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Equation 6 · Part 13 · One Model, Many Modalities: What Multimodal Systems Actually Share

Numerator: 1

L=−1B∑i=1Blog⁡exp⁡(⟨ui,vi⟩/τ)∑j=1Bexp⁡(⟨ui,vj⟩/τ),\mathcal{L} = -\frac{1}{B} \sum_{i=1}^{B} \log \frac{\exp(\langle u_i, v_i \rangle / \tau)}{\sum_{j=1}^{B} \exp(\langle u_i, v_j \rangle / \tau)},
11

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

…and colleagues showed that this simple pre-training task, applied to 400 million image–text pairs collected from the internet, matched the accuracy of the original ResNet-50 on ImageNet zero-shot without using any of the 1.28 million training examples that network was trained on [ 1 ] . A later variant replaces the softmax with a pairwise sigmoid loss that does not require a global view of the batch’s pairwise similarities for normalisation, and the authors report training a model to 84.5% ImageNet zero-shot…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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