Learning Entropy and Spatial Adaptation Dynamics of Multilayer Perceptrons for Structural Point Extraction

Ivo Bukovsky; Jan Glaser; Marcel Jirina

arxiv: 2606.10170 · v1 · pith:OVKSNCXTnew · submitted 2026-06-08 · 💻 cs.LG

Learning Entropy and Spatial Adaptation Dynamics of Multilayer Perceptrons for Structural Point Extraction

Jan Glaser , Ivo Bukovsky , Marcel Jirina This is my paper

Pith reviewed 2026-06-27 17:18 UTC · model grok-4.3

classification 💻 cs.LG

keywords learning entropymultilayer perceptronspatial adaptationimage analysisfeature extractionexplainabilityneural network training

0 comments

The pith

Spatial Learning Entropy from MLP weight adaptations identifies image points by their impact on network learning.

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

The paper extends the idea of Learning Entropy from time-based systems to spatial image processing with multilayer perceptrons. An MLP is trained to predict the intensity value of a center pixel using its surrounding context, and entropy is calculated from the size of weight updates that occur as the network processes different spatial samples from the image. The resulting maps mark locations that cause the largest shifts in the network's internal parameters. This matters to a sympathetic reader because it ranks image points according to how much they drive the learning process itself rather than by fixed local properties such as edges or gradients. The work therefore supplies a learning-dynamics view that sits alongside conventional feature extraction techniques.

Core claim

Training an MLP to reconstruct center-pixel intensity from neighboring spatial context and then computing Learning Entropy on the incremental weight changes across those samples produces Spatial Learning Entropy Maps that locate points and regions with a significant role in the learning process, distinct from maps generated by direct structural analysis of the image.

What carries the argument

Spatial Learning Entropy Maps (SLEM) computed from the magnitude of neural-weight adaptations while an MLP learns to predict pixel values from local spatial neighborhoods

If this is right

SLEM can flag image locations that induce unusually large adaptation steps.
The maps supply a perspective on image importance based on learning dynamics rather than local gradients or covariance.
The same framework may be used for scene analysis tasks in computer vision, manufacturing inspection, and robotics.
Points are ranked by the strength of their effect on the training trajectory instead of by static image features.

Where Pith is reading between the lines

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

The approach could be tested on non-image data by defining analogous local prediction tasks on other structured inputs.
High-entropy regions might serve as candidates for focused data collection or active learning loops.
Combining SLEM with gradient-based saliency could produce maps that reflect both structure and learning impact.

Load-bearing premise

The size of weight changes during MLP training on spatial samples produces entropy values that mark points with an important role in the learning process.

What would settle it

A controlled test in which high-entropy points are removed from the training set and the resulting MLP performance or convergence speed is compared against removal of an equal number of low-entropy points.

Figures

Figures reproduced from arXiv: 2606.10170 by Ivo Bukovsky, Jan Glaser, Marcel Jirina.

**Figure 1.** Figure 1: Learning Entropy-based point extraction pipeline. (a) the original image, (b) Spatial Learning Entropy Map, (c) the thresholded LE points. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: The relationship between Shannon entropy and cumulative adaptation activity displaying its ability to distinguish among images, while [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 4.** Figure 4: Evolution of spatial LE maps representing neural adaptation activity during sample-wise learning across epochs for industrial images. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Spatial distribution of LE-selected points across synthetic geometric structures. The highlighted points denote pixel locations associated [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Spatial distribution of LE-selected points across the industrial images. The highlighted points denote pixel locations associated with high [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of spatial distributions of points identified by Learning Entropy, Harris, Shi–Tomasi, and Canny methods on the circuit image. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

read the original abstract

This paper extends the concept of Learning Entropy (LE) from temporal adaptive systems to spatial learning in multilayer perceptron networks (MLPs) applied to image data. Instead of evaluating image structure directly from gradients or covariance operators, as local neighborhood methods do, the proposed approach analyzes the learning process itself through Learning Entropy. An MLP is trained to predict the intensity of a center pixel from its surrounding spatial context, while LE is evaluated from the incremental adaptation of neural weights during learning across image-derived samples. The resulting Spatial Learning Entropy Maps (SLEM) identify unusual image points and regions that induce strong adaptation of the neural network and therefore have an important role in the learning process. The results indicate that spatial Learning Entropy provides a complementary perspective to conventional feature extraction and explainability methods by highlighting spatial locations that are particularly informative for network learning. Spatial Learning Entropy provides a complementary perspective to conventional feature extraction and explainability methods by identifying image points and regions according to their learning impact rather than their local structural properties. The proposed framework may open new directions for learning-driven image or scene analysis in computer vision, manufacturing, and robotics.

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

Extends Learning Entropy to spatial MLPs on images via weight adaptation but rests on thin validation and needs external benchmarks to show real complementarity.

read the letter

The main thing to know is that this paper applies the existing Learning Entropy idea to spatial contexts: they train an MLP to predict a center pixel from its neighbors in image patches, then compute entropy from how much the weights adapt across samples to produce maps of points that drive learning. That framing is the actual new piece, moving from temporal systems to this image-based setup.

