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REVIEW 3 major objections 5 minor 73 references

ARTreeFormer: A Faster Attention-based Autoregressive Model for Phylogenetic Inference

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read ARTreeFormer proves that phylogenetic node embeddings can be computed by a fixed-point iteration with uniform convergence rate, yielding roughly 10x faster generation and 6x faster training while matching ARTree's approximation accuracy.

desk verdict A genuinely faster ARTree with a sound convergence theorem, but the printed Algorithm 1 doesn't match the proved recurrence and the stopping rule is unspecified; worth refereeing after fixing those. read the letter →

arxiv 2507.18380 v1 pith:E5CLHM26 submitted 2025-07-24 q-bio.PE

Tianyu Xie , Yicong Mao , Cheng Zhang This is my paper · ORCID
classification q-bio.PE MSC 92D1568T0762F15
keywords phylogeneticinferenceautoregressivemodelfixed-pointiterationattentionmechanismtopologicalnodeembeddingsvariationalBayesiantreetopologygenerationvectorizedcomputation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

ARTreeFormer tries to establish that the slowest part of ARTree—computing topological node embeddings by sequential tree traversals—can be replaced by a fixed-point iteration that converges at the same rate for every binary tree and every number of leaves. Because the iteration is just matrix–vector products and matrix squaring, it vectorizes across batched trees and nodes, which ARTree's traversal-based method cannot do. The paper also swaps ARTree's local graph-message-passing rounds for a single attention-based global readout. Together these changes yield roughly 10x faster tree generation and 6x faster training on standard phylogenetics benchmarks, with approximation accuracy matching or slightly better than ARTree's. If true, the result makes deep autoregressive models of tree topologies practical for larger taxon sets, including datasets with 100 taxa.

What carries the argument

The load-bearing object is the interior adjacency matrix $A_n$ of the tree topology, paired with the leaf-interior cross adjacency matrix $C_n$; they encode the fixed-point system $F_n = (A_n/3)F_n + C_n/3$ whose solution is the embedding matrix. Theorem 1 shows $\rho(A_n)\leq 2\sqrt{2}$ for every binary tree by applying a diagonal similarity transform that leaves eigenvalues unchanged but bounds all row sums by $2\sqrt{2}$, then using the Perron-Frobenius theorem. This yields the uniform linear convergence rate in Corollary 1, and Algorithm 1's power trick repeatedly squares the iteration operator to reach accuracy in $O(\log M_\varepsilon)$ matrix operations. The other mechanism is the attention-based global message passing block: a learnable query vector attends over all node features in one pass to form a global tree representation, which is then combined with sinusoidal positional embeddings to score each edge for the next leaf addition.

What would settle it

Run Algorithm 1 with the same epsilon used in the experiments on a large set of random binary trees (for example, 200 leaves) and compare the final iterates to the exact two-pass ARTree embeddings; if the relative error exceeds epsilon or the iteration count grows with the number of leaves, the uniform-convergence and embedding-fidelity claims are refuted. Alternatively, exhibiting any binary tree whose interior subgraph has spectral radius greater than $2\sqrt{2}$ would falsify Theorem 1.

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Extended reading notes

Core claim

ARTreeFormer's central claim is that ARTree's topological node embeddings—defined by minimizing Dirichlet energy with one-hot leaf encodings—can be computed as the solution of a linear system rather than by tree traversal. Writing the embedding matrix as $F_n$, the system is $F_n = (A_n/3)F_n + C_n/3$, where $A_n$ is the adjacency matrix of the subgraph induced by internal nodes and $C_n$ encodes leaf-to-internal connections. The paper proves that every such interior subgraph of a binary tree has spectral radius at most $2\sqrt{2}$, so the fixed-point iteration $F_n^{(m+1)} = (A_n/3)F_n^{(m)} + C_n/3$ converges linearly with rate at most $2\sqrt{2}/3$, independent of tree shape and leaf count; squaring the iteration operator (the power trick) makes the iteration count logarithmic. Combined with a one-pass attention-based global message passing scheme, the full generation pipeline becomes batch-vectorizable. The experiments on maximum parsimony, tree density estimation, and variational Bayesian phylogenetic inference report matching or improved accuracy with approximately 10x faster generation and 6x faster training.

Load-bearing premise

The practical equivalence to ARTree's embeddings rests on the stopping rule in Algorithm 1, which halts when successive iterates differ by less than a threshold epsilon; the convergence theorems bound only the error relative to the exact solution, and the paper does not prove that the successive-difference rule keeps the true error within the required tolerance, nor does it report the epsilon value used in the experiments.

