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# Tree Tensor Network

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  1. arXiv

    Decision diagrams stop counting subfunctions: ATDDs use cut-matrix rank to give one canonical form on any vtree

    Tree decision diagrams (TDDs) measure width by counting distinct subfunctions across each vtree cut, a count blind to linear dependence among those subfunctions. Replacing the count with the rank of the cut matrix yields algebraic tree decision diagrams (ATDDs), whose width is the factor rank and which have exactly one representation per function and vtree. ATDDs are exponentially more succinct than TDDs and quasi-polynomially more succinct than structured deterministic DNNFs, while keeping polynomial-time model counting, weighted model counting and equivalence checking.

    Alexis de Colnet（First author）
    Algebraic Tree Decision DiagramTree Tensor NetworkKnowledge CompilationFactor RankTree Decision Diagram
  2. arXiv

    AWT uses activation-derived diagonal preconditioning to close 12–60% of the tensor-network compression perplexity gap on Llama, Ministral, and Qwen

    The authors propose Activation-aware Weight Tensorization (AWT), a training-free, solver-agnostic calibration-time preconditioner that applies an activation-derived diagonal equivalent reparameterization to each weight matrix before an unchanged TT/TTN solver and deploys it with only an input-side elementwise rescaling. Across Llama 3.1 8B, Ministral 8B, and Qwen2.5 7B at 2–6 compression, AWT consistently improves vanilla tensorization: it closes 12–35% of the WikiText perplexity gap under single-operator replacement and 27–60% under Llama multi-operator suffix replacement, with gains transferring to HellaSwag and ARC-Challenge.

    Sapienza University of Rome
    Alessandro Beatini（First author）
    Activation-aware Weight TensorizationTensor-Network CompressionTree Tensor NetworkModel compressionLarge language models

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