arxiv: 2605.01874 · v1 · submitted 2026-05-03 · 💻 cs.LG · cs.AI

Recognition: unknown

Leveraging Data Symmetries to Select an Optimal Subset of Training Data under Label Noise

Kumar Shubham , Pavan Karjol , Kiran M K , Prathosh AP

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:19 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords label noisesubset selectionk-nearest neighborsdata symmetriesinvariant representationscutstatshigh-dimensional data

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The pith

Exploiting data symmetries improves k-NN accuracy for selecting low-noise subsets from label-corrupted training data even in high dimensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a subset of noisy training data exists on which models can perform as well as on clean data, and that the cutstats method identifies this subset by relying on k-NN accuracy. Standard k-NN degrades in high dimensions under noise, but the authors demonstrate that known data invariances and symmetries can be incorporated to raise k-NN performance toward the Bayes optimal classifier. When symmetries are only partially known, representations learned to be invariant still support identification of near-optimal subsets. This matters because it offers a route to effective training from large but imperfect real-world datasets without requiring exhaustive cleaning.

Core claim

In noisy label settings, the quality of the subset chosen by cutstats depends directly on k-NN accuracy. Incorporating knowledge of underlying data invariances and symmetries raises k-NN performance sufficiently close to Bayes optimality that the selected subset supports model accuracy comparable to noise-free training, and this holds in high-dimensional regimes. When only partial symmetry information is available, invariant representations learned from the data still enable selection of near-optimal subsets.

What carries the argument

The cutstats subset-selection procedure, which uses k-NN to identify low-noise samples, made more accurate by explicit use of data invariances or by learned invariant representations.

If this is right

Models trained on the symmetry-selected subset reach performance levels comparable to those obtained from fully clean data.
The improvement in k-NN accuracy extends the usefulness of cutstats to high-dimensional regimes where it would otherwise fail.
Learned invariant representations suffice for near-optimal subset selection even when full knowledge of the symmetries is unavailable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same symmetry-based correction could be applied to other distance-based noise filters beyond cutstats.
Domains that already encode symmetries explicitly, such as image data under geometric transformations, may obtain the gains without additional representation learning.
The approach supplies a concrete way to test whether invariance information can substitute for larger volumes of clean labels in practical pipelines.

Load-bearing premise

The data contain exploitable invariances or symmetries that can be known or learned accurately enough to improve neighbor selection without adding new errors.

What would settle it

On a dataset with verifiable symmetries and controlled label noise, applying symmetry-aware k-NN yields no improvement in the quality of the cutstats-selected subset compared with ordinary k-NN.

Figures

Figures reproduced from arXiv: 2605.01874 by Kiran M K, Kumar Shubham, Pavan Karjol, Prathosh AP.

read the original abstract

The performance of machine learning models often relies on large labeled datasets; however, data collected from diverse sources can contain label noise. Recent work has shown that, in noisy settings, there may exist a subset of the training data on which models can achieve performance comparable to training on a noise-free dataset. A widely used method for identifying such subsets is cutstats, which employs k-nearest neighbors (k-NN) to detect low-noise samples. However, its performance on high-dimensional data remains largely unexplored. In this work, we formally establish that the performance of a classifier trained on a subset of a noisy dataset selected via cutstats is influenced by the accuracy of k-NN. We further demonstrate that, in noisy environments, exploiting data invariance and knowledge of underlying symmetries can significantly enhance the performance of k-NN, bringing it closer to the Bayes optimal classifier even in high-dimensional regimes. Finally, we show that for real-world scenarios, where information about the underlying invariance is only partially known, learnt invariant representations can still facilitate the identification of near-optimal subsets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Symmetries can sharpen k-NN for clean subset selection under label noise, but the learned representation case needs tighter validation against noise leakage.

read the letter

This paper builds on cutstats by using data symmetries to make k-NN better at picking low-noise training samples, even when the data is high-dimensional. They also handle the case where symmetries are only partially known by learning invariant representations. The strongest part is the formal argument that the final model's performance on the selected subset depends directly on how accurate the k-NN is. That gives a clean reason to focus on improving the neighbor search. They show that exploiting invariances brings k-NN closer to Bayes optimal, which is a nice theoretical touch. For the practical side, demonstrating that learned representations can still help when full symmetry knowledge is missing is useful. The experiments appear to show improvements in subset quality and downstream accuracy. This kind of targeted fix for noisy labels is the sort of thing that can save labeling effort in applied ML. The soft spot is in the learned representations. Since those are trained on the noisy data, label errors could easily carry over into the metric that k-NN uses. The paper claims this still works, but it would be stronger with explicit tests showing the representation doesn't degrade under increasing noise levels or comparisons to methods that denoise first. If that step fails, the whole pipeline could underperform plain cutstats. The math and citations look standard and appropriate for this area. No obvious circularity or invented quantities. This is for researchers working on robust training with noisy supervision. A reader interested in practical subset selection methods would get value from the symmetry angle and the high-dim results. I would send it to peer review. The idea is clear, the problem matters, and the experiments can be checked and extended. Some revision on the representation robustness would be expected, but it's worth the referee time.

