The Four Facets of Determinism in Large Language Models: Numerical, Computational, Syntactic, and Semantic

Large language models are not deterministic systems. Even when presented with identical input, they may produce slightly different results. This variation arises from both the numerical properties of computation and the probabilistic mechanisms of text generation. Understanding the different forms of determinism that influence this behavior helps explain why models vary and how users can manage that variability. These forms are numerical, computational, syntactic, and semantic.

Numerical determinism

At the lowest level, determinism depends on how numbers are represented and processed. Large language models rely on floating-point arithmetic, which cannot represent real numbers exactly. Each operation rounds results to a limited precision. Because of this, addition and multiplication are not associative. For example, when a = 1020, b = -1020, and c = 3, the result of ((a + b) + c) is 3, while (a + (b + c)) is 0 when computed in double precision. These differences occur because rounding errors depend on the order of operations. On GPUs, thousands of operations are executed simultaneously. The order of execution and rounding can differ slightly between runs, which makes exact numerical reproducibility difficult to achieve. This limitation defines the boundaries of numerical determinism.

Computational determinism

Computational determinism describes whether an algorithm performs the same sequence of operations in the same order every time it runs. Large language models perform extensive parallel processing, where computations may be split across multiple processors. Even when the algorithm is identical, minor differences in scheduling, optimization, or asynchrony can lead to small numerical differences. Maintaining strict computational determinism would require fixed hardware conditions, execution order, and software versions. In most user-facing systems, these variables are abstracted away, so computational determinism cannot be guaranteed.

Syntactic determinism

Syntactic determinism refers to the consistency of the model’s output at the level of exact wording. Language models generate text by sampling one token at a time from a probability distribution. When the temperature or other sampling parameters are greater than zero, randomness enters this process by design. Two identical prompts can therefore produce different word sequences. Setting temperature to zero or restricting the token selection space through top-k or top-p sampling makes the process nearly deterministic, as the model always selects the most probable next token. This ensures stability in the literal sequence of words but often reduces stylistic variation and naturalness.

Semantic determinism

Semantic determinism concerns the stability of meaning. Even when the exact wording differs, an LLM can consistently produce outputs that convey the same ideas and reasoning. When a prompt defines a clear goal, specifies format and scope, and provides relevant context, the model’s probability distribution becomes concentrated around a narrow set of interpretations. For example, the instruction “Write a 100-word summary explaining the main human causes of climate change” consistently leads to answers focused on greenhouse gases, fossil fuels, and deforestation, even if the phrasing changes. Semantic determinism therefore captures the reproducibility of ideas rather than words.

Bringing the four forms together

These four forms of determinism describe stability at different levels. Numerical determinism concerns how numbers behave. Computational determinism concerns how operations are executed. Syntactic determinism concerns the literal text sequence. Semantic determinism concerns the stability of meaning. Each higher level tolerates more variability than the one below it. In practice, full determinism across all levels is unnecessary. For most uses, maintaining consistent meaning and reasoning is more valuable than reproducing exact numeric or textual forms.

Determinism and Hallucination

Hallucination and determinism describe different aspects of a language model’s behavior. Determinism concerns the consistency of responses, while hallucination concerns their factual accuracy. A model can be deterministic yet still generate incorrect information if the most probable response it has learned is wrong. Conversely, a non-deterministic model may produce varied outputs, some of which are correct and others not. Higher determinism ensures that the same statement is repeated reliably but does not guarantee that the statement is true. Clear and well-structured prompts can reduce both variability and factual errors by narrowing the model’s interpretive range, yet determinism alone cannot eliminate hallucination because it governs consistency rather than truthfulness.

What users can control

As a user, you have little control over the hardware or execution environment, but you can influence determinism through parameter settings and prompt design.

• Limited hardware control: Users typically cannot influence the model’s underlying hardware, floating-point precision, or internal execution path. These affect numerical and computational determinism but remain outside the user’s reach.
• Control through generation parameters: You can adjust several sampling parameters that directly influence how deterministic or natural the model’s text generation is. Choosing suitable values allows you to balance consistency with creativity.
  • Temperature: Lowering it to around 0.0–0.2 sharpens the probability distribution and makes responses highly repeatable, while higher values such as 0.7–1.0 introduce more variation and a natural writing style.
  • Top-p: Restricts token selection to the smallest set whose cumulative probability exceeds p. Smaller settings such as 0.1–0.3 make the output more deterministic, while values near 0.8–0.9 yield smoother, more natural phrasing.
  • Top-k: Limits selection to the k most likely tokens. Setting k = 1 removes randomness almost entirely, whereas k = 40–50 balances focus with stylistic diversity.
  • Seed: Fixing a random seed, for example 42, ensures that the same internal random sequence is used across runs, producing identical token choices when other settings remain constant. Leaving it unset allows small natural differences between runs.
  • Repetition or frequency penalty: Adjusts how strongly the model avoids repeating words. Lower values around 0.0–0.2 support deterministic phrasing, while moderate values of 0.5–1.0 encourage more varied wording.
  • Presence penalty: Controls the likelihood of introducing new topics. Fixed low values such as 0.0–0.2 promote stable focus, while 0.3–0.8 adds variety and new subject matter.
  • Max tokens and length penalty: Fixing a specific output length and using a length penalty of 1.0–1.2 ensures predictable structure. Allowing flexible length or keeping the penalty close to 1.0 produces a more natural and adaptive flow.
• Control through prompt design: The wording and structure of your prompt strongly affect semantic determinism.
  • Clear, specific, and structured prompts (for example, “List three key points in formal tone”) guide the model toward a narrow range of valid answers.
  • Vague or open-ended prompts widen the distribution of possible meanings and tones.
• Why you would increase determinism:
  • To achieve reproducible and consistent wording in professional or analytical contexts.To make results easier to verify, compare, and reuse.
  • To ensure predictable tone and structure across multiple generations.
• Why you might hesitate to increase determinism:
  • High determinism can make responses rigid or formulaic.Reduced randomness may suppress creativity, nuance, and adaptability.
  • It can narrow the exploration of alternative ideas or perspectives.
• Finding the balance:
  • Favor high determinism (low temperature, fixed seed, defined format) for accuracy, documentation, and controlled output.
  • Allow moderate randomness (slightly higher temperature or top-p) for tasks that benefit from variety, such as creative writing or brainstorming.

Conclusion

Determinism in large language models exists in several layers. Numerical and computational determinism describe reproducibility in how calculations occur, while syntactic and semantic determinism describe reproducibility in how ideas are expressed. Users cannot control the hardware environment but can improve consistency through parameter choices and well-designed prompts. Absolute determinism is unattainable in probabilistic systems, but by managing these factors carefully, users can achieve stable and reliable outputs suited to both precise and creative tasks.