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REVIEW 3 major objections 7 minor 24 references

In a minimal grid model of evolution, the size of space flips the system from compact replicators to runaway size-dominance via a nucleation-like transition.

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2026-07-31 14:16 UTC pith:6UGSFIRU

load-bearing objection Solid ALife methods paper: the L-gated compact-to-runaway split is real and cleanly controlled; the rest is useful programme extension, not a field reset. the 3 major comments →

arxiv 2607.28219 v1 pith:6UGSFIRU submitted 2026-07-30 q-bio.PE cs.NEnlin.CG

Hash Chemistry: Minimal Models for Evolutionary Growth of Complexity

Ilya Horiguchi , Hiroki Sayama This is my paper
classification q-bio.PE cs.NEnlin.CG
keywords artificial lifeartificial chemistryopen-ended evolutionspatial ecologylocal and dyadic interactionsnucleation-like transitionfinite-size effectsHash Chemistry
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.

Hash Chemistry is a family of deliberately simple evolutionary models in which a fixed hash function scores entities of any size, so the space of possible forms grows combinatorially as structures get larger. This paper reviews that family and then pushes its latest grid version, Structural Cellular Hash Chemistry, in two directions. First, making competition both spatially local and sometimes dyadic (pair-dependent) markedly improves population growth, pattern-size growth, and the diversity of forms explored. Second, on much larger grids, linear space size acts as a control knob for a stochastic jump: below a window near L≈300–320, replicators stay tiny; above it, a single structure often monopolizes replication and decouples success from the hash score. The authors separate the cause into a non-spatial bias (larger structures are sampled more often because contests pick cells at random) plus a finite-size boundary effect (open edges clip growing structures until the grid is big enough). The point is that a transparent minimal model can still exhibit multiscale open-ended dynamics and a clean scale-driven regime change.

Core claim

Extending Structural Cellular Hash Chemistry shows two concrete results: local and moderately dyadic competition substantially enrich its evolutionary dynamics relative to the original global individual-score setting; and, under global cell-seeded competition, grid size L controls a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, with the mechanism cleanly split into size-biased sampling feedback and an open-boundary finite-size effect confirmed by periodic-boundary controls that erase the L threshold while runaway structures settle at a scale-invariant fill fraction near 0.65.

What carries the argument

Structural Cellular Hash Chemistry (SCHC): replicators are connected components on an L×L grid, scored by a deterministic hash; contests are seeded by sampling active cells, and winners overwrite losers with death and mutation. The cardinality leap—combinatorial growth of possibility space with entity size—is the family’s core idea; the transition analysis hinges on size-biased cell sampling plus open versus periodic boundaries.

Load-bearing premise

The large-grid transition results assume a 32-bit surrogate hash is interchangeable enough with the original built-in hash that the reported size window and runaway behavior would still appear under the published scoring function.

What would settle it

Re-run the L=200–400 open-boundary scan with the original Mathematica Hash (or an exact match to its statistics) at the same mutation and death rates: if runaway fractions stay near zero below L≈300 and jump above it with dominant fill ≈0.65 under periodic boundaries, the claim holds; if the compact/runaway split vanishes or moves far from that window, it fails.

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

If this is right

  • Space size alone can reorganize evolutionary outcomes from score-driven compact forms to space-monopolizing giants without changing the competition rule.
  • Moderate locality and dyadic (pair-dependent) scoring can raise both complexity growth and pattern diversity in the same minimal model.
  • Realized fitness in these systems is emergent from interaction and medium geometry, not identical to the explicit hash score.
  • Periodic versus open boundaries give a clean experimental dial on whether finite-size clipping gates nucleation of runaway structures.
  • Hash Chemistry remains a usable testbed for dissecting open-ended evolution across scales with transparent mechanisms.

Where Pith is reading between the lines

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

  • The same size-biased sampling that drives runaway here may be a general hazard in any evolutionary algorithm that samples individuals proportional to spatial footprint or resource occupancy.
  • If dyadic scoring is what sustains unordered dominance networks, replacing the hash with other pair oracles (including learned evaluators) could be tested for the same diversity boost without changing the grid mechanics.
  • The reported ~0.65 fill fraction under runaway looks like a dynamic balance of copy growth versus per-cell death; sweeping death rate while holding L fixed should move that fraction in a predictable way.

