Completion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors

Guojing Cong; Tan Nguyen

REVIEW 4 major objections 6 minor 24 references

Completion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Modeling DrugMatrix as a 3D tensor and completing it with an attention-augmented factorization yields lower error and preserves rare gene signals that 2D and CP baselines flatten.

desk verdict Plausible tensor-completion setup for DrugMatrix, but the headline numbers aren't in the text and the random holdout doesn't match the real missingness. read the letter →

arxiv 2507.03024 v1 pith:EFM3QHYD submitted 2025-07-02 cs.LG cs.AIq-bio.QM

Tan Nguyen , Guojing Cong This is my paper · ORCID

classification cs.LGcs.AIq-bio.QM

keywords 3DtensorcompletionDrugMatrixtoxicogenomicsCPdecompositionattentionmechanismnon-negativefactorizationgeneexpressionimputationsparsedata

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

The paper tries to establish that a toxicogenomics database usually flattened into a matrix should instead be completed as a 3D tensor. Arranging DrugMatrix as tissue by gene by treatment, and factorizing it with a machine-learning-style tensor completion called ToxiTenCompl, yields lower validation error than the 2D matrix-completion baseline and a standard CP decomposition, while keeping the statistical distribution of predicted gene-expression values close to the real one. That matters because the database is dominated by near-zero changes, and the rare, large changes are the ones toxicologists care about but the ones mean-pulling methods lose. If correct, this gives a more faithful completed version of a large in-vivo toxicogenomics database and a template for completing other sparse biological tensors.

What carries the argument

The central object is a third-order tensor $\mathcal{X}\in\mathbb{R}^{R\times U\times I}$ built by mapping DrugMatrix's 2D rows and columns into tissue, gene, and treatment modes. ToxiTenCompl is a CP-style low-rank factorization into tissue, gene, and treatment factor matrices, with the predicted entry $\hat{y}_{r,u,i}=\sum_{d=1}^k r^{(d)}_r\,u^{(d)}_u\,i^{(d)}_i$ plus gene- and treatment-specific biases. Two additions carry the argument: an attention weight per latent component, computed by a softmax over component products, which lets the model modulate contributions for each tissue–gene–treatment triple; and a weighted MSE loss with a variance penalty $-\lambda\,\mathrm{Var}(\hat{y})$, which counteracts the pull toward the global mean in a dataset where 91.94% of fold changes are near zero. The non-negative version enforces non-negative factors after shifting the tensor, enabling tissue-factor cosine similarity clustering.

What would settle it

Retrain ToxiTenCompl with a tissue-stratified holdout that hides all brain and intestine entries (the tissues with the least data) and compare MAE and MSE against the 2D baseline; if the advantage disappears, the random-holdout gain does not transfer to the entries the completion is meant to fill.

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Extended reading notes

Core claim

The paper's central claim is that DrugMatrix, conventionally viewed as a 2D matrix of endpoints by treatments, is better modeled as a 3D tensor indexed by tissue, gene, and treatment, and completed by a gradient-descent factorization the authors call ToxiTenCompl. With an attention term and a weighted loss that counteracts the dominance of near-zero fold changes, ToxiTenCompl reaches lower validation MAE, MSE, and weighted MAE than the 2D ToxiCompl method and than generic CP decomposition; it also produces predictions whose distribution stays closer to the observed data and preserves rare over- and under-expression signals that the baselines pull toward the mean. A non-negative version yields tissue factor vectors whose cosine similarities mark closer relationships among bone marrow, kidney, and intestine. The paper interprets these results as evidence that preserving multi-way structure helps complete the sparsely observed transcriptomic part of DrugMatrix and can support tissue-level toxicology analysis.

Load-bearing premise

The evaluation assumes a random holdout of observed entries represents the missing entries, though the unobserved entries are absent in a systematic, tissue-dependent way.

