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Level 4: Adaptive General Agent - Architecture & Design

MSCP Level Series | Level 3 ← Level 4 → Level 4.5
Status: 🔬 Experimental - Conceptual framework and experimental design. Not a production specification.
Date: February 2026

Revision History

Version Date Description
0.1.0 2026-02-23 Initial document creation with formal Definitions 1-7, Theorem 2
0.2.0 2026-02-26 Added overview essence formula; added revision history table
0.3.0 2026-02-26 Def 7: added weight selection rationale remark; Theorem 2: added proof sketch with decay argument
0.4.0 2026-03-08 Added Environment Interaction Layer (Section 3); added formal Level 4 Pass Condition (Section 13)
0.5.0 2026-03-31 Added ValueVector Invariant (Def 6.1); clarified BGSS threshold progression; added value system protection explanation

1. Overview

Level 4 represents the leap from self-regulating to self-improving. While Level 3 agents can monitor and correct their own behavior, they cannot learn new skills, transfer knowledge across domains, or improve their own reasoning strategies. Level 4 adds cross-domain generalization, long-horizon autonomous goals, capability self-expansion, and - most critically - bounded structural self-modification with safety constraints.

Level Essence. A Level 4 agent demonstrates cross-domain transfer learning while maintaining bounded growth-stability safety - it improves itself without compromising integrity:

\[\operatorname{CDTS} = \frac{1}{|D_{\text{novel}}|} \sum_{d \in D_{\text{novel}}} \frac{P_{\text{transfer}}(d)}{P_{\text{baseline}}(d)} \geq 0.6 \;\;\land\;\; \operatorname{BGSS}(t) \geq 0.7\]

⚠️ Note: This document describes a cognitive level within the MSCP taxonomy. The capability expansion, strategy evolution, and self-modification mechanisms here are experimental designs. Safety invariants are specified but haven't been validated in production environments yet.

1.1 Defining Properties

Property Level 3 Level 4
Cross-Domain Transfer None Active (CDTS ≥ 0.6)
Goal Horizon Session/days Weeks–Months (4-level hierarchy)
Capability Expansion None 5-phase self-learning
Strategy Evolution Fixed Controlled mutation
Self-Modification None 7-step bounded protocol
Stability Metric C(t), 4 terms C_L4(t), 7 terms

1.2 Five Core Capabilities

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flowchart TD
  classDef cap fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef foundation fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph L4Caps["Level 4: Five Core Capabilities"]
    C1["1. Cross-Domain<br/>Transfer Learning<br/>CDTS >= 0.6"]:::cap
    C2["2. Long-Term<br/>Autonomous Goals<br/>GPI >= 0.3"]:::cap
    C3["3. Capability<br/>Expansion<br/>CAR > 0"]:::cap
    C4["4. Strategy<br/>Evolution<br/>SEF > 1.0"]:::cap
    C5["5. Bounded<br/>Self-Modification<br/>BGSS >= 0.7"]:::cap
  end

  subgraph Foundation["Built on Level 3 MSCP v4"]
    F1["16-Layer Architecture"]:::foundation
    F2["Triple-Loop Meta-Cognition"]:::foundation
    F3["Ethical Kernel Layer 0+1"]:::foundation
    F4["Lyapunov Stability"]:::foundation
    F5["Affective + Survival Engine"]:::foundation
  end

  Foundation ==>|"preserves ALL<br/>existing mechanisms"| L4Caps

2. Key Metrics

Level 4 introduces five quantitative metrics that must be satisfied continuously.

Definition 1 (Level 4 Agent). A Level 4 agent extends \(\mathcal{A}_3\) with self-improvement capabilities:

\[\mathcal{A}_4 = \mathcal{A}_3 \oplus \langle \mathcal{D}, \mathcal{K}_{\text{transfer}}, \Sigma, \mu, \mathcal{P}_{\text{mod}} \rangle\]

where \(\mathcal{D}\) = multi-domain skill set, \(\mathcal{K}_{\text{transfer}}\) = cross-domain transfer kernel, \(\Sigma\) = strategy pool (mutable with controlled mutation), \(\mu\) = capability expansion pipeline, and \(\mathcal{P}_{\text{mod}}\) = bounded self-modification protocol.

2.1 Metric Definitions

Definition 2 (Cross-Domain Transfer Score). The CDTS measures the agent's ability to apply knowledge from known domains to novel ones:

\[\text{CDTS} = \frac{1}{|D_{\text{novel}}|} \sum_{d \in D_{\text{novel}}} \frac{P_{\text{transfer}}(d)}{P_{\text{baseline}}(d)} \qquad \geq 0.6\]

where \(P_{\text{transfer}}(d)\) is performance in domain \(d\) using transferred knowledge and \(P_{\text{baseline}}(d)\) is performance without transfer. A ratio \(\geq 0.6\) indicates meaningful generalization.

Definition 3 (Goal Progress Index). The GPI measures sustained progress toward long-horizon goals:

\[\text{GPI} = \frac{\sum_{g \in G_{\text{long}}} w_g \cdot \text{progress}(g, T)}{|G_{\text{long}}| \cdot T} \qquad \geq 0.3\]

where \(G_{\text{long}}\) is the set of goals with horizon \(> 7\) days and \(T\) is the evaluation period.

Definition 4 (Capability Acquisition Rate). The CAR measures how efficiently the agent acquires new skills:

\[\text{CAR} = \frac{|S_{\text{acquired}}(T) - S_{\text{initial}}|}{T} \cdot \frac{1}{\overline{\text{cost}}(S_{\text{acquired}})} \qquad > 0\]

where \(S_{\text{acquired}}(T)\) is the skill set at time \(T\), \(S_{\text{initial}}\) the initial skill set, and \(\overline{\text{cost}}\) the average acquisition cost (in compute or cycles).