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

3 major / 7 minor

Summary. The manuscript reviews the Hash Chemistry family and presents two extensions of Structural Cellular Hash Chemistry (SCHC). First, it adds spatial interaction range D and dyadic interaction probability P, showing via systematic (D,P) sweeps that locality and moderate dyadicity improve successful growth, replicator size, and cumulative pattern diversity relative to the original global, individual-score setting. Second, using a GPU/JAX implementation at larger L, it reports that grid size controls a stochastic, nucleation-like shift between a compact-replicator regime (mean sizes ~2–3) and a runaway size-dominance regime (means O(10^3), maxima O(10^4–10^5)). The mechanism is decomposed into non-spatial size-biased cell sampling plus open-boundary finite-size clipping, supported by periodic-boundary controls (runaway at all tested L; dominant fill fraction ~0.65) and μ/p_death phase diagrams. The authors position Hash Chemistry as a minimal testbed for multiscale open-ended evolution.

Significance. If the reported mechanism holds, the work supplies a rare, mechanistically transparent minimal model in which a purely quantitative change in spatial scale flips evolutionary dynamics from score-driven compact replication to space-monopolizing size dominance, with an explicit non-spatial vs spatial decomposition. Strengths include systematic parameter heatmaps (30 runs), the open-vs-periodic boundary control that cleanly isolates the finite-size gate, mutation/death sensitivity diagrams, public code repositories, and an honest limitations section. The cardinality-leap framing and the demonstration that hash score is not realized fitness are useful for open-ended evolution and major-transitions discussions. The contribution is incremental relative to the authors’ prior SCHC and ALIFE pieces, but the synthesis plus the boundary-controlled transition analysis is a genuine advance for the artificial-life / minimal artificial-chemistry literature.

major comments (3)
  1. [§4.1–4.2, Methods §7.3, Table 3] §4.1–4.2 and Methods §7.3 / Table 3: Quantitative claims about the L≈300–320 transition window, runaway fractions, late/early ratios, and size–score anticorrelations (Table 2, Fig. 8–9) rest on a deterministic 32-bit surrogate hash, not Mathematica’s Hash. The paper only asserts qualitative trend agreement. Because the non-spatial size-bias feedback is score-mediated, a surrogate that systematically favors (or disfavors) large connected patterns could shift or erase the reported window. At minimum, re-run the coarse L scan (or a subset at L=200,300,320,400) under a closer hash match or several independent mix constants and report whether the compact/runaway dichotomy and ~0.65 fill fraction survive; otherwise narrow the claim to the JAX realization.
  2. [§4.1, Table 2, Fig. 8c–d, Fig. 9e] §4.1 and Limitations: The transition location and fine-scan runaway fractions are estimated from n=10 (size scans) and n=5 (sensitivity/boundary) replicates, with explicitly non-monotonic fine-scan fractions and broad first-crossing times. Welch/Mann–Whitney tests between L=300 and 320 are reported, but the stochastic nucleation picture needs uncertainty that matches the claim that L is a control parameter (e.g., bootstrap CIs on runaway fraction, survival curves for nucleation time, or substantially larger ensembles near the window). Without that, “L acts as a control parameter for a nucleation-like transition” is only weakly localized.
  3. [§3.1–3.2, Fig. 5d, Fig. 6] §3.2 / Fig. 5d: “Overall performance” is the raw product of successful-run count, mean replication size, and cumulative pattern types. These are on incommensurate scales and are filtered by post-hoc success/extinction/runaway criteria (including exclusion of the single explosive case at (D,P)=(10,0.6)). The product drives the claim that (D,P)=(L,0) is “not the best.” Either replace it with a pre-registered composite (e.g., z-scored average), report the three metrics without multiplication as the primary result, or show rank-robustness under alternative aggregations so the sweet-spot conclusion does not hinge on an ad hoc scalar.
minor comments (7)
  1. [Abstract, References [19],[20]] Abstract and §1 state arXiv date “30 Jul 2026” and cite ALIFE 2026 work as prior; ensure versioning and “to appear” citations are consistent at publication.
  2. [§3.1, Fig. 5] Fig. 5 heatmaps: color scales differ across panels and success counts occupy a narrow band (23–30); annotate excluded runs and define “meaningful population growth” operationally in the caption or Methods.
  3. [§7.3] Equation (1)–(2): state explicitly that the surrogate is not claimed to be cryptographically strong and give the exact normalization to [0,1]; a one-line check that score distribution on random small components is roughly uniform would help readers.
  4. [§4.2, Fig. 9a, §7.5] §4.2 periodic control uses 5,000 steps vs 20,000 open-boundary; note in the Fig. 9a caption that nucleation under periodic boundaries is fast enough that the shorter horizon is not comparing unequal steady states.
  5. [Table 1, §1] Table 1 is helpful; add a row or footnote clarifying that Spatial-dyadic SCHC and the large-L JAX study are the new contributions of this manuscript versus prior conference abstracts.
  6. [§3] Minor prose: “chessboard distance” should be defined once (Chebyshev/L∞); “dyadicity” is used clearly but could be glossed at first use for non-specialists.
  7. [Declarations] Code availability links are a strength; please pin commit hashes or release tags so the JAX surrogate and periodic flood-fill are bit-reproducible with the reported CSVs.

