Pith. sign in

REVIEW 5 major objections 8 minor 24 references

Semantic-space trajectory networks show that training on real labels builds denser, more centralized learning graphs than training on shuffled labels.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-31 00:39 UTC pith:LHDACGK2

load-bearing objection Useful cross-algorithm STN construction, but the headline funnel-vs-star claim for real vs shuffled labels collides with the paper’s own near-perfect train fits. the 5 major comments →

arxiv 2607.25122 v1 pith:LHDACGK2 submitted 2026-07-27 cs.LG

Semantic Space Search Trajectory Networks

Julian Agudelo , Alberto Tonda , Gabriela Ochoa , Vincent Guigue , Cristina Manfredotti , Evelyne Lutton This is my paper
classification cs.LG
keywords Search Trajectory NetworksSemantic spaceMachine LearningDeep Neural NetworksGeneralizationLabel randomizationAgglomerative clustering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Training a model is a path through candidate predictors. This paper builds graphs of those paths not in parameter space but in semantic space: the space of a model’s predictions on a fixed sample set. Prediction vectors are discretized and clustered into nodes, so any learner—neural net, boosted trees, or symbolic regression—can be placed on the same map and compared. On standard classification and regression tasks the graphs recover familiar differences: gradient methods funnel toward shared attractors, while symbolic regression stays more exploratory. When the same networks are trained on real versus fully shuffled labels, the graphs diverge in a consistent way: real labels yield denser, more efficient, more centralized networks; shuffled labels yield sparse, star-like, fragmented ones. Progressive label corruption smoothly turns the first pattern into the second. The result is a behavioral reading of generalization rooted in how algorithms and data jointly shape the path of predictions.

Core claim

Semantic space Search Trajectory Networks capture functional training dynamics from the interaction of learning algorithms and data. Across datasets, networks trained on real labels produce consistently denser, more efficient, and more centralized STNs than the same models trained on shuffled labels, separating generalization-like from memorization-like regimes by graph structure, while also recovering known qualitative differences among algorithm families.

What carries the argument

Semantic Space STNs: each model is a semantic vector of its predictions on a fixed sample set; vectors are discretized (argmax for classification, global quantile bins for regression) and aggregated into nodes by agglomerative clustering with complete linkage under normalized Hamming distance; directed edges count transitions across runs.

Load-bearing premise

The method assumes that clustering prediction vectors with a chosen distance threshold groups them into nodes that mark real stable functional states of learning, not artifacts of discretization or of how that threshold is set.

What would settle it

If changing the clustering threshold or the number of regression bins erased the density, efficiency, and centrality gaps between real-label and shuffled-label STNs—or flipped funnel topologies under real labels into star topologies and vice versa—the claimed structural signature of generalization would fail.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Heterogeneous learners can be compared on one semantic STN without aligning parameters or architectures.
  • Graph density, global efficiency, and centrality can serve as behavioral markers of generalization-like versus memorization-like training.
  • Progressive destruction of label structure should monotonically degrade those markers from funnel-like to isolated trajectories.
  • The same maps can expose basins, shared attractors, and exploratory versus gradient-like search across algorithm families.
  • Automating the clustering threshold would turn the construction into a routine diagnostic of training regimes.

Where Pith is reading between the lines

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

  • Semantic STN descriptors could be checked for correlation with flatness, mode-connectivity, or PAC-Bayes style generalization measures and used as cheap trajectory-level proxies.
  • The funnel-versus-star contrast may appear under milder breaks of input–label structure (partial noise, shift) without full shuffling.
  • If semantic trajectories are more stable under reparameterization than weight trajectories, STNs could help explain why distant parameter minima often generalize similarly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 8 minor

Summary. The manuscript introduces Semantic Space Search Trajectory Networks (SS-STNs), a method for building Search Trajectory Networks in the space of model predictions on a fixed sample set rather than in parameter/solution space. Semantic vectors are discretized (argmax labels for classification, global quantile bins for regression) and aggregated into nodes via agglomerative clustering with complete linkage under normalized Hamming distance, with a single threshold τ controlling granularity. The authors apply the method to MLPs, XGBoost, and symbolic regression on OpenML classification and regression benchmarks, recovering known qualitative differences between algorithm families, and then use it to contrast standard MLP training with the label-randomization regime of Zhang et al. (2017). The headline result is that real-label training yields denser, more efficient, more centralized (funnel-like) STNs, while shuffled-label training yields sparse, star-like STNs with isolated trajectories; a progressive label-corruption sweep on MNIST shows monotonic degradation of global efficiency, closeness, and PageRank. Code is publicly released.

