On Non-Interactive Simulation of Distributed Sources with Finite Alphabets

This work presents a Fourier analysis framework for the non-interactive source simulation (NISS) problem. Two distributed agents observe a pair of sequences $X^d$ and $Y^d$ drawn according to a joint distribution $P_{X^dY^d}$. The agents aim to generate outputs $U=f_d(X^d)$ and $V=g_d(Y^d)$ with a joint distribution sufficiently close in total variation to a target distribution $Q_{UV}$. Existing works have shown that the NISS problem with finite-alphabet outputs is decidable. For the binary-output NISS, an upper-bound to the input complexity was derived which is $O(\exp\operatorname{poly}(\frac{1}{\epsilon}))$. In this work, the input complexity and algorithm design are addressed in several classes of NISS scenarios. For binary-output NISS scenarios with doubly-symmetric binary inputs, it is shown that the input complexity is $\Theta(\log{\frac{1}{\epsilon}})$, thus providing a super-exponential improvement in input complexity. An explicit characterization of the simulating pair of functions is provided. For general finite-input scenarios, a constructive algorithm is introduced that explicitly finds the simulating functions $(f_d(X^d),g_d(Y^d))$. The approach relies on a novel Fourier analysis framework. Various numerical simulations of NISS scenarios with IID inputs are provided. Furthermore, to illustrate the general applicability of the Fourier framework, several examples with non-IID inputs, including entanglement-assisted NISS and NISS with Markovian inputs are provided.

PAC Learnability under Explanation-Preserving Graph Perturbations

Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs, enabling the model to leverage the complex relationships and dependencies in graph-structured data. A graph explanation is a subgraph which is an `almost sufficient' statistic of the input graph with respect to its classification label. Consequently, the classification label is invariant, with high probability, to perturbations of graph edges not belonging to its explanation subgraph. This work considers two methods for leveraging such perturbation invariances in the design and training of GNNs. First, explanation-assisted learning rules are considered. It is shown that the sample complexity of explanation-assisted learning can be arbitrarily smaller than explanation-agnostic learning. Next, explanation-assisted data augmentation is considered, where the training set is enlarged by artificially producing new training samples via perturbation of the non-explanation edges in the original training set. It is shown that such data augmentation methods may improve performance if the augmented data is in-distribution, however, it may also lead to worse sample complexity compared to explanation-agnostic learning rules if the augmented data is out-of-distribution. Extensive empirical evaluations are provided to verify the theoretical analysis.

Non-Linear Analog Processing Gains in Task-Based Quantization

In task-based quantization, a multivariate analog signal is transformed into a digital signal using a limited number of low-resolution analog-to-digital converters (ADCs). This process aims to minimize a fidelity criterion, which is assessed against an unobserved task variable that is correlated with the analog signal. The scenario models various applications of interest such as channel estimation, medical imaging applications, and object localization. This work explores the integration of analog processing components -- such as analog delay elements, polynomial operators, and envelope detectors -- prior to ADC quantization. Specifically, four scenarios, involving different collections of analog processing operators are considered: (i) arbitrary polynomial operators with analog delay elements, (ii) limited-degree polynomial operators, excluding delay elements, (iii) sequences of envelope detectors, and (iv) a combination of analog delay elements and linear combiners. For each scenario, the minimum achievable distortion is quantified through derivation of computable expressions in various statistical settings. It is shown that analog processing can significantly reduce the distortion in task reconstruction. Numerical simulations in a Gaussian example are provided to give further insights into the aforementioned analog processing gains.

Factorized Explainer for Graph Neural Networks

Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. To open the black-box of these deep learning models, post-hoc instance-level explanation methods have been proposed to understand GNN predictions. These methods seek to discover substructures that explain the prediction behavior of a trained GNN. In this paper, we show analytically that for a large class of explanation tasks, conventional approaches, which are based on the principle of graph information bottleneck (GIB), admit trivial solutions that do not align with the notion of explainability. Instead, we argue that a modified GIB principle may be used to avoid the aforementioned trivial solutions. We further introduce a novel factorized explanation model with theoretical performance guarantees. The modified GIB is used to analyze the structural properties of the proposed factorized explainer. We conduct extensive experiments on both synthetic and real-world datasets to validate the effectiveness of our proposed factorized explainer over existing approaches.

Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including $Fid_+$, $Fid_-$, and $Fid_\Delta$. Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics.

