlated across distinct nodes while temporally independent, i.e., it is spatially colored. We present a feasibility condition on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation., Comment: Accepted at the IEEE ICASSP 2024. Camera-Ready Version

While deep learning has been very successful in computer vision, real world operating conditions such as lighting variation, background clutter, or occlusion hinder its accuracy across several tasks. Prior work has shown that hybrid models -- combining neural networks and heuristics/algorithms -- can outperform vanilla deep learning for several computer vision tasks, such as classification or tracking. We consider the case of object tracking, and evaluate a hybrid model (PhyOT) that conceptualizes deep neural networks as ``sensors'' in a Kalman filter setup, where prior knowledge, in the form of Newtonian laws of motion, is used to fuse sensor observations and to perform improved estimations. Our experiments combine three neural networks, performing position, indirect velocity and acceleration estimation, respectively, and evaluate such a formulation on two benchmark datasets: a warehouse security camera dataset that we collected and annotated and a traffic camera open dataset. Results suggest that our PhyOT can track objects in extreme conditions that the state-of-the-art deep neural networks fail while its performance in general cases does not degrade significantly from that of existing deep learning approaches. Results also suggest that our PhyOT components are generalizable and transferable., Comment: Accepted at IEEE ICASSP 2024 on December 13, 2023

This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates spurious associations across pairs of nodes, rendering the problem much harder. To address the challenge of noise correlation and partial observability, we assign to each pair of nodes a feature vector computed from the time series data of observed nodes. The feature embedding is engineered to yield structural consistency: there exists an affine hyperplane that consistently partitions the set of features, separating the feature vectors corresponding to connected pairs of nodes from those corresponding to disconnected pairs. The causal inference problem is thus addressed via clustering the designed features. We demonstrate with simple baseline supervised methods the competitive performance of the proposed causal inference mechanism under broad connectivity regimes and noise correlation levels, including a real world network. Further, we devise novel technical guarantees of structural consistency for linear NDS under the considered regime., Comment: Accepted at The 38th AAAI Conference on Artificial Intelligence (Main Track). Final Camera-Ready Version

We present P2PL, a practical multi-device peer-to-peer deep learning algorithm that, unlike the federated learning paradigm, does not require coordination from edge servers or the cloud. This makes P2PL well-suited for the sheer scale of beyond-5G computing environments like smart cities that otherwise create range, latency, bandwidth, and single point of failure issues for federated approaches. P2PL introduces max norm synchronization to catalyze training, retains on-device deep model training to preserve privacy, and leverages local inter-device communication to implement distributed consensus. Each device iteratively alternates between two phases: 1) on-device learning and 2) peer-to-peer cooperation where they combine model parameters with nearby devices. We empirically show that all participating devices achieve the same test performance attained by federated and centralized training -- even with 100 devices and relaxed singly stochastic consensus weights. We extend these experimental results to settings with diverse network topologies, sparse and intermittent communication, and non-IID data distributions.

Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to interpret, and endowed with a corpus of mathematical results, rendering them natural candidates to serve as the basis for a theory of processing signals in more irregular domains. In this article, we provide an overview of the evolution of GSP, from its origins to the challenges ahead. The first half is devoted to reviewing the history of GSP and explaining how it gave rise to an encompassing framework that shares multiple similarities with SP. A key message is that GSP has been critical to develop novel and technically sound tools, theory, and algorithms that, by leveraging analogies with and the insights of digital SP, provide new ways to analyze, process, and learn from graph signals. In the second half, we shift focus to review the impact of GSP on other disciplines. First, we look at the use of GSP in data science problems, including graph learning and graph-based deep learning. Second, we discuss the impact of GSP on applications, including neuroscience and image and video processing. We conclude with a brief discussion of the emerging and future directions of GSP.

