The paper introduces an approximate fiber product to model multimodal embedding alignment and proposes an orthogonal decomposition of the shared embedding space.
BpForms and BcForms: Tools for concretely describing non-canonical polymers and complexes to facilitate comprehensive biochemical networks
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abstract
Although non-canonical residues, caps, crosslinks, and nicks play an important role in the function of many DNA, RNA, proteins, and complexes, we do not fully understand how networks of non-canonical macromolecules generate behavior. One barrier is our limited formats, such as IUPAC, for abstractly describing macromolecules. To overcome this barrier, we developed BpForms and BcForms, a toolkit of ontologies, grammars, and software for abstracting the primary structure of polymers and complexes as combinations of residues, caps, crosslinks, and nicks. The toolkit can help quality control, exchange, and integrate information about the primary structure of macromolecules into fine-grained global networks of intracellular biochemistry.
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Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment
The paper introduces an approximate fiber product to model multimodal embedding alignment and proposes an orthogonal decomposition of the shared embedding space.