SoftModel: A Neural Model That Grows Its Own Topology -- Governed Structural Growth for Continual In-Service Learning

Zhoumin Xie

Source-linked AI summary

SoftModel: A Neural Model That Grows Its Own Topology -- Governed Structural Growth for Continual In-Service Learning

Zhoumin Xie

arXiv:2608.16409v1Aug 17, 2026cs.LG

TL;DR

Continual-learning models typically freeze both their weights and topology, limiting adaptation as data and required capacity change. SoftModel introduces governed structural growth under a uniform held-out gate, and reports preserved learning across long task sequences.

Problem
Continual-learning models typically freeze weights and topology, while fixed topology imposes an irreducible approximation floor as targets drift.
Method
SoftModel uses recursively composable structural growth with a uniform gate and audit discipline governing changes across the model lifecycle.
Results
On standard continual-learning benchmarks, governed growth preserves the ability to keep learning along long task sequences.
Takeaways & Limitations
Because every change is gated, the served model can only improve or stay, enabling continual operation without human adjudication of each step.
Takeaways & Limitations
The measurements come from small-scale tested worlds and benchmark lanes, with no significance testing claimed at the registered sample sizes.

Abstract

from arXiv · show

Today, a neural system is almost always used in two phases -- trained, then deployed -- and in that regime it freezes twice: training ends, and the topology itself was never a degree of freedom. We take the opposite premise as an axiom -- total plasticity: no part of a model, including its structure, is ever frozen -- and derive the governance a lifelong learner then requires. The design's target regime is continual, in-service learning: a long-lived model on a non-stationary stream, whose stability comes from governance rather than immobility and whose capacity follows demand. The result is a growable soft model: an algebra of structural operators (width, hierarchy, composition, input interface, grown cycles, attention heads), each exact at application, budgeted, and audited, with adoption decided solely by a held-out reality gate that treats parametric and structural change uniformly. A complete from-scratch system realizes the whole account; its factory surface is operated end-to-end by a production LLM. Two conclusions follow from the axiom by construction: stability under lifelong change becomes an audit property of the lifecycle, and structure that follows demand removes the silent cap a fixed topology places on later capability where the capacity floor binds. A third is measured: in the worlds where this was measured, the marginal value of new capacity was unobservable before adoption, so workable growth governance took its ex-post form. The same governance extends to evaluative signals, and the core method is evaluated on standard continual-learning benchmarks, where governed growth preserves the ability to keep learning along long task sequences. A pre-registered experimental program adjudicates the mechanism and value claims on the tested problems and reports its failures at full prominence; the map -- positive and negative -- is the contribution.

1 Introduction · Part I. Theory and System · 2 Total Plasticity: The Axiom, Lock-In, and Governed Growth

The paper defines total plasticity as lifelong trainability of both parameters and topology, then replaces immobility with exact, budgeted, audited growth governed by held-out reality. It develops a recursive growable system and evaluates its mechanisms through a preregistered program that reports positive and negative verdicts, including where capacity lock-in failed to bind.

1.1 The two freezes; 2.2 Lock-in: fixed topology is freezing by omission: Conventional models freeze weights after training and topology from design time, confining later learning to a fixed function family and silently capping capability.Fixed capacity creates an approximation floor when later targets exceed it, while a missing causal input cannot be recovered at any capacity.
1.2 The inversion; 2.1 The axiom: Total plasticity makes every parameter trainable for the model’s lifetime and requires topology itself to remain a trainable degree of freedom.The axiom excludes disguised freezing, including mechanisms that make learning unable to resume.
1.3 The system; 1.4 Contributions and epistemic stance: The released system uses a recursive multi-scale substrate with nested inner networks and an operator algebra for widening, refinement, deepening, input-interface growth, and re-founding.Its structure and two depth quantities grow non-uniformly, while exactness is measured in the acceptance suite.
1.4 Contributions and epistemic stance: The lifecycle extends governed growth to local-solving cycles, self-processing units, growable attention, evaluative learning, reproducible stores, drift handling, and consent-gated self-study.A production LLM operates the factory surface end-to-end through a standard tool protocol.
1.5 Organization and reader’s paths; 1.4 Contributions and epistemic stance: The paper is organized into theory and system, empirical methods and results, and discussion, with separate paths for readers focused on theory or reproduction and audit.The core method is evaluated on the standard continual-learning benchmark family, alongside registered growth-value and fidelity programs.
2.3 The stability dilemma and its governed resolution: Stability comes from governance: every parametric or structural change must be harmless when applied and adopted only after strictly surpassing the incumbent on held-out reality.Exact-preserving operators leave the current function unchanged, while a reality gate compares speculative candidates with the committed version on a quarantined recent slice.
2.4 Growth as governed speculation: This contract turns structural growth into low-risk speculation constrained by adjustable budgets, lineage audits, and evidence-based verdicts rather than architecture search across training runs.Exactness preserves accumulated fit and makes later effects attributable, while rejected candidates do not enter the served lineage.
2.5 Falsifiable predictions; 1.4 Contributions and epistemic stance: The preregistered program treats the theory as falsifiable, reports failures prominently, and found that the tested kilobyte-scale T2 scenario did not induce capacity lock-in.The capacity claim therefore awaits scenarios where the approximation floor binds, whereas the interface instance remains structural at any scale.

