Sundeep Rangan

Sravan Reddy Chintareddy, Marco Mezzavilla, Sundeep Rangan et al.

The ever-growing demand for mobile data necessitates a transport network architecture that can withstand the 5G-and-beyond multi-Gbps traffic requirements. To cater for such unprecedented demand, studies are being conducted to incorporate TeraHertz (THz) communications in future mobile networks. In this paper, we consider an urban environment and evaluate the feasibility of THz wireless midhaul links for the transport networks between the Central Units (CU) and Distributed Units (DU) in a disaggregated 5G network architecture with functional splits. Our goal is to study the feasibility of midhaul links at 140 GHz by minimizing the number of required CUs to serve all the DUs. To this end, we define several policies for selecting CU and DU nodes in order to determine the peak data rate that can be supported over each link between a CU and DU. Our numerical results based on ray-tracing suggest that wireless links at 140 GHz with 3GPP option 2 as High Layer Split (HLS) represents a promising technology for midhaul transport networks.

Yu Li, Yuchen Zheng, Giles Hamilton-Fletcher et al.

This paper investigates the potential of vision-language models (VLMs) to assist people with blindness and low vision (pBLV) in navigation tasks. We evaluate state-of-the-art closed-source models, including GPT-4V, GPT-4o, Gemini-1.5-Pro, and Claude-3.5-Sonnet, alongside open-source models, such as Llava-v1.6-mistral and Llava-onevision-qwen, to analyze their capabilities in foundational visual skills: counting ambient obstacles, relative spatial reasoning, and common-sense wayfinding-pertinent scene understanding. We further assess their performance in navigation scenarios, using pBLV-specific prompts designed to simulate real-world assistance tasks. Our findings reveal notable performance disparities between these models: GPT-4o consistently outperforms others across all tasks, particularly in spatial reasoning and scene understanding. In contrast, open-source models struggle with nuanced reasoning and adaptability in complex environments. Common challenges include difficulties in accurately counting objects in cluttered settings, biases in spatial reasoning, and a tendency to prioritize object details over spatial feedback, limiting their usability for pBLV in navigation tasks. Despite these limitations, VLMs show promise for wayfinding assistance when better aligned with human feedback and equipped with improved spatial reasoning. This research provides actionable insights into the strengths and limitations of current VLMs, guiding developers on effectively integrating VLMs into assistive technologies while addressing key limitations for enhanced usability.

Evan Becker, Parthe Pandit, Sundeep Rangan et al.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the $\textit{Isolated Points Model}$ is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

Tao Li, Haozhe Lei, Hao Guo et al.

Millimeter-wave (mmWave) communication is a vital component of future generations of mobile networks, offering not only high data rates but also precise beams, making it ideal for indoor navigation in complex environments. However, the challenges of multipath propagation and noisy signal measurements in indoor spaces complicate the use of mmWave signals for navigation tasks. Traditional physics-based methods, such as following the angle of arrival (AoA), often fall short in complex scenarios, highlighting the need for more sophisticated approaches. Digital twins, as virtual replicas of physical environments, offer a powerful tool for simulating and optimizing mmWave signal propagation in such settings. By creating detailed, physics-based models of real-world spaces, digital twins enable the training of machine learning algorithms in virtual environments, reducing the costs and limitations of physical testing. Despite their advantages, current machine learning models trained in digital twins often overfit specific virtual environments and require costly retraining when applied to new scenarios. In this paper, we propose a Physics-Informed Reinforcement Learning (PIRL) approach that leverages the physical insights provided by digital twins to shape the reinforcement learning (RL) reward function. By integrating physics-based metrics such as signal strength, AoA, and path reflections into the learning process, PIRL enables efficient learning and improved generalization to new environments without retraining. Our experiments demonstrate that the proposed PIRL, supported by digital twin simulations, outperforms traditional heuristics and standard RL models, achieving zero-shot generalization in unseen environments and offering a cost-effective, scalable solution for wireless indoor navigation.