Editorial extensions

If this is right

The full DrugMatrix tensor can be reconstructed with lower expected error than the previous 2D completion, giving toxicologists a more faithful version of the roughly 580-million-entry database to mine.
Rare, biologically meaningful gene-expression shifts are less likely to be smoothed away, so downstream analyses of over- and under-expressed genes rest on more reliable imputed values.
Tissue factor clustering can be used to generate hypotheses about shared biology across organs; the paper specifically finds higher similarity among bone marrow, kidney, and intestine.
The gradient-descent, attention-augmented formulation establishes a practical alternative to classical alternating-minimization tensor completion for large sparse biological tensors.
Because treatment factors are explicit, the same tensor framework can be extended to higher dimensions with dose or time as a separate mode, a direction the paper names as future work.

Reading between the lines

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

Reading beyond the paper: the reported comparison is on a random holdout, so if DrugMatrix's real missingness is systematic (brain and intestine have far fewer observations than liver and kidney), the accuracy gain may not carry over to the entries the method is meant to fill.
A natural next experiment the paper does not run is a tissue-stratified holdout that withholds whole tissues, which would directly test whether the 3D model helps where data are genuinely absent rather than randomly missing.
The attention weights and tissue factors could be probed against known tissue-expression atlases or independent toxicology benchmarks; a match would turn the internal factor structure into an externally validated biological signal.
If the distribution-preservation result transfers across species, the same tensor completion could be used to fill rat-to-human extrapolation gaps, though the paper only gestures at that possibility.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is the first tensor-completion attack on DrugMatrix as far as the citations show, and the attention-warmed CP with a variance penalty is a reasonable engineering setup. But the current manuscript doesn't let you verify the headline numbers: no error values in the text, no code, no hyperparameter details, and the holdout scheme doesn't match the missingness pattern the model is supposed to fix.

What's new and what works: nobody else has applied 3D tensor completion to DrugMatrix, and the workflow (map the 2D matrix to tissue×gene×treatment, factor with CP, add an attention mechanism, weight the loss toward rare signals) is a sensible adaptation. Comparing against the authors' own ToxiCompl plus generic CP is a fair baseline choice. The non-negative tissue factors and cosine-similarity clustering are a nice exploratory aside, and the authors hedge the biology appropriately.

Soft spots, roughly in order. First, the central empirical claim lives only in figures. No MAE/MSE values, no error bars, no significance tests, no test-set size. That's not refereeable as-is. Second, the 'avoids central tendency' and 'preserves rare signals' results in Section 4.3 are properties the loss function explicitly encourages via the weighted MSE and the -λ Var(ŷ) term. Presenting those as empirical findings is circular; the paper never separates what the attention mechanism adds beyond the loss. Third, the cold-start holdout in §3.2 samples observed entries randomly, but DrugMatrix is missing in a tissue-dependent way (brain 0.55M vs liver 34.5M observations per Table 1). A random split is dominated by liver and kidney, so the gain may not transfer to the under-sampled tissues the completion is actually for. The authors concede BR and IN do worse in §5, which is honest, but it undercuts the 'completes DrugMatrix' framing. Fourth, small but real: the index-mapping equation in §3.1 looks off by a factor of 8, and the text contradicts itself on whether heart or brain is the exception in Figure 5. Also, the paper says 'completes the database' but only models transcriptomic endpoints, not histopathology, clinical chemistry, or hematology.

The citation pattern looks fine, and the ToxiCompl baseline is cited properly. This isn't a dishonest paper; it's an under-specified engineering report with an over-wide claim.

Who this is for: someone working on toxicogenomics imputation or tensor methods for biological matrices might read it for the idea, but not for numbers. It deserves a serious referee, but only with major revision: report actual numbers, add a missingness-aware evaluation, separate loss-induced behavior from model contributions, and provide code or a full configuration.

Referee Report

4 major / 6 minor

Summary. The manuscript proposes ToxiTenCompl, a CP-style tensor completion method for the DrugMatrix toxicogenomics database. The authors convert the DrugMatrix 2D matrix into a 3D tensor over tissues, genes, and treatment conditions; add an attention mechanism over latent factors; and train with a weighted MSE loss augmented by a variance penalty. They report that ToxiTenCompl achieves lower validation MAE, MSE, weighted MAE, and MaxAE than the 2D ToxiCompl baseline and the generic CP baseline, and that its predictions better match the original data distribution, especially for rare and extreme gene-expression signals. A non-negative variant gives tissue factor vectors whose cosine similarities are interpreted as tissue-tissue relationships. The paper concludes that the completed database is more accurate than previous completions and that the tensor approach is promising for cross-species toxicogenomics.