Significance. If the results hold, the paper makes a useful methodological contribution: STNs have been largely confined to low-dimensional or combinatorial search spaces, and a clustering-based location function in semantic space genuinely extends the tool to modern iterative learners while enabling cross-algorithm comparison on a common representation. The work ships several properties I weight positively: public reproducible code; a nearly parameter-free construction (a single threshold τ, with a granularity study in Fig. 3); a run-count robustness check (Fig. 4); an external experimental contrast (real vs. shuffled labels) rather than a self-referential metric; and a falsifiable, monotone dose–response pattern across the corruption sweep (Fig. 6) that is consistent in direction across all seven datasets in Table 4. The behavioral (prediction-space) view of generalization is a legitimate complement to loss-landscape analyses and of interest to both the EC/fitness-landscape and ML communities. However, the central qualitative claim of §5 currently rests on a characterization that appears inconsistent with the paper's own convergence numbers, and the quantitative separation is reported without

major comments (5)
  1. [§5, Fig. 5 vs. Table 5 (Appendix B)] The headline qualitative claim — shuffled labels yield star-shaped STNs whose runs 'converge to isolated end nodes' (§5, STNs Analysis; Fig. 5 caption: 'Shuffled labels yield isolated trajectories') — appears contradicted by the paper's own numbers. Semantic vectors are training-set predictions (§3; Table 1), and Table 5 reports final shuffled-regime train accuracy of 1.000±0.000 (CIFAR-10), 0.999 (Bioresponse), 0.994 (MNIST, Fashion-MNIST). Since the permutation is drawn once and shared across runs, terminal semantic vectors in the shuffled condition are (near-)identical across runs: for CIFAR-10 the pairwise normalized Hamming distance is exactly 0, and for MNIST it is bounded by ~0.012 ≪ τ=0.1. Complete-linkage agglomerative clustering must therefore merge all shuffled-regime terminal vectors into a single node at the stated τ values, producing disjoint paths that merge into one share
  2. [§5, Table 4 and preceding paragraph] The metric set in Table 4 was selected post hoc: 'we computed a broad collection of classical graph-theoretic descriptors. We, then, examined which measures most consistently differentiate the resulting networks' and report 'a subset of metrics exhibiting the strongest separation.' This is a selection-on-the-outcome procedure: with enough candidate descriptors, some will separate any two conditions. The claim that graph descriptors 'cleanly separate' the regimes therefore needs (a) the full list of computed descriptors with their values for both conditions, not only the strongest separators, and/or (b) a multiple-comparison correction or a held-out confirmation (e.g., select descriptors on a subset of datasets, evaluate on the rest). Relatedly, each cell of Table 4 is a point value from a single aggregated network; with R=20 runs the authors can and should bootstrap over runs (or jackkni
  3. [§5, Figs. 5–6 and Table 4; §3] No sensitivity analysis supports the headline comparison. τ is chosen manually per dataset 'for readability' (Fig. 1 caption; §3), and Table 4 / Fig. 6 report the real-vs-shuffled separation and the corruption sweep at a single τ per dataset. Since τ controls node granularity and hence every reported graph metric, the paper should show that the direction of the separation (density, efficiency, centrality: real > shuffled) and the monotonic degradation in Fig. 6 persist across a range of τ values, not only at the chosen one. Similarly, the shuffled condition uses a single stored permutation per dataset and the corruption sweep a single stored draw per p; the robustness of Table 4 and Fig. 6 to resampling the permutation/corruption should be checked, since run-to-run seed variation does not probe this source of variance at all.
  4. [§5, Table 4] The reported separation may be partly a graph-size artifact rather than a regime signature. Density and global efficiency decrease mechanically with node count, and the shuffled condition plausibly generates larger graphs (memorization takes longer per Zhang et al., and disjoint trajectories visit more distinct semantic states), while real-label runs quickly collapse onto shared states, yielding small, dense graphs by construction. The paper reports neither |N| and |E| per condition nor trajectory lengths, so the reader cannot tell whether the metric gaps reflect topology or merely size. Please report node/edge counts and trajectory-length statistics for both conditions, and add a size-controlled comparison (e.g., normalize metrics against degree-preserving randomized baselines of the same size, or compare at matched |N| via τ adjustment) to establish that the separation is structural.
  5. [§5 and Abstract/Conclusions] The generalization claims are calibrated beyond the evidence. All of §5 uses a single shallow MLP (3×512, SGD, no regularization variation) at modest performance (e.g., 49% on CIFAR-10, Table 3), yet the abstract and §5 frame the result as characterizing 'neural network generalization' and 'offering an alternative perspective on the study of generalization.' The Zhang et al. regime is famously architecture- and optimizer-sensitive; whether the funnel/star contrast survives depth, width, weight decay, batch size, or a second architecture family is unknown. Either temper the claims to the studied setting or add at least one additional architecture/optimizer condition. This is a claim-calibration issue, not a correctness issue, but it touches the paper's third stated contribution.
minor comments (8)
  1. [§3] The statement that 'the only hyperparameter in this methodology is the threshold τ' is inaccurate: the regression pipeline introduces the quantile bin count (10, Fig. 2 caption), and the classification pipeline fixes argmax discretization. Please qualify the claim.
  2. [Figures 1–12] τ is rendered as '¿' in every figure label (e.g., '¿ = 0:1'), apparently a font/encoding problem; colons in decimal numbers ('0:1') also appear. Please fix for the final version.
  3. [§3, notation] The trajectory-set notation '{⟨ŷ0,...,ŷT⟩(r)}r=R r=1' is garbled; presumably r = 1,…,R. Also, N is overloaded for sample count, node set, and semantic dimension at various points.
  4. [Fig. 11 (Appendix C)] The regression panels are labeled 'Accuracy (better = higher)'; this should be R².
  5. [Appendix A.2] Global efficiency on a directed STN with unreachable pairs: please state how disconnected ordered pairs are handled (distance = ∞ contributes 0?) and whether shortest paths respect edge direction, since trajectories are directed.
  6. [References] Reference [7] (Fenoglio et al.) carries the DOI/arXiv identifier 10.48550/arXiv.1504.04909, which is the MAP-Elites paper (Mouret & Clune), not the cited work — likely a copy-paste error. Reference [14] uses the same arXiv number, confirming the mix-up.
  7. [§4, Fig. 4] The robustness-to-run-count check is shown only for the real-label regime on two dataset/algorithm pairs; a one-line confirmation that the shuffled-regime networks are similarly stable would strengthen §5, where R=20 is used.
  8. [§5, Experimental setup] For regression, please state explicitly how 'shuffled labels' are constructed (permutation of continuous targets?) and how the quantile discretization interacts with a permuted target vector.