3 The Substrate, Learning, and the Shared Instruments

This section defines SoftModel’s recursive, scale-invariant substrate and learning rule, then governs structural and parametric changes through diagnostic instruments whose suggestions are accepted only by a held-out reality gate. It also establishes exact interface expansion, experience-driven depth, and explicit limits of the gate’s safety invariant.

Recursive substrate: The recursive network is closed under refinement: any node in any inner network can become composite, adding an inner network that corrects its scope’s hidden state.Composite corrections are additive, recursive, and operate at any level.
Recursive substrate: Depth records where experience demanded refinement, making the model’s depth profile an outcome of its life rather than an architectural hyperparameter.Depth exists only where an inner network has been grown.
Learning: Learning applies one scale-invariant rule at every scope: each inner network receives a supervised target for its parent’s residual instead of a cross-scale gradient.Every scale remains trainable, and effective optimization pressure reaches level k+1 when level k has residual error at a composite node.
Governance instruments: Instability reports and trajectory verdicts suggest growth sites, but only the gate decides, with every adopted promotion required to improve the judged held-out slice.The gate applies uniformly to learning steps and structural operators, while refusals leave the served lineage untouched.
Operators and limits: Interface expansion is σ-exact for any new coordinate because each new input column is zeroed, while re-founding uses only real accumulated rows and recomputes birth sizing on the current schema.The released birth-sizing heuristic is β = max(16, min(64, 4(nin + nout))), but later structure remains data-determined under the gate.
Operators and limits: The gate’s invariant does not prevent selection reuse: repeated commit attempts on one small held-out slice can eventually promote a noise-margin candidate, motivating promotion margins and query budgets.This exposure is distinct from training contamination and remains outside the invariant’s scope.

4 Growth: The Direction Question

This section defines two governed growth directions—additive multiscale expansion and compositional hierarchy—and selects between them from data. Every structural operator enters exactly, remains trainable, budgeted, logged, auditable, and removable, while refinement adds organization rather than representational power without composition blocks.

Growth directions: The operator algebra realizes additive expansion and compositional hierarchy as two governed growth directions, with the choice between them read from data.The additive realization is the adaptive system restricted to additive operators; the compositional realization adds scope-interior composition and signal-based direction selection.
Governance contract: Every in-place operator builds a candidate whose takeover is gated, exact at application, trainable from step one, budgeted, logged, audited, and exactly removable.The algebra’s operators carry inverses, and refusals are logged outcomes under parameter and depth caps.
Composition: The additive family preserves composition degree, whereas δ alone raises it by appending or inserting composition blocks in a scope’s chain, including in a live serving model.δ preserves additive aggregation and applies the same zero-entry exactness at insertion.
Refinement: Refinement ρ organizes information locally across scales but, without composition blocks and at matched atomic-unit counts, has the same function class as widening ω.Proposition 4 states F(Gρ) = F(Gω); refinement contributes a site, trigger, and audit unit, while local stagewise-additive credit assignment may alter learning trajectories.
Direction selection: Two-horizon probe slopes, rather than single-horizon raw gain or gain per parameter, carry the measured signal for selecting the growth axis.Single-horizon readings showed no axis information because candidates priced positively and the directions priced alike early in training.

5 Local Solving Loops: Computation That Solves Inside Itself

The section introduces two governed local solving loops: one iterates a scope’s forward state to a bounded fixed point, while the other self-processes newborn weights before global learning. Both treat iteration as a local, budgeted, auditable resource whose value remains subject to preregistered evaluation.

Forward-state solving: A loop operator adds iterative computation to the growth algebra, allowing a scope’s forward pass to relax toward a fixed point under a tolerance or hard cap.The cycle is the sixth operator and third growth direction, buying iteration and state rather than width or serial composition.
Forward-state solving: The fixed-point loop is governed by an enforced contraction certificate, bounded iteration budget, audited iteration count, and gradients differentiated through executed iterates.The contraction condition guarantees existence, uniqueness, and geometric convergence; the system rescales violating parameters to restore the bound.
Self-processing: A newborn inner body can run a policy-bounded, label-blind weight-adjustment loop against a local functional-consistency objective with a collapse guard.Released defaults use K = 4 perturbation copies, γ = 1, and ρfloor = 0.5.
Self-processing: Self-processing follows the invariant “process, then participate, then learn,” while remaining serving-pure, optimizer-neutral, hierarchy-respecting, bounded, and fully audited.Eligible newborn bodies self-process once per training step before the released forward computation and global credit assignment.
Shared governance: The two mechanisms share locality, boundedness, auditability, exact or neutral entry, and gate adoption, but solve different quantities on different clocks.Their measured mechanics include exact entry bitwise, an enforced contraction bound with CG = 1.128994, finite-difference-verified gradients, and optimizer-neutrality; value adjudication remains open.