Circularity Check

0 steps flagged

No significant circularity: L-transition and mechanism decomposition are empirical outcomes of stated update rules plus controls, not predictions forced by definition or fit.

full rationale

The paper’s load-bearing claims are simulation phenomenology under explicitly stated competition, sampling, death, and mutation rules (Algorithms/§7), not closed-form predictions fitted to a target curve. Hash scores are fixed deterministic oracles used as selection inputs; realized fitness is explicitly distinguished from the hash and is allowed to decouple (negative size–score correlation in the runaway regime). The size-biased sampling argument (selection probability ≈ 2 s_i / N_active) is a direct consequence of cell-uniform contest seeding, used to explain an observed instability rather than to define the observed sizes. The finite-size half of the mechanism is independently tested by the periodic-boundary control, which removes the L threshold while leaving competition and scoring unchanged and yields a scale-invariant ~0.65 fill fraction—falsifiable structure that does not reduce to the open-boundary inputs by construction. Heavy citation of prior Hash Chemistry papers defines and situates the model family being extended; those citations are not used as uniqueness theorems or as the sole warrant for the new L-window, runaway fractions, or boundary decomposition. No fitted-input-called-prediction, self-definitional loop, or renamed external empirical law is present. The JAX hash-surrogate caveat is a soundness/transfer concern, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 2 invented entities

The work is a defined artificial chemistry, not a derivation from nature. Load-bearing choices are modeling axioms (hash-as-oracle, connected components as individuals, cell-level global sampling, open boundaries, copy-with-death/mutation) plus free simulation parameters (L, μ, p_death, D, P, k, thresholds for ‘success’ and ‘runaway’). No new physical entities. Claims rest on these rules producing the reported phenomenology under the stated ensembles.

