TopoPrune: Robust Data Pruning via Unified Latent Space Topology

Arjun Roy; Kaushik Roy; Manish Nagaraj; Prajna G. Malettira

arxiv: 2602.02739 · v2 · submitted 2026-02-02 · 💻 cs.LG · cs.AI

TopoPrune: Robust Data Pruning via Unified Latent Space Topology

Arjun Roy , Prajna G. Malettira , Manish Nagaraj , Kaushik Roy This is my paper

Pith reviewed 2026-05-16 08:06 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords data pruningpersistent homologytopological data analysislatent embeddingsdataset reductionrobustnesstransferabilitymanifold approximation

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The pith

Topology-based pruning on latent embeddings ranks samples by structural complexity to enable stable high-ratio dataset reduction.

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

The paper seeks to replace unstable geometric pruning with a topological alternative that treats the latent space as having intrinsic stable structure rather than relying on fragile distance measurements. Geometric approaches degrade when embeddings are perturbed or when the pruning method is applied to a new network architecture, whereas topology is designed to remain invariant under small deformations. TopoPrune first builds a global low-dimensional embedding via a topology-aware manifold approximation, then applies differentiable persistent homology locally to score each point by its structural complexity and remove the least complex ones. If the approach holds, large-scale dataset reduction becomes practical without repeated architecture-specific tuning or sensitivity to feature noise.

Core claim

TopoPrune establishes a unified dual-scale topological framework that first utilizes a topology-aware manifold approximation to establish a global low-dimensional embedding of the dataset and subsequently employs differentiable persistent homology to perform a local topological optimization on the manifold embeddings, ranking samples by their structural complexity. This produces high accuracy and precision at significant pruning rates such as 90 percent, together with robustness to noise perturbations of latent feature embeddings and superior transferability across diverse network architectures.

What carries the argument

Dual-scale topological optimization: a topology-aware manifold approximation that produces a global low-dimensional embedding, followed by differentiable persistent homology that ranks embedded points by structural complexity.

If this is right

Pruning rates of 90 percent become feasible while preserving high accuracy and precision.
Performance remains stable under noise added to latent feature embeddings.
The same pruning procedure transfers effectively to networks with different architectures.
Data-efficient learning can be grounded in topology rather than geometry for greater reliability.

Where Pith is reading between the lines

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

The same two-scale topological ranking could be applied to active learning or core-set selection tasks that currently rely on distance-based scores.
If the method works on image embeddings, an immediate extension would be to test whether it produces comparable gains on text or graph embeddings without retraining the pruner.
Persistent homology scores might serve as a drop-in replacement for uncertainty or diversity heuristics in other data-selection pipelines.
The observed cross-architecture stability suggests that one pruned subset could be reused across an entire model family, reducing the computational cost of repeated pruning experiments.

Load-bearing premise

A topology-aware manifold approximation combined with differentiable persistent homology can reliably rank samples by structural complexity and outperform extrinsic geometric methods in stability and transfer.

What would settle it

A head-to-head test on the same noisy latent embeddings from two different architectures where a standard geometric pruner achieves higher final test accuracy than TopoPrune at a 90 percent pruning ratio.

read the original abstract

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade during cross-architecture transfer or in the presence of feature noise. We introduce TopoPrune, a framework which resolves this challenge by leveraging topology to capture the stable, intrinsic structure of data. TopoPrune operates at two scales, (1) utilizing a topology-aware manifold approximation to establish a global low-dimensional embedding of the dataset. Subsequently, (2) it employs differentiable persistent homology to perform a local topological optimization on the manifold embeddings, ranking samples by their structural complexity. We demonstrate that our unified dual-scale topological approach ensures high accuracy and precision, particularly at significant dataset pruning rates (e.g., 90%). Furthermore, through the inherent stability properties of topology, TopoPrune is (a) exceptionally robust to noise perturbations of latent feature embeddings and (b) demonstrates superior transferability across diverse network architectures. This study demonstrates a promising avenue towards stable and principled topology-based frameworks for robust data-efficient learning.