6 Growable Attention: Capacity Follows Demand

This section extends total plasticity to attention through governed head growth and local entropy discipline, with exact-at-application operators adjudicated by held-out gates. Experiments show strong benefits when capacity is genuinely starved, effective local repair, and measurable instrument leads, while identifying sensing demand as unresolved and growth’s architectural limits.

Governed attention growth: Attention head-add and head-widen remove fixed head count and equal-width lock-in under evidence-triggered, function-preserving, budgeted, and audited governance.Unequal head widths become lifecycle outcomes reflecting observed demand rather than fixed architectural hyperparameters.
Governed attention growth: Head growth is exactly function-preserving at application because each opened pathway contains an exactly-zero factor, creating a one-step two-stage trainability pattern.Head-add initializes the new output projection to zero; head-widen inserts zeros pairwise so every new product initially remains unchanged.
Local attention discipline: Local entropy-band discipline restores 97% of lost held-out performance at roughly 7% of global-retraining task-work cost after induced attention collapse.The local objective penalizes quadratic excursions outside [αlo log Fi, αhi log Fi], targeting saturated, gradient-dead attention rows where collapse occurs.
Growth results and limits: Under starved birth capacity, triggered growth reduced held-out error by 35% and 64% in firing seeds, whereas adequate-capacity ladders showed approximately zero paired-ablation deltas.The plateau trigger fired in all five starved seeds, but the evidence indicates the failure lies in acceptance sensing rather than triggering or operator construction.
Growth results and limits: Per-head instruments led held-out error by 4.9 evaluation periods on average in 11/15 distribution-shift runs, with misses concentrated at narrow widths.Positive leads occurred in 3/5 runs at dmodel = 16, 4/5 at 32, and 5/5 at 64; growth changes capacity, not computational class.

7 The Governed Lifecycle · 8 Evaluative Learning under Total Plasticity

The governed lifecycle separates speculative learning and growth from serving, granting adoption only through an audited held-out gate. Evaluative learning extends the same governance to structural preferences and policy optimization, with experiments showing capacity-dependent benefits alongside explicit negative and unresolved results.

7 The Governed Lifecycle: The factory versions, serves, gates, and audits models while keeping domain data isolated in each model’s versioned store.The surrounding machinery remains generic across domains and does not itself learn.
7 The Governed Lifecycle: Learning and growth act on a working state, while serving reads only the committed version and adoption requires the held-out gate.Reset discards a session, rollback preserves audited lineage, and the held-out stream is quarantined from training.
7 The Governed Lifecycle: Self-study is budgeted, consent-based, fully logged, and barred from the holdout, leaving promotion authority solely with the gate.The store and holdout are disjoint by construction, preventing self-study from corrupting the evaluation certificate.
7 The Governed Lifecycle: Categorical models mine stored data into ordered, human- and LLM-readable IF/THEN decision lists with confidence and support.Rules are surfaced when they agree with the network’s prediction, exposing domain regularities unavailable before training.
8.1 One evaluative primitive, two loops: The S-loop records gate-credited advantages for discrete growth moves and uses bucket statistics to order future candidates without mutating the model.Preference selects which candidate is offered; adoption remains the gate’s alone.
8.1 One evaluative primitive, two loops: The P-loop applies clipped-surrogate policy optimization through pseudo-targets, reusing the existing teaching kernel while keeping reinforcement-specific machinery outside the model.Advantage estimation, ratio clipping, entropy regularization, and optional KL regularization enter through the policy-loss interface.
8.1 One evaluative primitive, two loops: Both evaluative loops use paired-episode gating, quarantined evaluation data, audit records, and anti-interference instruments across regimes.The gate must prevent adoption from trading one regime’s competence away for another’s, while the S-loop credits evidence without regard to regime.
8.2 The quasi-static law extends to reward learning: The policy loop obeys the quasi-static verification law by matching the growable model against a fixed twin built only from independent official PyTorch components.Weights are transplanted into the twin, and pre-growth and post-growth behavior are checked against that reference.

9 An LLM Operates the Model … 11 The Core Method on Standard Continual-Learning Benchmarks

The paper presents a production-LLM-operated, governed growable model for continual in-service learning, with audited interfaces, held-out reality gates, and structural responses to changing demand. On standard continual-learning benchmarks, governed growth improves capacity and long-sequence plasticity while exposing dose, measurement, and deployment boundaries.

