LACE — Latent Adaptive Compression Engine

Semantic compression under physical channel constraints.
Does forced bottleneck induce structured cognitive emergence?

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Result (v2)

Yes — under the right constraint regime.

A phase transition governs emergence. Below a critical ratio N/K ≈ 25–30, VQ codebooks spontaneously separate retrieval-type and inference-type communications into distinct Voronoi regions — without explicit supervision.

Cognitive Emergence Law:

N/K < C · d_cog

where:

• d_cog = intrinsic cognitive separability of the input domain (Cohen's d = 2.45 on raw BPE tokens)
• C_emp = 0.391 ≈ 1/e = 0.368 (6.3% deviation explained by mean-field corrections)

Key findings:

• N/K < 25–30 is the only robust boundary (validated on 128 points, K×N×D sweep)
• Random reward outperforms MiniLM reward (2/3 vs 1/3 seeds significant at K=128, N/K=1.55)
• Cognitive structure is a property of operational language under compression, not an artifact of supervision
• d_cog is recoverable from raw syntactic features alone (CV accuracy 74.8%)
• 46 active codes out of 512 — 15 retrieval-dominant, 15 inference-dominant, 16 mixed

Optimal deployment parameter: K=16 (p=0.0034, survives Bonferroni correction)

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v1 Result (for reference)

47 concepts emerge spontaneously from 198 operational tasks.
Domain clustering: real (mean coherence 68.4%).
Retrieval/inference separation: not significant at K=512 (p̂=0.61).
→ v1 conclusion inverted by v2: compression was insufficient, not excessive.

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Architecture

Weighted BoW encoder → Spherical VQ codebook (K=16–512) → MLP decoder
Channel budget: 4–9 bits, equivalent to a 9–50 byte LoRa frame.

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Paper

LACE v2 — Cognitive Phase Transitions in Semantically Constrained Vector Quantization

Lafargue, T. (2026). Cognitive Phase Transitions in Semantically Constrained Vector Quantization: Emergent Retrieval/Inference Separation Under Physical Bandwidth Constraints (2.0). Zenodo. https://doi.org/10.5281/zenodo.19664121

• Zenodo DOI: 10.5281/zenodo.19664121
• HAL preprint: hal-05596229
• License: CC BY 4.0

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Dataset & Weights

→ ox-ox/lace-semantic-compression

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Related Work

• Patent FR2511116 — Hybrid State-Preserving Gateway for LLM inference over 2G/SMS/LoRa/satellite
• llama.cpp PR #20075 — Synchronized SSM Checkpointing for speculative decoding on hybrid MoE/SSM models
• llama.cpp PR #20649 — Mistral Small 4 (119B MoE) flake8 fix

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Citation

@misc{lafargue2026lace,
  author       = {Lafargue, Théophile},
  title        = {Cognitive Phase Transitions in Semantically Constrained Vector Quantization:
                  Emergent Retrieval/Inference Separation Under Physical Bandwidth Constraints},
  year         = {2026},
  version      = {2.0},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.19664121},
  url          = {https://doi.org/10.5281/zenodo.19664121}
}

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ox-ox / Théophile Lafargue — Pépite Paris-Saclay, Université Paris-Saclay