Mingsheng Yin, Yaqi Hu, Tommy Azzino et al.

Site-specific radio frequency (RF) propagation prediction increasingly relies on models built from visual data such as cameras and LIDAR sensors. When operating in dynamic settings, the environment may only be partially observed. This paper introduces a method to extract statistical channel models, given partial observations of the surrounding environment. We propose a simple heuristic algorithm that performs ray tracing on the partial environment and then uses machine-learning trained predictors to estimate the channel and its uncertainty from features extracted from the partial ray tracing results. It is shown that the proposed method can interpolate between fully statistical models when no partial information is available and fully deterministic models when the environment is completely observed. The method can also capture the degree of uncertainty of the propagation predictions depending on the amount of region that has been explored. The methodology is demonstrated in a robotic navigation application simulated on a set of indoor maps with detailed models constructed using state-of-the-art navigation, simultaneous localization and mapping (SLAM), and computer vision methods.

Oscar Stenhammar, Sundeep Rangan, Gábor Fodor et al.

The integration of accurate and reproducible wireless network simulations is a key enabler for research on open, virtualized, and intelligent communication systems. Network Digital Twins (NDTs) provide a scalable alternative to costly and time-consuming measurement campaigns, while enabling controlled experimentation and data generation for data-driven network design. In this paper, we present an open and user-friendly NDT framework that integrates controllable vehicular mobility with the site-specific ray tracer Sionna and the discrete-event ns-3 network simulator, enabling virtualized end-to-end modeling of wireless networks across the radio, network, and application layers. The proposed framework is particularly well-suited for dynamic vehicular networks and urban deployments, supporting realistic mobility, traffic dynamics, and the extraction of cross-layer metrics. To promote open-source initiatives, we release both the NDT implementation and a representative dataset generated from realistic vehicular and urban scenarios. The framework and dataset facilitate reproducible experimentation and benchmarking of machine learning-based quality of service prediction, network optimization, and intelligent network management algorithms, lowering the entry barrier for research on virtual and open wireless network services.

Golara Ahmadi Azar, Qin Hu, Melika Emami et al.

Hand gesture recognition (HGR) has gained significant attention due to the increasing use of AI-powered human-computer interfaces that can interpret the deep spatiotemporal dynamics of biosignals from the peripheral nervous system, such as surface electromyography (sEMG). These interfaces have a range of applications, including the control of extended reality, agile prosthetics, and exoskeletons. However, the natural variability of sEMG among individuals has led researchers to focus on subject-specific solutions. Deep learning methods, which often have complex structures, are particularly data-hungry and can be time-consuming to train, making them less practical for subject-specific applications. In this paper, we propose and develop a generalizable, sequential decoder of transient high-density sEMG (HD-sEMG) that achieves 73% average accuracy on 65 gestures for partially-observed subjects through subject-embedded transfer learning, leveraging pre-knowledge of HGR acquired during pre-training. The use of transient HD-sEMG before gesture stabilization allows us to predict gestures with the ultimate goal of counterbalancing system control delays. The results show that the proposed generalized models significantly outperform subject-specific approaches, especially when the training data is limited, and there is a significant number of gesture classes. By building on pre-knowledge and incorporating a multiplicative subject-embedded structure, our method comparatively achieves more than 13% average accuracy across partially observed subjects with minimal data availability. This work highlights the potential of HD-sEMG and demonstrates the benefits of modeling common patterns across users to reduce the need for large amounts of data for new users, enhancing practicality.

Amirreza Kiani, Ali Rasteh, Marco Mezzavilla et al.