Significance. If the quantitative claims held, the paper would make a useful applied contribution: it is a plausible next step beyond the 2D ToxiCompl baseline, it explicitly addresses the highly skewed distribution of DrugMatrix, and the non-negative tissue factors provide a concrete, interpretable output. The paper also deserves credit for framing completion as a machine-learning optimization problem rather than as a purely algebraic tensor routine, and for including a tissue-level analysis that goes beyond aggregate error. However, the reported evidence is substantially weaker than the claims: no numerical values, error bars, significance tests, or test-set sizes are given; all quantitative comparisons appear only in figures. The paper releases no code or data artifacts, and several load-bearing details of the method are underspecified. As presented, the manuscript is a reasonable research proposal but does not yet meet the reporting standard for a journal-level claim of improved completion accuracy.

major comments (4)

[Section 4.1-4.2, Figs. 2-3] The central quantitative claim of the paper, that ToxiTenCompl has lower MAE, MSE, weighted MAE, and MaxAE than ToxiCompl and CP, is supported only by figures; no numeric values, validation-set sizes, standard deviations, or significance tests are reported. Without these numbers, a reader cannot assess the magnitude of the claimed gains or whether the differences are within run-to-run noise. Please report the exact final metrics for each method, the number of holdout entries, and preferably confidence intervals or repeated-run statistics.
[Section 3.2, Section 5, Table 1] The random-entry holdout described in Section 3.2 does not match the systematic, tissue-dependent missingness of DrugMatrix. Table 1 shows that liver and kidney dominate the observed entries (34.5M and 19.0M, respectively), while brain and intestine have only 0.55M and 0.17M observations, and Section 5 concedes that ToxiTenCompl performs worse for tissues with little data. A random holdout therefore evaluates mostly liver and kidney entries, and aggregate MAE/MSE can improve even if the method is no better on brain and intestine or on entirely missing treatment-tissue blocks. Since the paper's goal is to complete the database, please add per-tissue error metrics and evaluate on a missingness-aware split, for example by holding out whole treatment-tissue blocks or by reporting errors separately for under-sampled tissues.
[Section 3.1, Eq. (1)] The tensor construction equation X_{r,u,i} <- G_{r*8*|U|+u, i} is dimensionally inconsistent and ambiguous. If R is the number of tissues (or tissue-platform combinations) and U is the number of unique genes, the row index of G should depend on r, u, and the platform in a way that is not captured by r*8*|U|+u; the factor 8 appears without definition, and the expression double-counts the gene index. Because this mapping defines the entire 3D tensor, the current description is not reproducible and may indicate an indexing bug. Please rewrite the mapping with explicit ranges and definitions of all indices.
[Section 3.4 and Section 4.3] The claims in Section 4.3 that ToxiTenCompl 'avoids central tendency' and 'preserves rare signals' are presented as empirical findings, but these behaviors are directly encouraged by the design of the loss function in Section 3.4: the weighted MSE assigns higher weights to over- and under-expressed genes, and the -lambda Var(yhat) term explicitly rewards prediction variance. The observed distributional behavior is therefore not an independent discovery; it is in part a consequence of the objective. Please reframe these statements as properties of the loss design, and provide a controlled comparison (e.g., with lambda=0 or with uniform weights) to show whether the tensor structure and attention mechanism add preservation of rare signals beyond what the loss itself enforces.

minor comments (6)

