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Equation 1 · Part 2 · How Robotics and Embodied AI Actually Work

Symbol f_θ

s^t+1=fθ(st,at),o^t+1∼pθ(o∣s^t+1)\hat{s}_{t+1} = f_\theta(s_t, a_t), \qquad \hat{o}_{t+1} \sim p_\theta(o \mid \hat{s}_{t+1})
fθf_\theta

What this part means

learned from a finite amount of real interaction and is wrong in ways that compound over an imagined rollout’s horizon — which is precisely the boundary the next section is about.

Its job in the formula

f_θ is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

The exposure is that fθf_\theta is learned from a finite amount of real interaction and is wrong in ways that compound over an imagined rollout’s horizon — which is precisely the boundary the next section is about.

The passage around this formula

…against s^t+1\hat{s}_{t+1} , a predicted latent state, thousands of times per second of imagined rollout, while the real robot only needs to execute the resulting action once per real control cycle. The exposure is that fθf_\theta is learned from a finite amount of real interaction and is wrong in ways that compound over an imagined rollout’s horizon — which is precisely the boundary the next section is about.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.