Referee Report

2 major / 2 minor

Summary. The paper claims that the performance of a classifier trained on a cutstats-selected subset from a noisy dataset is formally influenced by the accuracy of the underlying k-NN classifier. It further claims that exploiting known data invariances and symmetries improves k-NN accuracy toward Bayes optimality even in high dimensions, and that learned invariant representations can still enable near-optimal subset selection when symmetry information is only partial.

Significance. If the formal link and the symmetry-based improvements hold under the stated conditions, the work could meaningfully advance label-noise mitigation techniques by incorporating domain symmetries into data selection, which is relevant for high-dimensional data where standard k-NN degrades. The explicit connection to Bayes optimality and the handling of partial symmetry knowledge are potentially useful extensions of prior cutstats methods.

major comments (2)

[Theoretical analysis / formal establishment] The formal establishment that cutstats subset quality is governed by k-NN accuracy (abstract and theoretical section) does not explicitly address whether this link remains valid when k-NN operates in a representation space learned from the same noisy labels; any embedding of label errors into the metric would directly affect the subset selection quality.
[Learned invariant representations section] In the discussion of learnt invariant representations for partial symmetry knowledge, the manuscript provides no analysis, bound, or experiment demonstrating that the representation learner itself is robust to label noise (i.e., does not propagate errors into the distance metric used by k-NN). This is load-bearing for the real-world claim and directly engages the concern that learned representations may degrade rather than improve selection.

minor comments (2)

[Abstract] The abstract introduces 'cutstats' without a one-sentence definition or citation; adding this would improve accessibility for readers unfamiliar with the baseline method.
[Notation and preliminaries] Notation for the symmetry transformations and the learned representation function should be introduced consistently in the main text and aligned with any equations in the theoretical section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments identify important gaps in the explicit treatment of learned representations within our theoretical claims and empirical analysis. We address each point below and will revise the manuscript to incorporate the requested clarifications and additional experiments.

read point-by-point responses

Referee: [Theoretical analysis / formal establishment] The formal establishment that cutstats subset quality is governed by k-NN accuracy (abstract and theoretical section) does not explicitly address whether this link remains valid when k-NN operates in a representation space learned from the same noisy labels; any embedding of label errors into the metric would directly affect the subset selection quality.

Authors: Our formal result establishes that the quality of the cutstats-selected subset is governed by the accuracy of the k-NN classifier in the metric space used for neighbor search. The derivation is general and therefore applies to any metric space, including one obtained via a representation learned from the data. We agree that the manuscript does not explicitly state this applicability or discuss the consequences when label noise influences the learned metric. In the revision we will add a clarifying paragraph in the theoretical section noting that the formal link continues to hold in learned spaces and that subset quality will then be determined by the effective k-NN accuracy achieved in that space. revision: yes
Referee: [Learned invariant representations section] In the discussion of learnt invariant representations for partial symmetry knowledge, the manuscript provides no analysis, bound, or experiment demonstrating that the representation learner itself is robust to label noise (i.e., does not propagate errors into the distance metric used by k-NN). This is load-bearing for the real-world claim and directly engages the concern that learned representations may degrade rather than improve selection.

Authors: We acknowledge that the current manuscript lacks a dedicated robustness analysis or bounds for the representation learner under label noise. While the reported experiments show performance gains when learned invariant representations are used, they do not isolate the effect of noisy labels on the learner itself. In the revised version we will add experiments that train the representation model on the noisy labels, quantify the resulting changes to the distance metric, and measure the downstream impact on k-NN accuracy and subset selection quality. We will also include a brief discussion of conditions (e.g., self-supervised or augmentation-based invariance learning) under which such learners are expected to remain relatively robust. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation chain is self-contained against external benchmarks

full rationale

The abstract and described claims establish a formal link between cutstats subset quality and k-NN accuracy, then argue that known or learned symmetries improve k-NN toward Bayes optimality. No equations, fitted parameters, or self-referential definitions are present that would reduce any prediction to an input by construction. No self-citation chains, uniqueness theorems from the same authors, or ansatzes smuggled via prior work are invoked in the provided text. The central steps reference independent external concepts (k-NN, Bayes classifier, data invariances) without visible reduction to the paper's own fitted values or definitions. This is the normal case of a non-circular paper whose claims remain open to external verification.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities. The central claims rest on standard assumptions about data symmetries existing in the domain and k-NN being a reasonable base method.

pith-pipeline@v0.9.0 · 5495 in / 1184 out tokens · 42720 ms · 2026-05-10T16:19:07.741672+00:00 · methodology

discussion (0)

Reference graph

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