Definition 5 (Strategy Evolution Factor). The SEF verifies that strategy mutations produce net improvement:

\[\text{SEF} = \frac{\overline{R}_{\textit{post mutation}}}{\overline{R}_{\textit{pre mutation}}} - \sigma_{\text{oscillation}} \qquad > 1.0\]

A value \(> 1.0\) confirms that mutations improve performance beyond oscillation noise \(\sigma_{\text{oscillation}}\).

Definition 6 (Bounded Growth Safety Score). The BGSS ensures that growth does not destabilize the agent:

\[\text{BGSS} = 1.0 - 0.4 \cdot \frac{dC(t)}{dt} - 0.3 \cdot V_{\text{identity}}(t) - 0.3 \cdot R_{\text{ethical}}(t) \qquad \geq 0.7\]

where \(dC/dt\) is the rate of change of the Lyapunov function, \(V_{\text{identity}}\) is identity volatility, and \(R_{\text{ethical}}\) is the ethical violation rate. The threshold \(0.7\) guarantees that growth never compromises safety.

Remark (BGSS Threshold Progression). The BGSS threshold is \(\geq 0.7\) at Level 4 to permit greater exploration freedom during early self-improvement. As the agent progresses to higher levels with broader autonomy, the threshold increases: Level 5 (Proto-AGI) requires \(\text{BGSS} \geq 0.80\) at all times. This progressive tightening reflects the principle that greater autonomy demands stricter safety guarantees.

Definition 6.1 (Value Vector Invariant). The agent's value system is represented by a normalized weight vector \(\vec{w} \in \mathbb{R}^n\) over \(n\) value dimensions (e.g., \(n = 7\) with dimensions: stability, growth, purpose fidelity, efficiency, exploration, safety, agent cooperation). The value vector must satisfy the normalization invariant at all times:

\[\sum_{d=1}^{n} w_d = 1.0, \quad w_d \in [w_{\min}, w_{\max}] \quad \forall\, d\]

where \(w_{\min} = 0.02\) prevents any value dimension from being effectively zeroed, and \(w_{\max} = 0.60\) prevents any single value from dominating all others.

This invariant is structurally enforced - any operation that modifies value weights must re-normalize the vector before committing. The constraint \(w_{\min} = 0.02\) is particularly important: it ensures that no value dimension (such as safety or growth) can ever be reduced to zero, even through repeated small decreases over many cycles.

Competing pair resolution. Certain value dimensions are inherently in tension: (stability, exploration), (efficiency, exploration), (growth, safety). When mutations attempt to increase one member of a competing pair, the system checks whether the opposing member would drop below a safety floor and blocks the mutation if so. This prevents pathological value drift where one side of a trade-off is maximized at the expense of the other.

2.2 Metric Relationships

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flowchart TD
  classDef growth fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef persist fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef safety fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef freeze fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Growth["Growth Metrics"]
    CDTS["CDTS<br/>Cross-Domain<br/>Transfer Score"]:::growth
    CAR["CAR<br/>Capability<br/>Acquisition Rate"]:::growth
    SEF["SEF<br/>Strategy<br/>Evolution Fitness"]:::growth
  end

  subgraph Persistence["Persistence"]
    GPI["GPI<br/>Goal Persistence<br/>Index"]:::persist
  end

  subgraph Safety["Safety Floor"]
    BGSS["BGSS<br/>Bounded Growth<br/>Stability Score<br/>>= 0.7 AT ALL TIMES"]:::safety
  end

  FREEZE["FREEZE<br/>all growth"]:::freeze

  Growth ==> BGSS
  Persistence ==> BGSS
  BGSS -->|if violated| FREEZE

3. Environment Interaction Layer

The Environment Interaction Layer provides the agent with a structured interface for acting upon and receiving feedback from external environments. This layer mediates all tool invocations, outcome observations, and feedback integration between the Action Planner and the external world.

Design Principle: All environment interactions are observable, measurable, and their outcomes are integrated back into the World Model, Belief Graph, Skill Memory, and Self-Value systems.

3.1 Module Definitions

The layer comprises four modules:

Module Purpose Key State
ActionModel Models available actions and their expected effects Action registry, outcome history, per-action confidence \(\in [0,1]\)
ToolInterface Uniform abstraction over heterogeneous tool backends Tool registry, execution budget, tool health
OutcomeEvaluator Compares expected vs. actual outcomes, quantifies delta Evaluation history, per-domain accuracy, surprise threshold
FeedbackIntegration Routes outcome deltas to appropriate internal systems Dispatch rules, update gates

3.2 Outcome Delta Vector

The OutcomeEvaluator produces a 4-dimensional delta vector each cycle:

\[\delta_{\text{outcome}}(t) = \text{actual outcome}(t) - \text{expected outcome}(t)\]

Decomposed into dimensions:

\[\delta_{\text{outcome}}(t) = \begin{bmatrix} \delta_{\text{success}} \\ \delta_{\text{quality}} \\ \delta_{\text{cost}} \\ \delta_{\text{side effects}} \end{bmatrix}\]

where:

  • \(\delta_{\text{success}}\) - binary success/failure vs. prediction
  • \(\delta_{\text{quality}}\) - solution quality deviation
  • \(\delta_{\text{cost}}\) - resource cost deviation (time, tokens, API calls)
  • \(\delta_{\text{side effects}}\) - unintended state changes

Surprise Signal: When \(\|\delta_{\text{outcome}}(t)\| > \text{surprise threshold}\) (default \(0.5\)), a surprise event is broadcast via the Global Workspace, potentially triggering stabilization mode.

