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Equation 1 · Part 3 · Building a Multimodal AI Application That Actually Uses Its Inputs

Symbol A

ΔW=BA,B∈Rd×r, A∈Rr×k, r≪min⁡(d,k),\Delta W = BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, k),
AA

What this part means

A appears in the objective or constraint used by the optimization on the right.

Its job in the formula

A appears in the objective or constraint used by the optimization on the right.

The passage around this formula

When the adapter route is chosen, the engineering default within it is equally clear: adapt, do not retrain. Low-Rank Adaptation freezes the pretrained weights and injects a pair of small trainable matrices into selected layers, so that a weight update is expressed as a low-rank product rather than a dense matrix the size of the original layer, ΔW=BA,B∈Rd×r, A∈Rr×k, r≪min⁡(d,k)\Delta W = BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, k). with the forward pass computing h = W0W_0 x + Δ\Delta W x against the frozen base weight W0W_0 . The…

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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.

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Sources cited in the surrounding passage

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