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Equation 4 · Part 10 · How AI for Science and Medicine Actually Works

addition

xt=αˉt x0+1−αˉt ϵ,x^0=fθ(xt,t),x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, t),
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

The larger change is in how coordinates are produced. Rather than a Structure Module built on rotations and translations, AlphaFold3 uses a diffusion module that operates directly on raw atom coordinates and a coarse token representation, without rotational frames at all. Diffusion models are trained on a simple, general task: take a true data point, corrupt it with noise at a known level, and train a network to recover the original from the corrupted version. For coordinates x0x_0 noised to xtx_t at noise level t , xt=αˉt x0+1−αˉt ϵ,x^0=fθ(xt,t)x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, t). with ϵ\epsilon drawn from a standard normal distribution and fθf_\theta the trained network. Generating a structure then means starting from coordinates that are…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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