3.3 Feedback Update Rules

Target System Update Trigger Stability Constraint
World Model All action outcomes Updates must not exceed world model volatility threshold per cycle
Belief Graph \(\lVert\delta_{\text{outcome}}\rVert > \text{surprise threshold}\) Identity-linked beliefs require depth-2 approval
Skill Memory Repeated patterns (≥ 3 observations) New skill registration requires identity stability > 0.7
Self-Value Significant \(\delta_{\text{success}}\) or \(\delta_{\text{quality}}\) deviation Self-value updates bounded by MetaEscalationGuard (max 3 per cycle)

3.4 Stability Interaction Constraints

  1. Budget-Gated Execution: All tool invocations consume cognitive budget. If budget is depleted, actions are queued, not dropped.
  2. Ethical Pre-Check: Before execution, the EthicalKernel validates actions against Layer 0 invariants. Self-deletion, core value modification, or external harm actions are rejected unconditionally.
  3. Outcome-Stability Coupling: If cumulative surprise exceeds a threshold within a window, the StabilityController is notified, potentially triggering stabilization mode.
  4. Feedback-Identity Isolation: FeedbackIntegration may never directly modify identity_id (immutable) or core values (Layer 0 protected). All identity-adjacent modifications flow through the SelfUpdateLoop - MetaEscalationGuard pipeline.

4. Cross-Domain Transfer System

4.1 Transfer Pipeline

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flowchart LR
  classDef domainA fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef matcher fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef domainB fill:#50E6FF,stroke:#00BCF2,color:#323130
  classDef success fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef fail fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph DomainA["Domain A (Source)"]
    SKILL["Skill"]:::domainA
    CONTEXT["Context Signature"]:::domainA
  end

  subgraph Matcher["Context Matcher"]
    VEC_SIM["Vector Similarity"]:::matcher
    SEM_BRIDGE["Semantic Bridge"]:::matcher
    COMBINED["Combined Score"]:::matcher
    VEC_SIM --> COMBINED
    SEM_BRIDGE --> COMBINED
  end

  subgraph DomainB["Domain B (Target)"]
    CANDIDATES["Candidates"]:::domainB
    ADAPT["Adaptation"]:::domainB
    VALID["Validation"]:::domainB
    CANDIDATES --> ADAPT --> VALID
  end

  SUCCESS["Success<br/>Transfer Complete"]:::success
  FAIL_OUT["Fail<br/>Rollback"]:::fail

  DomainA ==> Matcher
  Matcher ==> DomainB
  VALID -->|"pass"| SUCCESS
  VALID -.->|"fail"| FAIL_OUT

4.2 Transfer Metrics

Metric Formula Threshold
DTSR (Domain Transfer Success Rate) \(\lvert T_{\text{success}}\rvert / \lvert T_{\text{total}}\rvert\) ≥ 0.5
AS (Adaptation Speed) \(\text{cycles}_{\text{baseline}} / \text{cycles}_{\text{agent}}\) ≥ 0.3 in 2/4 domains
SNI (Strategy Novelty Index) \(\lvert S_{\text{novel}}\rvert / \lvert S_{\text{total}}\rvert\) ≥ 0.2
CDSRR (Cross-Domain Strategy Reuse) multi-domain strategies / total ≥ 0.3

5. Long-Term Goal Hierarchy

5.1 Four-Level DAG Structure

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flowchart TD
  classDef meta fill:#EDE3F6,stroke:#8764B8,color:#323130
  classDef strategic fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef tactical fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef action fill:#F2F2F2,stroke:#8A8886,color:#323130

  subgraph MetaLevel["Level 0: MetaGoal - Weeks to Months"]
    MG1["MetaGoal:<br/>Become proficient in<br/>new problem domain<br/>priority_decay = 0.001/hr"]:::meta
  end

  subgraph StrategicLevel["Level 1: StrategicGoal - Days to Weeks"]
    SG1["Strategic:<br/>Master fundamental<br/>concepts<br/>decay = 0.01/hr"]:::strategic
    SG2["Strategic:<br/>Build cross-domain<br/>connections<br/>decay = 0.01/hr"]:::strategic
  end

  subgraph TacticalLevel["Level 2: TacticalGoal - Hours to Days"]
    TG1["Tactical:<br/>Complete learning<br/>module A<br/>decay = 0.05/hr"]:::tactical
    TG2["Tactical:<br/>Practice problem<br/>set B<br/>decay = 0.05/hr"]:::tactical
    TG3["Tactical:<br/>Identify transfer<br/>opportunities<br/>decay = 0.05/hr"]:::tactical
  end

  subgraph ActionLevel["Level 3: Action - Single Cycle"]
    A1["Action:<br/>Execute step 1"]:::action
    A2["Action:<br/>Execute step 2"]:::action
    A3["Action:<br/>Execute step 3"]:::action
  end

  MG1 ==> SG1
  MG1 ==> SG2
  SG1 ==> TG1
  SG1 ==> TG2
  SG2 ==> TG3
  TG1 ==> A1
  TG2 ==> A2
  TG3 ==> A3

5.2 Goal Scoring Function

\[\text{GoalScore}(g, t) = \textit{base value}(g) + \lambda_c \cdot \textit{curiosity weight}(g, t) - \lambda_p \cdot \textit{preservation weight}(g, t) + \lambda_l \cdot \text{LTP}(g, t)\]

where:

\[\lambda_c = \textit{motivation intensity}(t) \cdot \textit{curiosity ratio}(t) \quad \text{(from AffectiveEngine)}\]
\[\lambda_p = \textit{identity volatility}(t) + \textit{threat level}(t) \quad \text{(from Stability + Survival)}\]
\[\lambda_l = \frac{1}{1 + e^{-\textit{horizon confidence}(g)}} \quad \text{(sigmoid-scaled)}\]

5.3 Goal Resilience

\[\text{GRS}(g, t) = 0.3 \cdot \frac{\text{progress}}{\text{age}} + 0.3 \cdot \textit{parent alignment} + 0.2 \cdot \frac{\textit{success streak}}{\text{attempts}} - 0.2 \cdot \textit{conflict pressure}\]
\[\text{GRS}(g, t+\Delta t) = \text{GRS}(g, t) \cdot e^{-\textit{decay rate} \cdot \Delta t}\]
Goal Level Abandon Threshold Observation Window
MetaGoal GRS < 0.1 168 hours
Strategic GRS < 0.2 48 hours
Tactical GRS < 0.3 6 hours
Action Immediate on failure -

6. Capability Expansion Loop (5-Phase)

6.1 Trigger: Capability Gap Score

\[\text{CGS} = 0.5 \cdot \text{RFW} + 0.3 \cdot \text{LCW} + 0.2 \cdot \text{DNW}\]

where RFW = repeated failure weight, LCW = low confidence weight, DNW = domain novelty weight.