Circularity Check

0 steps flagged

No significant circularity: empirical STN construction and graph metrics do not force the real-vs-shuffled structural claims by definition.

full rationale

The paper is a methods-plus-empirics contribution, not a first-principles derivation. Semantic-space STNs are built by discretizing prediction vectors, agglomerative clustering under normalized Hamming distance with threshold τ, and counting observed transitions; graph density, global efficiency, closeness, PageRank, and degree statistics are then standard descriptors of the resulting digraphs. The central claim—that real-label training yields denser, more efficient, more centralized STNs than shuffled-label training—is an experimental contrast (Zhang et al. randomization regime) measured after construction, not a quantity defined in terms of the conclusion and rediscovered. τ is chosen manually for readability but held fixed within each dataset across the real/shuffled pair, so the comparison is not a fitted-input-called-prediction. Citations to prior STN work (including co-author Ochoa) and to semantic GP supply background methodology; they do not import a uniqueness theorem that forces the funnel-vs-star or density gaps. Post-hoc narrative linking denser graphs to an “underlying function” is interpretive, not a self-definitional step. Any internal tension about whether complete-linkage clustering should merge shuffled terminals (a correctness/consistency concern) is outside the circularity criteria. No step reduces Eq./claim X to its own inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The central claims rest on treating prediction vectors as the right state space, Hamming-after-discretization as the right similarity, and one clustering threshold as defining comparable nodes across runs and algorithms. Algorithm hyperparameters and bin counts are fixed design choices; τ is the load-bearing free knob. No new physical entities are postulated—only a methodological graph object.