Long-term beamforming (LTBF) is a widely-used scalable alternative to instantaneous multi-user MIMO processing that leverages slowly varying spatial channel statistics. VLSI implementations require matrix inversion that become computationally challenging for massive MIMO systems with large number of antennas. In this work, we show that dominant interferers significantly degrade the numerical conditioning of the LTBF covariance matrix, leading to severe performance loss in finite-precision implementations of polynomial and conjugate gradient (CG) based inversion methods. To address this issue, we propose a subspace nulling approach that operates solely on long-term channel statistics and acts as an implicit preconditioning step for LTBF. By projecting the received signal onto the orthogonal complement of the dominant interference subspace, the proposed method reduces the eigenvalue spread of the covariance matrix and improves numerical stability. Through ray-tracing simulations in a realistic 5G scenario, we demonstrate that the proposed method substantially reduces the number of CG iterations required to achieve near-optimal performance across floating-point and fixed-point implementations while preserving the low-overhead nature of LTBF.

Yu Hao, Fan Yang, Hao Huang et al.

People with blindness and low vision (pBLV) encounter substantial challenges when it comes to comprehensive scene recognition and precise object identification in unfamiliar environments. Additionally, due to the vision loss, pBLV have difficulty in accessing and identifying potential tripping hazards on their own. In this paper, we present a pioneering approach that leverages a large vision-language model to enhance visual perception for pBLV, offering detailed and comprehensive descriptions of the surrounding environments and providing warnings about the potential risks. Our method begins by leveraging a large image tagging model (i.e., Recognize Anything (RAM)) to identify all common objects present in the captured images. The recognition results and user query are then integrated into a prompt, tailored specifically for pBLV using prompt engineering. By combining the prompt and input image, a large vision-language model (i.e., InstructBLIP) generates detailed and comprehensive descriptions of the environment and identifies potential risks in the environment by analyzing the environmental objects and scenes, relevant to the prompt. We evaluate our approach through experiments conducted on both indoor and outdoor datasets. Our results demonstrate that our method is able to recognize objects accurately and provide insightful descriptions and analysis of the environment for pBLV.

Amirreza Kiani, Ali Rasteh, Marco Mezzavilla et al.

Long-term beamforming substantially reduces the channel estimation and inversion overhead of conventional massive MU-MIMO receivers; yet, its construction still hinges on the inversion of a large Hermitian matrix, whose condition number deteriorates with the per-user SNR dynamic range. When this inversion is approximated in hardware via the conjugate gradient (CG) algorithm, the deterioration directly inflates the iteration count and, consequently, the energy and latency budget. We propose a hardware-friendly low-rank preconditioning framework that targets exactly this bottleneck. The preconditioner is constructed from the top eigenpairs of the long-term covariance matrix through a randomized complex eigenvalue decomposition (RC-EVD), whose inner QR factorizations are realized via a Cholesky-based scheme (QRC), confining the dominant cost to generalized matrix multiplication (GEMM) and small triangular solves that map naturally onto systolic arrays. We further show that performing the preconditioned CG inversion in the beamspace domain induces sparsification of the system matrix and provides additional convergence acceleration at negligible transformation cost. Ray-tracing simulations confirm that the joint scheme reduces the required CG iteration count by two to three while matching the post-equalization SINR of the exact inversion.

Yaqi Hu, Mingsheng Yin, Marco Mezzavilla et al.

The upper mid-band (FR3) has been recently attracting interest for new generation of mobile networks, as it provides a promising balance between spectrum availability and coverage, which are inherent limitations of the sub 6GHz and millimeter wave bands, respectively. In order to efficiently design and optimize the network, channel modeling plays a key role since FR3 systems are expected to operate at multiple frequency bands. Data-driven methods, especially generative adversarial networks (GANs), can capture the intricate relationships among data samples, and provide an appropriate tool for FR3 channel modeling. In this work, we present the architecture, link state model, and path generative network of GAN-based FR3 channel modeling. The comparison of our model greatly matches the ray-tracing simulated data.

Ruibin Chen, Haozhe Lei, Hao Guo et al.

