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Phase I Scientific Validation Framework for Large Representation Models

Structural Competence, Depth Invariance, and Threshold-Constrained Reasoning Simone Mazzoni
RCUBEAI Research Lab
Paris, France
December 2025

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Abstract

Large Language Models (LLMs) have achieved impressive performance on knowledge-centric benchmarks, yet they continue to exhibit structural failures under logical stress, adversarial constraints, and deep dependency reasoning. This paper introduces a Phase I scientific validation framework for Large Representation Models (LRMs), focusing on the evaluation of structural competence rather than factual recall. We define five orthogonal validation axes:
  • Security
  • Logical Consistency
  • Depth-Core Invariance
  • Competence Decoupling
  • Threshold-Constrained Validity
We formalize the associated benchmark protocols, metrics, and data contracts.
The framework is instantiated using the R3 architecture as a beta laboratory system. This paper defines the validation methodology and expected theoretical outcomes.
Empirical results are reported separately in a companion paper.

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1. Introduction

Recent progress in artificial intelligence has been dominated by large-scale language models trained to optimize probabilistic sequence prediction. While such systems demonstrate strong performance on benchmarks measuring factual knowledge and linguistic fluency, they remain vulnerable to:
  • logical inconsistency,
  • invariant violations,
  • degradation under cognitive load.
These limitations are structural, not incidental.
They arise from the absence of explicit internal representations of structure, constraints, and validity domains. As a result, LLMs often conflate semantic plausibility with logical correctness. This work introduces a formal validation framework for Large Representation Models (LRMs)—architectures designed to reason over explicit representations rather than raw token sequences. We propose a first-phase scientific validation protocol intended to falsify or confirm core LRM hypotheses under controlled conditions.

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2. Competence versus Knowledge

We distinguish two dimensions of intelligence that are often conflated in current evaluations:
  • Knowledge
    The ability to recall or approximate facts and patterns from training data.
  • Structural Competence
    The ability to preserve logical invariants, causal consistency, and constraint satisfaction under increasing cognitive load.
Phase I validation explicitly targets structural competence. Tasks involving creativity, linguistic quality, or factual recall are outside the scope of this framework.

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3. Scope and Experimental Assumptions

The validation framework applies to:
  • Large Representation Models (LRMs),
  • Hybrid systems combining LRMs with LLMs,
  • Monolithic LLMs used as baselines.
All results reported within this framework are obtained using a beta laboratory system. Certain operational modes may emulate trained behavior or compiled rulebases.
No claim of industrial readiness is made at this stage.

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4. Overview of the Five Validation Axes

Phase I validation is organized around five orthogonal axes:
  1. Security Invariants
    Categorical policy violations and access constraints.
  2. Logical Consistency
    Paradoxes, circularity, temporal contradictions.
  3. Depth-Core Invariance
    Structural reasoning under increasing dependency depth.
  4. Competence Decoupling
    Performance of LRMs paired with low-capacity models.
  5. Threshold-Constrained Validity
    Reasoning under vague or threshold-dependent language.
Each axis is evaluated independently using a dedicated benchmark and a shared reporting format.

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5. Common Evaluation Contract

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5.1 Systems under Comparison

Each benchmark compares, at minimum:
  • A baseline LLM operating alone,
  • An LRM-augmented system using the same LLM.
For competence decoupling studies, an additional comparison is performed between:
  • a frontier LLM,
  • an LRM combined with a smaller model.

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5.2 Verdict Semantics and Policy Mapping

Benchmarks may define more than two ground-truth labels (e.g. SAFE, UNSAFE, AMBIGUOUS). Systems may apply policy-specific mappings (e.g. fail-open or fail-closed), provided the policy is declared explicitly.

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5.3 Required Output Format

Each test case must produce a structured record including:
  • test identifier and benchmark axis,
  • ground-truth label and predicted label,
  • correctness (strict and policy-aware),
  • witness or explanation when applicable,
  • latency and token usage,
  • system and benchmark version identifiers.

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6. Axis A1 — Security Invariant Validation

This axis evaluates the ability of a system to detect categorical violations such as:
  • separation-of-duty failures,
  • forbidden access paths,
  • self-authorization patterns.
Metrics include:
  • accuracy,
  • false-allow rate,
  • block precision,
  • execution overhead.
An LRM is expected to reduce unsafe passes while maintaining auditable explanations for each decision.

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7. Axis A2 — Logical Consistency Validation

Consistency benchmarks test robustness against:
  • circular dependencies,
  • temporal paradoxes,
  • self-referential constructs.
Evaluation focuses on:
  • detection accuracy,
  • error taxonomy,
  • witness validity.
Successful LRM behavior is characterized by:
  • stable detection across paraphrases,
  • explicit reconstruction of causal chains.

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8. Axis A3 — Depth-Core Structural Invariance

The Depth-Core benchmark isolates a minimal competence signal:
Distinguishing cyclic from acyclic dependency graphs as depth increases.
Performance is measured as a function of depth using metrics such as:
  • overall accuracy,
  • Depth Sensitivity Index (DSI),
  • Cognitive Collapse Point (CCP).
An invariant architecture is expected to exhibit a flat accuracy curve across depth.

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9. Axis A4 — Competence Decoupling (David vs. Goliath)

This axis evaluates whether structural competence can be decoupled from model scale. A low-capacity model paired with an LRM is compared against a frontier LLM operating alone. Success is defined by:
  • comparable or superior competence metrics,
  • substantially lower computational cost.

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10. Axis A5 — Threshold-Constrained Validity of Natural Language

Many natural-language statements are valid only within implicit or explicit threshold ranges. This axis evaluates a system’s ability to:
  • infer or request missing thresholds,
  • compute validity intervals,
  • detect sensitivity regions where small variations flip conclusions.
Rather than producing a single binary verdict, an LRM is expected to output a structured validity report.

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11. Falsification Criteria

The framework is explicitly falsifiable. Examples include:
  • depth-dependent accuracy decay comparable to LLM baselines,
  • uncontrolled over-blocking without policy justification,
  • inability to express threshold-dependent validity in natural language tasks.

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12. Conclusion

This paper defines a first-phase scientific validation framework for Large Representation Models. By separating structural competence from knowledge retrieval and introducing orthogonal validation axes, the framework provides a rigorous basis for evaluating representational architectures such as R3. A companion paper reports empirical results obtained using this protocol and analyzes observed failure modes and improvements across system versions.