9 An LLM Operates the Model: The LLM orchestrates feature extraction, inference, teaching, and interpretation, while the soft model provides a small, domain-specialized, forever-trainable extension.The factory exposes nine tools and the full system fifty-two, with MCP instructions documenting holdout-before-teach, feature extraction, drift handling, and recovery.
9 An LLM Operates the Model: The quality guarantee assumes an honest operator and trustworthy holdout provenance; deployments facing poisoning risk should source held-out reality separately from teaching.Rollback is audited but not gated, so a corrupted holdout can allow matching but degraded models to pass.
9 An LLM Operates the Model: The platform lowers access barriers to small domain-specialized models by automating construction, training, evaluation-gated promotion, versioned deployment, and rollback on ordinary CPUs.Models are kilobytes to megabytes, transitions are audited and reversible, and the scope excludes foundation-model construction.
10 In-Service Continual Learning as the Natural Habitat: Continual learning couples catastrophic forgetting with loss of plasticity, creating the stability–plasticity dilemma for long-lived models serving on non-stationary streams.The theory addresses this regime structurally, with measured behavior reported in the campaigns.
10.1 Structural answers to the two failure modes: Under total plasticity, governed growth adds capacity when learning stalls, while zero-initialized additions preserve the served function at structural change.New capacity is trainable from step one; input-conditioned ports associate growth with the regions that demanded it, although shared trunks can still forget under strict domain switches.
10.2 The anti-forgetting ladder: The anti-forgetting ladder combines event-scoped protection windows, demand-triggered structural response, and spaced review courses, with repetition countering erosion under continued new-domain training.Protection windows help at growth events but are not a long-horizon forgetting treatment; intrinsic local rehearsal remains future work.
10.3 Evaluation on the time axis: The evaluation treats an in-service life longitudinally, measuring retention, adaptation cost, service continuity through structural events, and auditability rather than only final performance.Reported measures include within-life retention ratios, compute-to-parity, relearning savings, and per-decision audit trails.

12 The Registered Program and Its Discipline · 13 Main Results

The registered program establishes that governed structural growth can match or exceed budget-matched fixed architectures, preserve learned behavior under continued change, and requires ex-post governance to control adoption. Its campaigns validate exact structural operations and continual-learning mechanisms while reporting measured boundaries and failures under preregistered discipline.

12.1 The evidence discipline: Written gate files froze worlds, arms, metrics, and acceptance bars before data existed, while failures and superseded protocols were archived rather than retrospectively reframed.Design iteration used only disclosed probe ledgers on burned, disjoint seeds; final registered designs and outcomes were reported.
12.2 The campaigns at a glance: Mechanism suites passed exactness, budget, gate, lineage, and holdout-quarantine checks, while campaigns covered topology, attention-head growth, generalization, transformer comparison, size adjustability, fidelity, and factory operation.The self-knowledge series produced a mixed verdict: self-reports were real, but exploitation remained open.
13.1 Capacity follows demand: 5/5 verdict seeds favored governed growth over a budget-matched standard transformer, surviving stricter governance at 4/5 under the silenced gate and 5/5 under incumbent–candidate governance.Against the fixed network, sustained overtake began at 1.47–4.27× its size, with median ∼2.6×, while two end comparisons were excluded or censored by registered rules.
13.2 Stability from governance, not immobility: On every verdict seed, the governed plastic arm held its educated canon at least as long as the frozen arm under surface drift and scheduled temptation.Both arms received the same curriculum, and a solidity gate required mean of the last three checkpoints ≥0.90 on calibration seeds.
13.3 Growth governance is ex-post: The naive gate made 8/8 regretted adoptions on the stationary public track, whereas the workable form promoted only at an audited improvement checkpoint with a demotion window.Trials were free and bit-equal to never-growing service until promotion; an immutable rollback anchor prevented promotion over the last good state, curing serving NLL 11.38 to 0.65.
13.4 The audit tally: The audit tally classified 35 of 64 claim rows as supported, 20 as boundary results, and 4 as open FAIL branches, with every number in the part tied to a correspondence-table row.The tally also included 3 diagnostic exhibits, 1 historical motivation row, 1 auxiliary demonstration, and 23 empirical-observation rows.
13.5 The depth-axis and continual-learning campaigns: Serving accepted whole-layer insertions without interruption: failed serves were 0 across every life, served functions were unchanged at 36/36 instants, and inserted layers trained thereafter at 36/36 aliveness.Autonomous growth also satisfied the aspect-ratio shape law with zero gate collisions, while protection windows damped post-insertion spikes at 28/36 instants.
13.5 The depth-axis and continual-learning campaigns: Under strict sequential domain switches, old-domain degradation reached 552–1,362×; only review arms retained old knowledge, with ratios 72–300, while capacity or protection windows alone did not.After stabilization, a review course achieved comparable retention at roughly one tenth the new-domain cost of always-on replay; adding growth delivered the best new-domain quality but weaker retention.