Editorial extensions

If this is right

  • The number of iterations to reach a fixed error tolerance is bounded independently of tree topology and taxon count, so the embedding computation can be executed as batched tensor operations without per-tree branching.
  • ARTreeFormer attains roughly 10x faster generation and 6x faster training than ARTree while matching or improving approximation accuracy on maximum parsimony, tree density estimation, and variational Bayesian phylogenetic inference benchmarks.
  • Because the pipeline vectorizes across trees, large batch sizes become practical; on DS1, larger batches improve the KL divergence to the ground-truth tree distribution with only modest slowdown per iteration.
  • On 100-taxon influenza data, the method keeps marginal likelihood estimates far more stable than the long-run sampling baseline and much closer to the SBN reference than ARTree, a regime where ARTree degrades.
  • The fixed-point embedding scheme is a drop-in replacement for the two-pass harmonic embedding computation, so downstream models built on learnable topological features can adopt the same acceleration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same fixed-point scheme should extend to rooted or multifurcating trees and to any harmonic node-embedding computation on trees, since the proof structure only uses bounded degree; the paper states only unrooted binary trees.
  • The stopping-rule gap is the main practical risk: a direct comparison of final embeddings to exact two-pass embeddings on random trees would settle whether the speedup preserves the intended representation.
  • The single-query attention readout is a cheap global-pooling pattern that could transfer to other autoregressive structured-output models needing per-step global context without pairwise attention.
  • The power trick squares the iteration matrix each round, so the densest matrix products occur near the end; profiling batched GPU runs at 100 or more taxa would test whether the claimed $O(n^2\log M_\varepsilon)$ cost dominates in practice.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes ARTreeFormer, an autoregressive model for phylogenetic tree topologies that accelerates the earlier ARTree model. Two modifications are introduced: (i) the topological node embeddings, previously computed by a sequential two-pass tree traversal, are replaced by a vectorizable fixed-point iteration whose convergence rate is proved uniform over all binary tree topologies and leaf counts (Theorem 1, Corollary 1, Section 2.5); and (ii) the local GNN message passing is replaced by a global multi-head attention mechanism (Section 2.5). The method is evaluated on maximum parsimony reconstruction, tree topology density estimation, and variational Bayesian phylogenetic inference on the standard DS1-8 benchmarks plus an influenza data set up to 100 taxa, reporting comparable or better accuracy than ARTree with approximately 10x faster generation and 6x faster training.

Significance. If the technical issues are resolved, this is a useful contribution to Bayesian phylogenetic inference. The paper gives a self-contained proof (Theorem 1) that the spectral radius of the interior adjacency matrix of any binary tree is at most 2*sqrt(2), and Corollary 1 derives a uniform linear contraction rate for the embedding iteration; these are mathematically sound and provide a principled basis for vectorizing a previously traversal-bound computation. The empirical protocol is solid: ARTree results are reproduced from its official codebase, comparisons include external baselines (MrBayes, PAUP*, SBNs), the benchmark data are standard, and code and data are publicly available. The main weakness is that the written algorithm does not implement the proved iteration, and the stopping criterion is not connected to the proved error bound, so the paper's central claim that ARTreeFormer computes the ARTree embeddings is not established by the text as it stands.

major comments (3)
  1. [Section 2.5, Algorithm 1] Algorithm 1 as printed does not implement the fixed-point iteration of Eq. (11) or a valid power-trick acceleration. For m=1, the instruction computes F^(3)_n = bar_A^2_n F^(2)_n = bar_A^3_n F^(1)_n, whereas Eq. (11) requires F^(3)_n = (A_n/3)F^(2)_n + C_n/3; for m=2 the loop refers to F^(4)_n, which was never formed, and the update bar_A^(2m+1)_n = (bar_A^(2m)_n)^2 is actually bar_A^(4m)_n, not bar_A^(2m+1)_n. Consequently the written procedure neither follows the recurrence whose convergence is proved in Corollary 1 nor realizes the advertised log_2 M_epsilon iteration count. Please provide a correct version of the algorithm (for example, the plain one-step iteration of Eq. (11), or binary exponentiation applied to bar_A and bar_F) and state its complexity precisely.
  2. [Section 2.5, Algorithm 1 and Corollary 1] The stopping rule in Algorithm 1 is mismatched with the theoretical criterion. The text states that the required number of iterations M_epsilon is defined by ||F^(m)_n - F*_n||_2/n < epsilon, but the while loop stops on the successive difference ||F^(2m)_n - F^(2m-1)_n||_2 < epsilon. These two criteria are not equivalent: for a contraction with constant q = 2*sqrt(2)/3, the true error can be up to (1-q)^{-1} times the successive difference, which is a factor of about 17.5. Moreover, no epsilon value (or resulting M_epsilon) is reported anywhere in the paper. This gap means the paper does not establish that the embeddings produced by Algorithm 1 are within the claimed tolerance of the ARTree embeddings, and the reported speedups cannot be reproduced or checked without knowing epsilon. Please either stop on a certified upper bound for the true error, or derive the relationship between the successive-difference test and the true-error threshold, and report the epsilon used in all experiments.
  3. [Section 2.5, after Eq. (11)] The complexity claim that the power trick reduces the cost to O(B n^2 log_2 M_epsilon) is not justified as stated. Forming bar_A^(2m) by squaring bar_A^(2m-1) costs O(n^3) operations for a dense (2n-2) x (2n-2) matrix, and the paper does not show that the block structure of bar_A in Eq. (9) reduces the squaring cost to O(n^2). If the intended implementation instead uses sparse matrix-vector products, then the power trick is not needed for the asymptotic speedup and the complexity statement in Proposition 2 should be revised accordingly. This issue affects the theoretical contribution and the interpretation of Fig. 2.
minor comments (5)
  1. [Eq. (13)] The symbol d_h is used in the multi-head attention definition but never defined; it should be d/h, the per-head dimension.
  2. [Eq. (12) and surrounding text] The stated time complexity O(nd + d^2) for the attention block appears to omit the cost of the K and V projections, which are O(n d^2) for standard multi-head attention; please clarify what operations are included in the stated complexity.
  3. [Fig. 4] The label 'Maximum Pasimony' in the right panel contains a typo; it should read 'Maximum Parsimony'.
  4. [Section 2.5, before Fig. 3] The phrase 'We depict the the pipeline' contains a duplicated article; please correct it.
  5. [Theorem 1 proof] The proof applies the Perron-Frobenius theorem to a nonnegative matrix; the text says 'positive matrices', which should be 'nonnegative matrices' for accuracy.