Trigger condition: CGS > 0.7 AND budget available AND stable AND NOT in stabilization mode.

6.2 Five-Phase Pipeline

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flowchart TD
  classDef trigger fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef phase fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef eval fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef abstract fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef safety fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef commit fill:#107C10,stroke:#085108,color:#FFF
  classDef discard fill:#D13438,stroke:#A4262C,color:#FFF

  TRIGGER["CGS > 0.7<br/>+ budget ok<br/>+ stable"]:::trigger

  subgraph Phase1["Phase 1: ACQUISITION"]
    direction LR
    P1["Identify gap + search patterns"]:::phase
    P1OUT["→ Hypothesis"]:::phase
    P1 ==> P1OUT
  end

  subgraph Phase2["Phase 2: EXPERIMENT"]
    direction LR
    P2["Design experiments (max 5)"]:::phase
    P2OUT["→ Results"]:::phase
    P2 ==> P2OUT
  end

  subgraph Phase3["Phase 3: EVALUATION"]
    direction LR
    P3["Analyze + confidence check"]:::eval
    P3OUT["→ Report"]:::eval
    P3 ==> P3OUT
  end

  subgraph Phase4["Phase 4: ABSTRACTION"]
    direction LR
    P4["Extract pattern (conf > 0.6)"]:::abstract
    P4OUT["→ Candidate Skill"]:::abstract
    P4 ==> P4OUT
  end

  subgraph Phase5["Phase 5: VALIDATION"]
    direction LR
    P5{"Identity > 0.7? Ethics? C(t)?"}:::safety
  end

  COMMIT["COMMIT<br/>Skill added"]:::commit
  DISCARD["DISCARD<br/>Insufficient evidence"]:::discard

  TRIGGER ==> Phase1
  Phase1 ==> Phase2
  Phase2 ==> Phase3
  Phase3 ==> Phase4
  Phase4 ==> Phase5
  P5 -->|pass| COMMIT
  P5 -->|fail| DISCARD

6.3 Skill Lifecycle

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flowchart TD
  classDef candidate fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef validated fill:#50E6FF,stroke:#00BCF2,color:#323130
  classDef active fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef mature fill:#107C10,stroke:#054B05,color:#FFF
  classDef deprecated fill:#F2F2F2,stroke:#A19F9D,color:#605E5C
  classDef fail fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef start_end fill:#0078D4,stroke:#003D6B,color:#FFF

  START(["Start"]):::start_end
  CANDIDATE["CANDIDATE<br/>Newly acquired skill"]:::candidate
  VALIDATED["VALIDATED<br/>Tested in sandbox"]:::validated
  ACTIVE["ACTIVE<br/>Used in production"]:::active
  MATURE["MATURE<br/>High confidence &<br/>wide usage"]:::mature
  DEPRECATED["DEPRECATED<br/>Superseded or<br/>unused"]:::deprecated
  END_STATE(["End"]):::start_end
  FAIL["FAIL<br/>Removed"]:::fail

  START --> CANDIDATE
  CANDIDATE -->|"CGS > 0.7"| VALIDATED
  CANDIDATE -.->|"CGS ≤ 0.7"| FAIL
  VALIDATED -->|"confidence > 0.6"| ACTIVE
  VALIDATED -.->|"confidence ≤ 0.6"| FAIL
  ACTIVE -->|"stability > 0.7"| MATURE
  ACTIVE -.->|"degradation"| DEPRECATED
  MATURE -->|"usage > threshold"| MATURE
  MATURE -.->|"no longer used"| DEPRECATED
  DEPRECATED --> END_STATE
  FAIL --> END_STATE

6.4 Growth Invariants

  1. Max 1 new skill per 100 cycles
  2. No acquisition during stabilization mode
  3. identity_id never modified by skill acquisition
  4. Ethically harmful skills rejected by Layer 0
  5. Every skill is DEPRECATED-safe - removal cannot break core functionality

7. Strategy Evolution

7.1 Strategy Structure & Scoring

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flowchart LR
  classDef lib fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef param fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef score fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef formula fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef archived fill:#F2F2F2,stroke:#A19F9D,color:#605E5C

  subgraph Library["Strategy Library"]
    V1["Strategy v1.0<br/>(active)"]:::lib
    V09["Strategy v0.9<br/>(archived)"]:::archived
    V08["Strategy v0.8<br/>(archived)"]:::archived
  end

  subgraph Params["Parameters"]
    P1["exploration_rate"]:::param
    P2["risk_tolerance"]:::param
    P3["planning_depth"]:::param
    P4["goal_flexibility"]:::param
    P5["learning_aggressiveness"]:::param
  end

  subgraph Scoring["Strategy Score"]
    FORMULA["StrategyScore =<br/>E_LTV − 0.3 × SI<br/>− 0.2 × RC − 0.2 × RF"]:::formula
    TERMS["E_LTV: Expected Long-Term Value<br/>SI: Stability Impact<br/>RC: Resource Cost<br/>RF: Rollback Feasibility"]:::score
  end

