Datasets:

PureOne
/

Echo-Mirror-RSI

"""Bounded evolutionary optimizer-program search with response-gated echoes.
This is a small program-synthesis / learned-proposal experiment. The mutation,
selection, and evidence-acceptance algorithm is fixed. It is not unrestricted
recursive self-improvement. All operator-order predictions are local bracket
approximations; actual program losses determine selection.
"""
from __future__ import annotations
import argparse
import csv
import json
import time
from dataclasses import dataclass, asdict
from pathlib import Path
import numpy as np


@dataclass(frozen=True)
class Config:
    dimension: int = 24
    primitives: int = 12
    underlying_fields: int = 4
    responses: int = 2
    train_states: int = 4
    test_states: int = 24
    generations: int = 5
    candidate_budget: int = 12
    seeds: int = 8
    step_size: float = 0.15
    elite_count: int = 3
    score_tolerance: float = 1e-12
    seed_offset: int = 203611080


class Task:
    def __init__(self, seed, cfg):
        self.cfg = cfg
        rng = np.random.default_rng(cfg.seed_offset + 10000 * seed)
        d, m = cfg.dimension, cfg.primitives
        rot, _ = np.linalg.qr(rng.normal(size=(d, d)))
        eig = np.geomspace(0.04, 1., d)
        self.H = (rot * eig) @ rot.T
        basis = [np.eye(d)]
        for _ in range(cfg.underlying_fields - 1):
            o, _ = np.linalg.qr(rng.normal(size=(d, d)))
            p = (o * rng.uniform(.2, 4., d)) @ o.T
            basis.append(p)
        mixing = np.vstack((np.eye(cfg.underlying_fields),
            rng.dirichlet(np.ones(cfg.underlying_fields), size=m-cfg.underlying_fields)))
        preconditioners = np.einsum('ib,bjk->ijk', mixing, np.asarray(basis))
        self.maps = np.asarray([-p @ self.H for p in preconditioners])
        self.c = rng.normal(size=d); self.c /= np.linalg.norm(self.c)
        self.train = rng.normal(size=(cfg.train_states,d))
        self.train /= np.linalg.norm(self.train,axis=1)[:,None]
        test_rng = np.random.default_rng(cfg.seed_offset + 10000 * seed + 2222)
        self.test = test_rng.normal(size=(cfg.test_states,d))
        self.test /= np.linalg.norm(self.test,axis=1)[:,None]

    def loss(self,x):
        return float(.5*x @ self.H @ x)

    def response(self,x):
        return np.array([self.loss(x),self.c @ x])

    def anchor(self,x):
        g = self.H @ x
        dh = np.vstack((g,self.c))
        u = np.einsum('ijk,k->ji',self.maps,x)
        v = np.einsum('ijk,j->ki',self.maps,g)
        c = u.T @ v-v.T @ u
        k = dh @ u
        t = np.block([[c,k.T],[-k,np.zeros((len(k),len(k)))]])
        left,s,_ = np.linalg.svd(t)
        rank = int(np.count_nonzero(s>1e-10*max(s[0],1.)))
        a = left[:,:rank].T
        omega = a @ t @ a.T
        q = k[0]
        ell = np.r_[q,np.zeros(len(k))] @ a.T
        return {'x':x,'g':g,'dh':dh,'h':self.response(x),'u':u,'c':c,
                'k':k,'q':q,'t':t,'a':a,'omega':omega,'ell':ell,
                'gate':a[:,self.cfg.primitives:],'rank':rank}


class Grammar:
    def __init__(self,task):
        self.task = task
        self.m = task.cfg.primitives
        self.nodes = [{'base':i,'depth':0} for i in range(self.m)]

    @staticmethod
    def gates(params,h):
        logits=params[:,0]+params[:,1:] @ h
        weight=np.exp(logits-np.max(logits));weight/=weight.sum()
        derivative=weight[:,None]*(params[:,1:]-weight @ params[:,1:])
        return weight,derivative

    def coefficients(self,index,h,cache=None):
        if cache is None: cache={}
        if index in cache: return cache[index]
        node=self.nodes[index]
        if 'base' in node:
            b=np.eye(self.m)[node['base']]
            db=np.zeros((self.m,len(h)))
        else:
            params=node['params']; beta,derivative=self.gates(params,h)
            b=np.zeros(self.m);db=np.zeros((self.m,len(h)))
            for j,parent in enumerate(node['parents']):
                bp,dp=self.coefficients(parent,h,cache)
                b+=beta[j]*bp
                db+=beta[j]*dp+np.outer(bp,derivative[j])
        cache[index]=(b,db)
        return b,db

    def signature(self,index,anchor,cache=None):
        if cache is None:cache={}
        if index in cache:return cache[index]
        node=self.nodes[index]
        if 'base' in node:
            e=anchor['a'][:,node['base']].copy()
        else:
            params=node['params'];beta,derivative=self.gates(params,anchor['h'])
            e=np.zeros(anchor['rank'])
            for j,parent in enumerate(node['parents']):
                ep=self.signature(parent,anchor,cache)
                e+=beta[j]*ep+(anchor['ell'] @ ep)*(anchor['gate'] @ derivative[j])
        cache[index]=e
        return e

