arXiv subjects

Tadashi Wadayama

Publications and source records attributed to Tadashi Wadayama.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive Score-Based VAMP: Self-Tuning Hyperparameters via Tilted EM

Approximate-message-passing methods offer fast Bayesian inference for high-dimensional inverse problems, but their performance and state-evolution predictions rely on correctly specified module parameters. This paper develops an adaptive version of score-based vector approximate message passing (SC-VAMP). Each parameterized factor is updated by a local tilted expectation-maximization (EM) step that reuses the tilted moments already computed by the single-input single-output module interface. Under standard large-system state-evolution assumptions and identifiability conditions, the matched parameters form a Bayes-optimal population fixed point of the adaptive recursion. The argument is written separately for prior modules and likelihood/LMMSE modules, the latter using the Gaussian cavity induced by the VAMP transformed-error model. Numerical results for linear and one-bit Bernoulli-Gaussian compressed sensing show that the proposed updates recover near-oracle performance from strongly mismatched initializations.

eess.SP↗

arXiv2026

A Differentiable Covariance Calculus for Linear Gaussian Bayesian Networks

Linear Gaussian Bayesian networks, equivalently linear Gaussian structural equation models, recur across statistics, control, and communications; in the vector-valued setting that motivates this work, their nodes are vectors and their edges are matrices. Every quantity of interest is a function of sub-blocks of the joint covariance, which is itself a classical, differentiable map (the K-recursion) from the local edge and innovation parameters. Yet the resulting inference and estimation tasks are usually derived and implemented separately, per task and per topology. Taking this covariance chart as a single backend, we build on it a unified, differentiable covariance calculus in which each task reduces to a few linear-algebra primitives on the one covariance, and automatic differentiation returns every gradient in a single backward sweep, over arbitrary vector-valued directed acyclic graphs and parametrizations, including tied and structured ones. The calculus covers conditioning, conditional-independence testing through mutual information, maximum-likelihood estimation with hidden nodes, and the Slepian--Bangs Fisher information with the local identifiability and Cram\'er--Rao reliability it induces. It is validated on a linear Gaussian state-space model and a skip-connected (non-chain) extension against the Kalman recursions, d-separation, and the Cram\'er--Rao bound.

cs.IT↗

arXiv2026

Differentiable Conditional Mutual Information for Multi-Terminal Linear Gaussian Wireless Networks

The rate regions of multi-terminal Gaussian channels (multiple-access, broadcast, interference, relay) are delimited by conditional mutual informations $I(V_A;V_B\,|\,V_C)$ among groups of input and output nodes; bringing such channels under differentiable physical-layer design therefore hinges on evaluating any such conditional MI, and its gradient, on a unified computation graph. Modeling the network as a linear Gaussian directed acyclic graph (Gaussian-DAG), we obtain $I(V_A;V_B\,|\,V_C)$ in closed form: from the node-pair covariances produced by one K-recursion forward pass, it is a log-determinant difference of two sub-block Schur complements of the support covariance. The construction is built entirely from automatic-differentiation (AD) primitives, so any differentiable function of finitely many conditional MIs is end-to-end differentiable in the design parameters; this broad class includes linear objectives (weighted sum-rate, secrecy), the rate functions of standard multi-terminal rate regions, and non-linear composites of these. A single reverse-mode AD sweep yields the Wirtinger gradient with respect to all controllable factors at once, so any such objective can be handled by projected gradient iterations without problem-specific gradient derivation. We demonstrate the framework on three experiments: rate-region maximization for a two-user MIMO multiple-access channel, secure precoding on a MIMO wiretap channel, and the same rate-region objective applied to a larger multi-hop multiple-access network.

cs.IT↗

arXiv2026

Mutual Information Optimization via K-Recursion and Automatic Differentiation for Linear Gaussian Wireless Networks