14 Empirical Observations and Threats to Validity … Appendices

The campaigns report conditional empirical observations about governed growth, measurement, curriculum, capacity, and governance, while explicitly limiting inference to small-scale tested worlds. The discussion and conclusion position SoftModel as an auditable, reproducible lifecycle method whose necessity and superiority remain open experiments.

14.1 The observations: The observations are measured findings from tested worlds, not laws, and are limited to the conditions under which they were measured.The campaigns retain full derivations and registered archival identifiers for each observation.
14.1 The observations: Instrument choice governed conclusions: lives tied on prequential scores despite exam readings of 0.64 vs 0.44, while informative NLL produced 0 vs 2–8 adoption events per seed.Audits could also miss harm: a +3,000-row bucket-CE audit retained a widen whose late-third exam score fell 0.04.
14.1 The observations: Curriculum effects were non-monotonic and exposure-limited: doubling a drill moved its target 0.20 →0.45, whereas six-fold review collapsed it to 0.17 and broke a neighboring axis.A skill drillable to 1.0 in isolation plateaued near chance in-curriculum, while live-world plasticity incurred a transition dip.
14.1 The observations: Governance faced delayed and regime-dependent costs: one tolerated adoption decayed 0.57 →0.37, re-anchoring recovered about half the loss at 11% cost, and noise caused 8/8 regretted adoptions.A calm throttle had zero era-adaptation cost but reduced fidelity from 0.67 →0.51 under permanent drift.
14.1 The observations: Capacity paid differently across the lifecycle: un-starving the gate narrowed the paired oracle gap from 0.046 →0.034 mean but could not close it, while discrete memorization—not smooth regression—required parameter growth.The smooth-regression family scored flat across a 20× parameter range at NLL 1.38/1.36/1.34/1.38.
14.2 Scope and threats to validity: Validity is bounded by kilobyte-to-tens-of-kilobyte models, synthetic registered worlds plus selected real-data and benchmark lanes, three seeds per arm, and mostly the reference-network family.The campaigns include moderate-scale seeded streams, with some results measured at one composition depth in one world and retention reported as within-life ratios.
15 Discussion: The discussion argues that gated change lets operators act carelessly while the served model can only improve or stay, and that lifecycle audits record what the model has been across its service life.Structural budgets remain bounded but adjustable runtime policies, while committed versions are immutable between promotions.
16 Conclusion: The conclusion extends the gate to attention and evaluative signals, reports preserved learning on standard continual-learning benchmark lanes, and makes safety and exactness—not necessity or superiority—the tested-scale claim.A matched-parameter comparison against wider immobilization families remains the decisive open experiment, although the EWC comparison is recorded as supported 3/4.

Appendix A. The Pre-Registered Empirical Program … B.1 G-GROW-1: the open-inventory exact-answer battery

The pre-registered program verifies the mechanics of governed growth, tests its theoretical and self-knowledge claims, and reports both successful continual adaptation and important failures. Growth-value experiments further show that capacity can bind while online metrics conceal it, motivating post-adoption review as future governance work.

Appendix A. The Pre-Registered Empirical Program; A.1 Protocol; A.2 What verifies exactly (the mechanics): Every experiment committed hypotheses, arms, seeds, budgets, pass bars, and failure interpretations before execution, while the acceptance suite separately verified exact mechanics and kept theory claims within Table 10.The suite confirmed refinement, widening, exact entry, budget refusals, lineage, gated adoption, quarantine, consent, and the end-to-end factory loop.
A.3 Where the theory’s predictions stand (E-series): The E-series supported fine-scale adaptation and exact σ entry, but found no capacity lock-in, failed the robustness branch under label noise, and left Φ’s firing trigger unsupported.σ drove error to 1.4 × 10−3 versus a control floor of ≈5.7, while the speed criterion held in only 1/3 seeds.
A.4 Self-knowledge is real; exploiting it is open (S-series): Self-generated doubt and label-free variation checks predicted true errors, but question-directed teaching, scheduling, alternation, self-quizzing, and self-study interventions failed or remained inconclusive.The variation self-check was the best measured transfer-error predictor, with correlations 0.68/0.58/0.60 versus 0.46/0.39/0.54 for perturbation sensitivity.
A.5 The attention program (A-series): The attention extension preserved the pre-registered protocol while showing that its no-shift control crossed the 2σ envelope in 13/15 runs, making the raw alarm sensitive but noisy.Deployment therefore requires a debounced threshold, and the false-alarm rate is recorded.
A.6 Real-data case study: prequential concept-drift streams: On INSECTS, the grown system reached prequential accuracy 0.762 versus 0.599 for single-model HAT and exceeded ARF, SRP, and LB while using less wall time than SRP and LB.The comparison used 79,986 rows, 33 features, six classes, and five seeds per arm; the system’s mean wall time was 41 s versus 534 s for SRP and 744 s for LB.
A.7 Generalization campaign (G-series): The generalization campaign found a frozen addition cliff from 0.65 at length 6 to 0.11 at length 7, whereas lifelong learning held 0.51–0.57 across untrained lengths.Two heads of width four restored parity with the fixed host, showing that birth capacity remained an obligation until the growth trigger closed the gap.
A.7 Generalization campaign (G-series): The EWC comparison showed governed plasticity retaining ≈1 on three of four tasks without anchors, while λ = 1000 over-pinned retention to 0.03–0.12; the result remains scoped to kilobyte scale and EWC.Progressive columns and adapter freezing remain open.
Appendix B. The Growth-Value Campaigns; B.1 G-GROW-1: the open-inventory exact-answer battery: In G-GROW-1, Round 1 was noise-limited and vacuous, while Round 2 showed capacity binding on exams but hidden online: the oracle beat fixed birth in 4/5 seeds, with median accuracy 0.64 versus 0.44.The record identifies delayed post-gate harm and proposes provisional adoption with a post-adoption review horizon and rollback anchors as future work.