    def contracted_jet(self,index,anchor,cache=None):
        """Strong raw (b,s) first-jet baseline, without a skew quotient."""
        if cache is None:cache={}
        if index in cache:return cache[index]
        node=self.nodes[index]
        if 'base' in node:
            z=np.r_[np.eye(self.m)[node['base']],np.zeros(len(anchor['h']))]
        else:
            beta,derivative=self.gates(node['params'],anchor['h'])
            z=np.zeros(self.m+len(anchor['h']))
            for j,parent in enumerate(node['parents']):
                zp=self.contracted_jet(parent,anchor,cache)
                z+=beta[j]*zp
                z[self.m:]+=(anchor['q'] @ zp[:self.m])*derivative[j]
        cache[index]=z
        return z

    def add(self,parents,params,normalization_anchor):
        index=len(self.nodes)
        node={'parents':tuple(int(p) for p in parents),'params':params.copy(),
              'depth':1+max(self.nodes[int(p)]['depth'] for p in parents)}
        self.nodes.append(node)
        # Convex softmax mixtures preserve the global SPD/norm bound of the
        # primitive preconditioners. There is no anchor-fitted renormalization.
        return index

    def field(self,index,x):
        h=self.task.response(x)
        b,_=self.coefficients(index,h)
        u=np.einsum('ijk,k->ji',self.task.maps,x)
        return u @ b

    def full_jet(self,index,anchor,cache=None):
        b,db=self.coefficients(index,anchor['h'],cache)
        value=anchor['u'] @ b
        jac=np.einsum('i,ijk->jk',b,self.task.maps)+anchor['u'] @ db @ anchor['dh']
        return value,jac

    def score(self,left,right,anchor,mode):
        if mode=='minimal':
            cache={}
            e=self.signature(left,anchor,cache);f=self.signature(right,anchor,cache)
            return float(e @ anchor['omega'] @ f)
        if mode=='first_jet':
            cache={}
            z=self.contracted_jet(left,anchor,cache)
            w=self.contracted_jet(right,anchor,cache)
            return float(z @ anchor['t'] @ w)
        cache={}
        b,db=self.coefficients(left,anchor['h'],cache)
        c,dc=self.coefficients(right,anchor['h'],cache)
        if mode=='gate_blind':return float(b @ anchor['c'] @ c)
        if mode=='full_jacobian':
            y,dy=self.full_jet(left,anchor,cache)
            z,dz=self.full_jet(right,anchor,cache)
            return float(anchor['g'] @ (dz @ y-dy @ z))
        raise ValueError(mode)

    def execute(self,left,right,x,eta):
        y=x+eta*self.field(left,x)
        z=y+eta*self.field(right,y)
        return self.task.loss(z)/max(self.task.loss(x),1e-30)


def evaluate_program(grammar,pair,states,anchors,mode,cfg,rng=None,both=False):
    outcomes=[];order_accuracy=[];scoring_errors=[];full_errors=[]
    choices=[]
    left,right=pair
    for x,anchor in zip(states,anchors):
        if both:
            ab=grammar.execute(left,right,x,cfg.step_size)
            ba=grammar.execute(right,left,x,cfg.step_size)
            reverse=ba<ab
            value=min(ab,ba)
        else:
            if mode=='random_order':reverse=bool(rng.integers(0,2))
            else:reverse=grammar.score(left,right,anchor,mode)>cfg.score_tolerance
            i,j=(right,left) if reverse else (left,right)
            value=grammar.execute(i,j,x,cfg.step_size)
        outcomes.append(value);choices.append(int(reverse))
    return float(np.mean(outcomes)),choices


