Search arXivSearch

arXiv · 2210.17444

Multimodal Information Bottleneck: Learning Minimal Sufficient Unimodal and Multimodal Representations

Abstract

Learning effective joint embedding for cross-modal data has always been a focus in the field of multimodal machine learning. We argue that during multimodal fusion, the generated multimodal embedding may be redundant, and the discriminative unimodal information may be ignored, which often interferes with accurate prediction and leads to a higher risk of overfitting. Moreover, unimodal representations also contain noisy information that negatively influences the learning of cross-modal dynamics. To this end, we introduce the multimodal information bottleneck (MIB), aiming to learn a powerful and sufficient multimodal representation that is free of redundancy and to filter out noisy information in unimodal representations. Specifically, inheriting from the general information bottleneck (IB), MIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target and simultaneously constraining the mutual information between the representation and the input data. Different from general IB, our MIB regularizes both the multimodal and unimodal representations, which is a comprehensive and flexible framework that is compatible with any fusion methods. We develop three MIB variants, namely, early-fusion MIB, late-fusion MIB, and complete MIB, to focus on different perspectives of information constraints. Experimental results suggest that the proposed method reaches state-of-the-art performance on the tasks of multimodal sentiment analysis and multimodal emotion recognition across three widely used datasets. The codes are available at \url{https://github.com/TmacMai/Multimodal-Information-Bottleneck}.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sijie Mai, Ying Zeng, Haifeng Hu. 2022-12-05. Multimodal Information Bottleneck: Learning Minimal Sufficient Unimodal and Multimodal Representations. https://doi.org/10.1109/tmm.2022.3171679

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

Classical particle methods based on propagation of chaos (PoC) have been developed for solving mean-field stochastic differential equations and their associated nonlinear Fokker--Planck equations. However, direct PoC implementations are difficult to apply to high-dimensional problems because they require simulating and storing large numbers of interacting particles, often with high particle-particle interaction costs. Motivated by these limitations, we build on the recently proposed sequential propagation of chaos (SPoC) framework, which replaces the fully interacting particle system in PoC with a sequential interaction mechanism. Based on this structure, we present DeepSPoC, a neural particle method that embeds a neural density representation into the sequential particle dynamics. DeepSPoC simulates particles batch by batch, while the neural network represents the evolving empirical law and is substituted into the coefficients of the mean-field SDE, thereby replacing direct particle-particle interactions with particle-network interactions. In DeepSPoC, a recently developed normalizing flow model called KRnet is used to approximate the empirical measure of particles. Compared with direct particle implementations, DeepSPoC substantially reduces memory consumption and evaluates interaction terms more efficiently, thereby improving scalability for high-dimensional problems. We apply DeepSPoC to a wide range of mean-field equations and verify its effectiveness and computational advantages.

cs.LG