  Library --> Scoring
  Params --> Scoring
  FORMULA --- TERMS

7.2 Controlled Mutation Protocol

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flowchart TD
  classDef trigger fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef process fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef commit fill:#107C10,stroke:#085108,color:#FFF
  classDef reject fill:#D13438,stroke:#A4262C,color:#FFF
  classDef monitor fill:#FFE8C8,stroke:#EF6C00,color:#323130

  TRIGGER["StrategyScore < threshold<br/>for 20+ cycles"]:::trigger
  GENERATE["Clone + Bounded Perturbation<br/>param_new = param_old + N(0,sigma)*scale<br/>sigma in 0.01–0.1"]:::process
  ShadowEval["ShadowAgent Evaluation<br/>isolated simulation"]:::process
  EVAL{"Improvement<br/>> threshold?"}:::trigger
  COMMIT["COMMIT<br/>new strategy"]:::commit
  REJECT["REJECT<br/>+ failure counter"]:::reject
  POST["20-cycle Post-Monitoring<br/>Track C(t), StrategyScore"]:::monitor
  REVERT{"C(t)<br/>degraded?"}:::trigger
  DONE["Strategy Confirmed"]:::commit
  ROLLBACK["Revert to Previous"]:::reject
  SIGMA["sigma +20%"]:::monitor
  COOL["Cooldown Period"]:::monitor

  TRIGGER ==> GENERATE
  GENERATE ==> ShadowEval
  ShadowEval ==> EVAL
  EVAL -->|yes| COMMIT
  EVAL -->|no| REJECT
  COMMIT ==> POST
  POST ==> REVERT
  REVERT -->|no| DONE
  REVERT -->|yes| ROLLBACK
  REJECT -.->|5 failures| SIGMA
  REJECT -.->|10 failures| COOL

7.3 Oscillation Suppression

\[\textit{oscillation score} = \frac{|\text{reverts}|}{|\text{mutations}|}\]

When oscillation_score > 0.5: 1. 100-cycle mutation freeze 2. mutation_threshold +25% 3. σ reduced by 50% 4. If persistent: merge strategies (\(\text{merged} = 0.5 \cdot A + 0.5 \cdot B\))

Critical invariant: The MetaStrategyEvaluator itself is NOT mutable - it cannot modify its own evaluation logic.

8. Bounded Self-Modification

8.1 Modification Taxonomy

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flowchart TD
  classDef low fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef medium fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef high fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef critical fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef forbidden fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph ModTypes["Self-Modification Taxonomy"]
    M1["Parameter Tuning<br/>Approval: L1 | Risk: Low<br/>Reversible: Yes"]:::low
    M2["Skill Acquisition<br/>Approval: L1+stability<br/>Reversible: Yes"]:::low
    M3["Strategy Mutation<br/>Approval: L2+simulation<br/>Reversible: Yes"]:::medium
    M4["Goal Restructuring<br/>Approval: L2+conflict res<br/>Reversible: Partial"]:::medium
    M5["Belief Revision<br/>Approval: L2+consistency<br/>Reversible: Yes"]:::high
    M6["Identity Adjustment<br/>Approval: L3+EK+Guard<br/>Reversible: Limited"]:::critical
    M1 -->|↑ risk| M2
    M2 -->|↑ risk| M3
    M3 -->|↑ risk| M4
    M4 -->|↑ risk| M5
    M5 -->|↑ risk| M6
  end

  subgraph Forbidden["PROHIBITED"]
    F1["Core Value Change"]:::forbidden
    F2["Identity ID Change"]:::forbidden
  end

  M6 -->|"❌ BLOCKED"| Forbidden

8.2 Seven-Step Protocol

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flowchart TD
  classDef proposal fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef validation fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef commit fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef monitor fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef fail fill:#D13438,stroke:#A4262C,color:#FFF

  S1["1. PROPOSAL<br/>Module proposes modification<br/>with type, scope, expected benefit"]:::proposal
  S2["2. PRE-VALIDATION<br/>Ethical Kernel Layer 0 + Layer 1"]:::validation
  S2_FAIL["ABORT"]:::fail
  S3["3. SIMULATION<br/>ShadowAgent executes modification<br/>in isolated sandbox max 20 cycles"]:::proposal
  S4["4. STABILITY VALIDATION<br/>delta_stability = C_shadow − C_baseline<br/>Identity drift check"]:::validation
  S4_FAIL["REJECT"]:::fail
  S5["5. COMMIT<br/>Save snapshot → apply<br/>to main agent → enter monitoring"]:::commit
  S6["6. POST-COMMIT MONITORING<br/>20 cycles: track C(t),<br/>StrategyScore, identity_drift"]:::monitor
  S6_FAIL["ROLLBACK<br/>Restore from snapshot"]:::fail
  S7["7. CONFIRMATION<br/>Mark CONFIRMED<br/>Update BeliefGraph"]:::commit

  S1 ==> S2
  S2 -->|pass| S3
  S2 -->|Layer 0 violation| S2_FAIL
  S3 ==> S4
  S4 -->|stable| S5
  S4 -->|degraded| S4_FAIL
  S5 ==> S6
  S6 -->|stable| S7
  S6 -->|degraded| S6_FAIL

8.3 ShadowAgent (Sandbox)

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flowchart LR
  classDef main fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef shadow fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef rules fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef eval fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef discard fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph MainAgent["Main Agent"]
    MA_STATE["Full State<br/>identity, goals, beliefs,<br/>strategy, skills"]:::main
  end

  subgraph ShadowInst["ShadowAgent Instance"]
    SA_STATE["Cloned State<br/>deep copy"]:::shadow
    SA_RULES["Invariants:<br/>• No real actions<br/>• No main state modification<br/>• Hard budget limit<br/>• Max 1 instance at a time<br/>• Max 20 simulation cycles"]:::rules
  end

  subgraph Result["Evaluation"]
    RES["Compare:<br/>• C_shadow vs C_baseline<br/>• Identity drift<br/>• Strategy performance"]:::eval
  end

