MoEGate.forward: denominator

Read the equation

In MoEGate.forward, this statement defines or updates denominator. The top-k operation selects the largest scores. Ties and group masking affect which experts or entries survive the discrete boundary. The reduction aggregates values along the explicit source axis; preserving the axis and keep-dimension setting matters for the later broadcast. Expert choice and expert mixture weight are separate in this implementation. Correction bias participates in selection; the uncorrected sigmoid scores supply the routed weights.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read denominator as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

### norm gate to sum 1
        if self.top_k > 1 and self.norm_topk_prob:
            denominator = topk_weight.sum(dim=-1, keepdim=True) + 1e-20
            topk_weight = topk_weight / denominator
        topk_weight = topk_weight * self.routed_scaling_factor  # must multiply the scaling factor

denominator = topk_weight.sum(dim=-1, keepdim=True) + 1e-20

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