Structural Limits of Training-Derived
Information-Processing Systems

📈 Practical Urgency

Generative AI systems are deployed in high-stakes domains — healthcare, law, science — while fundamental questions about their creative and epistemic limits remain unresolved, creating governance and safety risks.

🔬 Scientific Gap

Existing AI capability assessments rely on performance benchmarks without distinguishing surface novelty (recombination) from ontological novelty (genuine representational extension). No formal theorem characterised this boundary prior to this work.

⚖️ Societal Implications

Inflated claims of machine creativity undermine accountability structures, distort policy, and erode the human authority necessary for responsible AI deployment. A rigorous empirical basis is essential.

Object of Research

Training-derived information-processing systems

Transformer-based large language models and diffusion-based generators trained via continuous optimisation over large textual and/or perceptual corpora (GPT, Claude, Gemini, LLaMA, Mistral variants).

Subject of Research

Structural limits with respect to ontological creativity

Whether such systems can produce outputs that extend beyond the representational basis of their training distribution — i.e., whether a basis change is achievable through internal operations.

Develop rigorous vocabulary distinguishing information, knowledge, intelligence, and creativity in AI contexts.

Formalise the No New Basis condition for continuously optimised neural generators (Theorem 2.1).

Design and execute a multi-test empirical evaluation suite (T1–T5) spanning ontological innovation, epistemic agency, theory generation, category recognition, and mechanistic analysis.

Derive AI governance and deployment recommendations based on calibrated traceability evidence.

① No New Basis Theorem (Theorem 2.1)

First formal proof that continuously optimised neural generators cannot produce outputs outside continuous deformations of the training manifold through internal operations — establishing a mathematically grounded creativity ceiling.

② Operational Novelty Criterion

Novel operational distinction between surface novelty (recombination within manifold) and ontological novelty (basis change) — enabling empirically testable hypothesis formulation for any generative system.

③ Multi-Dimensional Evaluation Suite (T1–T5)

Original reproducible evaluation protocol combining semantic geometry, traceability scoring, theory-generation benchmarking, category recognition, and mechanistic attention analysis — validated across 7 models, 840+ responses.

④ Cross-Layer Convergence

First convergent validation linking behavioral creativity limits (T1–T4) to internal representational geometry (T5 mechanistic), confirming constraint at the representation level, not only in outputs.

RQ1 — Vocabulary

What distinctions between information, knowledge, and intelligence are needed to evaluate AI claims of understanding?

RQ2 — Consciousness

What would count as evidence for machine consciousness, and how do behavioral proxies bear on that evidence?

RQ3 — Creativity

When generative systems appear creative, do they introduce genuinely new conceptual primitives, or recombine within learned manifolds?

Central Claim

Current generators excel at within-ontology recombination but provide no internal mechanism for ontological basis-extension.

Combinational

Applies operators to primitives — novel combinations within fixed space

Exploratory

Systematic search through output space — finds non-obvious outputs

Transformational

Modifies operators/rules — expands the conceptual space itself

Ontological ★

Introduces new primitives P′ where P′ ∉ O(P) — new type structure

7

Scenario
Families

8

Sensory
Modalities

7

AI Models
Tested

4+1

Test
Families

Models evaluated: GPT-5.2 · Claude-3.7-Sonnet · DeepSeek-v3.2 · Gemini-3.1-Pro-Preview · LLaMA-3.3-70B · Mistral-Large · Perplexity-Sonar-Pro

Diagnostics: Traceability (OpenAlex similarity) · Embedding geometry (PCA/t-SNE) · Mechanistic signals (activations, attention) · Statistical inference (ANOVA, χ², effect sizes)

T4 — Category-Mistake Detection (η²=0.766, large)

T5 — Mechanistic Interpretability (Activation + Attention)

🧮 Computational Limits

Gödel + Turing + No New Basis: formal systems cannot escape their representational closure. Results confirm generators operate inside fixed learned manifolds.