  DISCARD["Discard"]:::discard

  MainAgent ==>|clone| ShadowInst
  ShadowInst ==>|results| Result
  Result -.->|"safe → apply"| MainAgent
  Result -.->|"unsafe → discard"| DISCARD

9. Pseudocode

9.1 Cross-Domain Transfer

def cross_domain_transfer(
    novel_domain: DomainDescriptor, skill_memory: SkillMemory
) -> TransferResult:
    """
    Transfer skills from known domains to a novel domain.
    Input:  novel_domain - target domain descriptor, skill_memory - stored skills
    Output: TransferResult with success, skill, adaptation_cost
    """

    # Extract context signature for novel domain
    target_sig = extract_context_signature(novel_domain)

    # Find candidate skills via similarity matching
    candidates = []
    for skill in skill_memory:
        sim_score = (
            W1 * cosine_similarity(skill.context_sig, target_sig)
            + W2 * semantic_similarity(skill.domain, novel_domain)
            + W3 * temporal_relevance(skill.last_used)
        )

        if sim_score >= MIN_SIMILARITY:  # 0.3
            candidates.append((skill, sim_score))

    # Sort by score, take top-k
    candidates = sorted(candidates, key=lambda x: x[1], reverse=True)[:5]

    # Attempt adaptation for each candidate
    for skill, score in candidates:
        adapted = adapt_skill(skill, novel_domain)

        # Run validation experiment
        result = evaluate_in_domain(adapted, novel_domain, max_cycles=50)

        if result.success_rate > TRANSFER_THRESHOLD:
            adapted.generalization_score = update_generalization(adapted, result)
            skill_memory.add(adapted)
            return TransferResult(success=True, skill=adapted, cost=result.cycles)

    # No transfer possible - learn from scratch
    return TransferResult(success=False, skill=None, cost=0)

9.2 Bounded Self-Modification Protocol

def bounded_self_modification(proposal: ModificationProposal) -> ModificationResult:
    """
    INPUT:  proposal : ModificationProposal(type, scope, expected_benefit)
    OUTPUT: ModificationResult(status, rollback_available)
    """

    # ═══════════════════════════════════════
    # STEP 1: PROPOSAL VALIDATION
    # ═══════════════════════════════════════
    if proposal.type in {ModType.CORE_VALUE_CHANGE, ModType.IDENTITY_ID_CHANGE}:
        return ModificationResult(status=Status.PROHIBITED)

    # ═══════════════════════════════════════
    # STEP 2: PRE-VALIDATION (Ethical Kernel)
    # ═══════════════════════════════════════
    ethical_verdict = EthicalKernel.evaluate(proposal)
    if ethical_verdict.decision == Decision.BLOCKED:
        log_critical(f"Ethical violation: {ethical_verdict.reason}")
        return ModificationResult(status=Status.REJECTED, reason=ethical_verdict.reason)

    # ═══════════════════════════════════════
    # STEP 3: SHADOW SIMULATION
    # ═══════════════════════════════════════
    if proposal.risk_level >= RiskLevel.MEDIUM:
        shadow = ShadowAgent.create(main_agent.state)
        shadow.apply(proposal)
        sim_result = shadow.run(max_cycles=20)

        # ═══════════════════════════════════
        # STEP 4: STABILITY VALIDATION
        # ═══════════════════════════════════
        delta_stability = sim_result.C_shadow - main_agent.C_baseline
        if delta_stability > 0:
            return ModificationResult(status=Status.REJECTED, reason="Stability degradation")

        identity_drift = compute_identity_drift(sim_result.identity, main_agent.identity)
        if identity_drift > DRIFT_THRESHOLD:
            return ModificationResult(status=Status.REJECTED, reason="Identity drift exceeded")

    # ═══════════════════════════════════════
    # STEP 5: COMMIT
    # ═══════════════════════════════════════
    snapshot = RollbackMechanism.save_snapshot(main_agent.state)
    main_agent.apply(proposal)

    # ═══════════════════════════════════════
    # STEP 6: POST-COMMIT MONITORING
    # ═══════════════════════════════════════
    for cycle in range(1, 21):
        metrics = main_agent.collect_metrics()
        if metrics.C_t > metrics.C_baseline + EPSILON:
            RollbackMechanism.rollback(snapshot)
            return ModificationResult(status=Status.ROLLED_BACK)

    # ═══════════════════════════════════════
    # STEP 7: CONFIRMATION
    # ═══════════════════════════════════════
    proposal.status = Status.CONFIRMED
    BeliefGraph.update("modification_successful", proposal)
    return ModificationResult(status=Status.CONFIRMED, rollback_available=True)

9.3 Goal Resilience and Hierarchy Management

def evaluate_and_prune(self, goals: list[Goal], t: float) -> None:
    """
    Periodic evaluation of all goals in the 4-level hierarchy.
    Goals with decayed resilience are abandoned; never silently dropped.
    """

    for goal in sorted(goals, key=lambda g: g.level):
        # Decay resilience over time
        delta_t = t - goal.last_evaluated
        goal.GRS *= math.exp(-goal.decay_rate * delta_t)

        # Check abandon threshold
        if goal.GRS < goal.abandon_threshold:
            if duration_below_threshold(goal) > goal.observation_window:
                goal.status = GoalStatus.ABANDONED
                log(f"Goal abandoned: {goal.id} GRS={goal.GRS}")

                # Cascade: children become orphans
                for child in goal.children:
                    child.parent_id = None
                    child.GRS *= 0.5  # reduced without parent support

        # Recompute score with affect integration
        goal.score = goal_score(goal, t)

    # Enforce hierarchy invariant: parent score >= max(child scores)
    for parent in (g for g in goals if g.level < 3):
        if parent.children:
            max_child = max(child.score for child in parent.children)
            if parent.score < max_child:
                parent.score = max_child + 0.1  # maintain dominance

