Reducing Computational Complexity in Long-Context LLMs

Standard attention mechanisms scale quadratically with sequence length, creating a bottleneck for long-context applications. Spectral-LSH addresses this by introducing a compression technique that reduces the memory and compute footprint of prompts without sacrificing significant performance. By leveraging Krylov-projected locality-sensitive hashing (LSH), the method effectively maps high-dimensional token representations into a lower-dimensional space while preserving the semantic relationships necessary for accurate model inference.

Krylov-Projected Hashing for Semantic Preservation

The core innovation lies in the use of Krylov subspace projections to refine the hashing process. Unlike traditional LSH, which may suffer from collisions that degrade model accuracy, the Krylov-based approach captures the spectral properties of the attention matrix. This ensures that the compressed representation retains the most critical information from the original prompt. By projecting tokens into this subspace, the model can perform attention operations in a sub-quadratic time complexity, enabling the processing of significantly longer prompts than would be feasible with standard attention mechanisms.

Practical Implications for AI Engineering

This approach offers a pathway to deploying LLMs in environments where memory constraints are tight but context requirements are high. By compressing prompts before they reach the attention layers, developers can maintain high throughput and reduce latency. The sub-quadratic nature of Spectral-LSH makes it particularly well-suited for RAG pipelines and long-form document analysis, where the overhead of processing massive context windows often leads to diminishing returns in speed and cost-efficiency.