def one_run(seed,method,cfg):
    setup_start=time.perf_counter()
    task=Task(seed,cfg);grammar=Grammar(task)
    train_anchors=[task.anchor(x) for x in task.train]
    test_anchors=[task.anchor(x) for x in task.test]
    rng=np.random.default_rng(cfg.seed_offset+10000*seed+3333)
    mean=np.zeros((2,2,cfg.responses+1))
    std=2*np.ones_like(mean);std[:,:,0]=.8
    pool=list(range(cfg.primitives))
    records=[];diagnostics=[];best=None;best_train=float('inf')
    training_program_executions=0
    prediction_anchors=0
    start=time.perf_counter()
    setup_seconds=start-setup_start
    mode={'corrected':'minimal','generic_first_jet':'first_jet','full_jacobian':'full_jacobian',
          'gate_blind':'gate_blind','random_order':'random_order',
          'no_feedback':'minimal','frozen_proposer':'minimal','direct_tournament':'minimal'}[method]
    def held_out(pair):
        # Evaluation never changes the trained program or proposal state.
        # Tournament evaluates both orders; its additional test executions
        # are recorded, not hidden as a free local ordering oracle.
        local_rng=np.random.default_rng(cfg.seed_offset+seed+90000)
        return evaluate_program(grammar,pair,task.test,test_anchors,mode,cfg,local_rng,
                                both=method=='direct_tournament')[0]
    for generation in range(cfg.generations):
        number=cfg.candidate_budget//2 if method=='direct_tournament' else cfg.candidate_budget
        candidates=[]
        for _ in range(number):
            params=rng.normal(mean,std)
            pair=[]
            for side in range(2):
                parents=[]
                for _ in range(2):
                    options=list(range(cfg.primitives)) if rng.random()<.2 else pool
                    parents.append(int(rng.choice(options)))
                pair.append(grammar.add(parents,params[side],train_anchors[0]))
            loss,choices=evaluate_program(grammar,pair,task.train,train_anchors,mode,cfg,rng,
                                         both=method=='direct_tournament')
            training_program_executions+=cfg.train_states*(2 if method=='direct_tournament' else 1)
            prediction_anchors+=cfg.train_states if method not in ('random_order','direct_tournament') else 0
            candidates.append((loss,tuple(pair),params.copy(),choices))
            if loss<best_train:
                best_train=loss;best=tuple(pair)
        candidates.sort(key=lambda x:x[0])
        proposal_test_losses=[held_out(candidate[1]) for candidate in candidates]
        if method=='no_feedback':
            chosen=rng.choice(len(candidates),size=min(cfg.elite_count,len(candidates)),replace=False)
            elite=[candidates[i] for i in chosen]
        elif method=='frozen_proposer':
            elite=[]
        else:
            elite=candidates[:cfg.elite_count]
            elite_params=np.asarray([x[2] for x in elite])
            mean=.65*mean+.35*elite_params.mean(axis=0)
            std=np.clip(.8*std+.2*elite_params.std(axis=0),.12,2.4)
        pool=list(range(cfg.primitives)) if method=='frozen_proposer' else [index for c in elite for index in c[1]]
        test_loss=held_out(best)
        records.append({'seed':seed,'method':method,'generation':generation+1,
            'training_program_executions':training_program_executions,
            'train_best_loss_ratio':best_train,'heldout_loss_ratio':test_loss,
            'mean_proposed_training_loss_ratio':float(np.mean([c[0] for c in candidates])),
            'mean_proposed_heldout_loss_ratio':float(np.mean(proposal_test_losses)),
            'fraction_proposals_beating_initial_gd':float(np.mean(np.asarray(proposal_test_losses)<np.mean([
                grammar.execute(0,0,x,cfg.step_size) for x in task.test]))),
            'proposal_mean_change_norm':float(np.linalg.norm(mean)),
            'proposal_std_mean':float(np.mean(std)),
            'best_program_depth':max(grammar.nodes[i]['depth'] for i in best),
            'nodes_generated':len(grammar.nodes)-cfg.primitives,
            'minimal_signature_rank_min':min(a['rank'] for a in train_anchors),
            'minimal_signature_rank_max':max(a['rank'] for a in train_anchors),
            'test_program_executions':cfg.test_states*(number+1)*(2 if method=='direct_tournament' else 1)+cfg.test_states})
        # Independent diagnostic probes are never exposed to the proposer.
        # Their cost is evaluation overhead, excluded equally for all runs.
        if method=='corrected':
            for _,pair,_,_ in candidates:
                for x,anchor in zip(task.test[:4],test_anchors[:4]):
                    exact=grammar.score(*pair,anchor,'full_jacobian')
                    compiled=grammar.score(*pair,anchor,'minimal')
                    firstjet=grammar.score(*pair,anchor,'first_jet')
                    blind=grammar.score(*pair,anchor,'gate_blind')
                    ab=grammar.execute(*pair,x,cfg.step_size)
                    ba=grammar.execute(pair[1],pair[0],x,cfg.step_size)
                    gap=ab-ba
                    valid=abs(gap)>1e-12
                    diagnostics.append({'seed':seed,'generation':generation+1,
                        'depth':max(grammar.nodes[i]['depth'] for i in pair),
                        'compiled_error':abs(compiled-exact),'first_jet_error':abs(firstjet-exact),
                        'blind_error':abs(blind-exact),'exact_bracket':exact,
                        'actual_loss_order_gap':gap,'non_tie':int(valid),
                        'compiled_correct_actual_order':int((compiled<=cfg.score_tolerance)==(gap<=0)),
                        'blind_correct_actual_order':int((blind<=cfg.score_tolerance)==(gap<=0))})
    # All execute() calls evaluate both fields using the full primitive basis.
    # A primitive Jacobian is a supplied matrix here, not a queried black box.
    cost={'seed':seed,'method':method,'seconds_including_diagnostics':time.perf_counter()-start,
        'setup_seconds_including_task_and_anchor_construction':setup_seconds,
        'training_program_executions':training_program_executions,
        'training_primitive_field_evaluations':2*cfg.primitives*training_program_executions,
        'training_loss_calls_in_program_execution':4*training_program_executions,
        'prediction_score_count':prediction_anchors,
        'base_jacobian_matrices_available':cfg.primitives,
        'test_program_executions_all_checkpoints':sum(r['test_program_executions'] for r in records),
        'diagnostic_program_executions':2*len(diagnostics),
        'note':'Program/primitive-value budgets match in training. Compiler arithmetic, supplied Jacobians, model operations, and diagnostic overhead are separately disclosed; no total-FLOP or wall-clock matching claim.'}
    return records,diagnostics,cost


def write_csv(path,rows):
    with path.open('w',newline='') as f:
        writer=csv.DictWriter(f,fieldnames=list(rows[0]));writer.writeheader();writer.writerows(rows)