Circularity Check

0 steps flagged · score 1.0 of 10

No meaningful circularity; the fixed-point derivation is self-contained and the empirical comparisons are measured against independently reproduced baselines.

full rationale

The paper's central derivation is mathematical, not fitted. The topological node embeddings are defined by minimizing the Dirichlet energy in Eq. (5), reformulated as the harmonic condition in Eq. (8), rewritten as the fixed-point equation Eq. (10), and solved by the linear iteration Eq. (11). Theorem 1 proves a uniform spectral-radius bound of 2√2 for the interior adjacency matrix, and Corollary 1 derives the linear convergence rate 2√2/3 from that bound. These steps are self-contained equations and proofs; no prediction or empirical result is built into them. The accuracy comparisons in Section 3 are direct measurements against external benchmarks and baselines: PAUP* for maximum parsimony, MrBayes for ground-truth posteriors, and SBN variants for density estimation, with ARTree runtimes and results reproduced using the official ARTree codebase. The self-citations to Xie & Zhang (2023) and Zhang (2023) are used to define the ARTree generating process and the topological embedding convention; they are not invoked as an unverified external authority that forces the paper's conclusion. One issue noted in the text is that Algorithm 1 uses the successive-difference stopping criterion ||F^(2m)_n - F^(2m-1)_n||_2 >= epsilon, while Corollary 1 bounds the true error ||F^(m)_n - F*_n||_2, and the paper does not bridge these two quantities or report epsilon. This is a correctness and reproducibility gap, not circularity: it does not make the claimed result equivalent to its inputs by construction. There is also no fitted parameter renamed as a prediction, and no external result is repackaged under new coordinates. Overall, the derivation chain is self-contained, with only ordinary self-citation that is not load-bearing.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The algorithmic claims rely on standard linear algebra (Perron-Frobenius), the degree-3 structure of binary tree interiors, and the unproven expressiveness of a single-query attention block. Hyperparameters are inherited from ARTree; the stopping threshold epsilon is a free parameter whose value is not reported.

free parameters (6)
  • node feature dimension d = 100
    Set following ARTree (Xie & Zhang 2023); used in all experiments and affects model capacity and runtime.
  • number of attention heads h = 4
    Chosen by the authors; ablation in Appendix C.1 shows KL divergence is not very sensitive to h.
  • learning rate = 0.0001
    Same as ARTree; standard Adam optimizer setting.
  • batch size = 10 for TDE and VBPI
    Default batch size for ARTreeFormer; Figure 5 right shows batch size affects training accuracy and speed.
  • fixed-point stopping threshold epsilon = not specified in the paper
    Algorithm 1 and the convergence discussion depend on epsilon to balance speed and accuracy, but its value is never reported.
  • annealing schedule beta_t = min(1, 0.001 + t/200000) for parsimony; min(1, 0.001 + t/H) with H=100000 or 200000 for VBPI
    Chosen following Xie & Zhang (2023); affects the optimization trajectory.
assumptions (4)
  • standard math Perron-Frobenius theorem: the spectral radius of a nonnegative matrix is bounded by its maximum row sum
    Used in Theorem 1 to bound the spectral radius of the interior adjacency matrix by 2 sqrt(2).
  • domain assumption The interior subgraph of an unrooted bifurcating tree has maximum degree 3
    Used in Theorem 1's row-sum analysis; holds for the binary tree topologies that ARTree and ARTreeFormer generate.
  • standard math The harmonic system (8) has a unique solution equal to the Dirichlet energy minimizer
    The fixed-point iteration is claimed to compute the same topological node embeddings as ARTree's two-pass algorithm; this relies on the uniqueness of the solution to the Laplace equation with fixed boundary values.
  • ad hoc to paper A single-query attention block can capture tree-wide information sufficient for edge decisions
    The attention-based global message passing replaces L rounds of local GNN message passing; the paper provides no proof that one attention pass is as expressive for edge decision distributions.

