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recursive-self-improvement
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exact-arithmetic
certified-compilation
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aff9293 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 | """Auditable, bounded experiments; all favorable and unfavorable controls saved."""
from __future__ import annotations
import copy
import hashlib
import json
import math
from pathlib import Path
import platform
import sys
import time
import numpy as np
from synthesis import discover, digest, verify_tensor
from arithmetic import Kernel, NTTKernel, P
from native import build, NativeKernel, NativeNTTKernel
from tasks import reciprocal, exponential, reversion, catalan
from audit import CreditAccount, AnytimeGate, atomic_save
ROOT = Path(__file__).resolve().parents[1]
def arrayhash(x):
return hashlib.sha256(np.asarray(x,dtype='<i8').tobytes()).hexdigest()
def vector(seed,n,constant=1):
r=np.random.default_rng(seed).integers(0,P,n,dtype=np.int64)
r[0]=constant
return r
class Lab:
def __init__(self,root=ROOT,native=True):
self.root=Path(root)
self.config=json.loads((self.root/'experiment_config.json').read_text())
self.discovery=discover()
self.law=self.discovery['law']
self.native=build(self.law,self.root/'native_build') if native else {'available':False,'wall_seconds':0}
self.files={}
self.backend='native C++' if self.native['available'] else 'portable NumPy'
def save(self,name,data):
path=self.root/'results'/name
path.parent.mkdir(parents=True,exist_ok=True)
path.write_text(json.dumps(data,indent=2,sort_keys=True))
def kernel(self,cap=0,ntt=False):
if self.native['available']:
return NativeNTTKernel(self.law,self.native['library']) if ntt else NativeKernel(self.law,cap,self.native['library'])
return NTTKernel(self.law) if ntt else Kernel(self.law,cap)
def run_job(self,family,n,seed,cap=0,ntt=False):
# Generate task inputs outside the solver timer; this cost is shared and
# not called learning. Kernel construction and checking ARE inside.
f=vector(seed,n,0 if family=='exponential' else 1)
fshort=np.array([0,1,seed%19+1,seed%23+2,seed%13+1],dtype=np.int64)
b=vector(seed+9871,n,2)
start=time.perf_counter_ns()
k=self.kernel(cap,ntt)
if family=='reciprocal':
out=reciprocal(f,n,k)
elif family=='exponential':
out=exponential(f,n,k)
elif family=='reversion':
out=reversion(fshort,n,k)
elif family=='implicit_catalan':
out=catalan(n,k)
elif family=='convolution':
out=k.mul(f,b)
else:
raise ValueError('Unknown task family')
elapsed=time.perf_counter_ns()-start
record={'family':family,'length':n,'input_seed':seed,'cap':cap,'ntt':ntt,
'wall_ns':elapsed,'output_sha256':arrayhash(out),
'meter':k.meter.snapshot(),
'trace':[[a,b,count] for (a,b),count in sorted(k.trace.items())]}
return out,record
def train(self):
cfg=self.config
account=CreditAccount(cfg['bootstrap_ledger_units'])
disc=self.discovery['counts']
startup_charge=disc['rational_ops']+disc['pivot_tests']+disc['certificate_ops']
if not account.invest(startup_charge):
raise RuntimeError('Insufficient bootstrap credit')
cap=0
state=self.kernel(0).program()
records=[];service=[];audit=[]
training_wall_start=time.perf_counter()
for stage,n in enumerate(cfg['training_lengths']):
stage_start=time.perf_counter()
for rep in range(cfg['service_jobs_per_stage']):
seed=cfg['master_seed']+stage*1000+rep
out,live=self.run_job('reciprocal',n,seed,cap)
ref,base=self.run_job('reciprocal',n,seed,0)
if not np.array_equal(out,ref):
raise ArithmeticError('Service semantics changed')
account.service(base['meter']['ledger_units'],live['meter']['ledger_units'])
service.append({'stage':stage,'live':live,'reference':base})
seed=cfg['master_seed']+stage*1000+999
child_kernel=self.kernel(cap+1)
proposed=child_kernel.program(state['sha256'])
before,old=self.run_job('reciprocal',n,seed,cap)
after,new=self.run_job('reciprocal',n,seed,cap+1)
if not np.array_equal(before,after):
raise ArithmeticError('Candidate changed learning result')
