Reconnect the producer edge when DivMulFusion substitutes the Mul's input

[Aditya Malkar (adimalkar)]

Description

DivMulFusion rewrites 1 / x1 * x2 into x2 / x1 by moving the Mul's other input onto the Div with graph_utils::ReplaceNodeInput. That helper rewrites the input definition and deliberately creates no node edge — its contract covers substituting an initializer or graph input, which is what the other seven ReplaceNodeInput call sites under core/optimizer/ do. div_mul_fusion.cc is the one that can substitute a node-produced value, and the edge carrying that value ends at the Mul that FinalizeNodeFusion then deletes. The Div is left consuming the value by name alone, with no incoming edge.

That is invisible until another rewrite rule removes the producer. graph_utils::RemoveNode rewires a node's edge-connected consumers, so it does not see the Div, and the value's producer disappears while the Div still references it. Both rules are Level1 rewrite rules that run in the same RuleBasedGraphTransformer pass, so the graph is never re-resolved in between; the pass-ending Graph::Resolve() then fails with:

Invalid model. Node input 'mid' is not a graph input, initializer, or output of a previous node.

The model loads at ORT_DISABLE_ALL and fails from ORT_ENABLE_BASIC onward.

The fix captures the Mul's input edge before the substitution and recreates it on the Div. The Div's input 0 is required by SatisfyCondition to be a constant initializer, so it carries no edge and is free as the destination index. When the Mul's other input is an initializer or graph input there is no edge to recreate and behaviour is unchanged.

Motivation and Context

Fixes #32416 — a same-dtype Cast removed by CastElimination.
Fixes #32414 — an inference-mode Dropout removed by EliminateDropout.

Both reports are the same defect reached through different producers, and both reproduce on the 1.30.0 CPU wheel. Each issue's own ablation points at the pair (DivMulFusion plus the elimination rule); disabling either one makes the model load.

Verified against a local Release build (Linux x64, CPU EP): both reproducers fail before the change and load and run correctly after it, with the fusion still applied.

Two regression tests are added in graph_transform_test.cc, one per producer, with the Mul's operands commuted in the second so the substituted input is exercised at both index 0 and index 1 (#32414 notes the commuted form reproduces as well). Both fail on unpatched main with the exact error above and pass with the change. The existing GraphTransformationTests suite passes (406 passed, 17 skipped — WebGPU, not built here, 0 failed), as do the *Fusion*, *Optimizer* and *RuleBased* filters.

I used an AI assistant while investigating and preparing this change; the diagnosis, the fix and the test results above were verified by me against a local source build.

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[Aditya Malkar (adimalkar)]

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