The paper presents the graph signal processing (GSP) companion model that naturally replicates the basic tenets of classical signal processing (DSP) for GSP. The companion model shows that GSP can be made equivalent to DSP 'plus' appropriate boundary conditions (bc) - this is shown under broad conditions and holds for arbitrary undirected or directed graphs. This equivalence suggests how to broaden GSP - extend naturally a DSP concept to the GSP companion model and then transfer it back to the common graph vertex and graph Fourier domains. The paper shows that GSP unrolls as two distinct models that coincide in DSP, the companion model based on (Hadamard or pointwise) powers of what we will introduce as the spectral frequency vector $\lambda$, and the traditional graph vertex model, based on the adjacency matrix and its eigenvectors. The paper expands GSP in several directions, including showing that convolution in the graph companion model can be achieved with the FFT and that GSP modulation with appropriate choice of carriers exhibits the DSP translation effect that enables multiplexing by modulation of graph signals., Comment: arXiv admin note: text overlap with arXiv:2203.13791

While much effort has been devoted to deriving and analyzing effective convex formulations of signal processing problems, the gradients of convex functions also have critical applications ranging from gradient-based optimization to optimal transport. Recent works have explored data-driven methods for learning convex objective functions, but learning their monotone gradients is seldom studied. In this work, we propose C-MGN and M-MGN, two monotone gradient neural network architectures for directly learning the gradients of convex functions. We show that, compared to state of the art methods, our networks are easier to train, learn monotone gradient fields more accurately, and use significantly fewer parameters. We further demonstrate their ability to learn optimal transport mappings to augment driving image data., Comment: ICASSP 2023 Camera-Ready Version

The article reviews significant advances in networked signal and information processing, which have enabled in the last 25 years extending decision making and inference, optimization, control, and learning to the increasingly ubiquitous environments of distributed agents. As these interacting agents cooperate, new collective behaviors emerge from local decisions and actions. Moreover, and significantly, theory and applications show that networked agents, through cooperation and sharing, are able to match the performance of cloud or federated solutions, while offering the potential for improved privacy, increasing resilience, and saving resources.

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume partial observability, where the state evolution of only a subset of nodes comprising the network is observed. We devise a new feature vector computed from the observed time series and prove that these features are linearly separable, i.e., there exists a hyperplane that separates the cluster of features associated with connected pairs of nodes from those associated with disconnected pairs. This renders the features amenable to train a variety of classifiers to perform causal inference. In particular, we use these features to train Convolutional Neural Networks (CNNs). The resulting causal inference mechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity. The trained CNNs generalize well over structurally distinct networks (dense or sparse) and noise-level profiles. Remarkably, they also generalize well to real-world networks while trained over a synthetic network (realization of a random graph). Finally, the proposed method consistently reconstructs the graph in a pairwise manner, that is, by deciding if an edge or arrow is present or absent in each pair of nodes, from the corresponding time series of each pair. This fits the framework of large-scale systems, where observation or processing of all nodes in the network is prohibitive., Comment: Accepted at The 37th AAAI Conference on Artificial Intelligence (main track)

This paper introduces a $\textit{canonical}$ graph signal model defined by a $\textit{canonical}$ graph and a $\textit{canonical}$ shift, the $\textit{companion}$ graph and the $\textit{companion}$ shift. These are canonical because, under standard conditions, we show that any graph signal processing (GSP) model can be transformed into the canonical model. The transform that obtains this is the graph $z$-transform ($\textrm{G$z$T}$) that we introduce. The GSP canonical model comes closest to the discrete signal processing (DSP) time signal models: the structure of the companion shift decomposes into a line shift and a signal continuation just like the DSP shift and the GSP canonical graph is a directed line graph with a terminal condition reflecting the signal continuation condition. We further show that, surprisingly, in the canonical model, convolution of graph signals is fast convolution by the DSP FFT.

Forecasting graph-based time-dependent data has many practical applications. This task is challenging as models need not only to capture spatial dependency and temporal dependency within the data, but also to leverage useful auxiliary information for accurate predictions. In this paper, we analyze limitations of state-of-the-art models on dealing with temporal dependency. To address this limitation, we propose GSA-Forecaster, a new deep learning model for forecasting graph-based time-dependent data. GSA-Forecaster leverages graph sequence attention (GSA), a new attention mechanism proposed in this paper, for effectively capturing temporal dependency. GSA-Forecaster embeds the graph structure of the data into its architecture to address spatial dependency. GSA-Forecaster also accounts for auxiliary information to further improve predictions. We evaluate GSA-Forecaster with large-scale real-world graph-based time-dependent data and demonstrate its effectiveness over state-of-the-art models with 6.7% RMSE and 5.8% MAPE reduction.