Cellular wireless systems are witnessing the proliferation of frequency bands over a wide spectrum, particularly with the expansion of new bands in FR3. These bands must be supported in user equipment (UE) handsets with multiple antennas in a constrained form factor. Rapid variations in channel quality across the bands from motion and hand blockage, limited field-of-view of antennas, and hardware and power-constrained measurement sparsity pose significant challenges to reliable multi-band channel tracking. This paper formulates the problem of predicting achievable rates across multiple antenna arrays and bands with sparse historical measurements. We propose a transformer-based neural architecture that takes asynchronous rate histories as input and outputs per-array rate predictions. Evaluated on ray-traced simulations in a dense urban micro-cellular setting with FR1 and FR3 arrays, our method demonstrates superior performance over baseline predictors, enabling more informed band selection under realistic mobility and hardware constraints.

Haozhe Lei, Ya-Ting Yang, Tao Li et al.

This paper presents the Traffic Adaptive Moving-window Patrolling Algorithm (TAMPA), designed to improve real-time incident management during major events like sports tournaments and concerts. Such events significantly stress transportation networks, requiring efficient and adaptive patrol solutions. TAMPA integrates predictive traffic modeling and real-time complaint estimation, dynamically optimizing patrol deployment. Using dynamic programming, the algorithm continuously adjusts patrol strategies within short planning windows, effectively balancing immediate response and efficient routing. Leveraging the Dvoretzky-Kiefer-Wolfowitz inequality, TAMPA detects significant shifts in complaint patterns, triggering proactive adjustments in patrol routes. Theoretical analyses ensure performance remains closely aligned with optimal solutions. Simulation results from an urban traffic network demonstrate TAMPA's superior performance, showing improvements of approximately 87.5\% over stationary methods and 114.2\% over random strategies. Future work includes enhancing adaptability and incorporating digital twin technology for improved predictive accuracy, particularly relevant for events like the 2026 FIFA World Cup at MetLife Stadium.

Golara Ahmadi Azar, Melika Emami, Alyson Fletcher et al.

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to vectors that are close to one another by some metric in the embedding space. A basic question is how well can such embedding be learned? To study this problem, we consider a simple probability model for discrete data where there is some "true" but unknown embedding where the correlation of random variables is related to the similarity of the embeddings. Under this model, it is shown that the embeddings can be learned by a variant of low-rank approximate message passing (AMP) method. The AMP approach enables precise predictions of the accuracy of the estimation in certain high-dimensional limits. In particular, the methodology provides insight on the relations of key parameters such as the number of samples per value, the frequency of the terms, and the strength of the embedding correlation on the probability distribution. Our theoretical findings are validated by simulations on both synthetic data and real text data.

Haozhe Lei, Hao Guo, Tommy Svensson et al.

Modern wireless systems require not only position estimates, but also quantified uncertainty to support planning, control, and radio resource management. We formulate localization as posterior inference of an unknown transmitter location from receiver measurements. We propose Monte Carlo Candidate-Likelihood Estimation (MC-CLE), which trains a neural scoring network using Monte Carlo sampling to compare true and candidate transmitter locations. We show that in line-of-sight simulations with a multi-antenna receiver, MC-CLE learns critical properties including angular ambiguity and front-to-back antenna patterns. MC-CLE also achieves lower cross-entropy loss relative to a uniform baseline and Gaussian posteriors. alternatives under a uniform-loss metric.

Evan Becker, Parthe Pandit, Sundeep Rangan et al.

Generative Adversarial Networks (GANs) are a popular formulation to train generative models for complex high dimensional data. The standard method for training GANs involves a gradient descent-ascent (GDA) procedure on a minimax optimization problem. This procedure is hard to analyze in general due to the nonlinear nature of the dynamics. We study the local dynamics of GDA for training a GAN with a kernel-based discriminator. This convergence analysis is based on a linearization of a non-linear dynamical system that describes the GDA iterations, under an \textit{isolated points model} assumption from [Becker et al. 2022]. Our analysis brings out the effect of the learning rates, regularization, and the bandwidth of the kernel discriminator, on the local convergence rate of GDA. Importantly, we show phase transitions that indicate when the system converges, oscillates, or diverges. We also provide numerical simulations that verify our claims.