free parameters (3)
  • agglomerative clustering threshold τ = dataset-specific (e.g. 0.05–0.4 in figures)
    Sole explicit method hyperparameter; set manually per dataset/figure for readability and directly controls node count and apparent funnel/star structure (Section 3, Figures 1–6).
  • regression quantile bin count = 10
    Continuous predictions mapped to discrete codes before Hamming clustering; fixed at 10 global quantile bins without sensitivity study in the main claims.
  • MLP/XGBoost/SR training hyperparameters = as in Table 2
    Architecture, epochs, learning rates, tree depth, generations etc. (Table 2) shape trajectories; not tuned per dataset, but still free design choices that condition observed STNs.
axioms (4)
  • domain assumption A model's functional state for trajectory analysis is adequately captured by its vector of predictions on a fixed training sample set (semantic vector).
    Stated in Sections 2–3 as the basis for cross-algorithm comparability; excludes parameter-space geometry and calibration of continuous logits.
  • ad hoc to paper After label/argmax or quantile discretization, normalized Hamming distance with complete-linkage agglomerative clustering yields structure-preserving nodes of the optimization process.
    Core methodological choice in Section 3; alternatives (logit Euclidean space, other linkages/metrics) are argued against but not systematically ablated.
  • domain assumption Graph descriptors (density, global efficiency, closeness, PageRank, in-degree, degree std.) are meaningful summaries of learning dynamics and regime differences.
    Used in Section 5 and Appendix A to separate real vs shuffled regimes; authors note they do not claim optimality of these metrics.
  • domain assumption Multiple independent runs with varied initialization, fixed data and hyperparameters, sample the relevant semantic trajectory distribution for STN aggregation.
    Standard STN practice invoked in Sections 3–5 (R=30 or 20).
invented entities (1)
  • Semantic Space Search Trajectory Network (SS-STN) independent evidence
    purpose: Graph object whose nodes are clusters of discretized semantic vectors and whose edges are observed training transitions, enabling cross-family and cross-regime comparison.
    Named methodological construct combining prior STNs with EC-style semantic space; not an ontological claim beyond the graph built from data.

pith-pipeline@v1.2.0-grok45-kimik3 · 19001 in / 3143 out tokens · 77567 ms · 2026-07-31T00:39:46.529239+00:00 · methodology

0 comments
read the original abstract

Search Trajectory Networks (STNs) are a graph-based tool for visualizing and characterizing the behavior of optimization algorithms. STNs' reliance on discretization of the search space has largely confined them to low-dimensional or combinatorial settings. We introduce a methodology for constructing STNs in semantic spaces, defined as the space of a model's predictions on a fixed sample set. Our approach discretizes semantic vectors and aggregates them into network nodes via agglomerative clustering with complete linkage under a normalized Hamming distance. Since any predictor can be summarized by its semantic vector, this method enables comparison of learning dynamics across otherwise incomparable algorithm families. We apply semantic space STNs to classification and regression tasks solved using different machine learning algorithms, recovering known qualitative differences between them. Additionally, we use semantic space STNs to study neural network generalization by contrasting standard training with the label randomization regime of Zhang et al. (2017). The resulting STNs exhibit consistent structural differences, training on real labels produces denser, more efficient and more centralized graphs than training on shuffled labels. Together, our results show that semantic space STNs capture functional training dynamics arising from the interaction between learning algorithms and data, providing a tool for analyzing and comparing learning dynamics across machine learning models and training regimes.

Figures

Figures reproduced from arXiv: 2607.25122 by Alberto Tonda, Cristina Manfredotti, Evelyne Lutton, Gabriela Ochoa, Julian Agudelo, Vincent Guigue.

Figure 1
Figure 1. Figure 1: Semantic space STNs for MLP and XGBoost on the four classification datasets, aggregated over 30 runs. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Semantic space STNs for MLP, XGBoost and Symbolic Regression on the three regression datasets, ag [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of the agglomerative clustering threshold [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Robustness of semantic space STNs to the number of sampled trajectories. The global structure remains [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Semantic space STNs for MLPs trained under true and shuffled labels, over 20 runs. Real labels produce a [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Progressive label corruption on MNIST (784), over 20 runs. As the corruption level [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Semantic space STNs for MLP and XGBoost on the four classification datasets, aggregated over 30 runs. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Semantic space STNs for MLP, XGBoost and Symbolic Regression on the three regression datasets, ag [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Effect of the agglomerative clustering threshold [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Robustness of semantic space STNs to the number of sampled trajectories. The global structure remains [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Semantic space STNs for MLPs trained under true and shuffled labels, over 20 runs. Real labels produce a [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Progressive label corruption on MNIST (784), over 20 runs. As the corruption level [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

24 extracted references · 4 canonical work pages

  1. [1]

