Thursday, December 04, 2025
| Operation | Physics/Concept Domain | Computation Mode | Software/Hardware Reality | SIMD/ASM/HW Instructions | Typical Gain |
|---|---|---|---|---|---|
| Attention computation (QรKแต) | Quantum / Entanglement | 6D phase space (per mode) | Massive matmul (batch, heads, seq_len) | AVX-512 VNNI, AMX (Intel), Tensor Cores (NVIDIA) | ร10โ30 vs scalar |
| Token โ latent space projection | Quantum / Entanglement | 6D per particle (QED/QFT) | GEMV/GEMM dense | AVX-512, BF16/FP16, AMX Tile | ร20โ50 |
| Retrocausal update (bidirectional) | Quantum / Entanglement | CFT(2,0) M5-branes | 2 forward passes + fusion (BERT/xLSTM) | FMA SIMD + memory coalescing | ร8โ15 |
| Constructive interferences (soft attention) | Quantum / Entanglement | 6D SYM orbifolds | Softmax + weighted sum | AVX-512 exp + reduce, Tensor Cores | ร30 |
| Disentanglement/entanglement regularization | Quantum / Entanglement | Twistors 6Dโ4D | Gradient penalty + orthogonalization | Matmul + truncated SVD SIMD | ร15โ40 |
| Global "collapse" simulation | Quantum / Entanglement | 6D supersymmetric | Beam search, nucleus sampling (top-k/p) | AVX-512 gather + bitonic sort | ร100+ |
| Numerical squeezing | Quantum / Entanglement | 6D phase space QFT/CFT | Time-frequency resolution beyond Heisenberg | Non-linear FFT + simulated squeezed states | ร5โ20 |
| Simulated gravitational lensing | Relativistic / Gravitational | 6D geodesics or N-dim | Synthetic distortion for radar robustness | Ray marching + geodesic deformation GPU | ร3โ8 |
| Quasi-periodic torus breakdown | Chaos / Nonlinear Dynamics | N-dim symplectic | Breakdown to chaos via type-II intermittency | Symplectic integration + rotation number analysis | ร2โ5 |
| Volumetric cavitation tracking | Chaos / Nonlinear Dynamics | N-dim level-set | Tracking via level-set ฯ=0 until collapse | GPU-accelerated level-set + PDE solvers | ร10โ40 |
| Lyapunov exponents (Takens embedding) | Chaos / Nonlinear Dynamics | N-dim recurrence | Trajectory divergence detection โ pre-collapse | AVX-512 + recurrence matrix SIMD | ร15 |
| micro-Doppler extraction (symplectic invariants) | Signal / Micro-Doppler | N-dim invariants | Drone/gesture detection | Symplectic transforms + vectorized chirp FFT | ร20โ60 |
| Remote mechanical resonance | Signal / Micro-Doppler | N-dim Hilbert | Passive vibration detection (surveillance) | Hilbert transform + CWT SIMD | ร12โ30 |
| Classification via Lie/Symplectic groups | Signal / Micro-Doppler | N-dim Lie algebras | Geometric invariants on radar signatures | Complex moments + Lie algebra embeddings | ร8โ25 |
| Tensor matrix multiplication | Tensorial / ML | N-dim rank-4 | GEMM for transformers (attention, FFN) | Intel AMX (1Kร1K tiles), NVIDIA Tensor Cores FP8 | ร50โ200 |
| 3D tensor convolutions | Tensorial / Vision | 3DโN-dim | CNNs, vision transformers | Tensor Cores (NVIDIA), XMX (Intel Arc), TPUs | ร30โ100 |
| Rank-3/4 tensor contractions | Tensorial / Physics | N-dim contractions | Quantum circuit simulation, physics ML | AMX-BF16, AVX-512 BF16 + tiling | ร25โ80 |
| Arbitrary BigInt multiplication | Arithmetic / Crypto | Karatsuba N-dim | Karatsuba/Toom-Cook โ vectorized ASM | AVX-512IFMA, ADX, PCLMULQDQ | ร10โ50 |
| BigInt division (multi-precision) | Arithmetic / Crypto | Newton-Raphson N-dim | Vectorized Newton-Raphson | AVX-512 VPOPCNT + VPDPBUSD | ร8โ30 |
| BigInt โ decimal conversion | Arithmetic / I/O | N-dim division | Division by 10^n vectorized | AVX-512 + divisor network | ร20โ100 |
| Precise timestamping (cycle-level) | Timing / Low-level | Dimension-independent | Performance profiling, deterministic timing | RDTSC/RDTSCP + LFENCE, TSC_ADJUST | ร1000 vs chrono |
| Parallel benchmarking | Timing / Low-level | Multi-core independent | Invariant TSC multi-core | RDTSCP + CPUID barrier, AVX-512 gather | ร500 |