def main():
    parser=argparse.ArgumentParser();parser.add_argument('--seeds',type=int,default=8)
    parser.add_argument('--output',type=Path,default=Path(__file__).resolve().parents[1]/'results')
    args=parser.parse_args();cfg=Config(seeds=args.seeds)
    args.output.mkdir(exist_ok=True,parents=True)
    methods=['corrected','generic_first_jet','full_jacobian','gate_blind','random_order','no_feedback','frozen_proposer','direct_tournament']
    rows=[];diags=[];costs=[]
    for seed in range(cfg.seeds):
        for method in methods:
            r,d,c=one_run(seed,method,cfg);rows+=r;diags+=d;costs.append(c)
    summary=[]
    for method in methods:
        for generation in range(1,cfg.generations+1):
            part=[r for r in rows if r['method']==method and r['generation']==generation]
            x=np.asarray([r['heldout_loss_ratio'] for r in part])
            summary.append({'method':method,'generation':generation,'mean_heldout_loss_ratio':float(x.mean()),
                'std_heldout_loss_ratio':float(x.std(ddof=1)) if len(x)>1 else 0.,
                'median_heldout_loss_ratio':float(np.median(x)),
                'mean_train_best_loss_ratio':float(np.mean([r['train_best_loss_ratio'] for r in part])),
                'mean_proposed_training_loss_ratio':float(np.mean([r['mean_proposed_training_loss_ratio'] for r in part])),
                'mean_proposed_heldout_loss_ratio':float(np.mean([r['mean_proposed_heldout_loss_ratio'] for r in part])),
                'std_proposed_heldout_loss_ratio':float(np.std([r['mean_proposed_heldout_loss_ratio'] for r in part],ddof=1)) if len(part)>1 else 0.,
                'mean_fraction_proposals_beating_initial_gd':float(np.mean([r['fraction_proposals_beating_initial_gd'] for r in part])),
                'mean_best_program_depth':float(np.mean([r['best_program_depth'] for r in part]))})
    eq_errors={}
    for other in ['generic_first_jet','full_jacobian']:
        dif=[]
        for seed in range(cfg.seeds):
            for gen in range(1,cfg.generations+1):
                a=next(r for r in rows if r['seed']==seed and r['method']=='corrected' and r['generation']==gen)
                b=next(r for r in rows if r['seed']==seed and r['method']==other and r['generation']==gen)
                dif.append(abs(a['heldout_loss_ratio']-b['heldout_loss_ratio']))
        eq_errors[other]=max(dif)
    nontie=[d for d in diags if d['non_tie']]
    diagnostic_summary={'number_of_probes':len(diags),
        'max_compiler_bracket_absolute_error':max(d['compiled_error'] for d in diags),
        'max_firstjet_bracket_absolute_error':max(d['first_jet_error'] for d in diags),
        'max_gateblind_bracket_absolute_error':max(d['blind_error'] for d in diags),
        'mean_gateblind_bracket_absolute_error':float(np.mean([d['blind_error'] for d in diags])),
        'compiled_actual_order_accuracy':float(np.mean([d['compiled_correct_actual_order'] for d in nontie])),
        'gateblind_actual_order_accuracy':float(np.mean([d['blind_correct_actual_order'] for d in nontie])),
        'non_tie_probes':len(nontie),'equivalent_compiler_search_trajectory_max_difference':eq_errors}
    assert diagnostic_summary['max_compiler_bracket_absolute_error']<1e-9
    assert max(eq_errors.values())<1e-10
    out={'status':'Executed bounded optimizer-program evolution. The proposer learns parent choices and gate-parameter distributions from measured losses; mutation and selection algorithm remains fixed.',
        'config':asdict(cfg),'methods':methods,'aggregate':summary,'diagnostics':diagnostic_summary,'costs':costs,
        'scope':{'train':'four task starting states per independently generated quadratic system',
                 'heldout':'24 new initial states of the same quadratic system; never used for selection or distribution updates',
                 'not_tested':'new natural task families, LLMs, modification of the search algorithm itself, open-ended RSI',
                 'low_rank':'12 primitives are mixtures of four base linear fields, deliberately imposing a small response-relative form',
                 'repair_and_confirmation':'An earlier pilot with unbounded affine gates failed from held-out instability. Those outputs are preserved as v2_pilot_*; this convex-softmax repair uses fresh independent seed offset203611080, versus202611080 in the pilot.',
                 'protocol_changes':'The repair also removes anchor-fitted field normalization and uses primitive SPD norm bound4 (pilot bound1). Pilot-to-confirmation numerical changes are not a controlled single-factor comparison.',
                 'restricted_grammar_rank':'rankT is an exact compiler dimension for the convex grammar; minimality for this restricted grammar is not asserted.',
                 'stability':'Primitive preconditioners are SPD with norm at most4; every recursive gate is a convex mixture. H has norm1 and step0.15, so every actual update is a descent step, uniformly over states and program depth.',
                 'ordering':'bracket predicts leading order only; selected programs are evaluated on the actual nonlinear gated fields',
                 'budget':'each method executes240 training two-step programs per seed; direct tournament uses half as many candidates and evaluates both orders',
                 'additional_costs':'All actual program executions charge24 primitive field evaluations. Jacobian matrices are supplied; compiler arithmetic and evolutionary updates are not FLOP-matched.',
                 'baseline':'Generic first-jet and full-Jacobian methods are mathematically equivalent and reproduce the same search. No superiority to them in discovery quality is asserted.',
                 'oracle':'The explicitly supplied quadratic Hessian admits a Newton step that solves the task. This study is not a state-of-the-art optimization performance claim.'}}
    write_csv(args.output/'v2_program_search.csv',rows)
    write_csv(args.output/'v2_bracket_diagnostics.csv',diags)
    write_csv(args.output/'v2_program_costs.csv',costs)
    (args.output/'v2_program_summary.json').write_text(json.dumps(out,indent=2)+'\n')
    print(json.dumps({'final_results':[r for r in summary if r['generation']==cfg.generations],
                      'diagnostics':diagnostic_summary},indent=2))


if __name__=='__main__':main()

	"""Bounded evolutionary optimizer-program search with response-gated echoes.

