Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels
arXiv:2606.07713v1 Announce Type: new Abstract: The attention mechanism is the dominant computational bottleneck in modern transformer-based AI. Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck. We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) tha
Ongoing research into optimizing transformer models is driven by the increasing computational and energy costs associated with their scaling, pushing for more efficient architectures and implementations.
Reducing the memory traffic and energy consumption of transformer mechanisms has direct implications for the scalability, cost-efficiency, and environmental footprint of AI systems, enabling larger and more capable models.
The focus shifts from solely FLOP counts to memory access and energy efficiency as the primary bottleneck in transformer performance, driving new architectural and mathematical approaches.
- · AI hardware manufacturers
- · Cloud AI providers
- · Research institutions developing large AI models
- · AI software optimization firms
- · Developers relying on inefficient transformer implementations
More memory-efficient transformer kernels will allow for processing longer sequence lengths with existing hardware.
Reduced operational costs and energy consumption for large-scale AI deployments, accelerating AI adoption and innovation.
The freed-up compute and energy resources could enable the development of even more complex and agentic AI models or allow AI to be deployed more widely in resource-constrained environments.
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Read at arXiv cs.LG