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Cite this review

Pith. "Pith review of ARTreeFormer: A Faster Attention-based Autoregressive Model for Phylogenetic Inference." pith.science (2026). https://pith.science/paper/E5CLHM26

@misc{pith2026250718380,
  author       = {Pith},
  title        = {Pith review of: ARTreeFormer: A Faster Attention-based Autoregressive Model for Phylogenetic Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E5CLHM26}},
  note         = {Machine review of arXiv:2507.18380}
}
read the original abstract

Probabilistic modeling over the combinatorially large space of tree topologies remains a central challenge in phylogenetic inference. Previous approaches often necessitate pre-sampled tree topologies, limiting their modeling capability to a subset of the entire tree space. A recent advancement is ARTree, a deep autoregressive model that offers unrestricted distributions for tree topologies. However, its reliance on repetitive tree traversals and inefficient local message passing for computing topological node representations may hamper the scalability to large datasets. This paper proposes ARTreeFormer, a novel approach that harnesses fixed-point iteration and attention mechanisms to accelerate ARTree. By introducing a fixed-point iteration algorithm for computing the topological node embeddings, ARTreeFormer allows fast vectorized computation, especially on CUDA devices. This, together with an attention-based global message passing scheme, significantly improves the computation speed of ARTree while maintaining great approximation performance. We demonstrate the effectiveness and efficiency of our method on a benchmark of challenging real data phylogenetic inference problems.

Figures

Figures reproduced from arXiv: 2507.18380 by the authors.

Figure 1
Figure 1. An illustration of ARTree starting from the star-shaped tree topology with 3 leaf nodes. This figure is from Xie & Zhang (2023). Although ARTree enjoys unconfined support over the entire tree topology space and provides a more flexible family of variational distributions, it suffers from expensive computation costs (see Appendix E in Xie & Zhang (2023)) which makes it prohibitive for phylogenetic inference when the … view at source ↗
Figure 2
Figure 2. Time comparison between different models and devices. Left & Middle: Runtime of the node embedding module and message passing module for generating 128 tree topologies in a single batch using ARTree and ARTreeFormer. Right: The runtime of ARTreeFormer for generating 128 tree topologies with or without vectorization across batched tree topologies. CPU means running on a cluster of 16 2.4GHz CPUs, and CUDA means runni… view at source ↗
Figure 3
Figure 3. An illustration of ARTreeFormer for growing an ordinal tree topology τ4 of rank 4 to an ordinal tree topology τ5 of rank 5. In [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Performances of ARTree and ARTreeFormer on the maximum parsimony problem. Left: The estimated log probability log Q(τ ) versus the parsimony score P(τ,Y ) on DS1. For different tree topologies with the same parsimony score, the mean of the estimated log probabilities i…
Figure 5
Figure 5. Figure 5: Performance of ARTree and ARTreeFormer on the TDE task. Left: The training time (per iteration) and evaluation time (per evaluating the probabilities of 10 tree topologies) of ARTree and ARTreeFormer across eight benchmark data sets for TDE (averaged over 100 trials). …
Figure 6
Figure 6. Figure 6: Performances of different methods for VBPI. Left: the 10-sample lower bound as a function of the number of iterations on DS1. Middle: the variational approximation v.s. the ground truth of the marginal distribution of tree topologies on DS1. Right: Training time per it…
Figure 7
Figure 7. Figure 7: shows the performance of different methods on DS1. Both ARTree and ARTreeFormer provide more accurate probability estimates for the tree topologies on the two peaks of the posterior distribu￾tion, compared to SBN-EM and SBN-SGA. We see that ARTreeFormer can provide the…

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Works this paper leans on

73 extracted references · 62 canonical work pages

  1. [1]

    Attwood, Sarah C

    Stephen W. Attwood, Sarah C. Hill, David M. Aanensen, Thomas R. Connor, and Oliver G. Pybus. Phylogenetic and phylodynamic approaches to understanding and combating the early SARS-CoV-2 pandemic. Nature Reviews. Genetics, 23: 0 547 -- 562, 2022

    work page 2022

  2. [2]

    Flow network based generative models for non-iterative diverse candidate generation

    Emmanuel Bengio, Moksh Jain, Maksym Korablyov, Doina Precup, and Yoshua Bengio. Flow network based generative models for non-iterative diverse candidate generation. Advances in Neural Information Processing Systems, 34: 0 27381--27394, 2021

