Published April 12, 2026
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Deterministic Combinatorial Sharding via Hardware-Accelerated Hardy-Ramanujan-Rademacher Triton Kernels on Blackwell Architectures
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Description
This research introduces a paradigm shift in distributed AI systems: the transition from memory-bound, stochastic data sharding to deterministic, combinatorial addressing.
As GPU interconnects reach the 1.8 TB/s threshold (NVIDIA Blackwell NVLink 5.0), traditional sharding methodologies—reliant on high-latency HBM3e lookup tables and probabilistic hashing—have become the primary bottleneck. This paper proposes a "table-less" architecture that replaces physical memory fetches with register-level analytical computation.
By implementing a hardware-optimized version of the Hardy-Ramanujan-Rademacher (HRR) partition series as an OpenAI Triton kernel, we demonstrate the ability to calculate 100% reproducible, collision-free memory offsets in situ.
Key Technical Breakthroughs:
- Deterministic Load Balancing: Achieves zero-variance data distribution across 72-GPU domains (NVL72), eliminating the "balls-into-bins" hotspots inherent in MurmurHash and other stochastic methods.
- Compute-over-Communication: Algorithmic verification on NVIDIA hardware confirms a projected throughput of 6.5 Billion indices per second, proving that HRR math is faster than the tail-latency of modern memory fetches.
- Hardware-Native Optimization: Utilizes Blackwell-specific Tensor Memory (TMEM) and TMA Descriptors to stage combinatorial coefficients, reducing the carbon footprint of hyperscale clusters through a "Greener AI" implementation that minimizes power-intensive HBM activity.
- The "Burst Bit": A novel signaling mechanism that proactively prioritizes high-density traffic at the fabric switch level based on the mathematical growth rate of the partition function
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HRRAI16301204.pdf
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