    In: Goos, G., Hartmanis, J., Van Leeuwen, J., Van Den Bussche, J., Vianu, V

    Aggarwal, C.C., Hinneburg, A., Keim, D.A.: On the Surprising Behavior of Distance Metrics in High Di- mensional Space. In: Goos, G., Hartmanis, J., Van Leeuwen, J., Van Den Bussche, J., Vianu, V . (eds.) 10 A Preprint - July 29, 2026 Database Theory — ICDT 2001, vol. 1973, pp. 420–434. Springer Berlin Heidelberg, Berlin, Heidelberg (2001), http://link.spr...

    doi:10.1007/3-540-44503-x_27 2026

  2. [2]

    Proceedings of the National Academy of Sciences116(32), 15849–15854 (Aug 2019), http://arxiv.org/abs/1812.11118, arXiv:1812.11118 [stat.ML]

    Belkin, M., Hsu, D., Ma, S., Mandal, S.: Reconciling modern machine learning practice and the bias- variance trade-off. Proceedings of the National Academy of Sciences116(32), 15849–15854 (Aug 2019), http://arxiv.org/abs/1812.11118, arXiv:1812.11118 [stat.ML]

    Pith/arXiv arXiv 2019

  3. [3]

    Nearest Neighbor

    Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U.: When Is “Nearest Neighbor” Meaningful? In: Beeri, C., Buneman, P. (eds.) Database Theory — ICDT’99. pp. 217–235. Springer Berlin Heidelberg, Berlin, Heidelberg (1999)

    1999

  4. [4]

    Proceedings of ASIS, 199898, 161–172 (1998)

    Brin, S.: The pagerank citation ranking: bringing order to the web. Proceedings of ASIS, 199898, 161–172 (1998)

    1998

  5. [5]

    5281/zenodo.18060795

    Csárdi, G., Nepusz, T., Horvát, S., Traag, V ., Zanini, F., Noom, D.: igraph (Dec 2025),https://doi.org/10. 5281/zenodo.18060795

    2025

  6. [6]

    Draxler, F., Veschgini, K., Salmhofer, M., Hamprecht, F.A.: Essentially No Barriers in Neural Network Energy Landscape (Feb 2019),http://arxiv.org/abs/1803.00885, arXiv:1803.00885 [stat.ML]

    Pith/arXiv arXiv 2019

  7. [8]

    Garipov, T., Izmailov, P., Podoprikhin, D., Vetrov, D., Wilson, A.G.: Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs (Oct 2018),http://arxiv.org/abs/1802.10026, arXiv:1802.10026 [stat.ML]

    Pith/arXiv arXiv 2018

  8. [9]

    In: Varoquaux, G., Vaught, T., Millman, J

    Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring network structure, dynamics, and function using networkx. In: Varoquaux, G., Vaught, T., Millman, J. (eds.) Proceedings of the 7th Python in Science Conference. pp. 11 –

  9. [10]

    Information Processing Letters 31(1), 7–15 (1989),https://www.sciencedirect.com/science/article/pii/0020019089901026

    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31(1), 7–15 (1989),https://www.sciencedirect.com/science/article/pii/0020019089901026

    arXiv 1989

  10. [11]

    Keskar, N.S., Mudigere, D., Nocedal, J., Smelyanskiy, M., Tang, P.T.P.: On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima (Feb 2017),http://arxiv.org/abs/1609.04836, arXiv:1609.04836 [cs.LG]

    Pith/arXiv arXiv 2017

  11. [12]

    Lavinas, Y ., Aranha, C., Ochoa, G.: Search Trajectories Networks of Multiobjective Evolutionary Algorithms 13224, 223–238 (2022),https://link.springer.com/10.1007/978-3-031-02462-7_15, series Title: Lecture Notes in Computer Science

    work page doi:10.1007/978-3-031-02462-7_15 2022

  12. [13]

    In: Coello, C.A.C., Cutello, V ., Deb, K., Forrest, S., Nicosia, G., Pavone, M

    Moraglio, A., Krawiec, K., Johnson, C.G.: Geometric semantic genetic programming. In: Coello, C.A.C., Cutello, V ., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) Parallel Problem Solving from Nature - PPSN XII. pp. 21–31. Springer Berlin Heidelberg (2012)

    2012

  13. [14]

    https://doi.org/10.48550/ARXIV .1504.04909

    Mouret, J.B., Clune, J.: Illuminating search spaces by mapping elites (2015). https://doi.org/10.48550/ARXIV .1504.04909

