Equation 11 · Part 2 · Adapters, Native Pretraining, and Unified Tokens: The Main Multimodal Architectures, Compared
subscript
subscript
What this part means
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.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
The passage around this formula
The same cross-entropy objective a text-only language model uses is the entire training objective here — the only thing that changed is what is allowed to denote. Whether index names a subword, a 16-by-16 image patch code, or a discretised robot joint angle is invisible to the loss function; the difficulty this section documents is not in the objective but in keeping training numerically stable once the vocabulary spans quantities of such different statistical character.
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
Sources cited in the article section
- [6] A Generalist Agent ↗
- [7] Chameleon: Mixed-Modal Early-Fusion Foundation Models ↗
- [8] CM3: A Causal Masked Multimodal Model of the Internet ↗
These citations provide research context; check each source for the exact claim it supports.