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Published equation contexts

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)})

Why this formula appears here

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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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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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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Published contexts (1)

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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)})

Equation 1 · Foundation Models

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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