free parameters (5)
  • Spatial interaction range D and dyadic probability P = Swept D∈[0.1L,L], P∈[0,1]; highlighted optima near (0.2L,0.2) and moderate P≈0.4
    Swept experimentally; ‘sweet spots’ (e.g. moderate D and P≈0.2–0.4) are selected by outcome heatmaps, not predicted a priori.
  • Mutation rate μ and death probability p_death = default μ=0.002/0.999, p_death=0.001; sensitivity grids in Fig. 9c,d
    Defaults μ_eff=0.002, p_death=0.001; shown to move or erase the L threshold—controls on nucleation rate chosen by authors.
  • Runaway and success operational thresholds = mean size>100; successful-run filter as described in §3.1
    Runaway fraction uses final mean component size>100; Extension I filters extinction/no-growth and one explosive case—analysis depends on these cutoffs.
  • Grid size L and type count k = k=1000, n=10; L varied 100–400
    L is the scanned control parameter; k=1000 and n_initial=10 are fixed design choices affecting diversity and density.
  • Surrogate hash mixing constants c1..c4 = c1=0x9E3779B9, c2=0x85EBCA6B, c3=0x45D9F3B, c4=0x27D4EB2D
    Fixed 32-bit constants in Eq. (1)–(2) define the JAX score landscape; not derived from theory of open-endedness.
axioms (5)
  • domain assumption A deterministic hash (or surrogate) assigns a structure-dependent scalar in [0,1] that can be used for competition without equating that scalar to realized ecological fitness.
    Core Hash Chemistry premise from §1–2 and [15]; realized fitness is allowed to decouple when spatial interference dominates.
  • ad hoc to paper Replicating individuals are 8-connected components on an L×L grid; competition is seeded by sampling active cells (size-biased), winner’s padded box overwrites loser with per-cell death and mutation.
    SCHC update rules §7.1–7.2 / Algorithm 1; the size bias ≈2s_i/N_active is a direct consequence of this sampling axiom.
  • ad hoc to paper Open boundaries clip copied material outside the domain; this finite container is part of the medium that can suppress or allow nucleation.
    Stated in §7.2 and tested by periodic control in §4.2; load-bearing for the claim that L gates runaway only through the boundary.
  • ad hoc to paper Dyadic mode: with probability P, a hash of the ordered combined pair decides the winner via threshold 0.5, creating possibly non-transitive dominance.
    Extension I rule §7.2 step 5(b); inspired by LLM pairwise word evolution [29,30] but implemented via hash.
  • standard math Standard stochastic simulation practice: independent runs, Moore neighborhood flood-fill, and ensemble statistics suffice to characterize regimes.
    Background computational method; Welch/Mann–Whitney tests reported for the L=300 vs 320 jump.
invented entities (2)
  • Hash Chemistry / cardinality leap scoring of arbitrary-size entities no independent evidence
    purpose: Provide an unbounded, generic oracle so higher-order structures can enter selection without hand-designed fitness.
    Introduced in prior work [15] and used throughout; not a physical particle but a modeling entity. Independent evidence outside this paper is only other Hash Chemistry simulations, not external empirical validation.
  • Structural Cellular Hash Chemistry (connected-component replicators on a grid) no independent evidence
    purpose: Unite spatial ecology, explicit individuality, and efficient simulation for open-ended complexity growth.
    Defined in [18] and extended here; existence is by construction in silico.

pith-pipeline@v1.2.0-daily-grok45 · 22482 in / 4253 out tokens · 88218 ms · 2026-07-31T14:16:24.632759+00:00 · methodology

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read the original abstract

Hash Chemistry is a family of minimalistic evolutionary models in which a deterministic hash function assigns a scalar score to entities of arbitrary size, opening a combinatorially vast possibility space (a ``cardinality leap''). Since its introduction, the idea has been realized in several settings, from the original spatial formulation to a fast non-spatial variant and then to structural cellular models. Here we review the Hash Chemistry family as a coherent modeling framework and use it to explore how minimal systems can demonstrate the mechanisms behind multiscale open-ended evolutionary dynamics. The most recent model, Structural Cellular Hash Chemistry (SCHC), successfully demonstrated multiscale ecological interaction/adaptation and complexity growth of replicators in a computationally efficient manner. In this study, we first extend SCHC to incorporate spatial locality and dyadicity of competitive interactions among replicating structures. We show this extension substantially enhances SCHC's evolutionary dynamics. Furthermore, we explore SCHC in a significantly larger spatial domain using a GPU-accelerated implementation. We show that the size of the space acts as a control parameter for a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, and we separate the responsible mechanism into a non-spatial, size-biased sampling feedback and a finite-size spatial effect. Altogether, these results illustrate the rich potential of Hash Chemistry as a minimal, mechanistically transparent testbed for studying open-ended evolution across scales.

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Reference graph

Works this paper leans on

24 extracted references · 3 canonical work pages

  1. [2]

    Theory in Biosciences135(3), 131–161 (2016) https://doi.org/10.1007/ s12064-016-0229-7

    Banzhaf, W., Baumgaertner, B., Beslon, G., Doursat, R., Foster, J.A., McMullin, B., De Melo, V.V., Miconi, T., Spector, L., Stepney, S., White, R.: Defin- ing and simulating open-ended novelty: Requirements, guidelines, and chal- lenges. Theory in Biosciences135(3), 131–161 (2016) https://doi.org/10.1007/ s12064-016-0229-7

    2016

  2. [5]

    In: OEE4: The Fourth Workshop on Open-Ended Evolution, at the 2021 Conference on Artificial Life (ALIFE 2021), Prague, Czech Republic (online) (2021)