    2021

  3. [3]

    Blei, Alp Kucukelbir, and Jon D

    David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe. Variational inference: A review for statisticians. Journal of the American Statistical Association, 112: 0 859 -- 877, 2016

    work page 2016

  4. [4]

    Reweighted wake-sleep

    J \"o rg Bornschein and Yoshua Bengio. Reweighted wake-sleep. In Proceedings of the third International Conference on Learning Representations, 2015

    work page 2015

  5. [5]

    Alexandre Bouchard-C \^o t \'e , Sriram Sankararaman, and Michael I. Jordan. Phylogenetic inference via sequential M onte C arlo. Systematic Biology, 61: 0 579 -- 593, 2012

    work page 2012

  6. [6]

    Naesseth, and Itsik Pe'er

    Alex Chen, Philippe Chlenski, Kenneth Munyuza, Antonio Khalil Moretti, Christian A. Naesseth, and Itsik Pe'er. Variational combinatorial sequential monte carlo for bayesian phylogenetics in hyperbolic space. In The 28th International Conference on Artificial Intelligence and Statistics, 2025

    work page 2025

  7. [7]

    Learning phrase representations using RNN encoder-decoder for statistical machine translation

    Kyunghyun Cho, Bart Van Merri \"e nboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078, 2014

    arXiv 2014

  8. [8]

    Maximum likelihood of evolutionary trees is hard

    Benny Chor and Tamir Tuller. Maximum likelihood of evolutionary trees is hard. In The 9th Annual International Conference on Research in Computational Molecular Biology, 2005

    work page 2005

Show all 73 references
  1. [9]

    Fast and accurate deep network learning by exponential linear units (elus)

    Djork - Arn \' e Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network learning by exponential linear units (elus). In The fourth International Conference on Learning Representations, 2016. URL http://arxiv.org/abs/1511.07289

    2016 arXiv

  2. [10]

    Computational complexity of inferring phylogenies from dissimilarity matrices

    William HE Day. Computational complexity of inferring phylogenies from dissimilarity matrices. Bulletin of Mathematical Biology, 49 0 (4): 0 461--467, 1987

    1987

  3. [11]

    Deepseek-v2: A powerful open-source language model

    DeepSeek. Deepseek-v2: A powerful open-source language model. https://deepseek.com, 2024

    2024

  4. [12]

    The expansion of conservation genetics

    Rob DeSalle and George Amato. The expansion of conservation genetics. Nat. Rev. Genet., 5 0 (9): 0 702--712, September 2004. ISSN 1471-0056. doi:10.1038/nrg1425. URL http://dx.doi.org/10.1038/nrg1425

    2004 doi

  5. [13]

    Probabilistic path H amiltonian M onte C arlo

    Vu Dinh, Arman Bilge, Cheng Zhang, and Frederick A Matsen IV. Probabilistic path H amiltonian M onte C arlo. In Proceedings of the 34th International Conference on Machine Learning, pp.\ 1009--1018, July 2017. URL http://proceedings.mlr.press/v70/dinh17a.html

    2017

  6. [14]

    Beast: Bayesian evolutionary analysis by sampling trees

    Alexei J Drummond and Andrew Rambaut. Beast: Bayesian evolutionary analysis by sampling trees. BMC evolutionary biology, 7: 0 1--8, 2007

    2007

  7. [15]

    Establishment and lineage dynamics of the SARS-CoV-2 epidemic in the UK

    Louis du Plessis, John T McCrone, Alexander E Zarebski, Verity Hill, Christopher Ruis, Bernardo Gutierrez, Jayna Raghwani, Jordan Ashworth, Rachel Colquhoun, Thomas R Connor, Nuno R Faria, Ben Jackson, Nicholas J Loman, \'A ine O'Toole, Samuel M Nicholls, Kris V Parag, Emily S...

    2021

  8. [16]

    ChenRui Duan, Zelin Zang, Siyuan Li, Yongjie Xu, and Stan Z. Li. Phylogen: Language model-enhanced phylogenetic inference via graph structure generation. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024

    2024

  9. [17]

    u nther, Christian T Happi, Edward C Holmes, Brima Kargbo, Sakoba Ke \

    Gytis Dudas, Luiz Max Carvalho, Trevor Bedford, Andrew J Tatem, Guy Baele, Nuno R Faria, Daniel J Park, Jason T Ladner, Armando Arias, Danny Asogun, Filip Bielejec, Sarah L Caddy, Matthew Cotten, Jonathan D'Ambrozio, Simon Dellicour, Antonino Di Caro, Joseph W Diclaro, Sophie ...