[Section 4.3, Fig. 5] The figure caption says ToxiTenCompl predictions are closer to the input 'except for Heart (HE)', while the main text says the exception is brain tissue. Please correct this inconsistency and state explicitly which tissue(s) show larger deviation.
[Section 3.4] The text 'Var(yhat) measures the deviation of ground truth from the mean values of gene expression' is not a definition of the variance of predictions; please clarify whether the variance term is taken over the predicted values, over a mini-batch, or over the reconstructed tensor, and specify how lambda is selected.
[Section 3.2] The preprocessing details are underspecified: the z-score outlier threshold, the choice between Min-Max scaling and StandardScaler, and whether normalization is applied per transcript or per tissue are not stated. These choices can materially affect all reported metrics.
[Section 4.2] Please state how the validation holdout was constructed beyond 'randomly selected subset': the fraction of held-out entries, the random seed, and whether the same holdout was used for all three methods.
[Section 2.2 and throughout] There are several typographical errors that should be fixed before resubmission, including 'toxicogenomis-aware' in the Section 2.2 heading, 'ToxCompl' where ToxiCompl is meant, 'truggles' in Section 2.3, 'annotaitons' in Section 2.2, and 'withtin' in Section 1.
[Table 2] The caption states that the distribution includes 'test predictions made by the original (ToxiCompl) model', but the table itself lists only category percentages and does not explain how these categories were derived from the predicted values; please clarify.

Circularity Check

1 steps flagged · score 6.0 of 10

The distribution-preservation and rare-signal results reduce to the training loss; the holdout MAE/MSE comparison is independent.

self definitional [Section 3.4 (Custom Loss Functions and Metrics) vs. Section 4.3 (Prediction Distribution)]
"we adopt a revised, weighted MSE loss, assigning higher weights w_{r,u,i} to over- and under-expressed genes: L_weighted = 1/N Sum w_{r,u,i}(y_{r,u,i} - y_hat_{r,u,i})^2 - lambda * Var(y_hat). ... Weighted MSE loss balances overall prediction performance and performance for rare signals. ... ToxiTenCompl notably avoids the tendency to predict the mean of data (central tendency), a characteristic of the ToxiCompl predictions. ... ToxiTenCompl better preserves these significant variations, confirming it captures more nuanced biological responses in gene expression."

The training objective in Section 3.4 explicitly contains the properties that Section 4.3 reports as findings. The -lambda * Var(y_hat) term directly rewards prediction variance, which is the opposite of central tendency, and the per-entry weights w_{r,u,i} give extra importance to over- and under-expressed entries, i.e., rare signals. Therefore 'avoids central tendency' and 'better preserves rare signals' are consequences of the chosen loss by construction, not emergent properties revealed by the tensor or attention architecture. The comparison with ToxiCompl shows only that a model optimized with a variance-encouraging, rare-signal-weighted objective has more spread than one trained with plain MSE; it does not independently validate the 3D structure or attention mechanism.

full rationale

The core quantitative claim of the paper, lower validation MAE and MSE on a random holdout, is not circular: the ToxiTenCompl predictions are compared against ToxiCompl and CP on held-out entries, and no fitting of those baselines into the test set is described. The same-group ToxiCompl baseline is a normal comparison, not a load-bearing self-citation. The main circularity is confined to the distribution/rare-signal portion of the evaluation: the weighted MSE plus -lambda Var(y_hat) loss directly encodes the objectives that Section 4.3 then presents as empirical advantages. A separate external-validity concern (random holdout vs. systematic tissue-dependent missingness in DrugMatrix, acknowledged for BR/IN in Section 5) is a limitation of the evidence, not a circularity, and does not raise the score further. Overall, partial circularity: one prominent validation claim reduces by construction, while the holdout-error comparison retains independent content.

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

The central claim rests on the existence of a low-rank multilinear structure in DrugMatrix gene expression, on the validity of the row-to-tensor mapping, and on a random-holdout evaluation that may not match the true missing-data mechanism. In addition, several numeric choices (rank, lambda, weights, thresholds) are required to reproduce the claims, but are not specified in the text.