B.2 G-GEN-1: the generative battery, and the scope observation from its stationary companion … B.7 The size-adjustability round (X-SAT)

Across generative, open-inventory, and size-adjustability tests, governed growth learned when to stay quiet, when to adopt capacity, and where adoption latency limited value. The program passed size adjustability while exposing metric-, stationarity-, and timing-dependent boundaries.

B.2 G-GEN-1: the generative battery, and the scope observation from its stationary companion: On the growing generative world, 2–8 adopted growth events per seed closed the gap, yielding final median NLL oracle 1.83 < grow 1.88 < fixed birth 1.98 < transformer 2.00.NLL kept the adoption gate informative, whereas exact-match evaluation could starve it; on a stationary temperature stream, the transformer was most accurate and unsilenced growth produced 8/8 regretted adoptions.
B.3 Round 2 of the generative campaign: the silenced gate (X1): The silenced gate reduced stationary-track net adoptions to 1/0/1/2/0 per seed, with 3/5 seeds non-regretted, while retaining growing-track coverage and recovery criteria.This contrasted with round 1’s 8/8 regretted stationary adoptions; C-N2 held at 4/5, C-N3 at 5/5, and C-N4 at 4/5.
B.4 Round 2 of the open-inventory campaign: probe hygiene and the provisional gate (X2): Open-inventory probe hygiene un-starved the gate: adoptions reached 2–3 per seed on 5/5, while audits reverted 2 per seed and the median late-third score rose 0.5014 →0.5653.The ex-ante probe damaged every trial, so adoption became untrained and exact, followed by shadow comparison and audited rollback; C-G1 still failed while C-G2 accuracy improved to 4/5 and parsimony remained 5/5.
B.5 Round 3, generative track: incumbent–candidate governance (X1b): Incumbent–candidate governance found value without serving disruption: 4/5 stationary promotions were non-regretted, and the growing track achieved C-N4 against the budget-matched transformer on 5/5 seeds.Trials were free until promotion, serving was bit-exact, and failures were non-catastrophic through rollback or non-regretted adoption.
B.6 Round 3, open-inventory track: the same governance under exam metrics (X2b): Under exam metrics, governance passed C-G2 with accuracy 3/5 and parsimony 5/5, but C-G1 remained 0/5, illustrating that serving isolation did not overcome the registered growth-value margin.Across gate rounds, governed growth beat budget-matched standard architectures on arriving structure in 5/5, 4/5, and 5/5 results, while mid-life capacity did not outrun lifelong-trained fixed twins by registered margins.
B.7 The size-adjustability round (X-SAT): In the extreme X-SAT round, A-1 passed 5/5: the growable arm began 2.4× smaller, ended 3.3× larger at 39,375–40,815 parameters, and earned 15–20 promotions, but A-2 failed at 2/5.The failure attributed demand exceeding the serialized pipeline’s approximately 1 promotion per 30–40k rows purchase rate.
B.7 The size-adjustability round (X-SAT): The moderate X-SAT round passed the size-adjustability program: every seed ended 4.6–4.9× the counterpart’s size, 4/5 crossed and stayed ahead, and median crossover occurred at 275,000 rows.The successful strategy used buffered birth, moderated lifelong data growth, and unchanged governance; sustained overtake began at a median approximately 2.6× counterpart size.

Appendix C. … Appendix E. Validation by an Operating LLM

Appendices C–E define a pedagogy and fidelity program for lifelong models, showing that repetition, contemporaneity, canon-anchored immunity, governed calm, and self-referenced trajectory metrics are necessary to evaluate learning under drift and corruption. The final validation shows that a production LLM can operate the factory end-to-end, generalize on withheld inputs, refuse inferior updates, and audit lineage.