Mojtaba Sahraee-Ardakan, Melikasadat Emami, Parthe Pandit et al.

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization properties of neural networks. Many recent works analyze such models in a certain high-dimensional regime where the covariates are independent and the number of samples and the number of covariates grow at a fixed ratio (i.e. proportional asymptotics). In this work we show that for a large class of kernels, including the neural tangent kernel of fully connected networks, kernel methods can only perform as well as linear models in this regime. More surprisingly, when the data is generated by a kernel model where the relationship between input and the response could be very nonlinear, we show that linear models are in fact optimal, i.e. linear models achieve the minimum risk among all models, linear or nonlinear. These results suggest that more complex models for the data other than independent features are needed for high-dimensional analysis.

Zhongzheng Yuan, Tommy Azzino, Yu Hao et al.

Advanced wearable devices are increasingly incorporating high-resolution multi-camera systems. As state-of-the-art neural networks for processing the resulting image data are computationally demanding, there has been growing interest in leveraging fifth generation (5G) wireless connectivity and mobile edge computing for offloading this processing to the cloud. To assess this possibility, this paper presents a detailed simulation and evaluation of 5G wireless offloading for object detection within a powerful, new smart wearable called VIS4ION, for the Blind-and-Visually Impaired (BVI). The current VIS4ION system is an instrumented book-bag with high-resolution cameras, vision processing and haptic and audio feedback. The paper considers uploading the camera data to a mobile edge cloud to perform real-time object detection and transmitting the detection results back to the wearable. To determine the video requirements, the paper evaluates the impact of video bit rate and resolution on object detection accuracy and range. A new street scene dataset with labeled objects relevant to BVI navigation is leveraged for analysis. The vision evaluation is combined with a detailed full-stack wireless network simulation to determine the distribution of throughputs and delays with real navigation paths and ray-tracing from new high-resolution 3D models in an urban environment. For comparison, the wireless simulation considers both a standard 4G-Long Term Evolution (LTE) carrier and high-rate 5G millimeter-wave (mmWave) carrier. The work thus provides a thorough and realistic assessment of edge computing with mmWave connectivity in an application with both high bandwidth and low latency requirements.

Mingsheng Yin, Akshaj Veldanda, Amee Trivedi et al.

The millimeter wave (mmWave) bands have attracted considerable attention for high precision localization applications due to the ability to capture high angular and temporal resolution measurements. This paper explores mmWave-based positioning for a target localization problem where a fixed target broadcasts mmWave signals and a mobile robotic agent attempts to capture the signals to locate and navigate to the target. A three-stage procedure is proposed: First, the mobile agent uses tensor decomposition methods to detect the multipath channel components and estimate their parameters. Second, a machine-learning trained classifier is then used to predict the link state, meaning if the strongest path is line-of-sight (LOS) or non-LOS (NLOS). For the NLOS case, the link state predictor also determines if the strongest path arrived via one or more reflections. Third, based on the link state, the agent either follows the estimated angles or uses computer vision or other sensor to explore and map the environment. The method is demonstrated on a large dataset of indoor environments supplemented with ray tracing to simulate the wireless propagation. The path estimation and link state classification are also integrated into a state-of-the-art neural simultaneous localization and mapping (SLAM) module to augment camera and LIDAR-based navigation. It is shown that the link state classifier can successfully generalize to completely new environments outside the training set. In addition, the neural-SLAM module with the wireless path estimation and link state classifier provides rapid navigation to the target, close to a baseline that knows the target location.

Mojtaba Sahraee-Ardakan, Tung Mai, Anup Rao et al.

