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Equation 1 · Adapters, Native Pretraining, and Unified Tokens: The Main Multimodal Architectures, Compared

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θ(t+1)=θ(t)−η⋅1 ⁣[θ∈θbridge]⊙∇θ L(θ(t))\theta^{(t+1)} = \theta^{(t)} - \eta \cdot \mathbb{1}\!\left[\theta \in \theta_{\text{bridge}}\right] \odot \nabla_\theta \, \mathcal{L}(\theta^{(t)})

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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θ(t+1)\theta^{(t+1)}

Symbol θ^(t+1)

θ^(t+1) is part of the quantity the equation computes from the expression on the right.

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θ(t)\theta^{(t)}

Symbol θ^(t)

θ^(t) is one of the signed contributions combined to compute the quantity on the left.

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η\eta

Symbol eta

eta is one of the signed contributions combined to compute the quantity on the left.

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θ\theta

Symbol θ

θ is part of the quantity the equation computes from the expression on the right.

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θbridge\theta_{\text{bridge}}

Symbol theta_bridge

thetaba_bridge is one of the signed contributions combined to compute the quantity on the left.

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L\mathcal{L}

Symbol L

L is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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multiplication

multiplication

Multiply the quantities on either side.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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How to interpret it

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What the article says around this equation

None of these three papers claims the resulting bridge is unlimited in what it can carry. LLaVA’s own error analysis documents a case where the model answers confidently that strawberry-flavoured yoghurt is present in a fridge that in fact contains only yoghurt and strawberries, which the authors read as the model treating the image “as a bag of patches, failing to grasp the complex semantics within the image” [ 1 ] , and they separately note that recognising a specific product brand would require higher input resolution than the system uses. The bridge has a fixed information-carrying capacity, whether it is BLIP-2’s small set of learned query vectors or LLaVA’s single projection matrix,…
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None of these three papers claims the resulting bridge is unlimited in what it can carry. LLaVA’s own error analysis documents a case where the model answers confidently that strawberry-flavoured yoghurt is present in a fridge that in fact contains only yoghurt and strawberries, which the authors read as the model treating the image “as a bag of patches, failing to grasp the complex semantics within the image” [ 1 ] , and they separately note that recognising a specific product brand would require higher input resolution than the system uses. The bridge has a fixed information-carrying capacity, whether it is BLIP-2’s small set of learned query vectors or LLaVA’s single projection matrix, and everything the language side ever learns about the image has to fit through it. This is the formal shape of “freeze the backbones”: the gradient update is masked to zero everywhere except the bridge parameters θbridge\theta_{\text{bridge}} , so |θbridge\theta_{\text{bridge}}| — a few hundred million parameters in BLIP-2’s case, dramatically fewer than either tower — is the entire quantity being optimised, and θvision\theta_{\text{vision}} and θLM\theta_{\text{LM}} contribute a forward pass but never a gradient.

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Sources cited in the surrounding passage

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