Capacity Gains in MIMO Systems with Few-Bit ADCs Using Nonlinear Analog Operators

Analog to Digital Converters (ADCs) are a major contributor to the power consumption of multiple-input multiple-output (MIMO) receivers with large antenna arrays operating in the millimeter wave and terahertz carrier frequencies. This is especially the case in large bandwidth terahertz communication systems, due to the sudden drop in energy-efficiency of ADCs as the sampling rate is increased above 100MHz. Two mitigating energy-efficient approaches which have received significant recent interest are i) to reduce the number of ADCs via analog and hybrid beamforming architectures, and ii) to reduce the resolution of the ADCs which in turn decreases power consumption. However, decreasing the number and resolution of ADCs leads to performance loss -- in terms of achievable rates -- due to increased quantization error. In this work, we study the application of practically implementable nonlinear analog operators such as envelop detectors and polynomial operators, prior to sampling and quantization at the ADCs, as a way to mitigate the aforementioned rate-loss. A receiver architecture consisting of linear analog combiners, nonlinear analog operators, and few-bit ADCs is designed. The fundamental information theoretic performance limits of the resulting communication system, in terms of achievable rates, are investigated under various assumptions on the set of implementable analog operators. Various numerical evaluations and simulations of the communication system are provided to compare the set of achievable rates under different architecture designs and parameters. Circuit simulations {in a 65 nm CMOS technology} exhibiting the generation of envelope detectors and polynomial operators are provided, and their power consumption is compared.

Optimal Distributed Fault-Tolerant Sensor Fusion: Fundamental Limits and Efficient Algorithms

Distributed estimation is a fundamental problem in signal processing which finds applications in a variety of scenarios of interest including distributed sensor networks, robotics, group decision problems, and monitoring and surveillance applications. The problem considers a scenario where distributed agents are given a set of measurements, and are tasked with estimating a target variable. This work considers distributed estimation in the context of sensor networks, where a subset of sensor measurements are faulty and the distributed agents are agnostic to these faulty sensor measurements. The objective is to minimize i) the mean square error in estimating the target variable at each node (accuracy objective), and ii) the mean square distance between the estimates at each pair of nodes (consensus objective). It is shown that there is an inherent tradeoff between satisfying the former and latter objectives. The tradeoff is explicitly characterized and the fundamental performance limits are derived under specific statistical assumptions on the sensor output statistics. Assuming a general stochastic model, the sensor fusion algorithm optimizing this tradeoff is characterized through a computable optimization problem. Finding the optimal sensor fusion algorithm is computationally complex. To address this, a general class of low-complexity Brooks-Iyengar Algorithms are introduced, and their performance, in terms of accuracy and consensus objectives, is compared to that of optimal linear estimators through case study simulations of various scenarios.

Quantifying the Capacity Gains in Coarsely Quantized SISO Systems with Nonlinear Analog Operators

The power consumption of high-speed, high-resolution analog to digital converters (ADCs) is a limiting factor in implementing large-bandwidth mm-wave communication systems. A mitigating solution, which has drawn considerable recent interest, is to use a few low-resolution ADCs at the receiver. While reducing the number and resolution of the ADCs decreases power consumption, it also leads to a reduction in channel capacity due to the information loss induced by coarse quantization. This implies a rate-energy tradeoff governed by the number and resolution of ADCs. Recently, it was shown that given a fixed number of low-resolution ADCs, the application of practically implementable nonlinear analog operators, prior to sampling and quantization, may significantly reduce the aforementioned rate-loss. Building upon these observations, this work focuses on single-input single-output (SISO) communication scenarios, and i) characterizes capacity expressions under various assumptions on the set of implementable nonlinear analog functions, ii) provides computational methods to calculate the channel capacity numerically, and iii) quantifies the gains due to the use of nonlinear operators in SISO receiver terminals. Furthermore, circuit-level simulations, using a 65 nm Bulk CMOS technology, are provided to show the implementability of the desired nonlinear operators in the analog domain. The power requirements of the proposed circuits are quantified for various analog operators.

Lattices from Linear Codes: Source and Channel Networks

In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework is presented which involves fine discretization of the source and channel variables followed by communication over the resulting discretized network. In order to evaluate fundamental performance limits, convergence results for information measures are provided under the proposed discretization process. Using this framework, we consider point-to-point source coding and channel coding with side-information, distributed source coding with distortion constraints, the function reconstruction problems (two-help-one), computation over multiple access channel, the interference channel, and the multiple-descriptions source coding problem. We construct lattice-like codes for general sources and channels, and derive inner-bounds to set of achievable rates and distortions in these communication scenarios.

MIMO Systems with One-bit ADCs: Capacity Gains using Nonlinear Analog Operations

Analog to Digital Converters (ADCs) are a major contributor to the energy consumption on the receiver side of millimeter-wave multiple-input multiple-output (MIMO) systems with large antenna arrays. Consequently, there has been significant interest in using low-resolution ADCs along with hybrid beam-forming at MIMO receivers for energy efficiency. However, decreasing the ADC resolution results in performance loss -- in terms of achievable rates -- due to increased quantization error. In this work, we study the application of practically implementable nonlinear analog operations, prior to sampling and quantization at the ADCs, as a way to mitigate the aforementioned rate-loss. A receiver architecture consisting of linear analog combiners, implementable nonlinear analog operators, and one-bit threshold ADCs is designed. The fundamental information theoretic performance limits of the resulting communication system, in terms of achievable rates, are investigated under various assumptions on the set of implementable nonlinear analog functions. In order to justify the feasibility of the nonlinear operations in the proposed receiver architecture, an analog circuit is introduced, and circuit simulations exhibiting the generation of the desired nonlinear analog operations are provided.