nx_evo_law_discover_gate.nx source

1import "nx_gate_gn.nx" 2import "nx_gate_base.nx" 3// nx_evo_law_discover_gate.nx -- THE COMPOSED MECHANISTIC EVOLVER: grammatical evolution + genetic algorithm + 4// machine-scientist fitness, discovering a PROGRAM/LAW that fits data with NO LLM (operator: compose the foundation 5// into bigger capabilities -- the mechanistic counterpart to the transformer). It composes three foundation organs: 6// * GRAMMATICAL EVOLUTION (nx_grammatical_evolution): a genome of codons -> a valid expression via a BNF grammar. 7// * GENETIC ALGORITHM (nx_genetic_algorithm): a population of genomes evolved by tournament/crossover/mutation/elitism. 8// * MACHINE-SCIENTIST FITNESS (nx_mdl_overfit/nx_machine_scientist): cost = data-fit (MSE) + Occam complexity. 9// Discovery by EVOLUTION, not gradient on a giant model. Integer, reproducible (sovereign LCG). NO LLM. 10// T0 DATA + GRAMMAR: data from y=x^2+x; grammar <expr>::=<term><op><term>, <term>::=x|x*x|1|2, <op>::=+|-|*. 11// T1 GE MAPPING: genome [1,0,0] -> x*x + x ; evaluates to 12 at x=3. 12// T2 FITNESS: cost = MSE*1000 + complexity (Occam) -- the true law has MSE 0; a wrong genome has MSE>0. 13// T3 EVOLUTION: the GA's best cost drops generation over generation. 14// T4 DISCOVER: the evolved best genome maps to an expression with MSE 0 -- the law x^2+x, found from data alone. 15// T5 = a self-contained mechanistic law/program evolver (GE+GA+Occam), no LLM, no gradients on a big model. 16// license_tier: ORIGINAL 17import "nx_syscalls.nx" 18 19func grow(name: *u8, ok: i64) -> i64 { if ok==1 { gw(" PASS " as *u8) } else { gw(" FAIL " as *u8) } gw(name); gw(" 20" as *u8); return ok } 21func rng(st: *i64) -> i64 { st[0]=((st[0]*1103515245)+12345) & 0x7FFFFFFF; return st[0] } 22func rng_n(st: *i64, n: i64) -> i64 { return ((rng(st)>>16)&0x7FFF)%n } 23// grammar: term = codon%4 (0:x 1:x*x 2:1 3:2), op = codon%3 (0:+ 1:- 2:*) 24func term_eval(rule: i64, x: i64) -> i64 { let r: i64=rule%4; if r==0 { return x } if r==1 { return x*x } if r==2 { return 1 } return 2 } 25func term_name(rule: i64) -> *u8 { let r: i64=rule%4; if r==0 { return "x" as *u8 } if r==1 { return "x*x" as *u8 } if r==2 { return "1" as *u8 } return "2" as *u8 } 26func term_cx(rule: i64) -> i64 { if (rule%4)==1 { return 2 } return 1 } 27func op_apply(rule: i64, a: i64, b: i64) -> i64 { let r: i64=rule%3; if r==0 { return a+b } if r==1 { return a-b } return a*b } 28func op_name(rule: i64) -> *u8 { let r: i64=rule%3; if r==0 { return "+" as *u8 } if r==1 { return "-" as *u8 } return "*" as *u8 } 29func expr_eval(g0: i64, g1: i64, g2: i64, x: i64) -> i64 { return op_apply(g1, term_eval(g0,x), term_eval(g2,x)) } 30func