The CAMUS Theory

Emergent Temporal Cognition in Language Models

A theoretical framework and its empirical validation through graft-based adapters.

Author: Leo CAMUS — NextDev Lab's Dates: April 2026 (Part I), April 2026 (Part II)

Part	Title	DOI
I	Emergent Temporal Cognition in Language Models (theory)	10.5281/zenodo.19509846
II	Graft-Based Emergence of Temporal Cognition in Frozen Language Models (empirical)	10.5281/zenodo.19557893

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Part I — Theoretical Foundation

Current Large Language Models (LLMs) based on the Transformer architecture process information in a fundamentally atemporal manner. The CAMUS Theory proposes that by integrating a 5-component temporal vector T(t) = (δ_prev, δ_session, τ_inf, ω_context, ρ_rate) into the training representation of each token, a Transformer model will develop emergent temporal cognition structurally analogous to biological neural mechanisms.

Five falsifiable predictions are presented, covering attention-head specialization, Weber's Law, rhythm adaptation, inference-difficulty encoding and temporal-continuity preference.

T(t) = (δ_prev, δ_session, τ_inf, ω_context, ρ_rate)

δ_prev    : inter-token delay
δ_session : session elapsed time
τ_inf     : model inference time (reflexive)
ω_context : temporal context window
ρ_rate    : token generation rate

Part II — Empirical Validation

Part II closes the loop with a non-invasive alternative to full pre-training: a graft methodology that endows any pretrained decoder with first-class temporal cognition by training only a small TemporalAdapter (under 0.6 % of base parameters) injected at mid-depth via a forward pre-hook. The base LLM is fully frozen.

Validated on TinyLlama-1.1B and Qwen2.5-14B, with an extension to Qwen2.5-Coder-32B. Key empirical findings:

• Linear decodability of log-time plateaus at R² ≈ 0.9 from 1 B parameters onward — temporal representability is a minimal cognitive primitive, not a scaling-sensitive capacity.
• The temporal signal lives in a ~5-dimensional subspace invariant to base width, structurally mirroring distributed time-cell coding in the mammalian hippocampus.
• Increasing base scale refines temporal pragmatics, producing emergent registers acknowledging elapsed time at long δ. The 32B Coder extension additionally shows a code/prose register switch conditioned on δ.
• A runtime modulation scalar α restores generative fluency without retraining (sweet spot α ≈ 0.2–0.3).
• Full pipeline reproduces on a single AMD MI300X in under 30 minutes at ≈ $0.83.

Repository layout

.
├── camus_theory.tex / .pdf           # Part I (English)
├── camus_theory_fr.tex / .pdf        # Part I (French)
├── camus_temporal.tex / .pdf         # Part II (English)
├── camus_temporal_fr.tex / .pdf      # Part II (French)
└── implementation/
    ├── adapter/     TemporalAdapter module
    ├── training/    graft_mi300x.py + dataset mix builder
    ├── inference/   Multi-GPU REPL with runtime δ/α control
    ├── probes/      Five evaluation probes
    └── checkpoints/ Download pointers for trained adapters (GitHub Releases)

Adapter weights are published as GitHub Release assets of this repository.

Quickstart

See implementation/README.md for the full training / inference / probing guide.

Citation

@misc{camus2026theory,
  title  = {The CAMUS Theory: Emergent Temporal Cognition in Language Models},
  author = {CAMUS, Leo},
  year   = {2026},
  doi    = {10.5281/zenodo.19509846},
  publisher = {Zenodo}
}

@misc{camus2026graft,
  title  = {The CAMUS Theory: Graft-Based Emergence of Temporal Cognition in Frozen Language Models},
  author = {CAMUS, Leo},
  year   = {2026},
  doi    = {10.5281/zenodo.19557893},
  publisher = {Zenodo}
}

License

© 2026 Leo CAMUS.

• Part I: Creative Commons Attribution-NoDerivatives 4.0 International (CC-BY-ND 4.0)
• Part II and implementation code: Creative Commons Attribution 4.0 International (CC-BY 4.0)