Datasets in the computer vision academic research community are primarily static. Once a dataset is accepted as a benchmark for a computer vision task, researchers working on this task will not alter it in order to make their results reproducible. At the same time, when exploring new tasks and new applications, datasets tend to be an ever changing entity. A practitioner may combine existing public datasets, filter images or objects in them, change annotations or add new ones to fit a task at hand, visualize sample images, or perhaps output statistics in the form of text or plots. In fact, datasets change as practitioners experiment with data as much as with algorithms, trying to make the most out of machine learning models. Given that ML and deep learning call for large volumes of data to produce satisfactory results, it is no surprise that the resulting data and software management associated to dealing with live datasets can be quite complex. As far as we know, there is no flexible, publicly available instrument to facilitate manipulating image data and their annotations throughout a ML pipeline. In this work, we present Shuffler, an open source tool that makes it easy to manage large computer vision datasets. It stores annotations in a relational, human-readable database. Shuffler defines over 40 data handling operations with annotations that are commonly useful in supervised learning applied to computer vision and supports some of the most well-known computer vision datasets. Finally, it is easily extensible, making the addition of new operations and datasets a task that is fast and easy to accomplish.

This paper focuses on finite-time in-network computation of linear transforms of distributed graph data. Finite-time transform computation problems are of interest in graph-based computing and signal processing applications in which the objective is to compute, by means of distributed iterative methods, various (linear) transforms of the data distributed at the agents or nodes of the graph. While finite-time computation of consensus-type or more generally rank-one transforms have been studied, systematic approaches toward scalable computing of general linear transforms, specifically in the case of heterogeneous agent objectives in which each agent is interested in obtaining a different linear combination of the network data, are relatively less explored. In this paper, by employing ideas from algebraic geometry, we develop a systematic characterization of linear transforms that are amenable to distributed in-network computation in finite-time using linear iterations. Further, we consider the general case of directed inter-agent communication graphs. Specifically, it is shown that \emph{almost all} linear transformations of data distributed on the nodes of a digraph containing a Hamiltonian cycle may be computed using at most $N$ linear distributed iterations. Finally, by studying an associated matrix factorization based reformulation of the transform computation problem, we obtain, as a by-product, certain results and characterizations on sparsity-constrained matrix factorization that are of independent interest., Comment: Presented at the 54th Annual Asilomar Conference on Signals, Systems, and Computers, 2020

Vertex based and spectral based GSP sampling has been studied recently. The literature recognizes that methods in one domain do not have a counterpart in the other domain. This paper shows that in fact one can develop a unified graph signal sampling theory with analogous interpretations in both domains just like sampling in traditional DSP. To achieve it, we introduce a spectral shift $M$ acting in the spectral domain rather than shift $A$ that acts in the vertex domain. This leads to a GSP theory that starts from the spectral domain, for example, linear shift invariant (LSI) filtering in the spectral domain is with polynomials $P(M)$. We then develop GSP vertex and spectral domain dual versions for each of the four standard sampling steps of subsampling, decimation, upsampling, and interpolation. We show how GSP sampling reduces to DSP sampling when the graph is the directed time cycle graph. Simple examples illustrate the impact of choices that are available in GSP sampling., Comment: V2: Added missing space in arXiv title, V3: Revised paper following journal review

Unsupervised time series clustering is a challenging problem with diverse industrial applications such as anomaly detection, bio-wearables, etc. These applications typically involve small, low-power devices on the edge that collect and process real-time sensory signals. State-of-the-art time-series clustering methods perform some form of loss minimization that is extremely computationally intensive from the perspective of edge devices. In this work, we propose a neuromorphic approach to unsupervised time series clustering based on Temporal Neural Networks that is capable of ultra low-power, continuous online learning. We demonstrate its clustering performance on a subset of UCR Time Series Archive datasets. Our results show that the proposed approach either outperforms or performs similarly to most of the existing algorithms while being far more amenable for efficient hardware implementation. Our hardware assessment analysis shows that in 7 nm CMOS the proposed architecture, on average, consumes only about 0.005 mm^2 die area and 22 uW power and can process each signal with about 5 ns latency., Comment: Accepted for publication at ICASSP 2021

Graph neural networks (GNNs) extend convolutional neural networks (CNNs) to graph-based data. A question that arises is how much performance improvement does the underlying graph structure in the GNN provide over the CNN (that ignores this graph structure). To address this question, we introduce edge entropy and evaluate how good an indicator it is for possible performance improvement of GNNs over CNNs. Our results on node classification with synthetic and real datasets show that lower values of edge entropy predict larger expected performance gains of GNNs over CNNs, and, conversely, higher edge entropy leads to expected smaller improvement gains.

