Beyond Projection: A General Framework for Self-Evolution - From Neural Intelligence to All Domains

V12.0 - Academic Edition (2026-02-06 11:17, Beijing Time / UTC+8) -> CATH 4.2 data leakage , being redesigned This paper presents a scalable mathematical principle for self-evolution that transcends artificial intelligence and applies to diverse domains requiring autonomous optimization. Through rigorous theoretical analysis and systematic empirical validation across five standard benchmarks (CATH, CIFAR-10, CIFAR-100, MedMNIST, TOX21) with varying mechanism counts (K5, K8, K10, K22) and 100 training-inference combinations each, we demonstrate that this framework behaves as predicted by geometric principles, not as a fixed architectural pattern. Core Contribution: Projection-orthogonality duality as a universal principle for self-evolution Four integrated dimensions: Spatial (Projection/Orthogonality), Temporal (Current/Next State), Value (Coherence/Divergence), Embodied (Perception/Action) Mathematical formalization of why dot-product architectures asymptotically approach but never transcend training data boundaries First empirical validation elevating orthogonal generation from domain-specific technique to universal mathematical principle New in V12.0: Systematic Empirical Validation: 100 training-inference combinations across three benchmarks under Pure ID Training (no OOD exposure) Scalability Principle (Section 3.7): Mathematical foundation proving orthogonal generation exhibits predictable scaling properties grounded in geometric principles Benchmark Results: CATH 4.2 data leakage , being redesigned CIFAR-10: AUROC 71.3% → 90.0% (+18.7%), FPR@95 86.2% → 46.2% (-40.0%) CIFAR-100: AUROC 68.3% → 74.1% (+5.8%), FPR@95 92.7% → 82.9% (-9.8%) MedMNIST: AUROC 83.5% → 92.7% (+9.2%), Far-OOD reaches 95.9% TOX21: Delivers near-state-of-the-art results at a minimal computational cost Five Key Empirical Findings: Cross-domain universality to protein structure (94.15% vs. 68% SOTA with minimal training data) Cross-domain universality across natural and medical imaging Task-adaptive scalability (optimal K correlates with task complexity) Real-world applicability (95.9% Far-OOD detection in medical imaging) Far-OOD advantage as emergent property (inverts conventional expectations) Breaking ID-OOD trade-off (simultaneous improvement in both metrics) Feature-Space Mirror Augmentation: Orthogonal transformation based on Householder reflection and cluster centers for enhanced Tier 1 applications Theoretical-Empirical Loop Completion: Section 3 (mathematical foundations) → Section 3.7 (scalability formalization) → Section 4.5 (empirical validation) Distinction Clarification: True OOD detection (never-seen distributions) vs. pseudo-OOD classification (pre-exposed outliers) Key Features: Complete mathematical foundations (Appendix A: Projection, Orthogonal Complement, Exterior Algebra, Gram-Schmidt, Dynamical Systems, Lie Algebras) Implementation guidelines for AI researchers and domain engineers (Appendix B) Falsifiable predictions across multiple domains (Chapter 7) Open questions for collaborative research (Chapter 8) Speculative extension on knowledge field advection and trans-intuitive cross-domain mapping (Chapter 10) Dual-structure design: Rigorous derivation (Chapters 1-9) + Speculative conjecture (Chapter 10), separated by author attribution Keywords: Projection-Orthogonality Duality, Self-Evolution, Autonomous Optimization, Cross Product, Transformer Architecture, Universal Framework, Complementary Operations, Yin-Yang Philosophy, AGI, Knowledge Field Advection, Exterior Product, Lie Bracket, Graph Neural Networks, Weisfeiler-Leman Test, Antiparallelism, OOD Detection, Scalability Principle, CIFAR-10, CIFAR-100, MedMNIST Version History: V12.0 (2026-01-27): add CATH 4.2 data leakage , being redesigned V11.0 (2026-01-03): Empirical Validation Edition with systematic experiments across three benchmarks, scalability principle formalization, 100 training-inference combinations per dataset, Pure ID Training protocol, five key empirical findings, feature-space mirror augmentation, theoretical-empirical loop completion V10.0 (2026-01-02): Academic Edition with complete Chapter 3 revision, 3-tier orthogonal application hierarchy, dual roles of orthogonal axes, formal mathematical tool suite (exterior product/Lie bracket/Gram-Schmidt), Rodrigues rotation formula proof, corrected NLP/GNN terminological misunderstandings V9.0 (2025-12-31): Added speculative Chapter 10 on Knowledge Field Advection, "Xiang" (象) correspondence hypothesis from Yi Jing, trans-intuitive mapping mechanism V8.0 (2025-12-30): Added philosophical context and Yin-Yang complementarity perspective, refined cross-domain applications V7.0 (2025-12-30): Revised Academic Edition, enhanced cross-product explanation with Lorentz force analogy V6.0 (2025-12-29): Academic Edition, complete mathematical formulation with appendices Contact for collaboration: yzb3001313@gmail.com, 382909119@qq.com License: Creative Commons Attribution 4.0 International (CC BY 4.0) Note on Originality: This framework represents original theoretical work with first empirical validation. The mathematical duality of projection-orthogonality as a universal self-evolution engine is proposed and now empirically validated here for the first time. Note on Structure: This paper uses author attribution at the conclusion of Chapter 9 to demarcate rigorously-derived and empirically-validated framework (Chapters 1-9) from speculative extension (Chapter 10).