	This is a small program-synthesis / learned-proposal experiment. The mutation,
	selection, and evidence-acceptance algorithm is fixed. It is not unrestricted
	recursive self-improvement. All operator-order predictions are local bracket
	approximations; actual program losses determine selection.
	"""
	from __future__ import annotations
	import argparse
	import csv
	import json
	import time
	from dataclasses import dataclass, asdict
	from pathlib import Path
	import numpy as np


	@dataclass(frozen=True)
	class Config:
	dimension: int = 24
	primitives: int = 12
	underlying_fields: int = 4
	responses: int = 2
	train_states: int = 4
	test_states: int = 24
	generations: int = 5
	candidate_budget: int = 12
	seeds: int = 8
	step_size: float = 0.15
	elite_count: int = 3
	score_tolerance: float = 1e-12
	seed_offset: int = 203611080


	class Task:
	def __init__(self, seed, cfg):
	self.cfg = cfg
	rng = np.random.default_rng(cfg.seed_offset + 10000 * seed)
	d, m = cfg.dimension, cfg.primitives
	rot, _ = np.linalg.qr(rng.normal(size=(d, d)))
	eig = np.geomspace(0.04, 1., d)
	self.H = (rot * eig) @ rot.T
	basis = [np.eye(d)]
	for _ in range(cfg.underlying_fields - 1):
	o, _ = np.linalg.qr(rng.normal(size=(d, d)))
	p = (o * rng.uniform(.2, 4., d)) @ o.T
	basis.append(p)
	mixing = np.vstack((np.eye(cfg.underlying_fields),
	rng.dirichlet(np.ones(cfg.underlying_fields), size=m-cfg.underlying_fields)))
	preconditioners = np.einsum('ib,bjk->ijk', mixing, np.asarray(basis))
	self.maps = np.asarray([-p @ self.H for p in preconditioners])
	self.c = rng.normal(size=d); self.c /= np.linalg.norm(self.c)
	self.train = rng.normal(size=(cfg.train_states,d))
	self.train /= np.linalg.norm(self.train,axis=1)[:,None]
	test_rng = np.random.default_rng(cfg.seed_offset + 10000 * seed + 2222)
	self.test = test_rng.normal(size=(cfg.test_states,d))
	self.test /= np.linalg.norm(self.test,axis=1)[:,None]

	def loss(self,x):
	return float(.5*x @ self.H @ x)

	def response(self,x):
	return np.array([self.loss(x),self.c @ x])

	def anchor(self,x):
	g = self.H @ x
	dh = np.vstack((g,self.c))
	u = np.einsum('ijk,k->ji',self.maps,x)
	v = np.einsum('ijk,j->ki',self.maps,g)
	c = u.T @ v-v.T @ u
	k = dh @ u
	t = np.block([[c,k.T],[-k,np.zeros((len(k),len(k)))]])
	left,s,_ = np.linalg.svd(t)
	rank = int(np.count_nonzero(s>1e-10*max(s[0],1.)))
	a = left[:,:rank].T
	omega = a @ t @ a.T
	q = k[0]
	ell = np.r_[q,np.zeros(len(k))] @ a.T
	return {'x':x,'g':g,'dh':dh,'h':self.response(x),'u':u,'c':c,
	'k':k,'q':q,'t':t,'a':a,'omega':omega,'ell':ell,
	'gate':a[:,self.cfg.primitives:],'rank':rank}


	class Grammar:
	def __init__(self,task):
	self.task = task
	self.m = task.cfg.primitives
	self.nodes = [{'base':i,'depth':0} for i in range(self.m)]

	@staticmethod
	def gates(params,h):
	logits=params[:,0]+params[:,1:] @ h
	weight=np.exp(logits-np.max(logits));weight/=weight.sum()
	derivative=weight[:,None]*(params[:,1:]-weight @ params[:,1:])
	return weight,derivative

	def coefficients(self,index,h,cache=None):
	if cache is None: cache={}
	if index in cache: return cache[index]
	node=self.nodes[index]
	if 'base' in node:
	b=np.eye(self.m)[node['base']]
	db=np.zeros((self.m,len(h)))
	else:
	params=node['params']; beta,derivative=self.gates(params,h)
	b=np.zeros(self.m);db=np.zeros((self.m,len(h)))
	for j,parent in enumerate(node['parents']):
	bp,dp=self.coefficients(parent,h,cache)
	b+=beta[j]*bp
	db+=beta[j]*dp+np.outer(bp,derivative[j])
	cache[index]=(b,db)
	return b,db

	def signature(self,index,anchor,cache=None):
	if cache is None:cache={}
	if index in cache:return cache[index]
	node=self.nodes[index]
	if 'base' in node:
	e=anchor['a'][:,node['base']].copy()
	else:
	params=node['params'];beta,derivative=self.gates(params,anchor['h'])
	e=np.zeros(anchor['rank'])
	for j,parent in enumerate(node['parents']):
	ep=self.signature(parent,anchor,cache)
	e+=beta[j]ep+(anchor['ell'] @ ep)(anchor['gate'] @ derivative[j])
	cache[index]=e
	return e

