CIv7-LLM: Latent Collapse Detection via Compression-Aligned Concept Geometry

Hypothesis Structural failures in reasoning traces generated by Large Language Models (LLMs) can be robustly detected by analysing latent representations, attention flows, and intermediate outputs through the lens of algorithmic compressibility, conceptual geometry, and joint compression divergence. These collapses manifest as discontinuities in the latent CoT (Chain-of-Thought) dynamics and can be interpreted as the dual of symbolic substrate faults in CIv7-ECA, forming a mirrored system grounded in the principle of Joint Compression as Shared Structure Discovery (Sutskever).

Such discontinuities are detectable via:

Latent compressibility divergence (BDM or NML over hidden state trajectories)
Failure of joint compression between CoT(X) and domain structure(Y) (Sutskever)
Collapse of semantic attractors in CoT manifolds (embedding space bifurcation)
Gradient flow torsion and persistent cohomology failures (Walch, Hodge duality)
Circuit motif destabilisation across transformer layers (Anthropic Circuit Tracer)
Misalignment between human conceptual clusters and latent token groupings (Shani et al.)
Semantic drift in high-attention regions with low motif entropy (Riedel & Zenil)
Phase discontinuities in training-state transition curves (SASR, Chen et al.)
Mode collapse in symbolic reasoning paths (RL fine-tuning instability)
Latent manifold torsion corresponding to ECA symbolic bifurcations (CIv7-ECA)
MCMC topology shift during local exploration in solution spaces (Vivier-Ardisson et al.)
Universal motif failure in graph-structured input-to-latent pipelines (GFSE, Chen et al.)
Translation instability across embedding spaces (vec2vec leakage) (Jha et al.)
Algebraic symmetry loss in attention-MLP cycles (Langlands duality, Hodge)
Symbolic faultline transfer from external substrates (CIv7-ECA) into latent transformer breakdown

Rationale

Joint Compression Principle (Sutskever 2024): Compression is prediction. Structural failures arise when X (e.g., semantic content) and Y (e.g., target CoT) fail to compress jointly. This implies a shared latent structure has broken—i.e., a fault.
CIv7-ECA ↔ CIv7-LLM: Symbolic substrates evolve in observable 2D arrays (ECA), while LLMs manifest structure internally. CIv7-LLM hypothesises that symbolic discontinuities in ECA predict latent collapses in LLMs, and vice versa—via joint compression alignment.
Hodge Geometry in Transformers: Attention layers form geometric relationships (Picard group), MLPs capture algebraic invariants (Néron-Severi), stabilised by Hodge numbers. Discontinuities arise from torsion collapse in this dual geometry.
MDL-Based Fault Surfaces: Following Grünwald & Roos, LLM collapses correspond to local minima or discontinuities in the MDL surface of the predictor’s latent structure—analogous to symbolic motif disruption in ECA.
GFSE & Graph-Latent Failures: Topological encodings from graph inputs (e.g., reasoning trees) can fail to preserve structural signals across transformer layers—detectable via positional-structural encodings.
SASR & Gradient Diagnostics: Adaptive curriculum switching reflects the instability between CoT memorisation and generalisation. Faults emerge when training dynamics drift outside optimal divergence zones (KL/∇ norms).
Latent Inversion & Leakage (vec2vec): Translation of internal states into other model geometries (via Jha et al.) shows that failure zones are transferable and interpretable through joint embedding manifolds.

Cross-Hypothesis Integration: CIv7-ECA ↔ CIv7-LLM

Shared Substrate Principle: CIv7-ECA operates over external symbolic evolution; CIv7-LLM over internal latent space evolution. Both are governed by principles of algorithmic compression, fault geometry, and motif-induced phase transitions.
Bidirectional Causality: Symbolic anomalies in ECA generate fault-like divergence patterns in LLM CoT spaces; conversely, LLM latent collapses signal missing or unstable motif alignments in symbolic substrates.
Experimental Co-Compression: Compression divergence between ECA-evolved sequences and their LLM-predicted CoT trajectories can serve as a universal structural break signal. This is a direct instantiation of Ilya’s joint compression gap.

Future Work

Joint Training Regimes: Train LLMs to predict ECA substrate evolutions and identify structural breaks, thereby grounding their CoT traces in compressible, symbolic causal transitions.
Latent Fault Line Atlas: Map discontinuities in transformer latent spaces using BDM, curvature, and joint motif decomposability. Cross-reference with symbolic ECA fault patterns.
Neural Langlands Machines: Build models whose architectural topology enforces cohomological alignment across symbolic (ECA) and neural (LLM) domains.
Causal Inference as Compression Geometry: Develop a shared formalism for causal discovery as failure of compressibility in structured, dual-view systems.

Supporting Literature

Sutskever (2024) – Compression as Prediction
Hodge et al. – Algebraic and Topological Transformer Bias
Shani et al. – Compression-Meaning Divergence
Chen et al. – SASR: Adaptive Curriculum in Reasoning
Vivier-Ardisson – MCMC Layers as Differentiable Reasoning
Jha et al. – Universal Embedding Geometry (vec2vec)
Chen et al. – GFSE: Cross-Domain Graph Structure Learning
Anthropic – Circuit Tracer
Riedel & Zenil – Symbolic Rule Decomposition
Ha & Schmidhuber – World Models and Fault Simulability
Dijkstra et al. – Reality Signal Thresholding in Imagination
Zhang et al. – Intelligence at the Edge of Chaos
CIv7-ECA Hypothesis – Symbolic Substrate Fault Geometry