Diffusion-Based Feature Denoising with NNMF for Robust handwritten digit multi-class classification

Hiba Adil Al-kharsan; R\'obert Rajk\'o

arxiv: 2603.29917 · v3 · submitted 2026-03-31 · 💻 cs.CV

Diffusion-Based Feature Denoising with NNMF for Robust handwritten digit multi-class classification

Hiba Adil Al-kharsan , R\'obert Rajk\'o This is my paper

Pith reviewed 2026-05-14 21:01 UTC · model grok-4.3

classification 💻 cs.CV

keywords handwritten digit classificationdiffusion denoisingNNMFhybrid CNN featuresadversarial robustnessmulti-class classificationfeature space defense

0 comments

The pith

Diffusion denoising of hybrid NNMF-CNN features sustains robust multi-class handwritten digit classification under attack.

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

The paper extends an earlier two-class method to ten-class digit recognition by first building a hybrid feature vector: non-negative matrix factorization supplies interpretable parts-based components while a convolutional network supplies learned deep features. These combined vectors are then diffused by successively adding Gaussian noise in feature space, and a separate denoiser network is trained to recover the original clean vectors from the corrupted ones. The restored representations are passed to a classifier whose performance is measured on both clean data and inputs perturbed by AutoAttack. Experiments indicate that the diffusion-augmented hybrid model remains effective and retains strong accuracy even when attacked, although a plain CNN baseline still edges it out in raw performance. A sympathetic reader would care because the approach shows how a lightweight feature-space defense can be added to existing extractors to improve resilience without retraining the entire pipeline.

Core claim

Training a denoiser on gradually noised hybrid NNMF-CNN feature vectors allows recovery of clean representations from adversarially perturbed inputs, thereby preserving high multi-class classification accuracy on handwritten digits in both clean and attacked regimes.

What carries the argument

Hybrid feature representation formed by concatenating NNMF-derived interpretable components with CNN deep features, subjected to a diffusion process of added Gaussian noise and reversed by a trained feature denoiser before classification.

If this is right

The diffusion step in feature space extends the prior two-class framework to reliable ten-class digit recognition while preserving adversarial resistance.
Hybrid NNMF-CNN vectors cleaned by the denoiser support competitive accuracy against AutoAttack without retraining the base CNN.
Feature-level diffusion acts as an additive defense that leaves the original feature extractors unchanged.
The method maintains powerful classification performance in both baseline and adversarial multi-class settings.

Where Pith is reading between the lines

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

The same feature-space denoising might transfer to other image domains where adversarial robustness is required without full model retraining.
NNMF's parts-based decomposition could yield more interpretable denoised features than CNN representations alone.
Varying the noise schedule or testing stronger attacks would expose the operating range of this defense.

Load-bearing premise

A denoiser trained only on gradually noised versions of the hybrid features will reliably undo the effects of adversarial perturbations in the ten-class setting without introducing new errors.

What would settle it

A measurable drop in test-set accuracy under AutoAttack when the diffusion denoiser is added, compared with the undefended hybrid model, would falsify the robustness benefit.

read the original abstract

This work presents a robust multi-class classification framework for handwritten digits that combines diffusion-driven feature denoising with a hybrid feature representation. Inspired by our previous work on brain tumor classification, the proposed approach operates in a feature space to improve the robustness to noise and adversarial attacks. This manuscript is submitted as an extended abstract rather than a full-length press-ready paper. First, the input images are converted into tight, interpretable exemplification using Non-negative Matrix Factorization (NNMF). In parallel, special deep features are extracted using a computational neural network (CNN). These integral features are combined into a united hybrid representation. The main objective of this work is to extend our previously validated two-class framework to a multi-class handwritten digit classification scenario. To improve robustness, a step diffusion operation is used in the feature space by gradually adding Gaussian noise. A feature denoiser network is trained to reverse this operation and rebuild clean representations from tilted inputs. The courteous features are then applied for multi-class classification. The suggested method is evaluated in both baseline and adversarial settings using AutoAttack. The experimental outcome present that the diffusion-based hybrid model is both effective and robust, the CNN baseline models outperforming while maintain powerful classification performance. These results explain the activity of feature-level diffusion defense for reliable multi-class handwritten digit classification.

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

This is a straightforward extension of the authors' prior two-class work to ten-class MNIST using a hybrid NNMF-CNN feature space and a diffusion denoiser, but the abstract supplies no numbers, ablations, or clean-accuracy checks to support the robustness claim.

read the letter

The paper moves the authors' earlier brain-tumor setup to handwritten digits. They extract NNMF factors and CNN embeddings, combine them into a hybrid vector, add gradual Gaussian noise, train a denoiser to reverse it, and classify the cleaned features. The abstract states that this beats a plain CNN under AutoAttack while keeping strong performance, and it is explicit that the work is an extension rather than a new framework.

Referee Report

4 major / 2 minor

Summary. The manuscript proposes a hybrid feature representation combining Non-negative Matrix Factorization (NNMF) for interpretable exemplars with CNN-extracted deep features for multi-class handwritten digit classification. It extends a prior two-class framework by applying a diffusion process that gradually adds Gaussian noise in the hybrid feature space, training a denoiser network to recover clean representations from perturbed inputs, and using these for classification. The central claim is that this diffusion-based denoising yields a model that is both effective and more robust than CNN baselines under AutoAttack.