	def contracted_jet(self,index,anchor,cache=None):
	"""Strong raw (b,s) first-jet baseline, without a skew quotient."""
	if cache is None:cache={}
	if index in cache:return cache[index]
	node=self.nodes[index]
	if 'base' in node:
	z=np.r_[np.eye(self.m)[node['base']],np.zeros(len(anchor['h']))]
	else:
	beta,derivative=self.gates(node['params'],anchor['h'])
	z=np.zeros(self.m+len(anchor['h']))
	for j,parent in enumerate(node['parents']):
	zp=self.contracted_jet(parent,anchor,cache)
	z+=beta[j]*zp
	z[self.m:]+=(anchor['q'] @ zp[:self.m])*derivative[j]
	cache[index]=z
	return z

	def add(self,parents,params,normalization_anchor):
	index=len(self.nodes)
	node={'parents':tuple(int(p) for p in parents),'params':params.copy(),
	'depth':1+max(self.nodes[int(p)]['depth'] for p in parents)}
	self.nodes.append(node)
	# Convex softmax mixtures preserve the global SPD/norm bound of the
	# primitive preconditioners. There is no anchor-fitted renormalization.
	return index

	def field(self,index,x):
	h=self.task.response(x)
	b,_=self.coefficients(index,h)
	u=np.einsum('ijk,k->ji',self.task.maps,x)
	return u @ b

	def full_jet(self,index,anchor,cache=None):
	b,db=self.coefficients(index,anchor['h'],cache)
	value=anchor['u'] @ b
	jac=np.einsum('i,ijk->jk',b,self.task.maps)+anchor['u'] @ db @ anchor['dh']
	return value,jac

	def score(self,left,right,anchor,mode):
	if mode=='minimal':
	cache={}
	e=self.signature(left,anchor,cache);f=self.signature(right,anchor,cache)
	return float(e @ anchor['omega'] @ f)
	if mode=='first_jet':
	cache={}
	z=self.contracted_jet(left,anchor,cache)
	w=self.contracted_jet(right,anchor,cache)
	return float(z @ anchor['t'] @ w)
	cache={}
	b,db=self.coefficients(left,anchor['h'],cache)
	c,dc=self.coefficients(right,anchor['h'],cache)
	if mode=='gate_blind':return float(b @ anchor['c'] @ c)
	if mode=='full_jacobian':
	y,dy=self.full_jet(left,anchor,cache)
	z,dz=self.full_jet(right,anchor,cache)
	return float(anchor['g'] @ (dz @ y-dy @ z))
	raise ValueError(mode)

	def execute(self,left,right,x,eta):
	y=x+eta*self.field(left,x)
	z=y+eta*self.field(right,y)
	return self.task.loss(z)/max(self.task.loss(x),1e-30)


	def evaluate_program(grammar,pair,states,anchors,mode,cfg,rng=None,both=False):
	outcomes=[];order_accuracy=[];scoring_errors=[];full_errors=[]
	choices=[]
	left,right=pair
	for x,anchor in zip(states,anchors):
	if both:
	ab=grammar.execute(left,right,x,cfg.step_size)
	ba=grammar.execute(right,left,x,cfg.step_size)
	reverse=ba<ab
	value=min(ab,ba)
	else:
	if mode=='random_order':reverse=bool(rng.integers(0,2))
	else:reverse=grammar.score(left,right,anchor,mode)>cfg.score_tolerance
	i,j=(right,left) if reverse else (left,right)
	value=grammar.execute(i,j,x,cfg.step_size)
	outcomes.append(value);choices.append(int(reverse))
	return float(np.mean(outcomes)),choices