    Stepney, S.: Modelling and measuring open-endedness. In: OEE4: The Fourth Workshop on Open-Ended Evolution, at the 2021 Conference on Artificial Life (ALIFE 2021), Prague, Czech Republic (online) (2021). http://workshops.alife.org/oee4/ 23

    2021

  3. [7]

    Artificial Life30(3), 417–438 (2024) https://doi.org/10.1162/ artl a 00406

    Borg, J.M., Buskell, A., Kapitany, R., Powers, S.T., Reindl, E., Tennie, C.: Evolved open-endedness in cultural evolution: A new dimension in open-ended evolution research. Artificial Life30(3), 417–438 (2024) https://doi.org/10.1162/ artl a 00406

    2024

  4. [8]

    Artificial Life7(3), 225–275 (2001) https://doi.org/10.1162/106454601753238636

    Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial chemistries—a review. Artificial Life7(3), 225–275 (2001) https://doi.org/10.1162/106454601753238636

    work page doi:10.1162/106454601753238636 2001

  5. [9]

    MIT Press, ??? (2015)

    Banzhaf, W., Yamamoto, L.: Artificial Chemistries. MIT Press, ??? (2015). https: //doi.org/10.7551/mitpress/9780262029438.001.0001

    arXiv 2015

  6. [10]

    In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation, pp

    Chan, B.W.-C.: Towards large-scale simulations of open-ended evolution in con- tinuous cellular automata. In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation, pp. 127–130 (2023). https://doi.org/10. 1145/3583133.3590670

    arXiv 2023

  7. [12]

    Artificial Life31(1), 81–95 (2024) https://doi.org/10

    Sayama, H., Nehaniv, C.L.: Self-reproduction and evolution in cellular automata: 25 years after evoloops. Artificial Life31(1), 81–95 (2024) https://doi.org/10. 1162/artl a 00451

    2024

  8. [15]

    Artificial Life25(2), 104–116 (2019) https://doi.org/10.1162/artl a 00283

    Sayama, H.: Cardinality leap for open-ended evolution: Theoretical considera- tion and demonstration by Hash Chemistry. Artificial Life25(2), 104–116 (2019) https://doi.org/10.1162/artl a 00283

    doi:10.1162/artl 2019

  9. [16]

    In: 2024 IEEE Congress on Evolutionary Computation (CEC), pp

    Sayama, H.: Non-spatial Hash Chemistry as a minimalistic open-ended evolu- tionary system. In: 2024 IEEE Congress on Evolutionary Computation (CEC), pp. 1–7. IEEE, ??? (2024). https://doi.org/10.1109/CEC60901.2024.10611791 . Preprint at https://arxiv.org/abs/2404.18027

    Pith/arXiv arXiv 2024

  10. [17]

    In: The 2024 Conference on Artificial Life (ALIFE)

    Sayama, H.: Hash chemistry on a cellular grid: An open-ended artificial chemistry 24 system with computational efficiency and nontrivial spatio-temporal dynamics. In: The 2024 Conference on Artificial Life (ALIFE). MIT Press, ??? (2024). https: //doi.org/10.1162/isal a 00762

    doi:10.1162/isal 2024

  11. [18]

    In: 2025 IEEE Symposium on Computational Intelligence in Artificial Life and Cooperative Intelligent Systems (ALIFE-CIS), pp

    Sayama, H.: Structural cellular hash chemistry. In: 2025 IEEE Symposium on Computational Intelligence in Artificial Life and Cooperative Intelligent Systems (ALIFE-CIS), pp. 1–7. IEEE, ??? (2025). https://doi.org/10.1109/ ALIFE-CIS64968.2025.10979829 . Preprint at https://arxiv.org/abs/2412.12790

    arXiv 2025

  12. [19]

    In: The 2026 Conference on Artificial Life (ALIFE), Late-Breaking Abstract (2026)

    Sayama, H.: Local and dyadic interactions enrich evolutionary dynamics in struc- tural cellular hash chemistry. In: The 2026 Conference on Artificial Life (ALIFE), Late-Breaking Abstract (2026)

    2026

  13. [20]

    In: Proceedings of the Artificial Life Conference 2026 (ALIFE 2026)

