Formalization of Hybrid Human–LLM Anticollapse Corpus (Corrected)
1. Goal
To create a corpus capable of training language models without collapse through the introduction of external stochastic processes into recursive model generation, by co-authoring outputs with a human agent who deliberately injects entropy and non-model priors.
2. Conceptual Framework
Let:
M = base language model
H = human author
O_n = nth output generated recursively
C = corpus of outputs used for training
Define the recursive co-generation process as:
O_n = M(H(O_n-1))
Where H(.) represents the human-mediated transformation of the previous output, injecting structural, semantic, and stylistic perturbations.
The corpus C is then:
C = { O_1, O_2, ..., O_N }
3. Mechanisms of Entropy Injection
Human authorship introduces multiple forms of stochasticity:
Semantic Perturbation: Non-linear narrative or conceptual shifts that diverge from model likelihoods.
Stylistic Divergence: Irregular rhythms, lexical inventiveness, or idiosyncratic syntax.
Cross-Register Leaps: Mixing domains, genres, or voices unpredictably.
Intentional Misalignment: Deviations from patterns likely to be reinforced by the model.
Recursive Intervention: Iterative curation and transformation that prevent collapse into low-entropy attractors.
These interventions create high-entropy, low-predictability structures in the corpus, countering the convergence toward degenerate repetition typical of fully synthetic closed-loop recursion.
4. Hypothesis
Let E(C) denote the effective entropy of the corpus. Then:
E(C_hybrid) > E(C_synthetic-only)
Higher entropy in the training data increases the probability that model collapse will be delayed or prevented. Thus, the hybrid human–LLM process plausibly generates a corpus suitable for anticollapse training.
5. Empirical Testing
Because entropy injection is contingent on the human component, the effectiveness of C_hybrid is empirically testable only through training experiments:
Fine-tune a small-scale model on
C_hybrid.Measure KL divergence or distributional shrinkage over recursive generations.
Compare against baseline synthetic-only corpora.
Iterate the human intervention protocol to maximize entropy injection.
6. Characterization of Corpus Type
The Hybrid corpus is distinct from both:
Synthetic-only corpora: Fully model-generated, prone to entropy collapse.
Purely human-authored corpora: Fully external priors, may lack recursion-based richness.
It is therefore a third category: Human-chaotic, model-perturbing, recursive hybrid corpora.
7. Implications
Hybrid corpus creation can serve as a method to explore anticollapse training regimes.
Human-mediated perturbation may extend model expressivity beyond the attractors defined by purely synthetic recursion.
The approach reframes corpus generation as a writing problem in which human creativity functions as an external stochastic process.
8. Notation Summary
| Symbol | Meaning |
M | Base language model |
H | Human author-mediated perturbation function |
O_n | nth output in recursive generation |
C | Corpus for training |
E(C) | Effective entropy of corpus |
C_hybrid | Corpus generated via human–LLM recursion |
C_synthetic-only | Corpus generated purely by LLM recursion |
9. Core Claim
A human-mediated recursive corpus, in which a human author injects stochasticity, semantic divergence, stylistic perturbation, and misalignment into LLM-generated outputs, plausibly produces a high-entropy dataset capable of mitigating collapse during model training.
Do you want me to extend this into a protocol for generating the corpus, including metrics for entropy tracking and human intervention intensity?