Deep learning has achieved great success in recognizing video actions, but the collection and annotation of training data are still quite laborious, which mainly lies in two aspects: (1) the amount of required annotated data is large; (2) temporally annotating the location of each action is time-consuming. Works such as few-shot learning or untrimmed video recognition have been proposed to handle either one aspect or the other. However, very few existing works can handle both issues simultaneously. In this paper, we target a new problem, Annotation-Efficient Video Recognition, to reduce the requirement of annotations for both large amount of samples and the action location. Such problem is challenging due to two aspects: (1) the untrimmed videos only have weak supervision; (2) video segments not relevant to current actions of interests (background, BG) could contain actions of interests (foreground, FG) in novel classes, which is a widely existing phenomenon but has rarely been studied in few-shot untrimmed video recognition. To achieve this goal, by analyzing the property of BG, we categorize BG into informative BG (IBG) and non-informative BG (NBG), and we propose (1) an open-set detection based method to find the NBG and FG, (2) a contrastive learning method to learn IBG and distinguish NBG in a self-supervised way, and (3) a self-weighting mechanism for the better distinguishing of IBG and FG. Extensive experiments on ActivityNet v1.2 and ActivityNet v1.3 verify the rationale and effectiveness of the proposed methods.

Existing few-shot learning (FSL) methods usually assume base classes and novel classes are from the same domain (in-domain setting). However, in practice, it may be infeasible to collect sufficient training samples for some special domains to construct base classes. To solve this problem, cross-domain FSL (CDFSL) is proposed very recently to transfer knowledge from general-domain base classes to special-domain novel classes. Existing CDFSL works mostly focus on transferring between near domains, while rarely consider transferring between distant domains, which is in practical need as any novel classes could appear in real-world applications, and is even more challenging. In this paper, we study a challenging subset of CDFSL where the novel classes are in distant domains from base classes, by revisiting the mid-level features, which are more transferable yet under-explored in main stream FSL work. To boost the discriminability of mid-level features, we propose a residual-prediction task to encourage mid-level features to learn discriminative information of each sample. Notably, such mechanism also benefits the in-domain FSL and CDFSL in near domains. Therefore, we provide two types of features for both cross- and in-domain FSL respectively, under the same training framework. Experiments under both settings on six public datasets, including two challenging medical datasets, validate the our rationale and demonstrate state-of-the-art performance. Code will be released.

Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying graph structure, as in social, biological, and many other domains. This paper explores 1)how graph signal processing (GSP) can be used to extend CNN components to graphs in order to improve model performance; and 2)how to design the graph CNN architecture based on the topology or structure of the data graph., Comment: To be published on IEEE Signal Processing Magazine

Few-shot learning (FSL) aims at recognizing novel classes given only few training samples, which still remains a great challenge for deep learning. However, humans can easily recognize novel classes with only few samples. A key component of such ability is the compositional recognition that human can perform, which has been well studied in cognitive science but is not well explored in FSL. Inspired by such capability of humans, to imitate humans' ability of learning visual primitives and composing primitives to recognize novel classes, we propose an approach to FSL to learn a feature representation composed of important primitives, which is jointly trained with two parts, i.e. primitive discovery and primitive enhancing. In primitive discovery, we focus on learning primitives related to object parts by self-supervision from the order of image splits, avoiding extra laborious annotations and alleviating the effect of semantic gaps. In primitive enhancing, inspired by current studies on the interpretability of deep networks, we provide our composition view for the FSL baseline model. To modify this model for effective composition, inspired by both mathematical deduction and biological studies (the Hebbian Learning rule and the Winner-Take-All mechanism), we propose a soft composition mechanism by enlarging the activation of important primitives while reducing that of others, so as to enhance the influence of important primitives and better utilize these primitives to compose novel classes. Extensive experiments on public benchmarks are conducted on both the few-shot image classification and video recognition tasks. Our method achieves the state-of-the-art performance on all these datasets and shows better interpretability.