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

TopoPrune pairs a topology-aware manifold step with differentiable persistent homology to rank and prune samples, aiming for stability where pure geometric pruning breaks.

read the letter

The paper's core move is to treat data pruning as a topological problem rather than a purely geometric one. It first builds a low-dimensional embedding that respects the data's manifold structure, then applies differentiable persistent homology on those embeddings to score samples by local structural complexity and decide what to keep. This dual-scale setup is the concrete novelty, and it rests on the known bottleneck stability of persistent homology to argue for resistance to noise in the latent features and better behavior when the underlying network changes. That framing is clear and directly targets a documented weakness in existing pruning work that relies on extrinsic distances or angles. The abstract does a straightforward job laying out why those methods degrade under perturbation or transfer, and the topological alternative follows logically from standard TDA results without obvious internal contradictions. The stress-test note is right that no hidden inconsistency appears in the construction itself. What remains thin is the experimental side. Claims of strong accuracy at 90% pruning, noise robustness, and cross-architecture gains are stated at a high level, but without seeing the actual numbers, baselines, controls, or ablations on each scale it is hard to judge effect size or whether the differentiability approximations preserve enough of the theoretical guarantees. The manifold approximation step could also introduce its own sensitivities if the topology preservation is not tight. This is the kind of paper that belongs in the data-efficient training literature. People working on pruning for large models or on topological methods in ML would get value from the framing and the proposed pipeline, even if they end up adapting pieces rather than using the whole thing. It is coherent enough on its own terms to deserve referee time rather than a desk reject, mainly because the motivation is practical and the topological grounding is real. I would send it for review but flag the need for fuller experimental reporting and checks on the differentiable homology implementation.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces TopoPrune, a data pruning framework that operates at two scales in latent space: a topology-aware manifold approximation for global low-dimensional embedding, followed by differentiable persistent homology for local optimization that ranks samples by structural complexity. The central claim is that this unified topological approach delivers high accuracy and precision at aggressive pruning rates (e.g., 90%), exceptional robustness to noise perturbations in feature embeddings, and superior transferability across network architectures, outperforming extrinsic geometric methods due to the stability properties of topology.

Significance. If the empirical results and stability arguments hold, the work would supply a topology-grounded alternative to geometric pruning that could improve data efficiency and cross-architecture reliability in large-scale training. The explicit appeal to bottleneck stability of persistent homology and the dual-scale construction constitute a clear methodological contribution if supported by reproducible experiments.

major comments (1)

The abstract states that the method 'ensures high accuracy and precision, particularly at significant dataset pruning rates (e.g., 90%)' and is 'exceptionally robust to noise perturbations,' yet no quantitative metrics, baseline comparisons, ablation controls, or error bars are referenced. Without these, the load-bearing performance claims cannot be evaluated.

minor comments (1)

The description of the 'topology-aware manifold approximation' and the precise formulation of the differentiable persistent homology loss would benefit from an explicit equation or pseudocode block to clarify how the ranking by structural complexity is computed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and for highlighting the need for clearer support of the performance claims. We address the single major comment below.

read point-by-point responses

Referee: The abstract states that the method 'ensures high accuracy and precision, particularly at significant dataset pruning rates (e.g., 90%)' and is 'exceptionally robust to noise perturbations,' yet no quantitative metrics, baseline comparisons, ablation controls, or error bars are referenced. Without these, the load-bearing performance claims cannot be evaluated.

Authors: We agree that the abstract would be strengthened by directly referencing quantitative results. The full manuscript reports these metrics in Section 4 (Experiments), including accuracy retention at 90% pruning rates, comparisons against geometric and random baselines, ablations isolating the manifold embedding and persistent homology stages, and error bars computed over multiple random seeds and noise levels. To resolve the concern, we will revise the abstract to incorporate specific numbers and references to these results (e.g., accuracy at aggressive pruning rates and measured degradation under feature noise). revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard topological properties

full rationale

The paper's central pipeline—topology-aware manifold approximation followed by differentiable persistent homology for sample ranking—draws on established stability theorems of persistent homology (e.g., bottleneck distance) and manifold learning techniques that are independent of the target pruning task. No equation reduces a prediction to a fitted parameter by construction, no load-bearing claim rests solely on self-citation, and no ansatz is smuggled via prior work by the same authors. The abstract and method description treat topological stability as an external mathematical fact rather than a derived result internal to the pruning objective. This is the expected honest non-finding for a method paper that applies known tools without redefining them in terms of the output metric.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that topology provides stable intrinsic structure where extrinsic geometry fails, plus the technical premise that differentiable persistent homology can optimize and rank samples on manifold embeddings.

axioms (1)

domain assumption Topology captures the stable, intrinsic structure of data better than extrinsic geometry for pruning purposes.
Invoked in abstract to explain why geometric methods are unstable and why the topological approach resolves the challenge.

pith-pipeline@v0.9.0 · 5502 in / 1213 out tokens · 52733 ms · 2026-05-16T08:06:40.241692+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

employs differentiable persistent homology to perform a local topological optimization on the manifold embeddings, ranking samples by their structural complexity... through the inherent stability properties of topology

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