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine learning community that highly over-parameterized neural networks achieve zero training error, and yet they are able to generalize well over the test samples. This phenomenon is captured by the so called double descent curve, where the generalization error starts decreasing again after the interpolation threshold. A series of recent works tried to explain such phenomenon for simple models. In this work, we analyze the asymptotics of estimation error in ridge estimators for convolutional linear models. These convolutional inverse problems, also known as deconvolution, naturally arise in different fields such as seismology, imaging, and acoustics among others. Our results hold for a large class of input distributions that include i.i.d. features as a special case. We derive exact formulae for estimation error of ridge estimators that hold in a certain high-dimensional regime. We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.

Abbas Khalili, Sundeep Rangan, Elza Erkip

Communication in high frequencies such as millimeter wave and terahertz suffer from high path-loss and intense shadowing which necessitates beamforming for reliable data transmission. On the other hand, at high frequencies the channels are sparse and consist of few spatial clusters. Therefore, beam alignment (BA) strategies are used to find the direction of these channel clusters and adjust the width of the beam used for data transmission. In this work, a single-user uplink scenario where the channel has one dominant cluster is considered. It is assumed that the user transmits a set of BA packets over a fixed duration. Meanwhile, the base-station (BS) uses different probing beams to scan different angular regions. Since the BS measurements are noisy, it is not possible to find a narrow beam that includes the angle of arrival (AoA) of the user with probability one. Therefore, the BS allocates a narrow beam to the user which includes the AoA of the user with a predetermined error probability while minimizing the expected beamwidth of the allocated beam. Due to intractability of this noisy BA problem, here this problem is posed as an end-to-end optimization of a deep neural network (DNN) and effects of different loss functions are discussed and investigated. It is observed that the proposed DNN based BA, at high SNRs, achieves a performance close to that of the optimal BA when there is no-noise and for all SNRs, outperforms state-of-the-art.

Melikasadat Emami, Mojtaba Sahraee-Ardakan, Parthe Pandit et al.

Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, precise reasoning for this behavior is still unknown. This paper provides a rigorous explanation of this property in the special case of linear RNNs. Although this work is limited to linear RNNs, even these systems have traditionally been difficult to analyze due to their non-linear parameterization. Using recently-developed kernel regime analysis, our main result shows that linear RNNs learned from random initializations are functionally equivalent to a certain weighted 1D-convolutional network. Importantly, the weightings in the equivalent model cause an implicit bias to elements with smaller time lags in the convolution and hence, shorter memory. The degree of this bias depends on the variance of the transition kernel matrix at initialization and is related to the classic exploding and vanishing gradients problem. The theory is validated in both synthetic and real data experiments.

Huaijiang Zhu, Manali Sharma, Kai Pfeiffer et al.

Real-world applications require light-weight, energy-efficient, fully autonomous robots. Yet, increasing autonomy is oftentimes synonymous with escalating computational requirements. It might thus be desirable to offload intensive computation--not only sensing and planning, but also low-level whole-body control--to remote servers in order to reduce on-board computational needs. Fifth Generation (5G) wireless cellular technology, with its low latency and high bandwidth capabilities, has the potential to unlock cloud-based high performance control of complex robots. However, state-of-the-art control algorithms for legged robots can only tolerate very low control delays, which even ultra-low latency 5G edge computing can sometimes fail to achieve. In this work, we investigate the problem of cloud-based whole-body control of legged robots over a 5G link. We propose a novel approach that consists of a standard optimization-based controller on the network edge and a local linear, approximately optimal controller that significantly reduces on-board computational needs while increasing robustness to delay and possible loss of communication. Simulation experiments on humanoid balancing and walking tasks that includes a realistic 5G communication model demonstrate significant improvement of the reliability of robot locomotion under jitter and delays likely to experienced in 5G wireless links.

Melikasadat Emami, Mojtaba Sahraee-Ardakan, Parthe Pandit et al.