We present a differentiable framework for end-to-end mutual information (MI) optimization over linear Gaussian directed acyclic graphs (DAGs). The framework targets network-wide design under global constraints, such as a total transmit power budget, and covers MIMO precoding, amplify-and-forward relays, RIS-aided channels, and branching/merging topologies within a common linear Gaussian model. Its core ingredient is a \emph{K-recursion} that analytically propagates all node-pair covariances along the DAG in topological order, including non-adjacent cross-covariances that are necessary for correctly handling branching and merging paths. The resulting covariances yield a closed-form log-determinant expression for the end-to-end MI as a smooth function of the controllable factors. Complex-valued reverse-mode automatic differentiation on this K-recursion then returns the exact Wirtinger gradient at every controllable factor in a single backward sweep, and projected gradient ascent (PGA) is used to maximize the MI under the global constraints. Because no closed-form gradient expression per topology is required, the same topology-agnostic implementation applies to any linear Gaussian DAG. A single topology-agnostic implementation is applied to four representative DAG classes: single-link MIMO, a diamond DAG, a two-hop AF relay, and input-covariance shaping. The same implementation reaches the classical water-filling optimum in the settings where it is available and yields MI improvements in non-single-link topologies without using topology-specific gradient formulas. A further experiment on a multi-layer Gaussian network (11 nodes, 5 layers) illustrates applicability to nontrivial multi-layer topologies for which no closed-form gradient is available.

cs.IT↗

arXiv2026

Physics-Aware Linearized ADMM and Its Unrolling

Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.

eess.SP↗

arXiv2026

Federated Learning with Hypergradient-based Online Update of Aggregation Weights

Federated learning using mobile and Internet of Things devices requires not only the ability to handle heterogeneity of clients' data distributions but also high adaptability to varying communication environments. We propose FedHAW (Federated Learning with Hypergradient-based update of Aggregation Weights) that implements online updates of aggregation weights. FedHAW updates the aggregation weights by using hypergradient, the gradient of the objective function with respect to the weights, which can be calculated with low computational overhead. Simulation results show that the proposed method possesses high generalization performance in heterogeneous environments and high robustness to communication errors.

cs.LG↗

arXiv2026

LLM-Steered Power Allocation for Parallel QPSK-AWGN Channels

Large language models (LLMs) are increasingly being explored as high-level decision modules in closed-loop systems, but their stochastic nature makes safe integration challenging. In this paper, we propose LLM-Steered Power Allocation, a dual-process architecture for parallel QPSK channels inspired by Kahneman's System 1/System 2 framework. A fast numerical optimizer (System 1) continuously performs projected gradient ascent on a weighted mutual-information objective, while an LLM navigator (System 2) periodically interprets natural-language policies and updates only the channel weights and the operational power budget. The LLM never manipulates the power-allocation variables directly, and constraint satisfaction is enforced structurally by the optimizer. To mitigate LLM unreliability, we further incorporate multi-layer guardrails including normalization, exponential moving-average smoothing, and fallback mechanisms. Numerical experiments on an 8-channel system show that, with a fixed optimization core and unchanged system prompt, different natural-language policies induce qualitatively different operating points, including throughput-oriented allocation, channel prioritization, power-aware operation, and channel shutdown. In addition, under an abrupt channel-gain reversal, the proposed system autonomously reconfigures its steering signals and reduces the final mutual-information spread by 60% compared with the optimizer alone. These results suggest that LLMs can serve as policy interpreters for safe, flexible reconfiguration of communication-system optimizers without controller reimplementation.

cs.IT↗

arXiv2026

Computationally Efficient Sparse Signal Recovery via Linear Sketching and Deep Unfolding

This paper provides a sparse signal recovery algorithm, DU-PSISTA (Deep Unfolded-Periodic Sketched Iterative Shrinkage-Thresholding Algorithm), which aims to balance computational efficiency and accuracy for recovering high-dimensional sparse signals, and a convergence analysis under sufficient conditions. DU-PSISTA introduces a random matrix projection known as sketching to reduce the dimensionality of gradient computations and periodically alternates between the standard ISTA and the sketched variant. This hybrid structure enables flexible control over the trade-off between accuracy and computational complexity through a pre-configurable period parameter. The algorithm includes many parameters to be tuned such as step sizes and thresholding factors so that we incorporate deep unfolding that optimizes the parameters through data-driven training, enabling the algorithm to adaptively improve convergence speed and performance. We show that the proposed method achieves a linear-type contraction to a neighborhood of the true sparse signal with properly selected parameters. The analysis provides an interpretation for the effectiveness of the hybrid structure to improve recovery accuracy. Numerical experiments confirm that our method achieves comparable recovery performance to conventional deep unfolded ISTA while reducing computational complexity, especially when the period parameter and sketch size are properly selected. The results are also consistent with the theoretical insights.

