Extremum Encoding for Joint Baseband Signal Compression and Time-Delay Estimation for Distributed Systems

The ubiquitous time-delay estimation (TDE) problem becomes nontrivial when sensors are non-co-located and communication between them is limited. Building on the recently proposed "extremum encoding" compression-estimation scheme, we address the critical extension to complex-valued signals, suitable for radio-frequency (RF) baseband processing. This extension introduces new challenges, e.g., due to unknown phase of the signal of interest and random phase of the noise, rendering a na\"ive application of the original scheme inapplicable and irrelevant. In the face of these challenges, we propose a judiciously adapted, though natural, extension of the scheme, paving its way to RF applications. While our extension leads to a different statistical analysis, including extremes of non-Gaussian distributions, we show that, ultimately, its asymptotic behavior is akin to the original scheme. We derive an exponentially tight upper bound on its error probability, corroborate our results via simulation experiments, and demonstrate the superior performance compared to two benchmark approaches.

Estimating the Number and Locations of Boundaries in Reverberant Environments with Deep Learning

Underwater acoustic environment estimation is a challenging but important task for remote sensing scenarios. Current estimation methods require high signal strength and a solution to the fragile echo labeling problem to be effective. In previous publications, we proposed a general deep learning-based method for two-dimensional environment estimation which outperformed the state-of-the-art, both in simulation and in real-life experimental settings. A limitation of this method was that some prior information had to be provided by the user on the number and locations of the reflective boundaries, and that its neural networks had to be re-trained accordingly for different environments. Utilizing more advanced neural network and time delay estimation techniques, the proposed improved method no longer requires prior knowledge the number of boundaries or their locations, and is able to estimate two-dimensional environments with one or two boundaries. Future work will extend the proposed method to more boundaries and larger-scale environments.

A Unified View on Learning Unnormalized Distributions via Noise-Contrastive Estimation

This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning unnormalized distributions, which have been independently proposed and studied in separate research communities, through the lens of NCE. This unified view offers new insights into existing estimators. Specifically, for exponential families, we establish the finite-sample convergence rates of the proposed estimators under a set of regularity assumptions, most of which are new.

RF Challenge: The Data-Driven Radio Frequency Signal Separation Challenge

This paper addresses the critical problem of interference rejection in radio-frequency (RF) signals using a novel, data-driven approach that leverages state-of-the-art AI models. Traditionally, interference rejection algorithms are manually tailored to specific types of interference. This work introduces a more scalable data-driven solution and contains the following contributions. First, we present an insightful signal model that serves as a foundation for developing and analyzing interference rejection algorithms. Second, we introduce the RF Challenge, a publicly available dataset featuring diverse RF signals along with code templates, which facilitates data-driven analysis of RF signal problems. Third, we propose novel AI-based rejection algorithms, specifically architectures like UNet and WaveNet, and evaluate their performance across eight different signal mixture types. These models demonstrate superior performance exceeding traditional methods like matched filtering and linear minimum mean square error estimation by up to two orders of magnitude in bit-error rate. Fourth, we summarize the results from an open competition hosted at 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2024) based on the RF Challenge, highlighting the significant potential for continued advancements in this area. Our findings underscore the promise of deep learning algorithms in mitigating interference, offering a strong foundation for future research.

FaceFolds: Meshed Radiance Manifolds for Efficient Volumetric Rendering of Dynamic Faces

3D rendering of dynamic face captures is a challenging problem, and it demands improvements on several fronts$\unicode{x2014}$photorealism, efficiency, compatibility, and configurability. We present a novel representation that enables high-quality volumetric rendering of an actor's dynamic facial performances with minimal compute and memory footprint. It runs natively on commodity graphics soft- and hardware, and allows for a graceful trade-off between quality and efficiency. Our method utilizes recent advances in neural rendering, particularly learning discrete radiance manifolds to sparsely sample the scene to model volumetric effects. We achieve efficient modeling by learning a single set of manifolds for the entire dynamic sequence, while implicitly modeling appearance changes as temporal canonical texture. We export a single layered mesh and view-independent RGBA texture video that is compatible with legacy graphics renderers without additional ML integration. We demonstrate our method by rendering dynamic face captures of real actors in a game engine, at comparable photorealism to state-of-the-art neural rendering techniques at previously unseen frame rates.

A Joint Data Compression and Time-Delay Estimation Method For Distributed Systems via Extremum Encoding

Motivated by the proliferation of mobile devices, we consider a basic form of the ubiquitous problem of time-delay estimation (TDE), but with communication constraints between two non co-located sensors. In this setting, when joint processing of the received signals is not possible, a compression technique that is tailored to TDE is desirable. For our basic TDE formulation, we develop such a joint compression-estimation strategy based on the notion of what we term "extremum encoding", whereby we send the index of the maximum of a finite-length time-series from one sensor to another. Subsequent joint processing of the encoded message with locally observed data gives rise to our proposed time-delay "maximum-index"-based estimator. We derive an exponentially tight upper bound on its error probability, establishing its consistency with respect to the number of transmitted bits. We further validate our analysis via simulations, and comment on potential extensions and generalizations of the basic methodology.

Improved Evidential Deep Learning via a Mixture of Dirichlet Distributions

This paper explores a modern predictive uncertainty estimation approach, called evidential deep learning (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their strong empirical performance, recent studies by Bengs et al. identify a fundamental pitfall of the existing methods: the learned epistemic uncertainty may not vanish even in the infinite-sample limit. We corroborate the observation by providing a unifying view of a class of widely used objectives from the literature. Our analysis reveals that the EDL methods essentially train a meta distribution by minimizing a certain divergence measure between the distribution and a sample-size-independent target distribution, resulting in spurious epistemic uncertainty. Grounded in theoretical principles, we propose learning a consistent target distribution by modeling it with a mixture of Dirichlet distributions and learning via variational inference. Afterward, a final meta distribution model distills the learned uncertainty from the target model. Experimental results across various uncertainty-based downstream tasks demonstrate the superiority of our proposed method, and illustrate the practical implications arising from the consistency and inconsistency of learned epistemic uncertainty.

Operator SVD with Neural Networks via Nested Low-Rank Approximation

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called nesting for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.

On Computationally Efficient Learning of Exponential Family Distributions

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a novel loss function and a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family. Further, we show that our estimator can be interpreted as a solution to minimizing a particular Bregman score as well as an instance of minimizing the \textit{surrogate} likelihood. We also provide finite sample guarantees to achieve an error (in $\ell_2$-norm) of $\alpha$ in the parameter estimation with sample complexity $O({\sf poly}(k)/\alpha^2)$. Our method achives the order-optimal sample complexity of $O({\sf log}(k)/\alpha^2)$ when tailored for node-wise-sparse Markov random fields. Finally, we demonstrate the performance of our estimator via numerical experiments.

Score-based Source Separation with Applications to Digital Communication Signals

We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by maximum a posteriori estimation with an $\alpha$-posterior, across multiple levels of Gaussian smoothing. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature and the recovery of encoded bits from a signal of interest, as measured by the bit error rate (BER). Experimental results with RF mixtures demonstrate that our method results in a BER reduction of 95% over classical and existing learning-based methods. Our analysis demonstrates that our proposed method yields solutions that asymptotically approach the modes of an underlying discrete distribution. Furthermore, our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme, shedding additional light on its use beyond conditional sampling.