    Horiguchi, I., Sayama, H.: Space-size-driven transition of evolutionary dynam- ics in structural cellular hash chemistry. In: Proceedings of the Artificial Life Conference 2026 (ALIFE 2026). MIT Press, ??? (2026). To appear

    2026

  14. [21]

    Oxford University Press, Oxford (1997)

    Maynard Smith, J., Szathm´ ary, E.: The Major Transitions in Evolution. Oxford University Press, Oxford (1997). https://doi.org/10.1093/oso/9780198502944. 001.0001

    arXiv 1997

  15. [22]

    Pro- ceedings of the National Academy of Sciences97(9), 4463–4468 (2000) https: //doi.org/10.1073/pnas.97.9.4463

    Adami, C., Ofria, C., Collier, T.C.: Evolution of biological complexity. Pro- ceedings of the National Academy of Sciences97(9), 4463–4468 (2000) https: //doi.org/10.1073/pnas.97.9.4463

    work page doi:10.1073/pnas.97.9.4463 2000

  16. [23]

    Physica D42(1–3), 12–37 (1990) https://doi.org/10.1016/ 0167-2789(90)90064-V

    Langton, C.G.: Computation at the edge of chaos: Phase transitions and emer- gent computation. Physica D42(1–3), 12–37 (1990) https://doi.org/10.1016/ 0167-2789(90)90064-V

    1990

  17. [24]

    Oxford University Press, New York (1993)

    Kauffman, S.A.: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, New York (1993)

    1993

  18. [25]

    (eds.): Adaptive Networks: Theory, Models and Applica- tions

    Gross, T., Sayama, H. (eds.): Adaptive Networks: Theory, Models and Applica- tions. Springer, ??? (2009)

    2009

  19. [26]

    Computers & Mathemat- ics with Applications65(10), 1645–1664 (2013) https://doi.org/10.1016/j.camwa

    Sayama, H., Pestov, I., Schmidt, J., Bush, B.J., Wong, C., Yamanoi, J., Gross, T.: Modeling complex systems with adaptive networks. Computers & Mathemat- ics with Applications65(10), 1645–1664 (2013) https://doi.org/10.1016/j.camwa. 2012.12.005

    doi:10.1016/j.camwa 2013

  20. [27]

    In: 2007 IEEE Symposium on Artificial Life, pp

    Sayama, H.: Generative network automata: A generalized framework for model- ing complex dynamical systems with autonomously varying topologies. In: 2007 IEEE Symposium on Artificial Life, pp. 214–221 (2007). https://doi.org/10.1109/ ALIFE.2007.367799 . IEEE

    arXiv 2007

  21. [28]

    In: Adaptive 25 Networks: Theory, Models and Applications, pp

    Sayama, H., Laramee, C.: Generative network automata: A generalized framework for modeling adaptive network dynamics using graph rewritings. In: Adaptive 25 Networks: Theory, Models and Applications, pp. 311–332. Springer, ??? (2009). https://doi.org/10.1007/978-3-642-01284-6 15

    work page doi:10.1007/978-3-642-01284-6 2009

  22. [29]

    In: 2025 IEEE Symposium on Computational Intelligence in Artificial Life and Cooperative Intelligent Sys- tems (ALIFE-CIS), pp

    Suzuki, R., Arita, T.: Evolutionary ecology of words. In: 2025 IEEE Symposium on Computational Intelligence in Artificial Life and Cooperative Intelligent Sys- tems (ALIFE-CIS), pp. 1–7 (2025). https://doi.org/10.1109/ALIFE-CIS64968. 2025.10979831 . IEEE

    arXiv 2025

  23. [30]

    In: Proceedings of the 39th Annual Conference of the Japanese Society for Artificial Intelligence, pp

    Suzuki, R., Arita, T.: Evolutionary ecology of words (in japanese). In: Proceedings of the 39th Annual Conference of the Japanese Society for Artificial Intelligence, pp. 1–4251425 (2025). JSAI

    2025

  24. [31]

    Software available at http://github.com/jax-ml/jax (2018) 26

    Bradbury, J., Frostig, R., Hawkins, P., Johnson, M.J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., Zhang, Q.: JAX: Composable Transformations of Python+NumPy Programs. Software available at http://github.com/jax-ml/jax (2018) 26

    2018