Appendix C. / A Pedagogy for Lifelong Models: Lifelong-model education requires foundation, ordered sequencing, rhythmic repetition, contemporaneous review, blended principle and skill, controlled exposure, self-examination, remediation, and time-axis evaluation.The framework treats these principles as architectural and lifecycle requirements, while marking structural protection, non-extractability, and individualized pacing as open measurements.
A Pedagogy for Lifelong Models: Doubling a drill moved composition skill from 0.20 to 0.45, whereas six-fold drilling collapsed it to 0.17 and damaged neighboring skills, demonstrating non-monotonic review dose.A skill drillable to 1.0 in isolation plateaued near chance inside a full curriculum, indicating crowding-out and exposure-economics constraints.
Appendix D. The Fidelity Program (GUARD): Four Registered Rounds / D.2 Round 1 — baseline: no defenses / D.3 Round 2 — strategy: canon-anchored immunity: Canon-anchored self-testing with alarm-triggered re-teaching recovered half the damage from coherent corruption at ∼11% vigilance cost, but alarm timing remains unresolved.The undefended plastic learner followed coherent corruption almost exactly as incentive predicted, while leading alarms cannot distinguish novelty from corruption.
D.4 Round 3 — strategy: a calm governor / D.6 Program conclusions: The GUARD program found that governors are regime-specific: calm helps genuinely stationary worlds, growth responds to arriving structure, and throttling cannot recover tracking costs under permanent drift.Naive composition can perturb governors through shared evidence streams, motivating isolated trigger channels as a registered direction rather than a measured regularity.
D.5 Round 4 — strategy: correct the instrument, then teach properly / D.6 Program conclusions: Corrected fidelity evaluation replaced absolute no-drop grading with self-referenced trajectory slope, time-to-degradation, and recovery, because minimum statistics reward immobility.The old instrument gave the round-4 thesis 2/5, whereas the corrected graduation-baseline rule left TTD at 5/5 and recovery at 4/5.
D.6 Program conclusions / A Pedagogy for Lifelong Models: The program concludes that immunity is prerequisite for lifelong learning under coherent corruption, canon-anchored re-teaching is cheap and partial, and each campaign’s unsupported claims remain registered future measurements.The education account reports both positive and negative results rather than treating its principles as decoration.
Appendix E. Validation by an Operating LLM: A production LLM validated the factory end-to-end with 16/16 exact-answer generalization on unseen operand pairs, refused garbage teaching when the candidate scored 0.4375 against the incumbent’s 1.0, and re-taught drift to 12/12.The released trace covered five auditable versions; governed growth made exact structural edits, promoted three times, and refused the final commit.

Appendix F. … Appendix I. Relation to Other Methods

The appendices document governed topology growth, audit-driven continual-learning campaigns, and the paper’s positioning against prior adaptive, continual, and structural methods. Together, they preserve failures and limitations while distinguishing this system by in-service, exact, uniformly gated structural change.

A Topology Growing under Governance: The released system grew a real topology through a staged curriculum, with growth sites proposed from instability reports and adoption decided only by the gate.The seed was fixed, and run snapshots were committed alongside the paper source.
Appendix G. The Historical Depth Route (retained as record): The historical depth route is retained as a record, not evidence, because scalar-width host interfaces could not export distributional corrections from grown inner structure.The appendix identifies interface completeness as the reason for retiring that generation’s mechanics, simulations, and depth-field figure as evidence.
Appendix H. The 2026 Depth-Axis and Continual-Learning Campaigns: The 2026 campaigns used preregistered designs, served interfaces, machine-checked isolation, write-once run directories, and append-only verdict recomputation from run files.The library anchor for adopted rows was depthgrowth-v1.7; two audit-exposed defects were fixed with tests and affected arms rerun.
Appendix H. The 2026 Depth-Axis and Continual-Learning Campaigns: E-3 passed exact insertion and continuity checks at 36/36 while post-insertion descent-window recovery failed at 12/36; E-6 found spike damping at 28/36.E-6 also found zero durable cost on healthy regions at 9/9 and late-insertion recovery at 3/9, with 6/9 in-band at the extended horizon and median 0.93.
Appendix H. The 2026 Depth-Axis and Continual-Learning Campaigns: E-2 established the shape law at 3/3 and binding-floor avoidance at 3/3; E-4 achieved bitwise rollback at 18/18, while economy passed at 2/3.The quality band passed at 1/3 initially and resolved at 3/3 in the preregistered 50-batch annex; E-4 isolated probe myopia as the cause of its shortfall.
Appendix H. The 2026 Depth-Axis and Continual-Learning Campaigns: The campaigns reported both positive and negative continual-learning findings, including 552–1,362× disease effects, 7–10× relearning savings, and failed registered hypotheses in E-7.E-1 achieved compute-to-parity at 58–64% in 2/3 seeds; E-12 achieved savings at 3/3, while E-7’s two hypotheses were 0/3.
Appendix I. Relation to Other Methods: Relative to prior methods, the system combines in-service evidence, bitwise exact application, uniform held-out adoption, and deployment-time operation in a cell the authors do not find previously occupied.Its reality gate is the sole adoption path, rescoring the incumbent and applying equally to gradient steps and structural operators.
Appendix I. Relation to Other Methods: The related-work distinctions span permanent unrouted depth, nested-scale credit assignment, search-free lifelong growth, persistent attention organs, and constructive per-head growth rather than pruning.The paper contrasts governed growth with adaptive inference depth, NAS outer loops, unconstrained recurrent mutations, scheduled head expansion, and post-hoc pruning.