Significance. If the quantitative claims were supported, the approach could offer a feature-space defense mechanism that leverages the interpretability of NNMF alongside deep features and diffusion denoising for adversarial robustness in multi-class settings. However, the extended-abstract format provides no metrics, ablations, or error analysis, so the potential impact cannot be assessed from the current text.

major comments (4)

[Abstract] Abstract: the claim that the diffusion-based hybrid model outperforms CNN baselines under AutoAttack is unsupported by any accuracy values, tables, figures, or error bars; no quantitative comparison is presented.
[Method] Method description: the assumption that a denoiser trained on gradually added Gaussian noise in the NNMF-CNN feature space will reverse AutoAttack perturbations (which maximize cross-entropy) is not verified; no analysis of the alignment between Gaussian noise and adversarial directions in that specific feature space is given.
[Experiments] Experiments: no ablation studies isolate the denoiser’s contribution to robustness versus the hybrid representation alone, nor any evaluation of whether the denoiser introduces misclassifications on clean data (e.g., between confusable digits such as 4/9).
[Abstract] Abstract and method: dataset details (e.g., MNIST or variant, train/test splits, number of classes confirmed as 10), AutoAttack parameters (epsilon, number of iterations), and training protocol for the denoiser are absent, preventing reproducibility or verification of the multi-class extension.

minor comments (2)

[Abstract] Abstract contains unclear or erroneous phrasing: 'courteous features' appears to be a typo for 'clean features'; 'tilted inputs' is ambiguous (likely intended as 'noisy inputs'); 'present' should read 'presents'; 'explain the activity' is vague and should be replaced with a precise statement of demonstrated efficacy.
[Abstract] The manuscript is explicitly submitted as an extended abstract; for a journal venue, the text would need expansion to include full experimental sections, figures showing clean vs. adversarial accuracy, and comparison to other defenses.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive feedback on our extended abstract. We acknowledge that the current format omits quantitative details and will incorporate the requested elements in the full manuscript revision.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the diffusion-based hybrid model outperforms CNN baselines under AutoAttack is unsupported by any accuracy values, tables, figures, or error bars; no quantitative comparison is presented.

Authors: We agree that the extended abstract provides no numerical accuracy values or tables. The claim is supported by experiments in the full paper; we will add tables, figures, and error bars comparing the hybrid diffusion model to CNN baselines under AutoAttack in the revision. revision: yes
Referee: [Method] Method description: the assumption that a denoiser trained on gradually added Gaussian noise in the NNMF-CNN feature space will reverse AutoAttack perturbations (which maximize cross-entropy) is not verified; no analysis of the alignment between Gaussian noise and adversarial directions in that specific feature space is given.

Authors: The denoiser is trained to recover from Gaussian perturbations in feature space as a proxy for robustness. While explicit alignment analysis between Gaussian noise and AutoAttack directions is not provided in the extended abstract, we will add a discussion of the rationale and any observed empirical alignment in the revised manuscript. revision: partial
Referee: [Experiments] Experiments: no ablation studies isolate the denoiser’s contribution to robustness versus the hybrid representation alone, nor any evaluation of whether the denoiser introduces misclassifications on clean data (e.g., between confusable digits such as 4/9).

Authors: We accept that ablations are missing from the extended abstract. In the full revision we will add studies isolating the denoiser’s effect on robustness and report clean-data accuracy to confirm no increase in errors on confusable classes such as 4/9. revision: yes
Referee: [Abstract] Abstract and method: dataset details (e.g., MNIST or variant, train/test splits, number of classes confirmed as 10), AutoAttack parameters (epsilon, number of iterations), and training protocol for the denoiser are absent, preventing reproducibility or verification of the multi-class extension.

Authors: As this is an extended abstract, such details were omitted for length. The work uses standard MNIST (10 classes, conventional splits). We will include all reproducibility information—dataset specification, AutoAttack parameters, and denoiser training protocol—in the revised full manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The manuscript describes a hybrid NNMF-CNN feature pipeline, followed by training a denoiser on gradually added Gaussian noise in feature space and applying it to adversarial inputs. No equations, fitted parameters, or derivations are supplied that would make any claimed robustness or classification accuracy equivalent to its own inputs by construction. The reference to prior two-class brain-tumor work is presented only as inspirational context for extending the same pipeline to ten-class MNIST; the load-bearing steps (feature extraction, diffusion schedule, denoiser training, and AutoAttack evaluation) are defined and measured independently within this paper. Consequently the central claims rest on experimental outcomes rather than self-referential reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. NNMF interpretability and diffusion reversal are treated as standard domain assumptions.

axioms (2)

domain assumption NNMF yields tight, interpretable exemplifications of digit images
Invoked in the first processing step without further justification in the abstract.
domain assumption A feature-space diffusion process with Gaussian noise can be reversed by a trained denoiser to recover robust representations
Central to the defense mechanism; assumed to hold for hybrid features.

pith-pipeline@v0.9.0 · 5537 in / 1349 out tokens · 37363 ms · 2026-05-14T21:01:53.365906+00:00 · methodology

Review history (2 revisions) →

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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

a step diffusion operation is used in the feature space by gradually adding Gaussian noise. A feature denoiser network is trained to reverse this operation
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

hybrid feature representation... NNMF... CNN... AutoAttack

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.