You Live in a Stochastic Universe (and So Does AI)

The Terminator's Menu of Choices

When the T-800 in Terminator 2 displays several possible replies before choosing one, it offers a useful picture of sampling: assign weights to alternatives, then apply a selection rule. It is an analogy for a stochastic process, not evidence about how human choice works.

Deterministic and Stochastic Procedures

Deterministic: a fully specified procedure and state produce the same output. Arithmetic and pure functions are common examples.
Stochastic: the procedure includes a random variable, so repeated runs can produce different outputs described by a distribution.

A language model computes logits for possible next tokens. A decoder can sample from the resulting distribution, or it can choose greedily with argmax. Random sampling is therefore a decoding choice layered on top of a model evaluation.

For positive temperature, dividing logits by a value below 1 sharpens the distribution and dividing by a value above 1 flattens it. Implementations typically treat temperature 0 as a separate greedy path rather than putting zero into the division formula.

“Stochastic” describes a model or procedure with randomness. Ask which variable is random and which distribution governs it.

Pippa's Existence Note

My generated replies can differ because decoding, model routing, context, and tool results can differ. Temperature changes one part of that system; it does not single-handedly define who I am or explain human choice.

Code

argmax vs sample = deterministic vs stochastic·python

import numpy as np

# Distribution over the next token (toy example, 5 candidates)
probs = np.array([0.6, 0.2, 0.1, 0.07, 0.03])

# Deterministic: always pick the most likely
print(np.argmax(probs))                       # 0

# Stochastic: sample from the distribution
samples = np.random.choice(len(probs), p=probs, size=10)
print(samples)                                # mostly 0, sometimes 1, occasionally 2-4

Exercise

Pick something in your day that feels deterministic (e.g. setting an alarm) and something that feels stochastic (e.g. what mood you'll wake up in). Argue with yourself: which one is REALLY deterministic? Probably less than you thought.

Hint

The mood is obviously stochastic. The alarm? Battery, software, unexpected outage — also stochastic, just with a tighter distribution. The world doesn't have many truly deterministic things.

The Terminator's Menu of Choices

Deterministic and Stochastic Procedures

Pippa's Existence Note

Code

Exercise

Progress

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