	def one_run(seed,method,cfg):
	setup_start=time.perf_counter()
	task=Task(seed,cfg);grammar=Grammar(task)
	train_anchors=[task.anchor(x) for x in task.train]
	test_anchors=[task.anchor(x) for x in task.test]
	rng=np.random.default_rng(cfg.seed_offset+10000*seed+3333)
	mean=np.zeros((2,2,cfg.responses+1))
	std=2*np.ones_like(mean);std[:,:,0]=.8
	pool=list(range(cfg.primitives))
	records=[];diagnostics=[];best=None;best_train=float('inf')
	training_program_executions=0
	prediction_anchors=0
	start=time.perf_counter()
	setup_seconds=start-setup_start
	mode={'corrected':'minimal','generic_first_jet':'first_jet','full_jacobian':'full_jacobian',
	'gate_blind':'gate_blind','random_order':'random_order',
	'no_feedback':'minimal','frozen_proposer':'minimal','direct_tournament':'minimal'}[method]
	def held_out(pair):
	# Evaluation never changes the trained program or proposal state.
	# Tournament evaluates both orders; its additional test executions
	# are recorded, not hidden as a free local ordering oracle.
	local_rng=np.random.default_rng(cfg.seed_offset+seed+90000)
	return evaluate_program(grammar,pair,task.test,test_anchors,mode,cfg,local_rng,
	both=method=='direct_tournament')[0]
	for generation in range(cfg.generations):
	number=cfg.candidate_budget//2 if method=='direct_tournament' else cfg.candidate_budget
	candidates=[]
	for _ in range(number):
	params=rng.normal(mean,std)
	pair=[]
	for side in range(2):
	parents=[]
	for _ in range(2):
	options=list(range(cfg.primitives)) if rng.random()<.2 else pool
	parents.append(int(rng.choice(options)))
	pair.append(grammar.add(parents,params[side],train_anchors[0]))
	loss,choices=evaluate_program(grammar,pair,task.train,train_anchors,mode,cfg,rng,
	both=method=='direct_tournament')
	training_program_executions+=cfg.train_states*(2 if method=='direct_tournament' else 1)
	prediction_anchors+=cfg.train_states if method not in ('random_order','direct_tournament') else 0
	candidates.append((loss,tuple(pair),params.copy(),choices))
	if loss<best_train:
	best_train=loss;best=tuple(pair)
	candidates.sort(key=lambda x:x[0])
	proposal_test_losses=[held_out(candidate[1]) for candidate in candidates]
	if method=='no_feedback':
	chosen=rng.choice(len(candidates),size=min(cfg.elite_count,len(candidates)),replace=False)
	elite=[candidates[i] for i in chosen]
	elif method=='frozen_proposer':
	elite=[]
	else:
	elite=candidates[:cfg.elite_count]
	elite_params=np.asarray([x[2] for x in elite])
	mean=.65mean+.35elite_params.mean(axis=0)
	std=np.clip(.8std+.2elite_params.std(axis=0),.12,2.4)
	pool=list(range(cfg.primitives)) if method=='frozen_proposer' else [index for c in elite for index in c[1]]
	test_loss=held_out(best)
	records.append({'seed':seed,'method':method,'generation':generation+1,
	'training_program_executions':training_program_executions,
	'train_best_loss_ratio':best_train,'heldout_loss_ratio':test_loss,
	'mean_proposed_training_loss_ratio':float(np.mean([c[0] for c in candidates])),
	'mean_proposed_heldout_loss_ratio':float(np.mean(proposal_test_losses)),
	'fraction_proposals_beating_initial_gd':float(np.mean(np.asarray(proposal_test_losses)<np.mean([
	grammar.execute(0,0,x,cfg.step_size) for x in task.test]))),
	'proposal_mean_change_norm':float(np.linalg.norm(mean)),
	'proposal_std_mean':float(np.mean(std)),
	'best_program_depth':max(grammar.nodes[i]['depth'] for i in best),
	'nodes_generated':len(grammar.nodes)-cfg.primitives,
	'minimal_signature_rank_min':min(a['rank'] for a in train_anchors),
	'minimal_signature_rank_max':max(a['rank'] for a in train_anchors),
	'test_program_executions':cfg.test_states(number+1)(2 if method=='direct_tournament' else 1)+cfg.test_states})
	# Independent diagnostic probes are never exposed to the proposer.
	# Their cost is evaluation overhead, excluded equally for all runs.
	if method=='corrected':
	for _,pair,_,_ in candidates:
	for x,anchor in zip(task.test[:4],test_anchors[:4]):
	exact=grammar.score(*pair,anchor,'full_jacobian')
	compiled=grammar.score(*pair,anchor,'minimal')
	firstjet=grammar.score(*pair,anchor,'first_jet')
	blind=grammar.score(*pair,anchor,'gate_blind')
	ab=grammar.execute(*pair,x,cfg.step_size)
	ba=grammar.execute(pair[1],pair[0],x,cfg.step_size)
	gap=ab-ba
	valid=abs(gap)>1e-12
	diagnostics.append({'seed':seed,'generation':generation+1,
	'depth':max(grammar.nodes[i]['depth'] for i in pair),
	'compiled_error':abs(compiled-exact),'first_jet_error':abs(firstjet-exact),
	'blind_error':abs(blind-exact),'exact_bracket':exact,
	'actual_loss_order_gap':gap,'non_tie':int(valid),
	'compiled_correct_actual_order':int((compiled<=cfg.score_tolerance)==(gap<=0)),
	'blind_correct_actual_order':int((blind<=cfg.score_tolerance)==(gap<=0))})
	# All execute() calls evaluate both fields using the full primitive basis.
	# A primitive Jacobian is a supplied matrix here, not a queried black box.
	cost={'seed':seed,'method':method,'seconds_including_diagnostics':time.perf_counter()-start,
	'setup_seconds_including_task_and_anchor_construction':setup_seconds,
	'training_program_executions':training_program_executions,
	'training_primitive_field_evaluations':2cfg.primitivestraining_program_executions,
	'training_loss_calls_in_program_execution':4*training_program_executions,
	'prediction_score_count':prediction_anchors,
	'base_jacobian_matrices_available':cfg.primitives,
	'test_program_executions_all_checkpoints':sum(r['test_program_executions'] for r in records),
	'diagnostic_program_executions':2*len(diagnostics),
	'note':'Program/primitive-value budgets match in training. Compiler arithmetic, supplied Jacobians, model operations, and diagnostic overhead are separately disclosed; no total-FLOP or wall-clock matching claim.'}
	return records,diagnostics,cost


	def write_csv(path,rows):
	with path.open('w',newline='') as f:
	writer=csv.DictWriter(f,fieldnames=list(rows[0]));writer.writeheader();writer.writerows(rows)