    2017

  10. [18]

    Felsenstein

    J. Felsenstein. Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of Molecular Evolution, 17: 0 268--276, 1981

    1981

  11. [19]

    Inferring Phylogenies

    Joseph Felsenstein. Inferring Phylogenies. Sinauer associates, 2 edition, 2004

    2004

  12. [20]

    Toward defining the course of evolution: minimum change for a specific tree topology

    Walter M Fitch. Toward defining the course of evolution: minimum change for a specific tree topology. Systematic Biology, 20 0 (4): 0 406--416, 1971

    1971

  13. [21]

    J. R. Garey, T. J. Near, M. R. Nonnemacher, and S. A. Nadler. Molecular evidence for A canthocephala as a subtaxon of R otifera. Mol. Evol., 43: 0 287--292, 1996

    1996

  14. [22]

    Schoenholz, Patrick F

    Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural message passing for quantum chemistry. ArXiv, abs/1704.01212, 2017

    2017 arXiv

  15. [23]

    S. B. Hedges, K. D. Moberg, and L. R. Maxson. Tetrapod phylogeny inferred from 18 S and 28 S ribosomal RNA sequences and review of the evidence for amniote relationships. Mol. Biol. Evol., 7: 0 607--633, 1990

    1990

  16. [24]

    D. A. Henk, A. Weir, and M. Blackwell. Laboulbeniopsis termitarius, an ectoparasite of termites newly recognized as a member of the L aboulbeniomycetes. Mycologia, 95: 0 561--564, 2003

    2003

  17. [25]

    Drummond

    Sebastian H \"o hna and Alexei J. Drummond. Guided tree topology proposals for Bayesian phylogenetic inference. Syst. Biol., 61 0 (1): 0 1--11, January 2012. ISSN 1063-5157. doi:10.1093/sysbio/syr074. URL http://dx.doi.org/10.1093/sysbio/syr074

    2012 doi

  18. [26]

    Efficient mixture learning in black-box variational inference

    Alexandra Hotti, Oskar Kviman, Ricky Mol \'e n, V \' ctor Elvira, and Jens Lagergren. Efficient mixture learning in black-box variational inference. In The Forty-first International Conference on Machine Learning, 2024

    2024

  19. [27]

    An introduction to variational methods for graphical models

    Michael I Jordan, Zoubin Ghahramani, Tommi S Jaakkola, and Lawrence K Saul. An introduction to variational methods for graphical models. Machine learning, 37: 0 183--233, 1999

    1999

  20. [28]

    Evolution of protein molecules

    Thomas H Jukes, Charles R Cantor, et al. Evolution of protein molecules. Mammalian protein metabolism, 3: 0 21--132, 1969

    1969

  21. [29]

    Variational phylodynamic inference using pandemic-scale data

    Caleb Ki and Jonathan Terhorst. Variational phylodynamic inference using pandemic-scale data. Mol. Biol. Evol., July 2022. ISSN 0737-4038, 1537-1719. doi:10.1093/molbev/msac154. URL http://dx.doi.org/10.1093/molbev/msac154

    2022 doi

  22. [30]

    D. P. Kingma and J. Ba. Adam: A method for stochastic optimization. In The third International Conference on Learning Representations, 2015

    2015

  23. [31]

    Kingma and Max Welling

    Diederik P. Kingma and Max Welling. Auto-encoding variational Bayes . In The second International Conference on Learning Representations, 2014

    2014

  24. [32]

    VaiPhy : a variational inference based algorithm for phylogeny

    Hazal Koptagel, Oskar Kviman, Harald Melin, Negar Safinianaini, and Jens Lagergren. VaiPhy : a variational inference based algorithm for phylogeny. In Advances in Neural Information Processing Systems, 2022

    2022

  25. [33]

    Lakner, P

    C. Lakner, P. van der Mark, J. P. Huelsenbeck, B. Larget, and F. Ronquist. Efficiency of M arkov chain M onte C arlo tree proposals in B ayesian phylogenetics. Syst. Biol., 57: 0 86--103, 2008

    2008

  26. [34]

    The estimation of tree posterior probabilities using conditional clade probability distributions

    Bret Larget. The estimation of tree posterior probabilities using conditional clade probability distributions. Syst. Biol., 62 0 (4): 0 501--511, July 2013. ISSN 1063-5157. doi:10.1093/sysbio/syt014. URL http://dx.doi.org/10.1093/sysbio/syt014

    2013 doi

  27. [35]

    Larget and D

    Bret R. Larget and D. L. Simon. Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees. Molecular Biology and Evolution, 16: 0 750--750, 1999

    1999

  28. [36]

    Trajectory balance: Improved credit assignment in GF lownets

    Nikolay Malkin, Moksh Jain, Emmanuel Bengio, Chen Sun, and Yoshua Bengio. Trajectory balance: Improved credit assignment in GF lownets. In Advances in Neural Information Processing Systems, 2022

    2022

  29. [37]

    Minimizing the average distance to a closest leaf in a phylogenetic tree

    Frederick A Matsen IV, Aaron Gallagher, and Connor O McCoy. Minimizing the average distance to a closest leaf in a phylogenetic tree. Systematic Biology, 62 0 (6): 0 824--836, 2013

