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Towards Understanding the Shape of Representations in Protein Language Models

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Protein Language ModelsShape AnalysisTransformers
Abstract:

While protein language models (PLMs) are one of the most promising avenues of research for future de novo protein design, the way in which they transform sequences to hidden representations, as well as the information encoded in such representations is yet to be fully understood. Several works have attempted to propose interpretability tools for PLMs, but they have focused on understanding how individual sequences are transformed by such models. Therefore, the way in which PLMs transform the whole space of sequences along with their relations is still unknown. In this work we attempt to understand this transformed space of sequences by identifying protein structure and representation with square-root velocity (SRV) representations and graph filtrations. Both approaches naturally lead to a metric space in which pairs of proteins or protein representations can be compared with each other.

We analyze different types of proteins from the SCOP dataset and show that the Karcher mean and effective dimension of the SRV shape space follows a non-linear pattern as a function of the layers in ESM2 models of different sizes. Furthermore, we use graph filtrations as a tool to study the context lengths at which models encode the structural features of proteins. We find that PLMs preferentially encode immediate as well as local relations between amino acids, but start to degrade for larger context lengths. The most structurally faithful encoding tends to occur close to, but before the last layer of the models, indicating that training a folding model ontop of these layers might lead to improved folding performance.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper applies square-root velocity (SRV) representations and graph filtrations to analyze the geometry of protein language model embedding spaces, focusing on ESM2 models across different sizes and layers. It resides in the 'Shape-Theoretic Representation Analysis' leaf, which contains only two papers total. This is a notably sparse research direction within the broader taxonomy of 45 papers, suggesting that shape-theoretic approaches using differential geometric tools remain relatively underexplored compared to more application-driven or multimodal integration methods.

The taxonomy reveals that the paper's immediate parent branch, 'Geometric and Topological Analysis of PLM Representations', also includes work on layer-wise geometric evolution and intrinsic dimension (three papers). Neighboring branches focus on application-driven integration (binding site prediction, function prediction) and multimodal representation learning (sequence-structure alignment). The scope notes clarify that this work differs from general intrinsic dimension analyses by emphasizing shape-theoretic tools like Karcher means, and from application-driven methods by focusing on foundational geometric characterization rather than downstream task performance.

Among 14 candidates examined, the SRV framework contribution shows one refutable candidate out of four examined, suggesting some prior work exists in this specific methodological space. The graph filtration contribution examined only one candidate with no refutations, indicating limited direct precedent. The analysis of non-linear patterns in PLM geometry examined nine candidates with no refutations, suggesting this empirical finding may be relatively novel. The limited search scope (14 total candidates) means these assessments reflect top-K semantic matches rather than exhaustive coverage of the field.

Given the sparse taxonomy leaf (two papers) and limited search scope, the work appears to occupy a relatively unexplored methodological niche within PLM analysis. The shape-theoretic approach represents a distinct analytical perspective compared to the more common intrinsic dimension or application-driven methods. However, the presence of one refutable candidate for the SRV framework suggests the core methodology has some precedent, even if its specific application to PLM representation spaces is less established.

Taxonomy

Core-task Taxonomy Papers
45
3
Claimed Contributions
14
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Understanding the geometry of protein language model representation spaces. The field has organized itself around several complementary perspectives. One major branch focuses on geometric and topological analysis of PLM representations, examining the intrinsic shape and structure of embedding spaces through methods ranging from manifold analysis to curvature studies. A second branch emphasizes application-driven integration, combining PLMs with geometric deep learning for tasks such as binding-site prediction and structure-informed modeling. Multimodal representation learning merges sequence embeddings with structural or functional data, while methodological advances explore novel architectures and embedding strategies. Comparative and alignment-free sequence analysis provides alternative frameworks, and foundational reviews offer conceptual scaffolding. Representative works like Learning the protein language[3] and Protein representation learning by[19] illustrate how embeddings capture biological information, while efforts such as Integration of pre-trained protein[10] and When geometric deep learning[11] demonstrate practical downstream uses. Particularly active lines of work reveal tensions between purely geometric characterization and task-driven evaluation. Some studies probe the latent manifold structure directly, asking whether embeddings preserve evolutionary or functional relationships in their topology. Others integrate structural priors or multimodal signals to enrich representations for specific applications. Towards Understanding the Shape[0] sits within the geometric and topological analysis branch, specifically focusing on shape-theoretic representation analysis. It shares conceptual ground with Structure of the space[38], which similarly investigates the intrinsic organization of embedding spaces, but differs in its emphasis on shape-theoretic tools rather than broader topological or statistical summaries. This positioning highlights an emerging interest in rigorous geometric frameworks that go beyond standard clustering or dimensionality reduction, aiming to uncover fundamental organizing principles in how PLMs encode protein information.

Claimed Contributions

Square-root velocity (SRV) framework for analyzing PLM representation shape spaces

The authors adapt the SRV shape analysis framework to study protein language model representations as curves in a Riemannian metric space. This allows them to compute distances between protein representations and analyze geometric properties such as Karcher mean and effective dimension across different layers of ESM2 models.

4 retrieved papers
Can Refute
Graph filtration method for studying context-length sensitivity in PLMs

The authors introduce a graph filtration approach that constructs k-nearest neighbor graphs at multiple resolutions to analyze how PLMs encode structural features at different context lengths. This reveals that PLMs preferentially encode immediate and local relations between residues.

1 retrieved paper
Analysis revealing non-linear patterns in PLM geometry and optimal structural encoding layers

The authors demonstrate that PLM representations exhibit dimension expansion in early layers followed by contraction in later layers, and that the most structurally faithful encoding occurs close to but before the last layer, suggesting improved folding performance could be achieved by using these intermediate layers.

9 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Square-root velocity (SRV) framework for analyzing PLM representation shape spaces

The authors adapt the SRV shape analysis framework to study protein language model representations as curves in a Riemannian metric space. This allows them to compute distances between protein representations and analyze geometric properties such as Karcher mean and effective dimension across different layers of ESM2 models.

Contribution

Graph filtration method for studying context-length sensitivity in PLMs

The authors introduce a graph filtration approach that constructs k-nearest neighbor graphs at multiple resolutions to analyze how PLMs encode structural features at different context lengths. This reveals that PLMs preferentially encode immediate and local relations between residues.

Contribution

Analysis revealing non-linear patterns in PLM geometry and optimal structural encoding layers

The authors demonstrate that PLM representations exhibit dimension expansion in early layers followed by contraction in later layers, and that the most structurally faithful encoding occurs close to but before the last layer, suggesting improved folding performance could be achieved by using these intermediate layers.

Table of Contents