Multimodal AI Is Just Tensor Algebra: The Linear Algebra Truth Behind Vision-Language Models

Author(s): DrSwarnenduAI

Originally published on Towards AI.

The Mathematical Symphony That Powers Billion-Dollar AI Systems

After reverse-engineering the mathematical foundations of GPT-4V, DALL-E, and Claude 3, I’ve discovered something profound: these systems that seem to “understand” images and text are performing a carefully orchestrated sequence of tensor operations that creates an emergent mathematical structure. The beauty isn’t in the complexity — it’s in how elegant mathematical principles from linear algebra, differential geometry, and information theory compose to create what we call “multimodal understanding.”

The article delves into the intricate mathematical foundations underpinning multimodal AI systems such as GPT-4V and DALL-E, highlighting how these technologies leverage tensor algebra and various mathematical concepts to achieve a sophisticated understanding of both images and text. It explores the role of linear transformations, attention mechanisms, and gradient descent in the formation of embeddings that facilitate multimodal understanding, while also discussing the potential limits and future directions of this rapidly evolving field.

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Published via Towards AI