What Makes Multi-modal Learning Better than Single (Provably) (2106.04538v2)

Abstract: The world provides us with data of multiple modalities. Intuitively, models fusing data from different modalities outperform their uni-modal counterparts, since more information is aggregated. Recently, joining the success of deep learning, there is an influential line of work on deep multi-modal learning, which has remarkable empirical results on various applications. However, theoretical justifications in this field are notably lacking. Can multi-modal learning provably perform better than uni-modal? In this paper, we answer this question under a most popular multi-modal fusion framework, which firstly encodes features from different modalities into a common latent space and seamlessly maps the latent representations into the task space. We prove that learning with multiple modalities achieves a smaller population risk than only using its subset of modalities. The main intuition is that the former has a more accurate estimate of the latent space representation. To the best of our knowledge, this is the first theoretical treatment to capture important qualitative phenomena observed in real multi-modal applications from the generalization perspective. Combining with experiment results, we show that multi-modal learning does possess an appealing formal guarantee.

A Theoretical Perspective on Multi-modal Learning

The paper "What Makes Multi-modal Learning Better than Single (Provably)" explores a critical question in the field of artificial intelligence and machine learning: can models fusing data from multiple modalities outperform their uni-modal counterparts, not just empirically, but also with theoretical justification? Despite the notable empirical success of multi-modal models in diverse applications, ranging from audio-visual learning to visual question answering, a rigorous theoretical framework has been lacking. This paper attempts to fill that gap by examining multi-modal learning through the lens of a popular fusion framework and providing the first theoretical treatment capturing qualitative phenomena observed in these models.

The authors focus on a framework where features from different modalities are encoded into a common latent space, which is then mapped into the task space. The paper establishes that multi-modal learning achieves a smaller population risk compared to using a subset of modalities, primarily due to a more accurate estimation of the latent space representation. This theoretical perspective challenges prior works that relied on strict assumptions concerning probability distributions across modalities and often ignored generalization performance.

Key Findings

The paper's key contributions are outlined as follows:

1. Theoretical Foundation for Multi-modal Advantage: The authors provide a theoretical proof showing that multi-modal learning can indeed outperform uni-modal learning in terms of a smaller population risk. This advantage is attributed to enhanced estimates of the latent representation, which is crucial for better generalization in learning tasks.
2. Structural Insights into Representation Quality: The authors formalize the concept of latent representation quality as a measure of how close a learned latent representation is to the true latent space. They establish a bound on this quality metric when using multiple modalities, thus offering a foundational principle for the selection and integration of modalities.
3. Empirical Results and Theoretical Validation: Through rigorous theoretical analysis and empirical studies, the paper demonstrates that multi-modal learning consistently results in superior latent representation quality compared to any subset of modalities. This is affirmed by experiments conducted on datasets with varying degrees of modality correlation.
4. Composite Framework of Multi-modal Learning: The examination of multi-modal learning is contextualized within a composite framework, prevalent in many existing empirical studies. Despite its common use, this framework's theoretical underpinnings had been underexplored until now.
5. Practical Implications and Guidelines: Practical guidance for modality selection is offered by comparing the empirical risk differences across various subsets of modalities. The authors suggest that using multiple modalities can enhance performance, especially when the number of samples is large and multiple modalities effectively minimize empirical risk.

Implications and Future Directions

The insights from this work have significant theoretical and practical implications for multi-modal AI systems. The establishment of a theoretical basis opens doors for more validated designs of multi-modal architectures that are robust and generalize well across diverse tasks. The findings encourage the exploration of new model architectures that maximize latent representation quality, thereby driving the development of more powerful AI systems.

One of the intriguing implications is the interplay between modality correlation and learning performance. The results suggest exploring combinations of modalities that maximize shared information while minimizing redundancy, which could revolutionize applications in areas like autonomous driving, healthcare, and multimedia search engines.

Looking forward, extensions of this theoretical framework could include relaxation of the assumptions regarding linearity in latent mappings, as well as expansion to non-linear or hierarchical representation paradigms. Another promising direction is the incorporation of these insights into optimization strategies that address practical challenges, such as dealing with incomplete modalities or imbalanced data streams, which are common in real-world applications.

In conclusion, this paper contributes substantially to understanding the theoretical mechanics behind the superior performance of multi-modal learning, paving the way for deeper insights and more effective AI systems in both academic research and practical deployment.