Shitong Wu

Shitong Wu, Sicheng Xu, Lingyi Chen et al.

Rate-distortion (RD) theory and its related formulations play a central role in understanding efficient information representation, but computing these quantities remains challenging in high-dimensional settings. Classical iterative methods such as the Blahut-Arimoto algorithm become impractical in high-dimensional domains due to the curse of dimensionality and the intractability of mutual-information terms. Recent advances in neural modeling and differentiable optimization offer a promising alternative through a learn-to-compute paradigm, in which probability distributions and objective functionals are represented by flexible neural parameterizations. This survey presents an overview of neural approaches for evaluating the RD-type objectives. We present three representative families of methods: variational inference, neural mutual-information estimation, and dual-form optimization. By reviewing their theoretical principles, algorithmic techniques, and consistency properties, we elucidate how these methods collectively transform classical RD-type problems into scalable differentiable objectives suitable for deep learning, though challenges remain in large-scale applications. Together, these perspectives offer promising avenues for scaling information-theoretic computation to complex, high-dimensional machine learning systems.

Lingyi Chen, Shitong Wu, Wenhao Ye et al.

The Blahut-Arimoto (BA) algorithm has played a fundamental role in the numerical computation of rate-distortion (RD) functions. This algorithm possesses a desirable monotonic convergence property by alternatively minimizing its Lagrangian with a fixed multiplier. In this paper, we propose a novel modification of the BA algorithm, wherein the multiplier is updated through a one-dimensional root-finding step using a monotonic univariate function, efficiently implemented by Newton's method in each iteration. Consequently, the modified algorithm directly computes the RD function for a given target distortion, without exploring the entire RD curve as in the original BA algorithm. Moreover, this modification presents a versatile framework, applicable to a wide range of problems, including the computation of distortion-rate (DR) functions. Theoretical analysis shows that the outputs of the modified algorithms still converge to the solutions of the RD and DR functions with rate $O(1/n)$, where $n$ is the number of iterations. Additionally, these algorithms provide $\varepsilon$-approximation solutions with $O\left(\frac{MN\log N}{\varepsilon}(1+\log |\log \varepsilon|)\right)$ arithmetic operations, where $M,N$ are the sizes of source and reproduced alphabets respectively. Numerical experiments demonstrate that the modified algorithms exhibit significant acceleration compared with the original BA algorithms and showcase commendable performance across classical source distributions such as discretized Gaussian, Laplacian and uniform sources.