A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help practitioners know when to use which explanation function. This paper proposes quantitative evaluation criteria for feature-based explanations: low sensitivity, high faithfulness, and low complexity. We devise a framework for aggregating explanation functions. We develop a procedure for learning an aggregate explanation function with lower complexity and then derive a new aggregate Shapley value explanation function that minimizes sensitivity., Comment: Accepted at IJCAI 2020

Graph convolutional neural networks (GCNNs) are a powerful extension of deep learning techniques to graph-structured data problems. We empirically evaluate several pooling methods for GCNNs, and combinations of those graph pooling methods with three different architectures: GCN, TAGCN, and GraphSAGE. We confirm that graph pooling, especially DiffPool, improves classification accuracy on popular graph classification datasets and find that, on average, TAGCN achieves comparable or better accuracy than GCN and GraphSAGE, particularly for datasets with larger and sparser graph structures., Comment: 5 pages, 2 figures, 2019 Asilomar Conference paper

The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based variant of classical SGD. We discuss local minima convergence guarantees and explore the simple but critical role of the stable-manifold theorem in analyzing saddle-point avoidance. For global optimization, we discuss annealing-based methods in which slowly decaying noise is added to D-SGD. Conditions are discussed under which convergence to global minima is guaranteed. Numerical examples illustrate the key concepts in the paper.

In Graph Signal Processing (GSP), data dependencies are represented by a graph whose nodes label the data and the edges capture dependencies among nodes. The graph is represented by a weighted adjacency matrix $A$ that, in GSP, generalizes the Discrete Signal Processing (DSP) shift operator $z^{-1}$. The (right) eigenvectors of the shift $A$ (graph spectral components) diagonalize $A$ and lead to a graph Fourier basis $F$ that provides a graph spectral representation of the graph signal. The inverse of the (matrix of the) graph Fourier basis $F$ is the Graph Fourier transform (GFT), $F^{-1}$. Often, including in real world examples, this diagonalization is numerically unstable. This paper develops an approach to compute an accurate approximation to $F$ and $F^{-1}$, while insuring their numerical stability, by means of solving a non convex optimization problem. To address the non-convexity, we propose an algorithm, the stable graph Fourier basis algorithm (SGFA) that we prove to exponentially increase the accuracy of the approximating $F$ per iteration. Likewise, we can apply SGFA to $A^H$ and, hence, approximate the stable left eigenvectors for the graph shift $A$ and directly compute the GFT. We evaluate empirically the quality of SGFA by applying it to graph shifts $A$ drawn from two real world problems, the 2004 US political blogs graph and the Manhattan road map, carrying out a comprehensive study on tradeoffs between different SGFA parameters. We also confirm our conclusions by applying SGFA on very sparse and very dense directed Erd\H os-R\'enyi graphs., Comment: 16 pages, 17 figures. Originally submitted in -IEEE Transactions on Signal Processing- on 01-Aug-2019. Resubmitted on 12-Jan-2020. Accept with mandatory minor revisions. Resubmitted again on 30-April-2020

The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original (primal) variable, wherein constraints satisfaction is controlled via the so-called dual variables. ALM is highly flexible with respect to how primal sub-problems can be solved, giving rise to a plethora of different primal-dual methods. The powerful ALM mechanism has recently proved to be very successful in various large scale and distributed applications. In addition, several significant advances have appeared, primarily on precise complexity results with respect to computational and communication costs in the presence of inexact updates and design and analysis of novel optimal methods for distributed consensus optimization. We provide a tutorial-style introduction to ALM and its variants for solving convex optimization problems in large scale and distributed settings. We describe control-theoretic tools for the algorithms' analysis and design, survey recent results, and provide novel insights in the context of two emerging applications: federated learning and distributed energy trading.

To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation, convolution, and sampling of graph signals as appropriate natural extensions of the corresponding DSP concepts. To define these for both the vertex and the graph frequency domains, we associate with generic data graph G and its graph shift A, a graph spectral shift M and a spectral graph Gs. This leads to a spectral GSP theory that parallels in the graph frequency domain the existing GSP theory in the vertex domain. The paper applies this to design and recovery sampling techniques for data supported by arbitrary directed graphs.

