Equation 4 · Part 2 · The Hardest Unsolved Problems in AI Agent Architecture
Symbol s
What this part means
everything true about the task — every file changed, every external call made, every fact established —.
Its job in the formula
s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol s→Article meaning
Where the article explains it
Applied to a long-running LLM agent, s is everything true about the task — every file changed, every external call made, every fact established — and b is whatever the agent’s context window currently represents.
The passage around this formula
A useful decomposition for what an agent needs to track is the belief it holds over the true state of its task, updated as new observations arrive. In the classical formalism, if b(s) is the agent’s probability distribution over possible states before an observation, a is the action just taken, o is the observation that followed, T is the environment’s transition model and O its observation model, the updated belief is
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
See this notation across published equations →
Sources cited in the article section
- [4] Planning and Acting in Partially Observable Stochastic Domains ↗
- [5] MemGPT: Towards LLMs as Operating Systems ↗
- [6] Compaction ↗
These citations provide research context; check each source for the exact claim it supports.