Gemini thinking budgets: an executed search analogy

A computed budget analogy

This lab executes breadth-first graph search in your browser. It illustrates a resource budget with observable work, rather than claiming to reproduce Gemini reasoning. The nodes, queue, expansions and returned route are computed from the selected adjacency list. No model weights, API, hidden reasoning, token usage, latency or price are involved. The connection to thinking models is a question to investigate: what happens when a process is stopped before it has found a supported answer? Actual model behavior requires measured evaluations; neither a graph-search success nor extra compute establishes language-model accuracy. Consult current provider documentation for configuration details because interfaces and supported models change.

Choose budget, graph and order

Expansion budget limits removals from the queue to two, five or twelve. Each removal includes the goal test, so discovering G as a neighbor is not yet a verified result. Graph chooses a direct edge, a branching route, or a disconnected goal. Neighbor order keeps each adjacency list as written or reverses it before enqueueing. Nodes are marked when enqueued, preventing repeated visits and cycles. The frontier contains discovered nodes still awaiting inspection. The displayed graph and expansion trace let you reproduce the queue with pencil and paper; no result is selected from a table of success labels.

Reproduce success and budget exhaustion

Choose Direct edge and two expansions. First remove S and enqueue G; then remove G, verify it and return S to G. Raising the budget to twelve still performs only two expansions. On Branching route with forward order and five expansions, the trace removes S, A, B, C and D. D discovers G, but E and G remain in the frontier and no route is returned yet. Twelve expansions remove E and then G, establishing S to A to D to G after seven removals. Reverse order visits B before A and finds the same shortest route after eight removals. These differences are actual traversal order, not an invented estimate of required reasoning.

Distinguish failure boundaries

Disconnected goal with twelve expansions visits seven reachable nodes and empties the frontier. It reports frontier exhausted, which differs from budget exhausted: more budget cannot add the missing edge. Two expansions stop with a nonempty frontier and cannot decide reachability. A returned route must consist entirely of graph edges, start at S and end at G. Breadth-first search yields a shortest unweighted route here, but this is neither a heuristic search nor a simulation of how an LLM forms an answer. The graph is tiny, deterministic and fully known; real tasks have uncertain evidence and errors that a larger budget may not fix.

Inspect and compare the trace

Play reveals eight stages over sixty inspection seconds; Pause freezes that position. Restart retains your choices and resets the timeline. Speed selects half, normal or double inspection pace without changing the computation. Timeline seeks directly to a chosen second. Changing a scenario pauses and starts a fresh trace. Only inspected stages expose their details, and the full computed JSON appears at sixty seconds. Scroll the result panel for the adjacency list, queue trace and route. Capture baseline retains a comparison, Replace baseline updates it and Clear baseline removes it. Notes persist locally and Export notes saves observations. Expand experiment enlarges the workspace. Compare the verified path and expansion count, not animation duration, when judging a budget change.