eess.SP↗

arXiv2026

Three-Module SC-VAMP for LDPC-Coded Nonlinear Channels

We propose a three-module extension of score-based VAMP (SC-VAMP) for signal recovery in nonlinear channels, where the received signal is obtained by applying a nonlinearity to a linear mixture of the transmitted signal, followed by additive Gaussian noise. The key idea is to introduce a latent variable representing the output of the linear mixing stage, which decomposes the inference problem into three modules: a likelihood module that handles the nonlinear observation via Gauss--Hermite quadrature, a coupling module that enforces the linear constraint between the transmitted signal and the latent variable via LMMSE estimation, and a denoiser module that incorporates the code constraint using belief propagation (BP) decoding. Each module exchanges extrinsic scalar-Gaussian messages with Onsager corrections derived from posterior variances that are computed in closed form or to quadrature accuracy. Numerical experiments with BPSK-modulated LDPC codewords transmitted through a hyperbolic tangent channel demonstrate that the proposed method achieves a clear waterfall in bit error rate (BER), with the gap to the capacity estimate narrowing as the block length increases from 128 to 2304. The framework provides a modular receiver architecture applicable to a broad class of nonlinear channels. Since only the likelihood module depends on the channel nonlinearity, the architecture readily adapts to other channel models by replacing a single module while leaving the coupling and decoder modules unchanged.

cs.IT↗

arXiv2026

Online Architecture Search for Compressed Sensing based on Hypergradient Descent

AS-ISTA (Architecture Searched-Iterative Shrinkage Thresholding Algorithm) and AS-FISTA (AS-Fast ISTA) are compressed sensing algorithms introducing structural parameters to ISTA and FISTA to enable architecture search within the iterative process. The structural parameters are determined using deep unfolding, but this approach requires training data and the large overhead of training time. In this paper, we propose HGD-AS-ISTA (Hypergradient Descent-AS-ISTA) and HGD-AS-FISTA that use hypergradient descent, which is an online hyperparameter optimization method, to determine the structural parameters. Experimental results show that the proposed method improves performance of the conventional ISTA/FISTA while avoiding the need for re-training when the environment changes.

eess.SP↗

arXiv2026

Score-Based VAMP with Fisher-Information-Based Onsager Correction

We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes.

cs.IT↗

arXiv2026

Mutual Information Estimation via Score-to-Fisher Bridge for Nonlinear Gaussian Noise Channels

We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher information estimated from the learned score function yields accurate estimates of MI through a Fisher integral representation for a variety of priors and channel nonlinearities. In this work, we propose a comprehensive theoretical foundation for the Score-to-Fisher bridge methodology, along with practical guidelines for its implementation. We also conduct extensive validation experiments, comparing our approach with closed-form solutions and a kernel density estimation baseline. The results of our numerical experiments demonstrate that the proposed method is both practical and efficient for MI estimation in nonlinear Gaussian noise channels. Additionally, we discuss the theoretical connections between our score-based framework and thermodynamic concepts, such as partition function estimation and optimal transport.

cs.IT↗

arXiv2026

Information Gradient for Directed Acyclic Graphs: A Score-based Framework for End-to-End Mutual Information Maximization

This paper presents a general framework for end-to-end mutual information maximization in communication and sensing systems represented by stochastic directed acyclic graphs (DAGs). We derive a unified formula for the (mutual) information gradient with respect to arbitrary internal parameters, utilizing marginal and conditional score functions. We demonstrate that this gradient can be efficiently computed using vector-Jacobian products (VJP) within standard automatic differentiation frameworks, enabling the optimization of complex networks under global resource constraints. Numerical experiments on both linear multipath DAGs and nonlinear channels validate the proposed framework; the results confirm that the estimator, utilizing score functions learned via denoising score matching, accurately reproduces ground-truth gradients and successfully maximizes end-to-end mutual information. Beyond maximization, we extend our score-based framework to a novel unsupervised paradigm: digital twin calibration via Fisher divergence minimization.

cs.IT↗

arXiv2025

Information Gradient for Nonlinear Gaussian Channel with Applications to Task-Oriented Communication

