arXiv:2409.17502v2 Announce Type: replace Abstract: Broadcast operations are widely used in scientific computing libraries, yet their mathematical formulation is often implicit and inconsistently represented in machine learning literature. This problem frequently leads to invalid equations when element-wise products are written despite mismatched tensor shapes. In this paper, we formalize such operations by introducing the broadcast product $\boxdot$, which explicitly extends the Hadamard product through shape-aligned element duplication. We provide a rigorous definition of the broadcast produ
The proliferation of complex AI models and the increasing sophistication of computing libraries necessitate more precise mathematical formalisms for common operations that were previously handled implicitly.
Formalizing broadcast operations improves the reliability and interpretability of scientific computing, reducing errors in AI and machine learning models, and potentially accelerating research and development.
The introduction of a rigorous definition for broadcast products will lead to more robust and less ambiguous mathematical representations in machine learning literature and software implementations.
- · AI/ML researchers
- · Scientific computing libraries
- · High-performance computing
Increased clarity and correctness in machine learning mathematical notation and implementations.
Improved efficiency and reduced debugging time for complex tensor operations in AI development.
Potentially enables more sophisticated and error-resistant model architectures by providing a clearer mathematical foundation for tensor interactions.
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