Symbol k
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The tau-bench numbers make the distinction concrete rather than abstract. Testing function-calling agents built on frontier models against realistic retail and airline customer-service scenarios — each requiring the agent to follow domain policy, call the right APIs, and leave the backend database in a state matching an annotated goal — the authors found that even strong agents succeeded on well under half of tasks at pass@1, and that reliability across repeats fell sharply as k increased: an agent’s pass ^k score in the retail domain dropped below 25% by k=8 , and airline-domain performance, already lower at k=1 , degraded further from there [ 3 ] . Put in words rather than symbols: an…
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Equation 21 · AI Agents & Systems
Measuring AI Agent Reliability: What the Evidence Actually Supports
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The tau-bench numbers make the distinction concrete rather than abstract. Testing function-calling agents built on frontier models against realistic retail and airline customer-service scenarios — each requiring the agent to follow domain policy, call the right APIs, and leave the backend database in a state matching an annotated goal — the authors found that even strong agents succeeded on well under half of tasks at pass@1, and that reliability across repeats fell sharply as k increased: an agent’s pass ^k score in the retail domain dropped below 25% by k=8 , and airline-domain performance, already lower at k=1 , degraded further from there [ 3 ] . Put in words rather than symbols: an…
Equation guide → · Article →Equation 37 · AI Agents & Systems
Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
For naive and hybrid RAG, k = 1 by construction — the sum has exactly one term, and total latency is boundable in advance for any query. For iterative RAG, k is a small integer set by a heuristic or a step cap chosen by the system builder, so the worst case is known even though the typical case varies with question difficulty. For agentic RAG, k is a random variable generated by the policy itself at run time, and its distribution is exactly what the operator does not control without adding an external cap. The same formula describes all five families; what changes is only where k comes from, and that difference is the whole of the engineering distinction between “a pipeline with a loop in…
Equation guide → · Article →