This paper considers the problem of neural decoding from parallel neural measurements systems such as micro-electrocorticography ($μ$-ECoG). In systems with large numbers of array elements at very high sampling rates, the dimension of the raw measurement data may be large. Learning neural decoders for this high-dimensional data can be challenging, particularly when the number of training samples is limited. To address this challenge, this work presents a novel neural network decoder with a low-rank structure in the first hidden layer. The low-rank constraints dramatically reduce the number of parameters in the decoder while still enabling a rich class of nonlinear decoder maps. The low-rank decoder is illustrated on $μ$-ECoG data from the primary auditory cortex (A1) of awake rats. This decoding problem is particularly challenging due to the complexity of neural responses in the auditory cortex and the presence of confounding signals in awake animals. It is shown that the proposed low-rank decoder significantly outperforms models using standard dimensionality reduction techniques such as principal component analysis (PCA).

Melikasadat Emami, Mojtaba Sahraee-Ardakan, Parthe Pandit et al.

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete. This task is made harder by the non-convexity of the underlying learning problems. We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems. This framework enables analyzing the effect of (i) over-parameterization and non-linearity during modeling; and (ii) choices of loss function, initialization, and regularizer during learning. Our model also captures mismatch between training and test distributions. As examples, we analyze a few special cases, namely linear regression and logistic regression. We are also able to rigorously and analytically explain the \emph{double descent} phenomenon in generalized linear models.

Parthe Pandit, Mojtaba Sahraee-Ardakan, Sundeep Rangan et al.

We consider the problem of inferring the input and hidden variables of a stochastic multi-layer neural network from an observation of the output. The hidden variables in each layer are represented as matrices. This problem applies to signal recovery via deep generative prior models, multi-task and mixed regression and learning certain classes of two-layer neural networks. A unified approximation algorithm for both MAP and MMSE inference is proposed by extending a recently-developed Multi-Layer Vector Approximate Message Passing (ML-VAMP) algorithm to handle matrix-valued unknowns. It is shown that the performance of the proposed Multi-Layer Matrix VAMP (ML-Mat-VAMP) algorithm can be exactly predicted in a certain random large-system limit, where the dimensions $N\times d$ of the unknown quantities grow as $N\rightarrow\infty$ with $d$ fixed. In the two-layer neural-network learning problem, this scaling corresponds to the case where the number of input features and training samples grow to infinity but the number of hidden nodes stays fixed. The analysis enables a precise prediction of the parameter and test error of the learning.

Parthe Pandit, Mojtaba Sahraee-Ardakan, Sundeep Rangan et al.

Deep generative priors offer powerful models for complex-structured data, such as images, audio, and text. Using these priors in inverse problems typically requires estimating the input and/or hidden signals in a multi-layer deep neural network from observation of its output. While these approaches have been successful in practice, rigorous performance analysis is complicated by the non-convex nature of the underlying optimization problems. This paper presents a novel algorithm, Multi-Layer Vector Approximate Message Passing (ML-VAMP), for inference in multi-layer stochastic neural networks. ML-VAMP can be configured to compute maximum a priori (MAP) or approximate minimum mean-squared error (MMSE) estimates for these networks. We show that the performance of ML-VAMP can be exactly predicted in a certain high-dimensional random limit. Furthermore, under certain conditions, ML-VAMP yields estimates that achieve the minimum (i.e., Bayes-optimal) MSE as predicted by the replica method. In this way, ML-VAMP provides a computationally efficient method for multi-layer inference with an exact performance characterization and testable conditions for optimality in the large-system limit.

Parthe Pandit, Mojtaba Sahraee-Ardakan, Arash A. Amini et al.

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with spiking or binary-valued data. We allow the process to depend on its past up to a lag $p$, for a general $p \ge 1$, allowing for more realistic modeling in many applications. We propose and analyze an $\ell_1$-regularized maximum likelihood estimator (MLE) under the assumption that the parameter tensor is approximately sparse. Rigorous analysis of such estimators is made challenging by the dependent and non-Gaussian nature of the process as well as the presence of the nonlinearities and multi-level feedback. We derive precise upper bounds on the mean-squared estimation error in terms of the number of samples, dimensions of the process, the lag $p$ and other key statistical properties of the model. The ideas presented can be used in the high-dimensional analysis of regularized $M$-estimators for other sparse nonlinear and non-Gaussian processes with long-range dependence.