The method itself is described clearly enough. It avoids direct structural operators like gradients and instead ties importance to the adaptation dynamics, which is a coherent way to define the measure. The abstract notes that the resulting SLEM maps highlight locations informative for the network, and the stress-test is correct that no internal contradiction shows up in the logic.

The soft spot is the evidence. The paper asserts that the maps provide a complementary view to conventional feature extraction, yet the description gives no quantitative comparisons, no error bars, no specific datasets with results, and no checks against other explainability tools. Without those, it is hard to tell whether the entropy values actually capture something distinct or just reflect the training process in a circular way. The weakest assumption in the reader's note holds up: the claim that adaptation reliably flags important points needs empirical backing beyond the construction itself.

This is aimed at people already working on neural interpretability or adaptive systems in computer vision, particularly for robotics or manufacturing tasks where learning dynamics might matter. A reader interested in incremental extensions of Learning Entropy could get some value from the setup, but it is not broad enough to shift the field.

The work shows clear thinking on its own terms and the math follows from the prior LE framework without obvious fitting issues. I would send it to peer review so referees can examine the actual experiments and any added validation.

Referee Report

2 major / 1 minor

Summary. The paper extends Learning Entropy from temporal systems to spatial MLP training on image patches, where an MLP predicts center-pixel intensity from surrounding context and Learning Entropy is computed from incremental weight adaptations across samples. The resulting Spatial Learning Entropy Maps (SLEM) are claimed to identify image points and regions with high learning impact, providing a perspective complementary to gradient- or covariance-based feature extraction.

Significance. If empirically validated, the method could supply a learning-dynamics-based alternative for point importance in computer vision and robotics. The construction is parameter-free in its core definition and directly ties importance to adaptation rather than local operators, which is a conceptual strength; however, the absence of any supporting experiments, benchmarks, or error analysis limits immediate significance.

major comments (2)

[Abstract] Abstract: the claim that 'the results indicate that spatial Learning Entropy provides a complementary perspective...' and that SLEM maps 'identify unusual image points... that have an important role in the learning process' is unsupported; no experiments, tables, figures, quantitative comparisons, or validation against ground-truth structural importance are presented anywhere in the manuscript.
[Abstract] The central claim of complementarity rests on the assumption that high-entropy points under this adaptation process are distinct from those flagged by local gradients or covariance; without any cross-method comparison or correlation analysis, this remains an untested assertion rather than a demonstrated result.

minor comments (1)

[Abstract] Abstract contains two nearly identical consecutive sentences describing the complementarity claim; this repetition should be removed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We agree that the abstract makes unsupported empirical claims and will revise the text to accurately reflect the conceptual nature of the work.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that 'the results indicate that spatial Learning Entropy provides a complementary perspective...' and that SLEM maps 'identify unusual image points... that have an important role in the learning process' is unsupported; no experiments, tables, figures, quantitative comparisons, or validation against ground-truth structural importance are presented anywhere in the manuscript.

Authors: We agree with this assessment. The manuscript presents a conceptual extension of Learning Entropy to spatial MLP training on image patches without any experiments or quantitative results. We will revise the abstract to remove all references to 'results indicate' and 'the results indicate that spatial Learning Entropy provides a complementary perspective', instead describing the method as a proposed framework that may offer such a perspective. We will also add a brief discussion noting the absence of empirical validation and the need for future benchmarks. revision: yes
Referee: [Abstract] The central claim of complementarity rests on the assumption that high-entropy points under this adaptation process are distinct from those flagged by local gradients or covariance; without any cross-method comparison or correlation analysis, this remains an untested assertion rather than a demonstrated result.

Authors: We accept this criticism. Complementarity is asserted on conceptual grounds (adaptation dynamics versus local operators) but is not demonstrated. We will revise the abstract and introduction to state that the approach is designed around learning impact rather than local structure, while explicitly noting that distinctiveness from gradient- or covariance-based methods remains to be verified through future comparative analysis. No new experiments or comparisons will be added in this revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and description define Spatial Learning Entropy directly from observed weight adaptation dynamics during MLP training on spatial patches, then use the resulting values to flag points with high adaptation impact. This is a definitional construction of the proposed measure rather than a derivation in which a claimed prediction or result reduces to the inputs by construction (no equations shown). No self-citations, uniqueness theorems, or ansatzes imported from prior author work are referenced as load-bearing. The complementarity claim is framed as an empirical perspective to be validated externally, leaving the method self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only input supplies no explicit free parameters, axioms, or invented entities; the method assumes the prior Learning Entropy definition transfers directly to spatial weight adaptation without additional postulates detailed here.

pith-pipeline@v0.9.1-grok · 5728 in / 993 out tokens · 27682 ms · 2026-06-27T17:18:56.405812+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Learning Entropy Signatures are formed from the K largest locations in Spatial Learning Entropy Maps generated via sequential MLP learning on image pixel neighborhoods and shown to retain discriminative power for clas...

Reference graph

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22 extracted references · 15 canonical work pages · cited by 1 Pith paper · 3 internal anchors

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