This paper studies the resilient distributed recovery of large fields under measurement attacks, by a team of agents, where each measures a small subset of the components of a large spatially distributed field. An adversary corrupts some of the measurements. The agents collaborate to process their measurements, and each is interested in recovering only a fraction of the field. We present a field recovery consensus+innovations type distributed algorithm that is resilient to measurement attacks, where an agent maintains and updates a local state based on its neighbors states and its own measurement. Under sufficient conditions on the attacker and the connectivity of the communication network, each agent's state, even those with compromised measurements, converges to the true value of the field components that it is interested in recovering. Finally, we illustrate the performance of our algorithm through numerical examples.

Explainable machine learning offers the potential to provide stakeholders with insights into model behavior by using various methods such as feature importance scores, counterfactual explanations, or influential training data. Yet there is little understanding of how organizations use these methods in practice. This study explores how organizations view and use explainability for stakeholder consumption. We find that, currently, the majority of deployments are not for end users affected by the model but rather for machine learning engineers, who use explainability to debug the model itself. There is thus a gap between explainability in practice and the goal of transparency, since explanations primarily serve internal stakeholders rather than external ones. Our study synthesizes the limitations of current explainability techniques that hamper their use for end users. To facilitate end user interaction, we develop a framework for establishing clear goals for explainability. We end by discussing concerns raised regarding explainability., Comment: ACM Conference on Fairness, Accountability, and Transparency 2020

Spatial and time-dependent data is of interest in many applications. This task is difficult due to its complex spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. To address these challenges, we propose Forecaster, a graph Transformer architecture. Specifically, we start by learning the structure of the graph that parsimoniously represents the spatial dependency between the data at different locations. Based on the topology of the graph, we sparsify the Transformer to account for the strength of spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. We evaluate Forecaster in the problem of forecasting taxi ride-hailing demand and show that our proposed architecture significantly outperforms the state-of-the-art baselines.

The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging to the set of global minima under certain technical assumptions. The paper presents simple methods for verifying that the required technical assumptions hold and illustrates it with a distributed target-localization application.

We study resilient distributed field estimation under measurement attacks. A network of agents or devices measures a large, spatially distributed physical field parameter. An adversary arbitrarily manipulates the measurements of some of the agents. Each agent's goal is to process its measurements and information received from its neighbors to estimate only a few specific components of the field. We present $\mathbf{SAFE}$, the Saturating Adaptive Field Estimator, a consensus+innovations distributed field estimator that is resilient to measurement attacks. Under sufficient conditions on the compromised measurement streams, the physical coupling between the field and the agents' measurements, and the connectivity of the cyber communication network, $\mathbf{SAFE}$ guarantees that each agent's estimate converges almost surely to the true value of the components of the parameter in which the agent is interested. Finally, we illustrate the performance of $\mathbf{SAFE}$ through numerical examples.

The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is assumed to possess a local objective function (assumed to be smooth, but possibly nonconvex). The paper considers algorithms for optimizing the sum function. A distributed algorithm of the consensus+innovations type is proposed which relies on first-order information at the agent level. Under appropriate conditions on network connectivity and the cost objective, convergence to the set of global optima is achieved by an annealing-type approach, with decaying Gaussian noise independently added into each agent's update step. It is shown that the proposed algorithm converges in probability to the set of global minima of the sum function.

Visual Dialog is a multimodal task of answering a sequence of questions grounded in an image, using the conversation history as context. It entails challenges in vision, language, reasoning, and grounding. However, studying these subtasks in isolation on large, real datasets is infeasible as it requires prohibitively-expensive complete annotation of the 'state' of all images and dialogs. We develop CLEVR-Dialog, a large diagnostic dataset for studying multi-round reasoning in visual dialog. Specifically, we construct a dialog grammar that is grounded in the scene graphs of the images from the CLEVR dataset. This combination results in a dataset where all aspects of the visual dialog are fully annotated. In total, CLEVR-Dialog contains 5 instances of 10-round dialogs for about 85k CLEVR images, totaling to 4.25M question-answer pairs. We use CLEVR-Dialog to benchmark performance of standard visual dialog models; in particular, on visual coreference resolution (as a function of the coreference distance). This is the first analysis of its kind for visual dialog models that was not possible without this dataset. We hope the findings from CLEVR-Dialog will help inform the development of future models for visual dialog. Our dataset and code are publicly available., Comment: 13 pages, 11 figures, 3 tables, accepted as a short paper at NAACL 2019