    2013

  30. [38]

    B. Mau, M. Newton, and B. Larget. Bayesian phylogenetic inference via M arkov chain M onte C arlo methods. Biometrics, 55: 0 1--12, 1999

    1999

  31. [39]

    Geophy: Differentiable phylogenetic inference via geometric gradients of tree topologies

    Takahiro Mimori and Michiaki Hamada. Geophy: Differentiable phylogenetic inference via geometric gradients of tree topologies. In The Thirty-seventh Annual Conference on Neural Information Processing Systems, 2023

    2023

  32. [40]

    Variational inference for monte carlo objectives

    Andriy Mnih and Danilo Jimenez Rezende. Variational inference for monte carlo objectives. In The Thirty-third International Conference on Machine Learning, 2016

    2016

  33. [41]

    Improved variational bayesian phylogenetic inference using mixtures

    Ricky Mol \'e n, Oskar Kviman, and Jens Lagergren. Improved variational bayesian phylogenetic inference using mixtures. Transactions on Machine Learning Research, 2024. ISSN 2835-8856

    2024

  34. [42]

    Blei, and Itsik Pe’er

    Antonio Khalil Moretti, Liyi Zhang, Christian Andersson Naesseth, Hadiah Venner, David M. Blei, and Itsik Pe’er. Variational combinatorial sequential M onte C arlo methods for B ayesian phylogenetic inference. In The Thirty-seventh Conference on Uncertainty in Artificial Intel...

    2021

  35. [43]

    Attending to graph transformers

    Luis M \"u ller, Mikhail Galkin, Christopher Morris, and Ladislav Ramp \'a s ek. Attending to graph transformers. Transactions on Machine Learning Research, 2024. ISSN 2835-8856

    2024

  36. [44]

    OpenAI. Gpt-4o. https://openai.com/blog/gpt-4o, 2024

    2024

  37. [45]

    PyTorch : An imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas K \"o pf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu...

    2019

  38. [46]

    Kosioreck, Tuan Anh Le, Chris J

    Tom Rainforth, Adam R. Kosioreck, Tuan Anh Le, Chris J. Maddison, Maximilian Igl, Frank Wood, and Yee Whye Teh. Tighter variational bounds are not necessarily better. In Proceedings of the 36th International Conference on Machine Learning, 2019

    2019

  39. [47]

    MrBayes 3.2: Efficient B ayesian phylogenetic inference and model choice across a large model space

    Fredrik Ronquist, Maxim Teslenko, Paul Van Der Mark, Daniel L Ayres, Aaron Darling, Sebastian H \"o hna, Bret Larget, Liang Liu, Marc A Suchard, and John P Huelsenbeck. MrBayes 3.2: Efficient B ayesian phylogenetic inference and model choice across a large model space. Systema...

    2012

  40. [48]

    A. Y. Rossman, J. M. Mckemy, R. A. Pardo-Schultheiss, and H. J. Schroers. Molecular studies of the B ionectriaceae using large subunit rDNA sequences. Mycologia, 93: 0 100--110, 2001

    2001

  41. [49]

    The neighbor-joining method: a new method for reconstructing phylogenetic trees

    Naruya Saitou and Masatoshi Nei. The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular biology and evolution, 4 0 (4): 0 406--425, 1987

    1987

  42. [50]

    Spielman

    Daniel A. Spielman. Spectral and Algebraic Graph Theory. 2025. URL http://cs-www.cs.yale.edu/homes/spielman/sagt/sagt.pdf

    2025

  43. [51]

    PAUP* : Phylogenetic analysis using parsimony

    David Swofford. PAUP* : Phylogenetic analysis using parsimony. version 4. http://paup. csit. fsu. edu/, 2003

    2003

  44. [52]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems, volume 30, 2017

    2017

  45. [53]

    Liangliang Wang, Alexandre Bouchard-C \^o t \'e , and A. Doucet. B ayesian phylogenetic inference using a combinatorial sequential M onte C arlo method. Journal of the American Statistical Association, 110: 0 1362 -- 1374, 2015

    2015

  46. [54]

    Sarma, Michael M

    Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E. Sarma, Michael M. Bronstein, and Justin M. Solomon. Dynamic graph CNN for learning on point clouds. ACM Transactions on Graphics (TOG), 38: 0 1 -- 12, 2018

    2018

  47. [55]

    Quantifying MCMC exploration of phylogenetic tree space

    Chris Whidden and Frederick A Matsen IV. Quantifying MCMC exploration of phylogenetic tree space. Syst. Biol., 64 0 (3): 0 472--491, May 2015. ISSN 1063-5157, 1076-836X. doi:10.1093/sysbio/syv006. URL http://dx.doi.org/10.1093/sysbio/syv006

    2015 doi

  48. [56]