	def main():
	parser=argparse.ArgumentParser();parser.add_argument('--seeds',type=int,default=8)
	parser.add_argument('--output',type=Path,default=Path(__file__).resolve().parents[1]/'results')
	args=parser.parse_args();cfg=Config(seeds=args.seeds)
	args.output.mkdir(exist_ok=True,parents=True)
	methods=['corrected','generic_first_jet','full_jacobian','gate_blind','random_order','no_feedback','frozen_proposer','direct_tournament']
	rows=[];diags=[];costs=[]
	for seed in range(cfg.seeds):
	for method in methods:
	r,d,c=one_run(seed,method,cfg);rows+=r;diags+=d;costs.append(c)
	summary=[]
	for method in methods:
	for generation in range(1,cfg.generations+1):
	part=[r for r in rows if r['method']==method and r['generation']==generation]
	x=np.asarray([r['heldout_loss_ratio'] for r in part])
	summary.append({'method':method,'generation':generation,'mean_heldout_loss_ratio':float(x.mean()),
	'std_heldout_loss_ratio':float(x.std(ddof=1)) if len(x)>1 else 0.,
	'median_heldout_loss_ratio':float(np.median(x)),
	'mean_train_best_loss_ratio':float(np.mean([r['train_best_loss_ratio'] for r in part])),
	'mean_proposed_training_loss_ratio':float(np.mean([r['mean_proposed_training_loss_ratio'] for r in part])),
	'mean_proposed_heldout_loss_ratio':float(np.mean([r['mean_proposed_heldout_loss_ratio'] for r in part])),
	'std_proposed_heldout_loss_ratio':float(np.std([r['mean_proposed_heldout_loss_ratio'] for r in part],ddof=1)) if len(part)>1 else 0.,
	'mean_fraction_proposals_beating_initial_gd':float(np.mean([r['fraction_proposals_beating_initial_gd'] for r in part])),
	'mean_best_program_depth':float(np.mean([r['best_program_depth'] for r in part]))})
	eq_errors={}
	for other in ['generic_first_jet','full_jacobian']:
	dif=[]
	for seed in range(cfg.seeds):
	for gen in range(1,cfg.generations+1):
	a=next(r for r in rows if r['seed']==seed and r['method']=='corrected' and r['generation']==gen)
	b=next(r for r in rows if r['seed']==seed and r['method']==other and r['generation']==gen)
	dif.append(abs(a['heldout_loss_ratio']-b['heldout_loss_ratio']))
	eq_errors[other]=max(dif)
	nontie=[d for d in diags if d['non_tie']]
	diagnostic_summary={'number_of_probes':len(diags),
	'max_compiler_bracket_absolute_error':max(d['compiled_error'] for d in diags),
	'max_firstjet_bracket_absolute_error':max(d['first_jet_error'] for d in diags),
	'max_gateblind_bracket_absolute_error':max(d['blind_error'] for d in diags),
	'mean_gateblind_bracket_absolute_error':float(np.mean([d['blind_error'] for d in diags])),
	'compiled_actual_order_accuracy':float(np.mean([d['compiled_correct_actual_order'] for d in nontie])),
	'gateblind_actual_order_accuracy':float(np.mean([d['blind_correct_actual_order'] for d in nontie])),
	'non_tie_probes':len(nontie),'equivalent_compiler_search_trajectory_max_difference':eq_errors}
	assert diagnostic_summary['max_compiler_bracket_absolute_error']<1e-9
	assert max(eq_errors.values())<1e-10
	out={'status':'Executed bounded optimizer-program evolution. The proposer learns parent choices and gate-parameter distributions from measured losses; mutation and selection algorithm remains fixed.',
	'config':asdict(cfg),'methods':methods,'aggregate':summary,'diagnostics':diagnostic_summary,'costs':costs,
	'scope':{'train':'four task starting states per independently generated quadratic system',
	'heldout':'24 new initial states of the same quadratic system; never used for selection or distribution updates',
	'not_tested':'new natural task families, LLMs, modification of the search algorithm itself, open-ended RSI',
	'low_rank':'12 primitives are mixtures of four base linear fields, deliberately imposing a small response-relative form',
	'repair_and_confirmation':'An earlier pilot with unbounded affine gates failed from held-out instability. Those outputs are preserved as v2_pilot_*; this convex-softmax repair uses fresh independent seed offset203611080, versus202611080 in the pilot.',
	'protocol_changes':'The repair also removes anchor-fitted field normalization and uses primitive SPD norm bound4 (pilot bound1). Pilot-to-confirmation numerical changes are not a controlled single-factor comparison.',
	'restricted_grammar_rank':'rankT is an exact compiler dimension for the convex grammar; minimality for this restricted grammar is not asserted.',
	'stability':'Primitive preconditioners are SPD with norm at most4; every recursive gate is a convex mixture. H has norm1 and step0.15, so every actual update is a descent step, uniformly over states and program depth.',
	'ordering':'bracket predicts leading order only; selected programs are evaluated on the actual nonlinear gated fields',
	'budget':'each method executes240 training two-step programs per seed; direct tournament uses half as many candidates and evaluates both orders',
	'additional_costs':'All actual program executions charge24 primitive field evaluations. Jacobian matrices are supplied; compiler arithmetic and evolutionary updates are not FLOP-matched.',
	'baseline':'Generic first-jet and full-Jacobian methods are mathematically equivalent and reproduce the same search. No superiority to them in discovery quality is asserted.',
	'oracle':'The explicitly supplied quadratic Hessian admits a Newton step that solves the task. This study is not a state-of-the-art optimization performance claim.'}}
	write_csv(args.output/'v2_program_search.csv',rows)
	write_csv(args.output/'v2_bracket_diagnostics.csv',diags)
	write_csv(args.output/'v2_program_costs.csv',costs)
	(args.output/'v2_program_summary.json').write_text(json.dumps(out,indent=2)+'\n')
	print(json.dumps({'final_results':[r for r in summary if r['generation']==cfg.generations],
	'diagnostics':diagnostic_summary},indent=2))


	if __name__=='__main__':main()