We propose a gradient-based framework for optimizing parametric nonlinear Gaussian channels via mutual information maximization. Leveraging the score-to-Fisher bridge (SFB) methodology, we derive a computationally tractable formula for the information gradient that is the gradient of mutual information with respect to the parameters of the nonlinear front-end. Our formula expresses this gradient in terms of two key components: the score function of the marginal output distribution, which can be learned via denoising score matching (DSM), and the Jacobian of the front-end function, which is handled efficiently using the vector-Jacobian product (VJP) within automatic differentiation frameworks. This enables practical parameter optimization through gradient ascent. Furthermore, we extend this framework to task-oriented scenarios, deriving gradients for both task-specific mutual information, where a task variable depends on the channel input, and the information bottleneck (IB) objective. A key advantage of our approach is that it facilitates end-to-end optimization of the nonlinear front-end without requiring explicit computation on the output distribution. Extensive experimental validation confirms the correctness of our information gradient formula against analytical solutions and demonstrates its effectiveness in optimizing both linear and nonlinear channels toward their objectives.

cs.IT↗

arXiv2025

Physics-Aware Sparse Signal Recovery Through PDE-Governed Measurement Systems

This paper introduces a novel framework for physics-aware sparse signal recovery in measurement systems governed by partial differential equations (PDEs). Unlike conventional compressed sensing approaches that treat measurement systems as simple linear systems, our method explicitly incorporates the underlying physics through numerical PDE solvers and automatic differentiation (AD). We present physics-aware iterative shrinkage-thresholding algorithm (PA-ISTA), which combines the computational efficiency of ISTA with accurate physical modeling to achieve improved signal reconstruction. Using optical fiber channels as a concrete example, we demonstrate how the nonlinear Schrödinger equation (NLSE) can be integrated into the recovery process. Our approach leverages deep unfolding techniques for parameter optimization. Numerical experiments show that PA-ISTA significantly outperforms conventional recovery methods. While demonstrated on optical fiber systems, the proposed framework provides a general methodology for physics-aware signal recovery applicable to a wide range of various PDE-governed measurement systems.

cs.IT↗

arXiv2025

Multi-Output Gaussian Processes for Graph-Structured Data

Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on multi-output Gaussian processes (MOGP), to capture both the correlation between vertices and the correlation between associated data. The proposed formulation is built on the definition of MOGP. This allows it to be applied to a wide range of data configurations and scenarios. Moreover, it has high expressive capability due to its flexibility in kernel design. It includes existing methods of Gaussian processes for graph-structured data as special cases and is possible to remove restrictions on data configurations, model selection, and inference scenarios in the existing methods. The performance of extensions achievable by the proposed formulation is evaluated through computer experiments with synthetic and real data.

cs.LG↗

arXiv2025

Physics-Aware Decoding for Communication Channels Governed by Partial Differential Equations

Digital communication systems inherently operate through physical media governed by partial differential equations (PDEs). In this paper, we introduce a physics-aware decoding framework that integrates gradient descent-based error correcting algorithms with PDE-based channel modeling using differentiable PDE solvers. At the core of our approach is gradient flow decoding, which harnesses gradient information directly from the PDE solver to guide the decoding process. We validate our method through numerical experiments on both the heat equation and the nonlinear Schrödinger equation (NLSE), demonstrating significant improvements in decoding performance. The implications of this work extend beyond decoding applications, establishing a new paradigm for physics-aware signal processing that shows promise for various signal detection and signal recovery tasks.

cs.IT↗

arXiv2024

Gradient Flow Decoding

This paper presents the Gradient Flow (GF) decoding for LDPC codes. GF decoding, a continuous-time methodology based on gradient flow, employs a potential energy function associated with bipolar codewords of LDPC codes. The decoding process of the GF decoding is concisely defined by an ordinary differential equation and thus it is well suited to an analog circuit implementation. We experimentally demonstrate that the decoding performance of the GF decoding for AWGN channels is comparable to that of the multi-bit mode gradient descent bit flipping algorithm. We further introduce the negative log-likelihood function of the channel for generalizing the GF decoding. The proposed method is shown to be tensor-computable, which means that the gradient of the objective function can be evaluated with the combination of basic tensor computations. This characteristic is well-suited to emerging AI accelerators, potentially applicable in wireless signal processing. The paper assesses the decoding performance of the generalized GF decoding in LDPC-coded MIMO channels. Our numerical experiments reveal that the decoding performance rivals that of established techniques like MMSE + BP. Furthermore, an exploration of score-based channel learning for capturing statistical properties is also provided.

cs.IT↗