AmelieSchreiber/toricblm-dataset-state-toricblm-structure-priority-balanced-3day-20260709t185034z-epoch-002
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Amelie Schreiber
AmelieSchreiber
AI & ML interests
Diffusion and flow matching models for proteins, small molecules, DNA, and RNA, protein language models, machine translation, equivariant attention mechanisms, LoRA, and QLoRA.
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updated a dataset about 1 month ago
AmelieSchreiber/toricblm-dataset-state-toricblm-structure-priority-balanced-3day-20260709t185034z-epoch-002 published a dataset about 1 month ago
AmelieSchreiber/toricblm-dataset-state-toricblm-structure-priority-balanced-3day-20260709t185034z-epoch-002 updated a dataset about 1 month ago
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Latest OpenAI Parameter Golf Competition Training Run BPB (<1K steps on a single 4090) See: ToricBLM, ToricGT, and TropicalGT methods
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ToricBLM: Thought Alcoves, Tropical Attention, and Small Models With Serious Geometry
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TropicalGT and ToricGT: Tropical, Toric, and Graph-Token Geometry for Auditable Reasoning
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In algebraic geometry, embedding tropical varieties into toric varieties relies on the process of tropicalization and the use of toroidal embeddings. Rather than embedding as geometric spaces, tropical varieties are embedded as polyhedral fans or cone complexes within the fans of target toric varieties to study compactifications and intersection theory.
Toric Varieties: Geometric varieties constructed from combinatorial data known as fans (collections of polyhedral cones). Tropicalization: A procedure that maps an algebraic variety X (typically a subvariety of an algebraic torus T) to a polyhedral complex in a real vector space via valuations. Toric Closures: When you embed a tropical variety in a compact toric variety, the boundary points correspond to limits of points in the variety going towards the boundary of the torus. Embedding Methodologies...Toric Compactification: Any tropical variety (a rational polyhedral fan) can be compactified by embedding it into a complete toric variety. The fan of the toric variety is chosen to contain the tropical variety as a subcomplex, which encodes the combinatorics of the compactification. Toroidal Embeddings: For varieties that are not strict toric varieties, they can often be mapped into toric varieties using the theory of toroidal embeddings. This involves equipping the tropicalized spaces (cone complexes) with balancing conditions and intersection theories.
Toric Varieties: Geometric varieties constructed from combinatorial data known as fans (collections of polyhedral cones). Tropicalization: A procedure that maps an algebraic variety X (typically a subvariety of an algebraic torus T) to a polyhedral complex in a real vector space via valuations. Toric Closures: When you embed a tropical variety in a compact toric variety, the boundary points correspond to limits of points in the variety going towards the boundary of the torus. Embedding Methodologies...Toric Compactification: Any tropical variety (a rational polyhedral fan) can be compactified by embedding it into a complete toric variety. The fan of the toric variety is chosen to contain the tropical variety as a subcomplex, which encodes the combinatorics of the compactification. Toroidal Embeddings: For varieties that are not strict toric varieties, they can often be mapped into toric varieties using the theory of toroidal embeddings. This involves equipping the tropicalized spaces (cone complexes) with balancing conditions and intersection theories.