# Validation work is an explicit cost of producing a successor.
checks=verify_tensor(self.law)[1]
investment=old['meter']['ledger_units']+new['meter']['ledger_units']+checks+len(json.dumps(proposed))
improvement=new['meter']['field_ops']<old['meter']['field_ops']
paid=account.invest(investment)
committed=paid and improvement
if committed:
cap+=1;state=proposed
event={'stage':stage,'length':n,'before_cap':cap-int(committed),'after_cap':cap,
'committed':committed,'candidate_sha256':proposed['sha256'],
'state_sha256':state['sha256'],'investment_units':investment,
'strict_arithmetic_gain':improvement,'paid':paid,
'parent_evaluation':old,'candidate_evaluation':new,
'account':account.snapshot(),'stage_wall_seconds':time.perf_counter()-stage_start}
records.append(event)
audit.append({'stage':stage,'candidate':proposed})
atomic_save(self.root/'results/checkpoint.json',
{'generation':stage+1,'program':state,'account':account.snapshot(),
'protocol_sha256':digest(cfg),'next_request':'bounded external job'})
atomic_save(self.root/f'results/checkpoint_{stage:02d}.json',
{'generation':stage+1,'program':state,'account':account.snapshot()})
result={'mode':'arithmetic objective; timings are diagnostic, not the promotion criterion',
'final_cap':cap,'commits':sum(x['committed'] for x in records),
'startup_discovery_units':startup_charge,'records':records,'service':service,
'programs':audit,'final_account':account.snapshot(),
'loop_wall_seconds_including_reference_audit':time.perf_counter()-training_wall_start,
'production_wall_seconds':sum(x['live']['wall_ns'] for x in service)/1e9+
sum((x['parent_evaluation']['wall_ns']+x['candidate_evaluation']['wall_ns'])/1e9 for x in records)+
self.discovery['wall_seconds']+self.native['wall_seconds'],
'reference_service_wall_seconds':sum(x['reference']['wall_ns'] for x in service)/1e9,
'accounting_note':'Production time includes discovery, native compilation, service and paired validation; reference reruns are research-only audit costs and are logged separately.'}
self.save('training.json',result)
return result
def same_child(self,final_cap):
cfg=self.config;rows=[]
for n in cfg['same_child_lengths']:
for rep in range(cfg['same_child_replicates']):
seed=710000+n*10+rep
child,child_record=self.run_job('reciprocal',n,seed,final_cap)
artifact=self.kernel(final_cap).program('counterfactual-fixed-parent-metadata')
for cap in range(final_cap+1):
old,record=self.run_job('reciprocal',n,seed,cap)
if not np.array_equal(old,child):
raise ArithmeticError('Same-child output mismatch')
fixed=verify_tensor(self.law)[1]+len(json.dumps(artifact))
rows.append({'length':n,'replicate':rep,'parent_cap':cap,
'candidate_cap':final_cap,'candidate_sha256':artifact['sha256'],
'identical_learned_output':True,
'parent_evaluation':record,'candidate_evaluation':child_record,
'meta_field_ops':record['meter']['field_ops']+child_record['meter']['field_ops'],
'meta_ledger_units':record['meter']['ledger_units']+child_record['meter']['ledger_units']+fixed,
'meta_wall_ns':record['wall_ns']+child_record['wall_ns']})
result={'definition':'Same fixed candidate artifact and task. Only the inherited arithmetic implementation used by the incumbent validation arm is intervened on.',
'not_a_claim':'This does not show that the proposal grammar or proof strategy improved.',
'rows':rows}
self.save('same_child.json',result)
return result
def holdout(self,final_cap,wall_cap):
cfg=self.config;rows=[]
methods=[('frozen_schoolbook',0,False),('arithmetic_lineage',final_cap,False),
('wall_gated_lineage',wall_cap,False),('static_cap4',4,False),
('static_full_envelope',20,False),('conventional_NTT',0,True)]
