The Intrinsic Non-Randomness of Large Language Models

Large Language Models (LLMs) are inherently deterministic systems, yet their ability to generate text that appears creative and varied has often raised questions about the true nature of their “randomness.” Recent research, published on arXiv, addresses this topic by introducing a new metric, Entropic Deviation (ED), to quantify the intrinsic non-randomness in token distributions generated by these models. This study offers an in-depth perspective on how internal structure and learned weights influence text generation, independently of semantic context.

Entropic Deviation is defined as the normalized KL divergence between a model's token distribution and a uniform distribution. The analysis was conducted on a vast dataset, comprising 31,200 generations. This sample covered seven different models, two main architectures – the widely used transformers and the newer state space models – nine prompt categories, three temperature settings, and five different languages, providing a robust comparative framework.

Architectures Compared: Transformer vs. State Space Models

The study's results highlight significant differences between architectures. For transformer models, even with semantically neutral prompts – such as empty strings, random characters, or nonsense syllables – an Entropic Deviation of approximately 0.30 was observed. This data is particularly relevant: it suggests that between 88% and 93% of the non-randomness found under semantic prompt conditions is intrinsic to the model's learned weights, rather than induced by the specific prompt context. This is a clear indication of how the model's “personality” is deeply rooted in its structure.

Furthermore, the research revealed that three widely used transformer families – Gemma, Llama, and Qwen – converge on nearly identical ED values. This occurs despite differences in training data and vocabularies used to train them, suggesting a fundamental and transversal property of this architecture. State space models, such as Mamba2, instead show a qualitatively different regime: they exhibit twice the Entropic Deviation of transformers, three times lower within-sequence variance, and massive sensitivity to temperature (with a correlation coefficient r = -0.78), unlike transformers which are almost immune to this parameter (r < 0.05). These differences are crucial for those who need to evaluate model performance and predictability in production environments.

Implications for Deployment and Data Sovereignty

Understanding the intrinsic randomness floor and architectural differences in token generation has direct implications for LLM deployment, both in cloud and self-hosted environments. The predictability of a model's behavior, particularly its sensitivity to parameters like temperature, is a key factor in optimizing resources and ensuring response stability. For organizations prioritizing data sovereignty and complete control over infrastructure, the choice of architecture and understanding its intrinsic properties become even more critical.

A model's ability to generate consistent and predictable output, even in the absence of strong semantic context, can influence the design of inference pipelines and system calibration. For example, a model with low within-sequence variance might be preferable for applications requiring high consistency. These aspects are fundamental for CTOs, DevOps leads, and infrastructure architects who must make informed decisions about the trade-offs between different solutions, especially when considering on-premise deployments where resource optimization and predictability are essential.

The Role of Language and Future Perspective

Cross-lingual experiments conducted with Qwen-32B added an additional layer of complexity and interest. The research demonstrated a stable gradient of Entropic Deviation across five different languages (English, Japanese, Chinese, Polish, and Arabic). This gradient shows no correlation with token “fertility” (i.e., how many tokens are needed to express a concept) and persists even when comparing two languages that share an identical tokenizer subset. This suggests that language itself modulates the randomness bound independently of tokenization.

These findings establish a structural lower bound on randomness in pre-trained Large Language Models, characterize how this bound differs across architectures, and demonstrate that language itself influences this bound independently of the tokenization process. For industry professionals, this means that the choice of an LLM is not solely based on its size or training data, but also on its intrinsic generation properties, which can significantly impact performance and reliability in real-world scenarios, especially in multilingual contexts or with stringent control requirements.