Current approaches for explaining machine learning models fall into two distinct classes: antecedent event influence and value attribution. The former leverages training instances to describe how much influence a training point exerts on a test point, while the latter attempts to attribute value to the features most pertinent to a given prediction. In this work, we discuss an algorithm, AVA: Aggregate Valuation of Antecedents, that fuses these two explanation classes to form a new approach to feature attribution that not only retrieves local explanations but also captures global patterns learned by a model. Our experimentation convincingly favors weighting and aggregating feature attributions via AVA., Comment: In AAAI-19 Workshop on Network Interpretability for Deep Learning

In this paper, we present a new approach to interpret deep learning models. By coupling mutual information with network science, we explore how information flows through feedforward networks. We show that efficiently approximating mutual information allows us to create an information measure that quantifies how much information flows between any two neurons of a deep learning model. To that end, we propose NIF, Neural Information Flow, a technique for codifying information flow that exposes deep learning model internals and provides feature attributions., Comment: ICASSP 2020 (shorter version appeared at AAAI-19 Workshop on Network Interpretability for Deep Learning)

This paper studies resilient distributed estimation under measurement attacks. A set of agents each makes successive local, linear, noisy measurements of an unknown vector field collected in a vector parameter. The local measurement models are heterogeneous across agents and may be locally unobservable for the unknown parameter. An adversary compromises some of the measurement streams and changes their values arbitrarily. The agents' goal is to cooperate over a peer-to-peer communication network to process their (possibly compromised) local measurements and estimate the value of the unknown vector parameter. We present SAGE, the Saturating Adaptive Gain Estimator, a distributed, recursive, consensus+innovations estimator that is resilient to measurement attacks. We demonstrate that, as long as the number of compromised measurement streams is below a particular bound, then, SAGE guarantees that all of the agents' local estimates converge almost surely to the value of the parameter. The resilience of the estimator -- i.e., the number of compromised measurement streams it can tolerate -- does not depend on the topology of the inter-agent communication network. Finally, we illustrate the performance of SAGE through numerical examples.

Visual dialog entails answering a series of questions grounded in an image, using dialog history as context. In addition to the challenges found in visual question answering (VQA), which can be seen as one-round dialog, visual dialog encompasses several more. We focus on one such problem called visual coreference resolution that involves determining which words, typically noun phrases and pronouns, co-refer to the same entity/object instance in an image. This is crucial, especially for pronouns (e.g., `it'), as the dialog agent must first link it to a previous coreference (e.g., `boat'), and only then can rely on the visual grounding of the coreference `boat' to reason about the pronoun `it'. Prior work (in visual dialog) models visual coreference resolution either (a) implicitly via a memory network over history, or (b) at a coarse level for the entire question; and not explicitly at a phrase level of granularity. In this work, we propose a neural module network architecture for visual dialog by introducing two novel modules - Refer and Exclude - that perform explicit, grounded, coreference resolution at a finer word level. We demonstrate the effectiveness of our model on MNIST Dialog, a visually simple yet coreference-wise complex dataset, by achieving near perfect accuracy, and on VisDial, a large and challenging visual dialog dataset on real images, where our model outperforms other approaches, and is more interpretable, grounded, and consistent qualitatively., Comment: ECCV 2018 + results on VisDial v1.0 dataset

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the underlying data generation, the direct interactions between measured entities, and the indirect effects of unmeasured processes on the observed data. The learning is posed as regularized empirical risk minimization. Details of the algorithm for learning the model are outlined. Experiments demonstrate the performance of the learned model on real data., Comment: arXiv admin note: substantial text overlap with arXiv:1705.03536

The growth in the number of devices connected to the Internet of Things (IoT) poses major challenges in security. The integrity and trustworthiness of data and data analytics are increasingly important concerns in IoT applications. These are compounded by the highly distributed nature of IoT devices, making it infeasible to prevent attacks and intrusions on all data sources. Adversaries may hijack devices and compromise their data. As a result, reactive countermeasures, such as intrusion detection and resilient analytics, become vital components of security. This paper overviews algorithms for secure distributed inference in IoT.

