MicroTensor Computing (MTC-8): An Architecture for Adaptive Sub-Byte GEMM, Spatial Octrees, and Prime Residue Arithmetic

Modern neural networks and scientific computing are dominated by uniform fixed-precision arithmetic (FP32, BF16, INT8, FP4) allocated across flat, monolithic memory buffers. While optimal for uniform dense distributions, this paradigm degrades severely in the presence of non-uniform dynamics, multi-scale energy variations, and heavy-tailed outliers. We introduce MicroTensor Computing (MTC-8), a geometric computational architecture based on localized micro-tensors, decoupled metadata interpretation, and hierarchical structural pointer composition. MTC-8 establishes three foundational principles: (1) Joint Precision Negotiation, which dynamically selects interacting block bit-depths by bounding forward matrix product error Delta(AB) <= epsilon rather than isolated reconstruction loss; (2) Spatial Octree Geometry, which extends micro-tensors to 3D 2x2x2 micro-cubes and leverages non-Archimedean vacuum pruning to collapse empty physical space; (3) Number-Theoretic Arithmetic, which introduces carry-free parallel Residue Number Systems (RNS) across prime moduli and balanced ternary (F3) multiplier-free linear algebra with an optimal radix economy (E approx 2.730). Empirical benchmarks demonstrate that on non-uniform multi-scale matrices where conventional INT4 collapses with 43.3% relative error, MTC-8 maintains strictly bounded error at 0.70% (43.1 dB SNR, a +14 dB gain over INT8) while achieving a 2.0x–2.5x compute kernel speedup (35.7 GFLOPS on CPU). In 3D physical fields, octree vacuum pruning delivers a 47.6x memory reduction (97.9% storage savings). In end-to-end 528K-parameter neural network experiments, pre-packed MTC layers achieve a 5.1x inference speedup over conventional INT8, while balanced ternary quantization-aware training compresses model parameters by 19.1x (from 2,069 KB to 108 KB) and converges with zero hardware multipliers in both forward and backward activation passes. Code, test harness, and single-command benchmarks: https://github.com/Sharexi/TensorPack