Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

Aditya Ravuri; Neil D. Lawrence

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Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

Aditya Ravuri, Neil D. Lawrence

, 2025.

Abstract

We propose a probabilistic interpretation of transformers as unrolled inference steps assuming a probabilistic Laplacian Eigenmaps model from the ProbDR framework. Our derivation shows that at initialisation, transformers perform “linear” dimensionality reduction. We also show that within the transformer block, a graph Laplacian term arises from our arguments, rather than an attention matrix (which we interpret as an adjacency matrix). We demonstrate that simply subtracting the identity from the attention matrix (and thereby taking a graph diffusion step) improves validation performance on a language model and a simple vision transformer.

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BibTeX


@Misc{transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps,
  title = 	 {Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements},
  author = 	 {Ravuri, Aditya and Lawrence, Neil D.},
  year = 	 {2025},
  url = 	 {/publications/transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps.html},
  abstract = 	 {We propose a probabilistic interpretation of transformers as unrolled inference steps assuming a probabilistic Laplacian Eigenmaps model from the ProbDR framework. Our derivation shows that at initialisation, transformers perform "linear" dimensionality reduction. We also show that within the transformer block, a graph Laplacian term arises from our arguments, rather than an attention matrix (which we interpret as an adjacency matrix). We demonstrate that simply subtracting the identity from the attention matrix (and thereby taking a graph diffusion step) improves validation performance on a language model and a simple vision transformer.
}
}

Endnote

%0 Generic
%T Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements
%A Aditya Ravuri
%A Neil D. Lawrence
%D 2025	
%F transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps
%U /publications/transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps.html
%X We propose a probabilistic interpretation of transformers as unrolled inference steps assuming a probabilistic Laplacian Eigenmaps model from the ProbDR framework. Our derivation shows that at initialisation, transformers perform "linear" dimensionality reduction. We also show that within the transformer block, a graph Laplacian term arises from our arguments, rather than an attention matrix (which we interpret as an adjacency matrix). We demonstrate that simply subtracting the identity from the attention matrix (and thereby taking a graph diffusion step) improves validation performance on a language model and a simple vision transformer.

RIS


TY  - GEN
TI  - Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements
AU  - Aditya Ravuri
AU  - Neil D. Lawrence
DA  - 2025/07/28	
ID  - transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps
UR  - /publications/transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps.html
AB  - We propose a probabilistic interpretation of transformers as unrolled inference steps assuming a probabilistic Laplacian Eigenmaps model from the ProbDR framework. Our derivation shows that at initialisation, transformers perform "linear" dimensionality reduction. We also show that within the transformer block, a graph Laplacian term arises from our arguments, rather than an attention matrix (which we interpret as an adjacency matrix). We demonstrate that simply subtracting the identity from the attention matrix (and thereby taking a graph diffusion step) improves validation performance on a language model and a simple vision transformer.

ER  -

APA


Ravuri, A. & Lawrence, N.D.. (2025). Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements.  Available from /publications/transformers-as-unrolled-inference-in-probabilistic-laplacian-eigenmaps.html.