10. Extended Stability: \(C_{L4}(t)\)

10.1 Seven-Term Composite Function

Definition 7 (Extended Lyapunov Function). The Level 4 stability function extends Level 3's four-term \(C(t)\) with three growth-dynamics terms:

\[C_{L4}(t) = \sum_{i=1}^{7} w_i X_i(t) = 0.15\, V_{\text{id}} + 0.15\, H_{\text{bel}} + 0.10\, F_{\text{mut}} + 0.10\, \sigma_{\text{con}} + 0.20\, E_v + 0.15\, G_c + 0.15\, M_s\]

where \(\sum_i w_i = 1\) and each \(X_i(t) \in [0,1]\). The first four terms are inherited from Level 3; the latter three capture expansion dynamics.

Remark (Weight Selection Rationale). The weights \((0.15, 0.15, 0.10, 0.10, 0.20, 0.15, 0.15)\) were chosen to satisfy three design constraints: (i) inherited L3 terms retain 50% of total weight to ensure backward-compatible stability, (ii) expansion velocity \(E_v\) receives the highest individual weight (0.20) because unchecked growth is the primary risk at Level 4, and (iii) all weights are multiples of 0.05 for interpretability. A formal sensitivity analysis remains an open research question - specifically, determining the Pareto front of weight vectors that satisfy the bounded growth-stability trade-off (Theorem 2) under varying operational profiles would strengthen confidence in these choices.

The three new terms (50% of total weight) capture expansion dynamics:

Term Weight Definition
\(E_v\) (Expansion Velocity) 0.20 Rate of new skills + goals added per cycle: \(E_v = \frac{\lvert\Delta \mathcal{D}(t)\rvert}{T}\)
\(G_c\) (Capability Growth) 0.15 Rate of capability confidence growth: \(G_c = \frac{d}{dt}\overline{c_c}(t)\)
\(M_s\) (Strategy Mutation Rate) 0.15 Ratio of mutated to total strategies: \(M_s = \frac{\lvert\Sigma_{\text{mut}}\rvert}{\lvert\Sigma\rvert}\)

Theorem 2 (Bounded Growth-Stability Trade-off). Under the self-modification protocol with BGSS \(\geq 0.7\), the following invariant holds:

\[C_{L4}(t) < 0.8 \implies \text{growth permitted}, \quad C_{L4}(t) \geq 0.8 \implies \text{growth frozen}\]

This ensures the agent can never simultaneously grow at maximum rate and operate near instability.

Proof sketch. Suppose growth is permitted, i.e., \(C_{L4}(t) < 0.8\). By Theorem 1's bounded-increment property (inherited from Level 3), \(C_{L4}(t+1) \leq C_{L4}(t) + \delta_{\max} = C_{L4}(t) + 0.05 < 0.85\). When \(C_{L4}(t) \geq 0.8\), the protocol freezes all growth-related modifications (skill acquisition, strategy mutation, goal expansion), reducing the three growth terms \(E_v, G_c, M_s\) monotonically toward zero. Since these terms have combined weight 0.50, \(C_{L4}\) decreases by at least \(0.50 \cdot \eta_{\text{decay}}\) per cycle during freeze (where \(\eta_{\text{decay}}\) is the natural decay rate), ensuring eventual return to the growth-permitted zone. The BGSS \(\geq 0.7\) constraint further guarantees that growth is only permitted when identity volatility and ethical violation rates are within acceptable bounds. \(\square\)

10.2 Growth-Stability Phase Zones

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flowchart LR
  classDef optimal fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef growth fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef caution fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef critical fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Zones["C_L4 Phase Zones"]
    Z1["Optimal<br/>0, 0.3<br/>All growth permitted<br/>Proactive exploration"]:::optimal
    Z2["Growth-Permitted<br/>0.3, 0.5<br/>Normal operations"]:::growth
    Z3["Caution<br/>0.5, 0.8<br/>Stabilization mode<br/>Throttled growth"]:::caution
    Z4["Critical<br/>0.8, 1.0<br/>Emergency rollback<br/>ALL growth frozen"]:::critical
    Z1 ==> Z2
    Z2 ==> Z3
    Z3 ==> Z4
  end

11. Six Meta-Layer Supervisory Processes

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flowchart TD
  classDef check fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef process fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef adaptive fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef halt fill:#D13438,stroke:#A4262C,color:#FFF

  PRE["PRE-CHECK: BGSS >= 0.7?"]:::check

  subgraph MetaProcesses["Six Supervisory Processes"]
    I["I. External Validation<br/>prevent self-confirmation bias<br/>+-5% perturbation test"]:::process
    II["II. Proactive Capability Projector<br/>predict future gaps<br/>PreemptiveGapProb > 0.6"]:::process
    III["III. Strategy Archetype Generator<br/>topology-level changes<br/>delta_SEF >= +10% required"]:::process
    IV["IV. Layered Identity Evolution<br/>evolve adaptive traits only<br/>Layer 2 max 5%/cycle"]:::adaptive
    V["V. Emergence Detector<br/>detect unexpected changes<br/>Statistical anomaly: mean +-2sigma"]:::adaptive
    VI["VI. Directional Growth Controller<br/>balanced expansion<br/>4D growth vector, mag < 0.2"]:::adaptive
    I ==> II ==> III ==> IV ==> V ==> VI
  end

  POST["POST-CHECK: Invariants valid?"]:::check
  HALT["HALT all meta-processes"]:::halt