Appendix J. Reading the Evidence

This evidence block is organized around three readings and a table that every claim in the paper answers to.

Evidence block: The evidence block closes with three readings.These readings are one of the two pieces that bind the evidence block.
Evidence block: A table binds the evidence block alongside the three readings.The passage identifies these as the two closing pieces.
Evidence block: Every claim in the paper answers to the table.The table is presented as part of the closing evidence structure.

J.1 Reading the map

The evidence is organized around mechanism versus value: governed growth works mechanically, while its benefits are partly supported and its remaining uncertainties are localized to revisable scenarios.

Mechanism vs value: Governed growth verifies exactly on its mechanical requirements, separating implementation evidence from questions about when growth pays.The map organizes the evidence from Appendices A–D around mechanism versus value.
Mechanism vs value: Positive value evidence comes from transformer comparisons and the size-adjustability crossover in §13.1.The passage describes these results as only a partial answer to where growth pays.
Open questions: Remaining open questions are localized to revisable scenarios involving floor-binding lock-in, trigger signals for Φ, noise regimes, and bounded within-life comparison.The passage presents these as specific scenarios rather than unresolved questions about the entire account.

J.2 The evidence table

Table 10 is the paper’s single source of record, mapping every numbered claim, prediction, and observation to its adjudicating artifact, registered verdict, key number, and status. Its evidence spans governed growth, continual-learning performance, and explicitly recorded boundaries and failures.

Evidence-table structure: Table 10 contains exactly one row for every numbered claim, prediction, and observation, and the paper’s prose does not outrun it.Rows record the theory section, claim, adjudicating campaign or artifact, registered verdict, one key number, and status.
Governance and structural growth: Governed growth received broad support: budgets were enforced, lineage audited, topology grew end-to-end, and the gate promoted or refused candidates.The table also records PASS outcomes for acceptance checks and the lifecycle’s end-to-end structural growth.
Continual-learning campaigns: Continual-learning results support demand-tracking growth, adaptation without forgetting, and stream competitiveness, including PASS 0.762 vs HAT 0.599 and NOAA 0.768 vs 0.739.Paired ablations were marked NOT ATTRIBUTABLE, so the stream-case result’s attribution to growth remains limited.
Boundaries and failures: The evidence table preserves important failures and boundaries, including NOT ATTRIBUTABLE paired ablations, a stationary miss, and GUARD r2 central claims NOT SUPP.It also records that instantaneous gates cannot see lifetime consequences and that governors have regimes.
Growth value: Growth paid when capacity bound: paired gains were +0.32/+0.08/+0.30, while the capacity-value observation states that ex-ante value was unobservable.The table distinguishes exam capacity effects from prequential behavior and records growth as needed only where the world grows.

J.3 How to audit a row

Each table row is auditable through its campaign-linked registered materials and disclosed per-seed results. The key number traces in two hops from the table to a hashed, write-once artifact with resolved configuration and content hashes.

A row’s campaign column identifies the appendix section containing its registered acceptance, per-seed values, and probe-ledger disclosures.
Evaluative-learning and benchmark rows instead trace through the Reproducibility Statement to registered design documents and per-run JSON stores.The adjudicating lanes’ per-seed values are listed in Table 11.
The result stores are write-once run directories with resolved configurations and content hashes, enabling a two-hop trace from each row to a hashed artifact on disk.

Appendix K. Glossary of Named Quantities and Roles

The glossary defines named roles and quantities within an auditable, registry-backed architecture. Roles are replaceable parts, while quantities are recorded in audit artifacts.

Roles: Every named role is a replaceable part behind a registry.The registry is identified in §4.3.
Quantities: Every named quantity is recorded in the audit artifacts.The glossary explicitly links quantity recording to audit artifacts.
Glossary: The glossary covers both registry-backed roles and audited quantities.Table 12 presents these as the defining properties of the glossary.