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Dear Hugging Face Team,

We are applying for the GPU Community Grant to showcase Forge: Foundational Optimization Representations from Graph Embeddings, recently published at TMLR ’26.

What is Forge?

Forge is the first pre-trained optimization model capable of producing meaningful, general-purpose embeddings for combinatorial optimization problems.

At a high level, Forge provides a unified representation space for optimization, similar to how foundational models transformed computer vision and natural language processing.

• Unsupervised Capabilities: Forge captures structural relationships between optimization problems in a way never demonstrated before. For example, it reproduces the classic King – Man + Woman ≈ Queen analogy in the optimization domain as Set Covering – (Vertex) Cover + (Bin) Packing ≈ Independent Set. Beyond analogies, Forge clusters unseen optimization instances with high accuracy, revealing latent structure across diverse problem families.

• Supervised Capabilities: The same pre-trained model can be fine-tuned for a wide range of downstream optimization tasks, including: predicting integrality gap, estimating linear relaxation quality, guiding search toward optimal solutions, selecting solver configurations, and identifying important variables

Forge is an important step toward a single foundational model serving multiple tasks, problem types, sizes, and difficulty levels and it opens up a new exciting research direction for the Optimization Community.

Why We Need GPU Support?

We have already built an initial Demo Space for Forge: https://huggingface.co/spaces/skadio/forge

However, Forge’s inference pipeline does not scale on CPU, making the current demo non-functional. With GPU support, we can build a full Space that:

• Predicts optimality gaps and relaxation bounds
• Generates solution guidance
• Clusters unseen optimization instances
• Demonstrates cross-task generalization from a single pre-trained model

Supported by this grant, this would be the first public demonstration of foundational modeling for combinatorial optimization. This is an important milestone for the optimization community to revive the success of pretrained models in CV and NLP to Optimization.

Given the chance, we would be happy to showcase Forge on Hugging Face and help catalyze a new wave of research around pretrained optimization models.

Thank you for your consideration.

Best,
Serdar Kadioglu