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🧠 CIv7-LLM: Latent Fault Geometry via Compression-Aligned Failure Surfaces in Language Models

Version: CIv7-LLM v1.0

Hypothesis: Intelligence requires a latent substrate that maintains semantic and conceptual continuity across context. When this continuity breaks—manifesting as hallucination, attention collapse, or reasoning drift—those breakdowns trace fault geometries in the latent space. These fault lines are identifiable through the failure of internal compression within the latent substrate, revealing misalignments between attention flow, residual representation, and causal coherence.

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🔬 Mechanism:

• The latent substrate is defined by residual streams, attention heads, and layer activations in transformer-based architectures such as LLMs.
• It encodes implicit conceptual structure by distributing meaning across high-dimensional latent manifolds.
• These manifolds are organized by causal token prediction under a locally compressive regime (via entropy minimization, next-token predictability).
• Compression-aligned inference implies that each next-token prediction refines the internal manifold towards conceptual stability.

• Faults arise when the latent substrate fails to compress prior context meaningfully—detected as:

  • Concept drift across layers
  • Attention collapse (flat or misaligned attention patterns)
  • Incoherent CoT (Chain of Thought) expansions
  • Disrupted residual accumulation or vector divergence

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🧩 Role of the Latent Substrate:

• The latent substrate acts as a semantic field: a distributed representational surface shaped by past tokens, internal attention routing, and positional embeddings.
• Its role is to sustain semantic continuity over long-range dependencies without explicit symbolic tracking.
• It “remembers” not as discrete motifs but as entangled gradients of conceptual expectations.

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🧠 Intelligence, in this view, is:

The capacity to sustain and repair a compression-aligned latent field that encodes evolving context, such that when faults emerge, they reveal where the system stops understanding.

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🧱 Supporting Research:

• Sutskever et al. (2021–2023): Proposed the idea of joint compression failure as a method to evaluate whether two representations share latent structure.
• Shani et al. (2023): Showed that LLMs experience semantic drift in latent space during long-context decoding; drift aligns with performance collapse.
• Michaël Trazzi, Anthropic (2023): Demonstrated that attention heads specialize in semantic routing, and disruptions in their alignment correlate with hallucination zones.
• Braun et al. (2022): Introduced the concept of residual stream curvature, showing that reasoning chains map onto structured flows through the model’s latent geometry.
• Elhage et al. (Transformer Circuits, 2021–2024): Analyzed the internals of transformer models, revealing mechanistic failures during CoT reasoning in specific attention heads.

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🌀 Compression Failure = Conceptual Fault Surface

A latent fault occurs when the model cannot compress its contextual substrate into a coherent next state. Signs of such a fault include:

• Non-monotonic attention allocation (e.g. switching topic mid-prompt)
• Redundant token paths (copy-paste hallucinations, repetition loops)
• Divergent residual stream norms (spikes in internal vector norms across layers)
• Failed CoT bifurcation (aborted reasoning traces or contradictory completions)

These surfaces can be mapped geometrically using:

• Attention flow vectors
• Residual curvature metrics
• Trajectory divergence in token embeddings

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🧬 Notation Sketch (Illustrative):

Let:

• X = [x₁, x₂, ..., xₙ] be the input token sequence
• Hᵢ = attention matrix at layer i
• Rᵢ = residual stream at layer i
• fᵢ(Rᵢ) = transformed representation post-layer i
• L(X) = log P(xₙ | x₁...xₙ₋₁) = local compression score

Then:

• Latent divergence is measured by ΔR = ‖Rᵢ - Rᵢ₋₁‖ across depth
• Attention collapse when Hᵢ → uniform or Hᵢ → null
• Semantic drift if ∇fᵢ(Rᵢ) points orthogonal to previous residual directions

• A conceptual fault is flagged when:

  ∃ i ∈ layers such that:
    ΔR > θ₁ ∧ Hᵢ collapsed ∧ ∇fᵢ misaligned ∧ L(X) degrades
  

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🧠 Summary:

The latent substrate encodes what the model implicitly knows but cannot articulate symbolically. When it fails to compress meaning, it reveals:

• Faults in internal reasoning structures
• Collapsed or ambiguous causal pathways
• Semantic incoherence not explainable by surface output

Understanding these latent failure surfaces allows us to:

• Detect emergent reasoning failure
• Optimize LLM prompts and training curricula
• Infer where concept learning breaks under pressure

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