Parthe Pandit, Mojtaba Sahraee, Sundeep Rangan et al.

Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the multi-layer network from its output. Maximum a priori (MAP) estimation is a widely-used inference method as it is straightforward to implement, and has been successful in practice. However, rigorous analysis of MAP inference in multi-layer networks is difficult. This work considers a recently-developed method, multi-layer vector approximate message passing (ML-VAMP), to study MAP inference in deep networks. It is shown that the mean squared error of the ML-VAMP estimate can be exactly and rigorously characterized in a certain high-dimensional random limit. The proposed method thus provides a tractable method for MAP inference with exact performance guarantees.

Alyson K. Fletcher, Sundeep Rangan

Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the networks from the outputs. Inference is also required for sampling during stochastic training on these generative models. This paper considers inference in a deep stochastic neural network where the parameters (e.g., weights, biases and activation functions) are known and the problem is to estimate the values of the input and hidden units from the output. While several approximate algorithms have been proposed for this task, there are few analytic tools that can provide rigorous guarantees in the reconstruction error. This work presents a novel and computationally tractable output-to-input inference method called Multi-Layer Vector Approximate Message Passing (ML-VAMP). The proposed algorithm, derived from expectation propagation, extends earlier AMP methods that are known to achieve the replica predictions for optimality in simple linear inverse problems. Our main contribution shows that the mean-squared error (MSE) of ML-VAMP can be exactly predicted in a certain large system limit (LSL) where the numbers of layers is fixed and weight matrices are random and orthogonally-invariant with dimensions that grow to infinity. ML-VAMP is thus a principled method for output-to-input inference in deep networks with a rigorous and precise performance achievability result in high dimensions.

Alyson K. Fletcher, Mojtaba Sahraee-Ardakan, Philip Schniter et al.

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse problems. We show that a computationally simple iterative message-passing algorithm can provably obtain asymptotically consistent estimates in a certain high-dimensional large-system limit (LSL) under very general parameterizations. Previous message passing techniques have required i.i.d. sub-Gaussian A matrices and often fail when the matrix is ill-conditioned. The proposed algorithm, called adaptive vector approximate message passing (Adaptive VAMP) with auto-tuning, applies to all right-rotationally random A. Importantly, this class includes matrices with arbitrarily poor conditioning. We show that the parameter estimates and mean squared error (MSE) of x in each iteration converge to deterministic limits that can be precisely predicted by a simple set of state evolution (SE) equations. In addition, a simple testable condition is provided in which the MSE matches the Bayes-optimal value predicted by the replica method. The paper thus provides a computationally simple method with provable guarantees of optimality and consistency over a large class of linear inverse problems.

Alyson K. Fletcher, Mojtaba Sahraee-Ardakan, Sundeep Rangan et al.

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. The proposed method, called Generalized Expectation Consistency (GEC), can be applied to both maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimation. Here we characterize its fixed points, convergence, and performance relative to the replica prediction of optimality.

Ulugbek S. Kamilov, Sundeep Rangan, Alyson K. Fletcher et al.

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. A novel method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector $\xbf$ is presented. The proposed algorithm is a generalization of a recently-developed EM-GAMP that uses expectation-maximization (EM) iterations where the posteriors in the E-steps are computed via approximate message passing. The methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear-nonlinear cascade models in dynamical systems and neural spiking processes. We prove that for large i.i.d. Gaussian transform matrices the asymptotic componentwise behavior of the adaptive GAMP algorithm is predicted by a simple set of scalar state evolution equations. In addition, we show that when a certain maximum-likelihood estimation can be performed in each step, the adaptive GAMP method can yield asymptotically consistent parameter estimates, which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. Remarkably, this result applies to essentially arbitrary parametrizations of the unknown distributions, including ones that are nonlinear and non-Gaussian. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of complex linear-nonlinear models with provable guarantees.