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As Large Language Models (LLMs) grow in size and context length, efficient inference strategies are essential to maintain low-latency token generation. Unfortunately, conventional tensor and data parallelism face diminishing returns when scaling across multiple devices. We propose a novel form—attention-level speculative parallelism (ALSpec)—that predicts self-attention outputs to execute subsequent operations early on separate devices. Our approach overlaps attention and non-attention computations, reducing the attention latency overhead at 128K context length by up to 5x and improving end-to-end decode latency by up to 1.65x, all without sacrificing quality. We establish the fundamental pillars for speculative execution and provide an execution paradigm that simplifies implementation. We show that existing attention-approximation methods perform well on simple information retrieval tasks, but they fail in advanced reasoning and math. Combined with speculative execution, we can approximate up to 90% of self-attention without harming model correctness. Demonstrated on Tenstorrent's NPU devices, we scale up LLM inference beyond current techniques, paving the way for faster inference in transformer models.