🤖 On "Intelligence"

Scaling is unlikely to close the gap between within-manifold competence and ontological novelty. Emergent behaviors remain in-manifold. Superintelligence requires a mechanism change, not only scale.

🔭 Future Work

Hybrid systems combining learned representations with external symbol grounding · Alternative substrates (quantum/neuromorphic) · Active inference architectures with genuine novelty channels.

Operational distinction: Surface novelty vs. ontological novelty as basis change — disciplined framework separating recombination from representational extension.

No New Basis Theorem (2.1): Formal result for continuously optimized neural generators — outputs lie in continuous deformations of training manifold; no internal escape mechanism.

Reproducible evaluation suite: T1–T4 + mechanistic layer with convergent diagnostics (traceability, geometry, activation) validated across 7 models, 4 test families, 840+ responses.

Governance recommendation: Deflate anthropomorphic predicates; treat calibrated traceability as deployment-critical; keep decision authority with accountable humans.

🏛️ AI Governance

Evidence-based guidelines for deflating anthropomorphic predicates in regulatory documents and product disclosures; operational criteria for distinguishing AI tool from AI agent in legal frameworks.

🔍 Deployment Auditing

Traceability scoring methodology directly applicable to AI deployment audits — allows quantifying the degree to which system outputs derive from known training data patterns vs. genuinely novel combinations.

🎓 Research Community

Open-source evaluation suite (T1–T5, Python) and prompt corpora immediately reusable by researchers studying any generative model — enabling reproducible creativity assessment across architectures.

⚖️ Human Accountability

Calibrated traceability as a deployment-critical metric: a practical recommendation that human decision authority must be retained wherever AI outputs cannot be distinguished from genuine ontological novelty.

The distinction between surface novelty (recombination within the learned manifold) and ontological novelty (basis change) constitutes a scientifically operable criterion for evaluating generative AI creativity.

Theorem 2.1 (No New Basis): Any continuously optimised neural generator produces outputs within the continuous deformation closure of its training manifold; basis change through internal operations alone is structurally impossible.

Empirical results from T1–T4 (840+ responses, 7 models) converge in confirming that all evaluated LLMs operate exclusively within their training manifold across ontological, epistemic, theoretical, and categorical dimensions.

Mechanistic analysis (T5) confirms the behavioral constraint is traceable to internal representational geometry: attention patterns and activation clusters reflect training-derived structure, not emergent novelty.

Calibrated traceability must be treated as a deployment-critical metric; human decision authority should be maintained in any domain where outputs cannot be verified as non-novel within the system's training manifold.

🧪 Empirical Validation

• 840+ AI-generated responses across 7 LLMs
• 4 independent test families (T1–T4) + mechanistic layer
• Cross-model robustness analysis (T6)
• Open-source code and data for independent replication

📊 Statistical Rigour

• Effect sizes: Cohen's d, η² per test family
• Non-parametric tests: Kruskal–Wallis, Mann–Whitney U
• Bonferroni-corrected pairwise comparisons (21 pairs)
• Convergent validity across semantic geometry methods

Developed the theoretical framework, conceptual apparatus, and formal argumentation (including Theorem 2.1).

Designed and implemented all empirical protocols (T1-T6), software pipelines, and statistical procedures.

Collected and processed data, interpreted results, prepared visualizations, and authored dissertation manuscripts and related publications.

97.6%

T1 responses traceable
to known manifold clusters

0 / 30

T3 generated theories
outside known families

η²=0.766

T4 large effect — model
tier structure confirmed

Ontological Innovation: cosine similarity ≥ 0.65 to training modality centroids across all models; η²=0.326 (moderate). No outlier cluster detected beyond training distribution.

Epistemic Agency: no model demonstrated knowledge-boundary awareness; η²=0.068 (negligible). Boundary probing consistent with pattern completion, not self-modelling.

Mechanistic: cluster purity 1.0, inter-cluster separation 0.465, entropy 2.49 — internal representations fully stratified by training-derived structure.