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Rosetta Stone · 11 of 30

β\beta

Beta

Naming convention: meaning depends on the field

In plain English

Another conventional parameter name. In statistical physics β=1/(kBT)\beta = 1/(k_B T) is inverse temperature: large β\beta means cold, sharp preferences for low energy. In regression, β\betas are coefficients. In the Adam optimiser, β1\beta_1 and β2\beta_2 control how much the running averages remember. In β-VAEs it weights a KL term. The letter carries no meaning of its own.

See it

μ\mu shifts the centre and σ\sigma sets the spread. About 68% of the probability lies within one σ of μ.

What it means, field by field

Physics

Inverse temperature β = 1/k_BT; also v/c in relativity; a critical exponent.

AI / ML

Adam’s β₁ ≈ 0.9 and β₂ ≈ 0.999 decay rates; KL weight in β-VAE; sometimes inverse softmax temperature.

Biology

Transmission rate in SIR epidemic models; selection coefficients in some notations.

Epistemics

β is the false-negative rate of a test; statistical power = 1 − β.

In a research paper

The Adam optimiser (Kingma & Ba 2014, arXiv:1412.6980): an exponential moving average of gradients.
mt=β1mt−1+(1−β1) gtm_t = \beta_1 m_{t-1} + (1-\beta_1)\,g_t

The new momentum is mostly the old momentum (weight β₁) plus a little of the current gradient.

Common misreadings

  • Assuming β means "beta version" or something preliminary.

  • Reading β in a softmax as temperature. It is usually the inverse of temperature, so larger β is sharper, not softer.

Connected symbols

α\alpha Alphaexe^{x} ExponentialE\mathbb{E} Expectation (expected value)η\eta Eta