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Why We Need New Benchmarks for Local Intrinsic Dimension Estimation

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Local intrinsic dimension estimationLIDLFLIPDDiffusion ModelsBenhamarkNormalizing FlowsESSNormal BundleNBLID
Abstract:

Recent advancements in algorithms for local intrinsic dimension (LID) estimation have been closely tied to progress in neural networks (NN). However, NN architectures are often tailored to specific domains, such as audio or image data, incorporating inductive biases that limit their transferability across domains. Moreover, existing LID estimation methods leveraging these architectures are typically evaluated on either overly simplistic benchmarks or domain datasets where the true LID is unknown, resulting in potentially erroneous evaluations. To close this research gap, we first isolate problematic aspects of LID estimation and leverage them to analyze the limitations of state-of-the-art methods. Our approach employs several techniques to create LID benchmarks for arbitrary domains, including the introduction of a method to transform any manifold into the domain while preserving the manifold structure, thereby addressing challenges posed by biases in neural network-based methods. Our comparative analysis reveals critical limitations and identifies new directions for future development in LID estimation methods. Code will be available on github when published.

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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 proposes a principled benchmarking framework for local intrinsic dimension (LID) estimation that addresses domain transferability and evaluation rigor. It resides in the 'Benchmarking and Evaluation Frameworks' leaf of the taxonomy, which contains only two papers total. This sparse population suggests that systematic evaluation infrastructure for LID estimation remains underdeveloped relative to the broader field, where estimation methods and applications dominate the taxonomy with over forty papers across multiple branches.

The taxonomy reveals that while estimation algorithms (nearest-neighbor, likelihood-based, deep learning methods) and applications (adversarial detection, generative model analysis) are well-populated, the evaluation infrastructure branch is notably thin. The paper's sibling, 'Estimating Local ID', represents foundational evaluation practices, while neighboring leaves in the same branch cover software packages and survey papers. The work diverges from the crowded 'Estimation Methods' branch by focusing on how to test methods rather than proposing new estimators, addressing a gap where algorithmic innovation has outpaced rigorous comparative assessment.

Among twenty-three candidates examined, none clearly refute the three core contributions. The principled benchmarking framework examined ten candidates with zero refutations, suggesting limited prior work on cross-domain evaluation protocols at this scale. The data transformation method for preserving manifold structure while changing domains also examined ten candidates without refutation, indicating novelty in addressing neural network inductive biases. The harder dataset variants examined three candidates, again with no overlapping prior work identified within this limited search scope.

Based on the top-twenty-three semantic matches examined, the work appears to occupy relatively unexplored territory within LID evaluation methodology. The sparse taxonomy leaf and absence of refuting candidates suggest the cross-domain benchmarking focus addresses an underserved need, though the limited search scope means potentially relevant work in adjacent evaluation or manifold learning communities may exist beyond these candidates.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
23
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: local intrinsic dimension estimation. The field is organized around five main branches that collectively address how to measure the effective dimensionality of data in local neighborhoods. Estimation Methods and Algorithms encompasses the diverse algorithmic approaches—ranging from classical nearest-neighbor techniques like those in Estimating Local ID[3] to more recent entropy-based and extreme-value methods such as Local Dimensional Entropy[1] and Generalized Ratios Estimator[4]. Bias Correction and Robustness focuses on refining these estimators to handle underestimation issues and noisy data, as seen in Underestimation Modification[5] and De-biasing ID[9]. Theoretical Foundations and Connections explores the mathematical underpinnings, linking local dimension to extreme value theory, score matching, and geometric perspectives on manifolds. Applications and Domain-Specific Uses demonstrates how local intrinsic dimension informs tasks from adversarial detection to AI-generated text identification, while Evaluation, Benchmarking, and Software provides the infrastructure—such as Scikit-Dimension[8] and Rdimtools[26]—for systematic comparison and reproducibility. A particularly active line of work centers on developing robust, scalable estimators that balance theoretical rigor with practical performance across diverse data types. Recent efforts like Novel ID Estimation[2] and Less is More[16] explore minimal-information approaches and geometric insights, while studies such as Bayesian LID Estimation[36] and Score Matching Connection[37] deepen the theoretical connections to probabilistic models. New Benchmarks LID[0] sits squarely within the Evaluation, Benchmarking, and Software branch, closely aligned with Estimating Local ID[3] in its emphasis on systematic assessment frameworks. Where Estimating Local ID[3] laid foundational evaluation practices, New Benchmarks LID[0] extends this tradition by introducing updated benchmarking protocols that address the growing diversity of estimation methods and application domains, helping practitioners navigate trade-offs between accuracy, computational cost, and robustness in contemporary high-dimensional settings.

Claimed Contributions

Principled benchmarking framework for LID estimation across domains

The authors develop a framework that transforms the same manifold into multiple domain representations while preserving its structure. This enables controlled cross-architecture testing and reveals that validation on simple synthetic manifolds does not guarantee similar performance across different domain networks.

10 retrieved papers
Harder variants of existing datasets targeting key manifold properties

The authors design more challenging versions of datasets from prior literature that specifically target key manifold characteristics such as non-uniform density, curvature, boundaries, thin manifolds, and nearby manifolds. These variants expose significant limitations in state-of-the-art LID estimation methods.

3 retrieved papers
Data transformations for stress-testing algorithms on unknown-LID datasets

The authors introduce controlled transformations (Monotonic Embedding, Ambient Space Extension, Auxiliary Dimension Injection, and Manifold Synthesis) that enable stress-testing of algorithms on datasets with unknown LID by evaluating performance before and after transformation and comparing to ground-truth LID differences imposed by the transformations.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Principled benchmarking framework for LID estimation across domains

The authors develop a framework that transforms the same manifold into multiple domain representations while preserving its structure. This enables controlled cross-architecture testing and reveals that validation on simple synthetic manifolds does not guarantee similar performance across different domain networks.

Contribution

Harder variants of existing datasets targeting key manifold properties

The authors design more challenging versions of datasets from prior literature that specifically target key manifold characteristics such as non-uniform density, curvature, boundaries, thin manifolds, and nearby manifolds. These variants expose significant limitations in state-of-the-art LID estimation methods.

Contribution

Data transformations for stress-testing algorithms on unknown-LID datasets

The authors introduce controlled transformations (Monotonic Embedding, Ambient Space Extension, Auxiliary Dimension Injection, and Manifold Synthesis) that enable stress-testing of algorithms on datasets with unknown LID by evaluating performance before and after transformation and comparing to ground-truth LID differences imposed by the transformations.

Table of Contents