order_rng=np.random.default_rng(22012027)
for family in ['exponential','reversion','implicit_catalan','convolution']:
for n in cfg['holdout_lengths']:
for rep in range(cfg['holdout_replicates']):
seed=cfg['holdout_seed']+n*100+rep
expected=None
for j in order_rng.permutation(len(methods)):
name,cap,ntt=methods[int(j)]
out,row=self.run_job(family,n,seed,cap,ntt)
if expected is None:expected=out
elif not np.array_equal(out,expected):
raise ArithmeticError('Held-out algorithm disagreement')
row.update({'method':name,'replicate':rep,'correct_vs_other_algorithms':True})
rows.append(row)
result={'status':'Fresh coefficient instances and control-flow families, but the same finite-field arithmetic contract.',
'families_not_used_for_promotion':['exponential','reversion','implicit_catalan','convolution'],
'rows':rows}
self.save('holdout.json',result)
return result
def hardware_gate(self):
cfg=self.config;cap=0;records=[]
rng=np.random.default_rng(813411)
for proposal,n in enumerate(cfg['hardware_audit_lengths'],1):
gate=AnytimeGate(proposal,cfg['hardware_alpha'])
pairs=[];parent_cap=cap
for t in range(cfg['hardware_audit_max_pairs']):
seed=8800000+proposal*10000+t
order=list(map(int,rng.permutation(2)));data={};outs={}
for j in order:
outs[int(j)],data[int(j)]=self.run_job('reciprocal',n,seed,cap+int(j))
if not np.array_equal(outs[0],outs[1]):
raise ArithmeticError('Hardware gate saw a semantic difference')
a,b=data[0]['wall_ns'],data[1]['wall_ns']
sign=1 if b<a else (-1 if b>a else 0)
gate.update(sign)
pairs.append({'trial':t,'order':order,'parent_ns':a,'candidate_ns':b,
'sign':sign,'parent_units':data[0]['meter']['ledger_units'],
'candidate_units':data[1]['meter']['ledger_units']})
if gate.accepted and t+1>=16:
break
if gate.accepted:cap+=1
records.append({'proposal':proposal,'length':n,'parent_cap':parent_cap,
'candidate_cap':parent_cap+1,'accepted':gate.accepted,
'after_cap':cap,'evidence':gate.snapshot(),'pairs':pairs})
result={'final_cap':cap,'accepted_proposals':sum(r['accepted'] for r in records),
'alpha':cfg['hardware_alpha'],'records':records,
'null':'For a proposal, conditional probability of a candidate timing win is at most one half on the sampled reciprocal workload.',
'limitations':'No distribution-free guarantee for future wall time; hardware-dependent outcomes; this gate is separate from the arithmetic lineage.'}
self.save('hardware_gate.json',result)
return result
def payback(self,cap):
cfg=self.config;rows=[];rng=np.random.default_rng(199903)
for rep in range(cfg['payback_jobs']):
seed=9100000+rep
pair={};outs={}
for j in rng.permutation(2):
outs[int(j)],pair[int(j)]=self.run_job('reciprocal',cfg['payback_length'],seed,cap if j else 0)
if not np.array_equal(outs[0],outs[1]):
raise ArithmeticError('Payback task mismatch')
rows.append({'replicate':rep,'frozen':pair[0],'evolved':pair[1]})
result={'deployed_cap':cap,'rows':rows,
'frozen_seconds':sum(r['frozen']['wall_ns'] for r in rows)/1e9,
'evolved_seconds':sum(r['evolved']['wall_ns'] for r in rows)/1e9,
'note':'A measured finite deployment workload, not a forecast. Subtract separately recorded discovery, compilation and all relevant proposal-validation costs before claiming net payback.'}
self.save('payback.json',result)
return result
def fixed_budget(self,cap,wall_cap):
cfg=self.config;rows=[]
methods=[('frozen_schoolbook',0,False),('arithmetic_lineage',cap,False),
('wall_gated_lineage',wall_cap,False),('static_cap4',4,False),
('static_full_envelope',20,False),('conventional_NTT',0,True)]
for name,d,ntt in methods:
spent=0;completed=0;wall=0.;hashes=[]
