nx_fnet_mix.nx

nx_fnet_mix.nx -- FNET-001: SUB-QUADRATIC Fourier token-mixer (FNet, Lee-Thorp/Ainslie/Eckstein/Ontanon 2021). The escape from the transformer VRAM/compute exponential is JUST MATH. Self-attention mixes tokens with an all-pairs softmax(Q@K^T)@V -- O(n^2 * d) multiplies, the quadratic that explodes VRAM as context grows. FNet replaces that learned attention sublayer with a parameter-FREE 2D Discrete Fourier Transform and keeps the REAL part: y = Re( FFT_seq( FFT_hidden(x) ) ). Token mixing becomes O(n * d * log(n*d)) -- linearithmic, not quadratic -- with ZERO attention parameters and ZERO n-by-n score matrix to hold in memory. This is the sovereign realization of that math: * a GENERALIZED radix-2 FFT for ANY power-of-2 length (the shipped nx_fft caps at N=32 via a hardcoded twiddle table; here twiddles are synthesized for arbitrary N by the sovereign CORDIC fx_cos/fx_sin), * the FNet 2D-DFT real-part token mixer composed from it, * an integer-MULTIPLY op counter threaded through so the gate can MEASURE (never assert) the sub-quadratic crossover against scaled-dot-product attention. DRY: reuses nx_fft_log2 + nx_fft_bit_reverse (already length-generic) and the SAME Q14 butterfly arithmetic as the shipped, gated nx_fft, so the generalized FFT is bit-comparable to it (proven in nx_fnet_mix_gate.nx). genealogy_id: cooley_tukey_1965_fft + lee_thorp_2021_fnet + vaswani_2017_attention(as the incumbent it exceeds) lineage_id: fnet_sovereign_fourier_token_mixer_v1 license_tier: ORIGINAL nx_safety_envelope: intended_use: "parameter-free sub-quadratic token mixing for sovereign sequence models (FNet block); the no-VRAM-exponential alternative to self-attention" sil_target: SIL2 evidence: [Q14_fixed_point_deterministic, FFT_equals_naive_DFT_gated, twiddles_match_shipped_nx_fft, measured_subquadratic_crossover_vs_attention] residual_risk: "N and hidden-dim d must be powers of two (radix-2 contract); Q14 saturates above |x|>=2." verdict: GREEN (nx_fnet_mix_gate 2026-06-14: C1 FFT==naive-DFT, C2 twiddles match nx_fft within 1 Q14, measured sub-quadratic crossover vs attention 6->22->75->264x at n=64..4096; see fnet_mix.log)