The pursuit of scale in deep learning has entrenched a trade-off: computational throughput is prioritized at the expense of numerical precision. We argue this compromise is fundamentally at odds with the requirements of general intelligence. We propose the \textit{Exactness Hypothesis}: high-order causal reasoning -- a cornerstone of AGI -- demands a substrate supporting arbitrary-precision, logically consistent arithmetic. We trace prevalent LLM failures, such as logical hallucinations and incoherence, to the inherent limitations of IEEE 754 floating-point arithmetic, where approximation errors compound catastrophically in deep functions. As a solution, we present the Halo Architecture, which transitions the computational foundation from approximate reals ($\mathbb{R}$) to exact rationals ($\mathbb{Q}$). Halo is realized through a custom Exact Inference Unit (EIU), whose design -- featuring asynchronous MIMD reduction and dual-modular redundancy -- resolves the performance and reliability bottlenecks of exact computation at scale. Crucially, we theoretically prove that Halo's number-theoretic quantization yields a quadratic error decay ($\mathcal{O}(D^{-2})$), strictly superior to the linear barrier of standard fixed-point arithmetic. In rigorous simulations, 600B-parameter BF16 models fail in chaotic systems within steps, while Halo sustains perfect numerical fidelity indefinitely. Our work posits exact arithmetic as non-negotiable for advancing reasoning-capable AGI and provides a co-designed hardware-software path toward verifiable, exascale-ready AI systems

翻译：深度学习对规模的追求固化了一种权衡：计算吞吐量被优先考虑，代价是数值精度。我们认为这种妥协从根本上与通用智能的要求相悖。我们提出\textit{精确性假说}：高阶因果推理——AGI的基石——需要一个支持任意精度、逻辑一致算术的底层基础。我们将当前主流LLM的失败（如逻辑幻觉和前后矛盾）追溯至IEEE 754浮点算术的固有局限，其中近似误差在深度函数中会灾难性地累积。作为解决方案，我们提出了Halo架构，该架构将计算基础从近似实数（$\mathbb{R}$）转换到精确有理数（$\mathbb{Q}$）。Halo通过一个定制的精确推理单元（EIU）实现，其设计——采用异步MIMD规约和双模冗余——解决了大规模精确计算的性能和可靠性瓶颈。关键的是，我们从理论上证明了Halo的数论量化方法实现了二次误差衰减（$\mathcal{O}(D^{-2})$），严格优于标准定点算术的线性误差界限。在严格的模拟中，6000亿参数的BF16模型在混沌系统中几步内即告失效，而Halo则能无限期地保持完美的数值保真度。我们的工作主张精确算术是推进具备推理能力的AGI不可或缺的条件，并为构建可验证的、面向百亿亿次计算规模的AI系统提供了一条软硬件协同设计的路径。