Many applications donot have the benefit of the laws of physics to derive succinct descriptive models for observed data. In alternative, interdependencies among $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are nowadays often captured by a graph or network $G$ that in practice may be very large. The network itself may change over time as well (i.e., as $G_k$). Tracking brute force the changes of time varying networks presents major challenges, including the associated computational problems. Further, a large set of networks may not lend itself to useful analysis. This paper approximates the time varying networks $\left\{G_k\right\}$ as weighted linear combinations of eigennetworks. The eigennetworks are fixed building blocks that are estimated by first learning the time series of graphs $G_k$ from the data $\{ x_{nk}, k>0 \}_{n=1}^{N}$, followed by a Principal Network Analysis procedure. The weights of the eigennetwork representation are eigenfeatures and the time varying networks $\left\{G_k\right\}$ describe a trajectory in eigennetwork space. These eigentrajectories should be smooth since the networks $G_k$ vary at a much slower rate than the data $x_{nk}$, except when structural network shifts occur reflecting potentially an abrupt change in the underlying application and sources of the data. Algorithms for learning the time series of graphs $\left\{G_k\right\}$, deriving the eigennetworks, eigenfeatures and eigentrajectories, and detecting changepoints are presented. Experiments on simulated data and with two real time series data (a voting record of the US senate and genetic expression data for the \textit{Drosophila Melanogaster} as it goes through its life cycle) demonstrate the performance of the learning and provide interesting interpretations of the eigennetworks.

Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically elude analysis, predictable spectral asymptotics can emerge for large scale networks. Previously published works successfully analyze large-scale networks described by undirected graphs and directed graphs with transpose-symmetric distributions, focusing on consensus acceleration filter design for time-invariant networks as an application. This work expands upon these results by enabling analysis of certain large-scale directed networks described by transpose-asymmetric distributions. Specifically, efficiently computable spectral density approximations are possible for transpose-asymmetric percolation network models with node-transitive symmetry group and normal mean matrix. Numerical simulations support the derived approximations and application to consensus filters.

Optimal design of consensus acceleration graph filters relates closely to the eigenvalues of the consensus iteration matrix. This task is complicated by random networks with uncertain iteration matrix eigenvalues. Filter design methods based on the spectral asymptotics of consensus iteration matrices for large-scale, random undirected networks have been previously developed both for constant and for time-varying network topologies. This work builds upon these results by extending analysis to large-scale, constant, random directed networks. The proposed approach uses theorems by Girko that analytically produce deterministic approximations of the empirical spectral distribution for suitable non-Hermitian random matrices. The approximate empirical spectral distribution defines filtering regions in the proposed filter optimization problem, which must be modified to accommodate complex-valued eigenvalues. Presented numerical simulations demonstrate good results. Additionally, limitations of the proposed method are discussed.

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to the graph shift operator, polynomial functions of the shift matrix perform filtering. An application considered in this paper, convergence acceleration filters for distributed average consensus may be viewed as lowpass graph filters periodically applied to the states. Design of graph filters depends on the shift matrix eigendecomposition. Consequently, random graphs present a challenge as this information is often difficult to obtain. Nevertheless, the asymptotic behavior of the shift matrix empirical spectral distribution provides a substitute for suitable random matrix models. This paper employs deterministic approximations for empirical spectral statistics from other works to propose optimization criteria for consensus acceleration filters, evaluating the results through simulation., Comment: 2017 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017)

Fifth generation~(5G) networks providing much higher bandwidth and faster data rates will allow connecting vast number of static and mobile devices, sensors, agents, users, machines, and vehicles, supporting Internet-of-Things (IoT), real-time dynamic networks of mobile things. Positioning and location awareness will become increasingly important, enabling deployment of new services and contributing to significantly improving the overall performance of the 5G~system. Many of the currently talked about solutions to positioning in~5G are centralized, mostly requiring direct line-of-sight (LoS) to deployed access nodes or anchors at the same time, which in turn requires high-density deployments of anchors. But these LoS and centralized positioning solutions may become unwieldy as the number of users and devices continues to grow without limit in sight. As an alternative to the centralized solutions, this paper discusses distributed localization in a 5G enabled IoT environment where many low power devices, users, or agents are to locate themselves without global or LoS access to anchors. Even though positioning is essentially a non-linear problem (solving circle equations by trilateration or triangulation), we discuss a cooperative \textit{linear} distributed iterative solution with only local measurements, communication and computation needed at each agent. Linearity is obtained by reparametrization of the agent location through barycentric coordinate representations based on local neighborhood geometry that may be computed in terms of certain Cayley-Menger determinants involving relative local inter-agent distance measurements., Comment: Technical Report