    ART ree: A deep autoregressive model for phylogenetic inference

    Tianyu Xie and Cheng Zhang. ART ree: A deep autoregressive model for phylogenetic inference. In Thirty-seventh Conference on Neural Information Processing Systems, 2023

    2023

  49. [57]

    Variational bayesian phylogenetic inference with semi-implicit branch length distributions

    Tianyu Xie, Frederick A Matsen IV, Marc A Suchard, and Cheng Zhang. Variational bayesian phylogenetic inference with semi-implicit branch length distributions. arXiv preprint arXiv:2408.05058, 2024 a

    2024 arXiv

  50. [58]

    Improving tree probability estimation with stochastic optimization and variance reduction

    Tianyu Xie, Musu Yuan, Minghua Deng, and Cheng Zhang. Improving tree probability estimation with stochastic optimization and variance reduction. Statistics and Computing, 34 0 (6): 0 186, 2024 b

    2024

  51. [59]

    Phylo VAE : Unsupervised learning of phylogenetic trees via variational autoencoders

    Tianyu Xie, Harry Richman, Jiansi Gao, Frederick A Matsen IV, and Cheng Zhang. Phylo VAE : Unsupervised learning of phylogenetic trees via variational autoencoders. In The Thirteenth International Conference on Learning Representations, 2025

    2025

  52. [60]

    W. Xie, P. O. Lewis, Y. Fan, L. Kuo, and M.-H. Chen. Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Syst. Biol., 60: 0 150--160, 2011

    2011

  53. [61]

    On layer normalization in the transformer architecture

    Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. In The Thirty-seventh International Conference on Machine Learning, pp.\ 10524--10533. PMLR, 2020

    2020

  54. [62]

    Yang and A

    Z. Yang and A. D. Yoder. Comparison of likelihood and B ayesian methods for estimating divergence times using multiple gene loci and calibration points, with application to a radiation of cute-looking mouse lemur species. Syst. Biol., 52: 0 705--716, 2003

    2003

  55. [63]

    Bayesian phylogenetic inference using DNA sequences: a Markov chain Monte Carlo method

    Ziheng Yang and Bruce Rannala. Bayesian phylogenetic inference using DNA sequences: a Markov chain Monte Carlo method. Molecular Biology and Evolution, 14 0 (7): 0 717--724, 1997

    1997

  56. [64]

    A. D. Yoder and Z. Yang. Divergence datas for M alagasy lemurs estimated from multiple gene loci: geological and evolutionary context. Mol. Ecol., 13: 0 757--773, 2004

    2004

  57. [65]

    Improved variational Bayesian phylogenetic inference with normalizing flows

    Cheng Zhang. Improved variational Bayesian phylogenetic inference with normalizing flows. In The Thirty-fourth Conference on Neural Information Processing Systems, 2020

    2020

  58. [66]

    Learnable topological features for phylogenetic inference via graph neural networks

    Cheng Zhang. Learnable topological features for phylogenetic inference via graph neural networks. In The Eleventh International Conference on Learning Representations, 2023

    2023

  59. [67]

    Generalizing tree probability estimation via B ayesian networks

    Cheng Zhang and Frederick A Matsen IV. Generalizing tree probability estimation via B ayesian networks. In The Thirty-second Conference on Neural Information Processing Systems, 2018

    2018

  60. [68]

    Variational Bayesian phylogenetic inference

    Cheng Zhang and Frederick A Matsen IV. Variational Bayesian phylogenetic inference. In The Seventh International Conference on Learning Representations, 2019

    2019

  61. [69]

    A variational approach to B ayesian phylogenetic inference

    Cheng Zhang and Frederick A Matsen IV. A variational approach to B ayesian phylogenetic inference. Journal of Machine Learning Research, 25 0 (145): 0 1--56, 2024

    2024

  62. [70]

    Zhang and M

    N. Zhang and M. Blackwell. Molecular phylogeny of dogwood anthracnose fungus ( D iscula destructiva) and the D iaporthales. Mycologia, 93: 0 355--365, 2001

    2001

  63. [71]

    Influenza research database: An integrated bioinformatics resource for influenza virus research

    Yun Zhang, Brian D Aevermann, Tavis K Anderson, David F Burke, Gwenaelle Dauphin, Zhiping Gu, Sherry He, Sanjeev Kumar, Christopher N Larsen, Alexandra J Lee, et al. Influenza research database: An integrated bioinformatics resource for influenza virus research. Nucleic acids ...

    2017

  64. [72]

    Phylo GFN : Phylogenetic inference with generative flow networks

    Ming Yang Zhou, Zichao Yan, Elliot Layne, Nikolay Malkin, Dinghuai Zhang, Moksh Jain, Mathieu Blanchette, and Yoshua Bengio. Phylo GFN : Phylogenetic inference with generative flow networks. In The Twelfth International Conference on Learning Representations, 2024

    2024

  65. [73]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.