aiqbench analysis
This research introduces a novel framework for probabilistic inference in high-treewidth graphical models by leveraging latent parametric structure within base tensor networks. By reparameterizing models into specific tensor network representations, the method enables efficient contraction and decomposition without requiring explicit prior knowledge of symmetries or other structural constraints. This advancement expands the tractability limits of inference algorithms, offering a significant theoretical step forward for complex probabilistic modeling in AI systems.
On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks
arXiv:2609.23774v1 Announce Type: new Abstract: Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings. Many existing methods improve efficiency by exploiting specific parametric structure, such as symmetries. However, they typically require such structure to be explicitly present, limiting their applicability to a broader range of graphical models. To address this limitation, we propose a framework where tractable inference is controlled by latent parametric structure exploitation, rather than requiring it to be explicitly present a priori. Our approach first reparameterises a graphical model as a specific tensor network representation, which we call a base tensor network. This representation yields two key properties that allow inference tractability to be controlled by parametric structure: 1) First, the complexity of inference is mainly determined by the parametric structure of a single tensor, called the base tensor. We characterise several tractable classes of base tensors for which the entire base tensor network can be contracted efficiently. 2) Second, decomposing the base tensor yields again a collection of base tensor networks. This allows inference to be naturally reduced to decomposing the base tensor into tractable components with sufficient parametric structure. We call this procedure parametric tensor decomposition. By exploiting parametric structure within the base tensor, our framework enables a novel view on inference beyond settings where such structure is explicitly present.
Abstract:Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings. Many existing methods improve efficiency by exploiting specific parametric structure, such as symmetries. However, they typically require such structure to be explicitly present, limiting their applicability to a broader range of graphical models. To address this limitation, we propose a framework where tractable inference is controlled by latent parametric structure exploitation, rather than requiring it to be explicitly present a priori. Our approach first reparameterises a graphical model as a specific tensor network representation, which we call a base tensor network. This representation yields two key properties that allow inference tractability to be controlled by parametric structure: 1) First, the complexity of inference is mainly determined by the parametric structure of a single tensor, called the base tensor. We characterise several tractable classes of base tensors for which the entire base tensor network can be contracted efficiently. 2) Second, decomposing the base tensor yields again a collection of base tensor networks. This allows inference to be naturally reduced to decomposing the base tensor into tractable components with sufficient parametric structure. We call this procedure parametric tensor decomposition. By exploiting parametric structure within the base tensor, our framework enables a novel view on inference beyond settings where such structure is explicitly present.
Artificial Intelligence (cs.AI)
arXiv:2609.23774 [cs.AI]
(or arXiv:2609.23774v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.23774 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 312 words
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