On Stronger Computational Separations Between Multimodal and Unimodal Machine Learning

TL;DR

The paper addresses whether multimodal data provably offers computational advantages over unimodal data in learning tasks, proposing an average-case framework and showing a stronger separation under a low-noise LPN assumption. It introduces a concrete bimodal construction that achieves polynomial-time learnability when both modalities are available, while unimodal learning remains intractable, and proves that such separations induce cryptographic key agreement protocols, suggesting these extreme advantages are likely rare in practice. The work highlights a fundamental distinction between computational and statistical benefits of multimodal learning and provides a cryptographic lens for evaluating the practicality of strong average-case separations. Overall, it provides a rigorous bridge between multimodal learning theory and cryptography, arguing that while average-case computational gains are possible, they may be limited to cryptographically structured distributions, whereas statistical benefits remain broadly plausible.

Abstract

Recently, multimodal machine learning has enjoyed huge empirical success (e.g. GPT-4). Motivated to develop theoretical justification for this empirical success, Lu (NeurIPS '23, ALT '24) introduces a theory of multimodal learning, and considers possible \textit{separations} between theoretical models of multimodal and unimodal learning. In particular, Lu (ALT '24) shows a computational separation, which is relevant to \textit{worst-case} instances of the learning task. In this paper, we give a stronger \textit{average-case} computational separation, where for ``typical'' instances of the learning task, unimodal learning is computationally hard, but multimodal learning is easy. We then question how ``natural'' the average-case separation is. Would it be encountered in practice? To this end, we prove that under basic conditions, any given computational separation between average-case unimodal and multimodal learning tasks implies a corresponding cryptographic key agreement protocol. We suggest to interpret this as evidence that very strong \textit{computational} advantages of multimodal learning may arise \textit{infrequently} in practice, since they exist only for the ``pathological'' case of inherently cryptographic distributions. However, this does not apply to possible (super-polynomial) \textit{statistical} advantages.

Theorems & Definitions (22)

• Definition 1.1: LPN assumption
• Theorem 1.2: Informal
• Theorem 1.3: Informal
• Definition 2.1
• Theorem 3.1: Separation
• proof
• Theorem 3.2
• proof
• Lemma 3.3: Chernoff Bound, cf. Theorem 2.1 janson2011random
• Theorem 3.4