    Pith/arXiv arXiv doi:10.48550/arxiv.1504.04909 2015

  14. [15]

    Pasadena, CA USA (2008),http://conference.scipy.org/proceedings/SciPy2008/paper_2/

    2008

  15. [16]

    In: Pérez Cáceres, L., Stützle, T

    Ochoa, G., Liefooghe, A., Lavinas, Y ., Aranha, C.: Decision/Objective Space Trajectory Networks for Multi- objective Combinatorial Optimisation. In: Pérez Cáceres, L., Stützle, T. (eds.) Evolutionary Computation in Combinatorial Optimization, vol. 13987, pp. 211–226. Springer Nature Switzerland (2023),https://link. springer.com/10.1007/978-3-031-30035-6_...

    work page doi:10.1007/978-3-031-30035-6_14 2023

  16. [17]

    Applied Soft Computing109, 107492 (2021)

    Ochoa, G., Malan, K.M., Blum, C.: Search trajectory networks: A tool for analysing and visualising the behaviour of metaheuristics. Applied Soft Computing109, 107492 (2021). https://doi.org/10.1016/j.asoc.2021.107492,https://www.sciencedirect.com/science/article/ pii/S1568494621004154

    arXiv 2021

  17. [18]

    In: Richter, H., Engelbrecht, A

    Ochoa, G., Verel, S., Daolio, F., Tomassini, M.: Local Optima Networks: A New Model of Combinatorial Fitness Landscapes. In: Richter, H., Engelbrecht, A. (eds.) Recent Advances in the Theory and Application of Fitness Landscapes, vol. 6, pp. 233–262. Springer Berlin Heidelberg (2014),https://link.springer.com/ 10.1007/978-3-642-41888-4_9

    work page doi:10.1007/978-3-642-41888-4_9 2014

  18. [19]

    Information Sciences609, 711–726 (Sep 2022),https: //linkinghub.elsevier.com/retrieve/pii/S0020025522007290 11 A Preprint - July 29, 2026

    Rodrigues, N.M., Malan, K.M., Ochoa, G., Vanneschi, L., Silva, S.: Fitness landscape analysis of convolutional neural network architectures for image classification. Information Sciences609, 711–726 (Sep 2022),https: //linkinghub.elsevier.com/retrieve/pii/S0020025522007290 11 A Preprint - July 29, 2026

    2022

  19. [20]

    In: Proceedings of the 5th International Confer- ence on Neural Information Processing Systems

    Vapnik, V .: Principles of risk minimization for learning theory. In: Proceedings of the 5th International Confer- ence on Neural Information Processing Systems. p. 831–838. NIPS’91, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1991)

    1991

  20. [21]

    Springer-Verlag New York, Inc

    Vapnik, V .N.: The nature of statistical learning theory. Springer-Verlag New York, Inc. (1995)

    1995

  21. [22]

    02113, arXiv:2503.02113 [cs.LG]

    Wilson, A.G.: Deep Learning is Not So Mysterious or Different (Jul 2025),http://arxiv.org/abs/2503. 02113, arXiv:2503.02113 [cs.LG]

    Pith/arXiv arXiv 2025

  22. [23]

    Zhang, C., Bengio, S., Hardt, M., Recht, B., Vinyals, O.: Understanding deep learning requires rethinking generalization (Feb 2017),http://arxiv.org/abs/1611.03530, arXiv:1611.03530 [cs.LG]

    Pith/arXiv arXiv 2017

  23. [24]

    Communications of the ACM64(3), 107–115 (Mar 2021),https://dl.acm.org/doi/10

    Zhang, C., Bengio, S., Hardt, M., Recht, B., Vinyals, O.: Understanding deep learning (still) requires rethinking generalization. Communications of the ACM64(3), 107–115 (Mar 2021),https://dl.acm.org/doi/10. 1145/3446776

    2021

  24. [25]

    In: Genetic Programming, pp

    Zhang, H., Chen, Q., Tonda, A., Xue, B., Banzhaf, W., Zhang, M.: MAP-elites with cosine-similarity for evolutionary ensemble learning. In: Genetic Programming, pp. 84–100. Springer Nature Switzerland (2023). https://doi.org/10.1007/978-3-031-29573-7_6 A Graph metrics Throughout this paper, we use several graph metrics as quantitative insights about semant...

    work page doi:10.1007/978-3-031-29573-7_6 2023