Equation 9 · Part 13 · Adapters, Native Pretraining, and Unified Tokens: The Main Multimodal Architectures, Compared
Ending index or upper bound: T
What this part means
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Its job in the formula
T appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Ending index or upper bound: T→Article meaning
The passage around this formula
Meta’s Chameleon commits to the same principle at a much larger scale and is candid that stability, not capability, was the hard engineering problem. It describes itself as “a family of early-fusion token-based mixed-modal models” that interleaves image and text tokens in one sequence, generating either kind at any position, and its authors state directly that this “requires a stable training approach from inception, an alignment recipe, and an architectural parameterization tailored for the early-fusion, token-based, mixed-modal setting” [ 7 ] . The paper documents the failure mode this addresses concretely: without a query-key normalisation step controlling the growth of attention logits,…
Learn the underlying idea
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Open the illustrated sums and products: repeat an operation over an index guide →
See this notation across published equations →
Sources cited in the surrounding passage
- [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.