# Exact shape model makes cost constant for non-NTT methods. NTT
# root setup is separately charged through measured counters.
while completed<1000:
out,r=self.run_job('reciprocal',cfg['budget_length'],9300000+completed,d,ntt)
units=r['meter']['ledger_units']
if spent+units>cfg['budget_ledger_units']:
# This look-ahead run belongs to audit, not the service
# budget; its full cost is explicitly disclosed.
lookahead={'units':units,'wall_ns':r['wall_ns']};break
spent+=units;wall+=r['wall_ns']/1e9;completed+=1;hashes.append(r['output_sha256'])
rows.append({'method':name,'completed':completed,'budget':cfg['budget_ledger_units'],
'spent_units':spent,'service_seconds':wall,'output_hashes':hashes,
'research_only_lookahead':lookahead})
result={'scope':'Equal warm-service abstract resource budgets; separate from end-to-end training budgets.',
'rows':rows}
self.save('fixed_budget.json',result)
return result
def e_simulation(self):
cfg=self.config;rng=np.random.default_rng(319127)
result=[]
for probability in [0.5,0.65,0.8]:
successes=0;stops=[]
for simulation in range(cfg['null_simulations']):
gate=AnytimeGate(1,cfg['hardware_alpha'])
for t in range(cfg['null_horizon']):
if gate.update(1 if rng.random()<probability else -1):
successes+=1;stops.append(t+1);break
result.append({'win_probability':probability,'accepted':successes,
'runs':cfg['null_simulations'],'horizon':cfg['null_horizon'],
'acceptance_fraction':successes/cfg['null_simulations'],
'mean_stopping_trial_if_accepted':float(np.mean(stops)) if stops else None})
output={'proposal':1,'allocated_alpha':cfg['hardware_alpha']/2,'results':result,
'interpretation':'Monte Carlo check of a proved gate, not evidence of AI capability.'}
self.save('e_simulation.json',output)
return output
def run(self):
totalstart=time.perf_counter()
self.save('discovery.json',self.discovery)
self.save('native_build.json',self.native)
self.save('environment.json',{'python':sys.version,'platform':platform.platform(),
'numpy':np.__version__,'backend':self.backend,
'hardware_scope':'Container CPU only; no GPU or user-PC benchmark',
'protocol_sha256':digest(self.config)})
training=self.train()
print('Training',training['commits'],'commits; cap',training['final_cap'],flush=True)
same=self.same_child(training['final_cap'])
hardware=self.hardware_gate()
print('Hardware gate',hardware['accepted_proposals'],'accepted; cap',hardware['final_cap'],flush=True)
holdout=self.holdout(training['final_cap'],hardware['final_cap'])
payback=self.payback(hardware['final_cap'])
budget=self.fixed_budget(training['final_cap'],hardware['final_cap'])
e=self.e_simulation()
self.save('experiment_run.json',{'completed':True,'wall_seconds':time.perf_counter()-totalstart,
'training_commits':training['commits'],'hardware_commits':hardware['accepted_proposals'],
'heldout_method_runs':len(holdout['rows']),'same_child_runs':len(same['rows']),
'payback_jobs':len(payback['rows']),'note':'All reported outcomes, including regressions and stronger conventional controls, are retained.'})
print('Completed experiments',time.perf_counter()-totalstart,flush=True)
if __name__=='__main__':
Lab(native='--portable' not in sys.argv).run()
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