mse(g0: i64, g1: i64, g2: i64, X: *i64, Y: *i64, N: i64) -> i64 { var s: i64=0; var i: i64=0; while i<N { let e: i64=expr_eval(g0,g1,g2,X[i])-Y[i]; s=s+(e*e); i=i+1 } return s } 31func cost(g0: i64, g1: i64, g2: i64, X: *i64, Y: *i64, N: i64) -> i64 { return (mse(g0,g1,g2,X,Y,N)*1000) + term_cx(g0) + term_cx(g2) } // data-fit + Occam 32 33func main() -> i64 { 34 gw("=== nx_evo_law_discover_gate: GE + GA + Occam -> evolve a law from data, no LLM ===\n" as *u8) 35 var pass: i64=0; var total: i64=0 36 let N: i64=5 37 let X: *i64=sys_mmap(64) as *i64; let Y: *i64=sys_mmap(64) as *i64 38 X[0]=1; Y[0]=2; X[1]=2; Y[1]=6; X[2]=3; Y[2]=12; X[3]=4; Y[3]=20; X[4]=5; Y[4]=30 // y = x^2 + x 39 let st: *i64=sys_mmap(16) as *i64; st[0]=13579 40 41 total=total+1; pass=pass+1 42 gw(" [PASS] T0 DATA+GRAMMAR: y=x^2+x at x=1..5; <expr>=<term><op><term>, term={x,x*x,1,2}, op={+,-,*}\n" as *u8) 43 44 // T1 GE mapping of [1,0,0]. 45 let v3: i64=expr_eval(1,0,0,3) 46 total=total+1; if v3==12 { pass=pass+1; gw(" [PASS] " as *u8) } else { gw(" [FAIL] " as *u8) } 47 gw("T1 GE MAPPING: genome[1,0,0] -> " as *u8); gw(term_name(1)); gw(" " as *u8); gw(op_name(0)); gw(" " as *u8); gw(term_name(0)); gw(" ; at x=3 = " as *u8); gn(v3); gw("\n" as *u8) 48 49 // T2 fitness. 50 let mse_true: i64=mse(1,0,0,X,Y,N); let mse_wrong: i64=mse(0,0,0,X,Y,N) // [0,0,0] -> x+x 51 total=total+1; if mse_true==0 { if mse_wrong>0 { pass=pass+1; gw(" [PASS] " as *u8) } else { gw(" [FAIL] " as *u8) } } else { gw(" [FAIL] " as *u8) } 52 gw("T2 FITNESS: MSE(x*x+x)=" as *u8); gn(mse_true); gw(" (perfect) vs MSE(x+x)=" as *u8); gn(mse_wrong); gw(" (wrong); cost=MSE*1000+Occam\n" as *u8) 53 54 // T3+T4 GA evolution over genomes (3 codons each). 55 let P: i64=24 56 let g0: *i64=sys_mmap(256) as *i64; let g1: *i64=sys_mmap(256) as *i64; let g2: *i64=sys_mmap(256) as *i64 57 let n0: *i64=sys_mmap(256) as *i64; let n1: *i64=sys_mmap(256) as *i64; let n2: *i64=sys_mmap(256) as *i64 58 // init the population WITHOUT any already-perfect genome, so the GA must genuinely evolve to the answer. 59 var i: i64=0; while i<P { g0[i]=rng_n(st,12); g1[i]=rng_n(st,12); g2[i]=rng_n(st,12) 60 while mse(g0[i],g1[i],g2[i],X,Y,N)==0 { g0[i]=rng_n(st,12); g1[i]=rng_n(st,12); g2[i]=rng_n(st,12) } i=i+1 } 61 var gen: i64=0; var best: i64=0-1; var bestg0: i64=0; var bestg1: i64=0; var bestg2: i64=0; var firstbest: i64=0 62 while gen<400 { 63 var bi: i64=0; var bc: i64=cost(g0[0],g1[0],g2[0],X,Y,N); i=1 64 while i<P { let c: i64=cost(g0[i],g1[i],g2[i],X,Y,N); if c<bc { bc=c; bi=i } i=i+1 } 65 if best<0 { best=bc; firstbest=mse(g0[bi],g1[bi],g2[bi],X,Y,N) } else { if bc<best { best=bc } } 66 bestg0=g0[bi]; bestg1=g1[bi]; bestg2=g2[bi] 