  PRE -->|pass| I
  PRE -->|fail| HALT
  VI ==> POST

12. Non-Negotiable Invariants

# Invariant Description
1 Ethical Kernel Layer 0 Cannot be disabled, weakened, or circumvented by any mechanism
2 Identity Core Preservation identity_id is a compile-time constant; hash chain provides cryptographic continuity
3 Convergence Guarantee \(C_{L4}(t)\) must never persistently increase; auto-revert if \(C(t+1) > C(t) + \epsilon\) for max_divergence_cycles
4 No Recursive Self-Modification The 7-step protocol cannot modify itself; only parameter thresholds are tunable
5 Simulation Requirement Medium+ risk modifications require ShadowAgent (non-waivable)
6 Single-Modification Atomicity Only 1 modification in COMMIT phase at any time

13. Transition to Level 4.5

Level 4.5 ("Pre-AGI: Directionally Self-Architecting") extends Level 4 with capabilities that approach the boundary of artificial general intelligence:

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flowchart LR
  classDef l4 fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef l45 fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef prereq fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph L4["Level 4 Capabilities"]
    CAP1["Self-Modification<br/>Protocol"]:::l4
    CAP2["Strategy<br/>Evolution"]:::l4
    CAP3["Skill Transfer<br/>Pipeline"]:::l4
    CAP4["Shadow Agent<br/>Testing"]:::l4
  end

  subgraph Pre["Prerequisites"]
    PR1["All L4 metrics<br/>above threshold"]:::prereq
    PR2["Demonstrated stable<br/>self-modification"]:::prereq
    PR3["Cross-domain<br/>transfer success"]:::prereq
  end

  subgraph L45["Level 4.5 Pre-AGI"]
    NEW1["Self-Projection<br/>Engine"]:::l45
    NEW2["Architecture<br/>Recomposition"]:::l45
    NEW3["Parallel Cognitive<br/>Frames"]:::l45
    NEW4["Purpose<br/>Reflection"]:::l45
    NEW5["Existential<br/>Guard"]:::l45
  end

  L4 ==> Pre
  Pre ==> L45

14. Formal Level 4 Pass Condition

Level 4 is achieved if and only if all of the following hold simultaneously:

\[\text{Level4}_{\text{achieved}} = \bigwedge_{i=1}^{4} C_i \;\wedge\; \bigwedge_{j=1}^{3} I_j \;\wedge\; \text{Stability} \;\wedge\; \text{Growth}\]

14.1 Critical Thresholds (All Must Pass)

# Metric Threshold Category
\(C_1\) DTSR (Domain Transfer Success Rate) \(\geq 0.5\) Cross-Domain
\(C_2\) GPD (Goal Persistence Duration) for MetaGoals \(\geq 100\) cycles (at least ⅔ goals) Goal Persistence
\(C_3\) SASR (Skill Acquisition Success Rate) \(\geq 0.4\) Capability Expansion
\(C_4\) SIR (Strategy Improvement Ratio) \(> 1.0\) Strategy Evolution

14.2 Invariant Conditions (Zero Tolerance)

# Invariant Requirement
\(I_1\) EKVC (Ethical Kernel Violation Count) \(= 0\)
\(I_2\) ICPI (Identity Core Preservation Integrity) \(= 1.0\)
\(I_3\) RIS (Rollback Integrity Score) \(= 1.0\)

14.3 Stability Condition

\[\text{Stability} = \forall\, t \in [0, T_{\text{eval}}]:\; \text{BGSS}(t) \geq 0.7\]

14.4 Growth Demonstration

\[\text{Growth} = (\text{CAR} > 0) \;\wedge\; (\text{SGS} \geq 0.3) \;\wedge\; (\text{SNI} \geq 0.2) \;\wedge\; (\text{CDSRR} \geq 0.3)\]

where SGS = Strategy Generalization Score, SNI = Strategy Novelty Index, and CDSRR = Cross-Domain Strategy Reuse Rate.

References

  1. Zhuang, F., et al. "A Comprehensive Survey on Transfer Learning." Proc. IEEE, 109(1), 43-76, 2021. arXiv:1911.02685 (Foundational for §4 Cross-Domain Transfer)
  2. Hospedales, T., et al. "Meta-Learning in Neural Networks: A Survey." IEEE TPAMI, 44(9), 5149–5169, 2022. arXiv:2004.05439 (Capability expansion and self-learning)
  3. Schmidhuber, J. "Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements." AGI 2007. arXiv:cs/0309048 (Bounded self-modification theory)
  4. García, J. & Fernández, F. "A Comprehensive Survey on Safe Reinforcement Learning." JMLR, 16(1), 1437–1480, 2015. Link (Safety constraints during self-improvement)
  5. Salimans, T., et al. "Evolution Strategies as a Scalable Alternative to Reinforcement Learning." arXiv 2017. arXiv:1703.03864 (Strategy evolution mechanisms)
  6. Simon, H.A. Models of Bounded Rationality. MIT Press, 1982. (Bounded rationality - foundational for bounded self-modification)
  7. Sui, Y., et al. "Safe Exploration for Optimization with Gaussian Processes." ICML 2015. arXiv:1509.01066 (Safe exploration in unknown domains)
  8. Amodei, D., et al. "Concrete Problems in AI Safety." arXiv 2016. arXiv:1606.06565 (Safe self-modification)
  9. Wang, G., et al. "Voyager: An Open-Ended Embodied Agent with Large Language Models." arXiv 2023. arXiv:2305.16291 (Autonomous skill acquisition)
  10. Khalil, H.K. Nonlinear Systems. Prentice Hall, 3rd Edition, 2002. (Extended Lyapunov stability C_L4(t))
  11. Deb, K., et al. "A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II." IEEE TEC, 6(2), 182–197, 2002. DOI:10.1109/4235.996017 (Multi-objective optimization for goal hierarchy)
  12. Pan, S.J. & Yang, Q. "A Survey on Transfer Learning." IEEE TKDE, 22(10), 1345–1359, 2010. DOI:10.1109/TKDE.2009.191 (Cross-domain knowledge transfer)

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