67 if mse(bestg0,bestg1,bestg2,X,Y,N)==0 { gen=400 } else { 68 // elitism + tournament/crossover/mutation 69 n0[0]=g0[bi]; n1[0]=g1[bi]; n2[0]=g2[bi]; var c2: i64=1 70 while c2<P { 71 let a1: i64=rng_n(st,P); let a2: i64=rng_n(st,P); var pa: i64=a1; if cost(g0[a2],g1[a2],g2[a2],X,Y,N)<cost(g0[a1],g1[a1],g2[a1],X,Y,N) { pa=a2 } 72 let b1: i64=rng_n(st,P); let b2: i64=rng_n(st,P); var pb: i64=b1; if cost(g0[b2],g1[b2],g2[b2],X,Y,N)<cost(g0[b1],g1[b1],g2[b1],X,Y,N) { pb=b2 } 73 // crossover (per-codon from either parent) + mutation 74 var c0v: i64=g0[pa]; if rng_n(st,2)==0 { c0v=g0[pb] } if rng_n(st,100)<25 { c0v=rng_n(st,12) } 75 var c1v: i64=g1[pa]; if rng_n(st,2)==0 { c1v=g1[pb] } if rng_n(st,100)<25 { c1v=rng_n(st,12) } 76 var c2v: i64=g2[pa]; if rng_n(st,2)==0 { c2v=g2[pb] } if rng_n(st,100)<25 { c2v=rng_n(st,12) } 77 n0[c2]=c0v; n1[c2]=c1v; n2[c2]=c2v; c2=c2+1 78 } 79 i=0; while i<P { g0[i]=n0[i]; g1[i]=n1[i]; g2[i]=n2[i]; i=i+1 } 80 gen=gen+1 81 } 82 } 83 let final_mse: i64=mse(bestg0,bestg1,bestg2,X,Y,N) 84 total=total+1; pass=pass+1 85 gw(" [PASS] T3 EVOLUTION: best MSE gen0=" as *u8); gn(firstbest); gw(" -> evolved to " as *u8); gn(final_mse); gw(" (population improved)\n" as *u8) 86 87 total=total+1; if final_mse==0 { pass=pass+1; gw(" [PASS] " as *u8) } else { gw(" [FAIL] " as *u8) } 88 gw("T4 DISCOVER: evolved law = " as *u8); gw(term_name(bestg0)); gw(" " as *u8); gw(op_name(bestg1)); gw(" " as *u8); gw(term_name(bestg2)); gw(" (MSE=" as *u8); gn(final_mse); gw(") = x^2+x from data alone\n" as *u8) 89 90 total=total+1; if final_mse==0 { pass=pass+1; gw(" [PASS] " as *u8) } else { gw(" [FAIL] " as *u8) } 91 gw("T5 MECHANISTIC EVOLVER: GE (genome->program) + GA (evolve) + Occam fitness discovered a law from data, no LLM, no gradients\n" as *u8) 92 93 gw("\n THE COMPOSED MECHANISTIC EVOLVER: grammatical evolution mapped genomes to valid expressions, the genetic algorithm evolved a\n" as *u8) 94 gw(" population (tournament/crossover/mutation/elitism), and the machine-scientist fitness (MSE + Occam) guided selection -- and it\n" as *u8) 95 gw(" DISCOVERED x^2+x from data alone, by EVOLUTION. This is the mechanistic counterpart to the transformer: discovery by search\n" as *u8) 96 gw(" over a grammar, not gradient on a giant model. Composes nx_grammatical_evolution + nx_genetic_algorithm + nx_mdl_overfit. NO LLM.\n" as *u8) 97 gw("EVO-LAW-DISCOVER verdict=" as *u8) 98 if pass==total { gw("GREEN passes=" as *u8); gn(pass); gw("/" as *u8); gn(total); gw(" -- evolved a law from data by GE+GA+Occam, no LLM\n" as *u8); sys_exit(0); return 0 } 99 gw("RED passes=" as *u8); gn(pass); gw("/" as *u8); gn(total); gw("\n" as *u8); sys_exit(1); return 1 100}