free parameters (6)

rank k = 300
Latent dimensionality for tissue, gene, and treatment factors; fixed to 300 in both ToxiTenCompl and ToxiCompl with no sensitivity analysis. The completion error depends on this choice.
variance penalty coefficient lambda
Weight on -lambda Var(yhat) in the loss (Section 3.4). Value is not reported; it directly controls the claimed distribution-preservation behavior.
per-sample loss weights w_{r,u,i}
Weights for over/under-expressed genes in the weighted MSE loss (Section 3.4). The weighting scheme is not specified, yet it drives the rare-signal MAE result.
z-score outlier threshold
Outliers are removed by 'statistical thresholding based on z-scores' (Section 3.2) but the threshold is never stated, changing the training set.
data normalization choice = Min-Max or StandardScaler
Either Min-Max scaling or StandardScaler is applied (Section 3.2) but not which one, nor the scaling range; this affects all subsequent values.
attention MLP architecture
The attention scores are computed from learned factor entries (Section 3.3) but the architecture, size, and whether side-information MLPs are used are unspecified.

assumptions (6)

domain assumption DrugMatrix rows can be losslessly rearranged into a 3D tensor with dimensions (tissue, gene, treatment) using the stated mapping.
Section 3.1 introduces the mapping X_{r,u,i} <- G_{r*8*|U|+u,i}; this assumes the original row index contains exactly the tissue/gene information needed and that the linear index formula is correct. The formula appears dimensionally questionable.
domain assumption A low-rank CP-style model with shared latent factors captures the biological signal in gene expression.
The model approximates each entry as a sum of rank-one products of tissue, gene, and treatment factors (Section 3.3). No evidence is given that DrugMatrix gene expression is approximately low-rank.
domain assumption A random holdout of observed entries has the same distribution as the missing entries.
Section 3.2 evaluates on a random subset of observed entries, but the real missing data are systematic across tissues and treatments, making this assumption questionable.
domain assumption The variance term and weights in the loss reflect biological importance rather than only statistical goals.
Section 3.4 defines the weighted loss with Var(yhat); the choice assumes that preserving variance and weighting rare signals is the right objective for toxicogenomic imputation.
domain assumption Non-negative factors after subtracting the minimum and clipping are biologically interpretable.
Section 4.4 uses the non-negative variant to cluster tissues; this assumes the resulting factor geometry reflects biological relationships rather than an artifact of the non-negativity transform.
standard math Standard SGD/ADAM optimization converges to a useful solution for this non-convex factorization.
The paper trains by gradient descent (Section 3.4) without discussing local optima, initialization, or convergence guarantees; this is a standard practical assumption.

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Cite this review

Pith. "Pith review of Completion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors." pith.science (2026). https://pith.science/paper/EFM3QHYD

@misc{pith2026250703024,
  author       = {Pith},
  title        = {Pith review of: Completion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFM3QHYD}},
  note         = {Machine review of arXiv:2507.03024}
}

read the original abstract

We explore applying a tensor completion approach to complete the DrugMatrix toxicogenomics dataset. Our hypothesis is that by preserving the 3-dimensional structure of the data, which comprises tissue, treatment, and transcriptomic measurements, and by leveraging a machine learning formulation, our approach will improve upon prior state-of-the-art results. Our results demonstrate that the new tensor-based method more accurately reflects the original data distribution and effectively captures organ-specific variability. The proposed tensor-based methodology achieved lower mean squared errors and mean absolute errors compared to both conventional Canonical Polyadic decomposition and 2-dimensional matrix factorization methods. In addition, our non-negative tensor completion implementation reveals relationships among tissues. Our findings not only complete the world's largest in-vivo toxicogenomics database with improved accuracy but also offer a promising methodology for future studies of drugs that may cross species barriers, for example, from rats to humans.

Figures

Figures reproduced from arXiv: 2507.03024 by the authors.

**Figure 1.** Workflow of ToxiTenCompl 3 A New 3D Approach for Completing DrugMatrix Our tensor completion algorithm, ToxiTenCompl, consists of several stages designed to handle the complexity and multi-dimensional structure of the DrugMatrix toxicogenomics dataset. This structured pipeline, detailed in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Overall MAE and MAE for rare signals: a comparison of ToxiTenCompl against the two baselines [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Validation MSE & MAE comparison between ToxiTenCompl and ToxiCompl. ToxiTenCompl achieved substantially [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Comparison of prediction distributions from ToxiCompl and ToxiTenCompl. ToxiTenCompl effectively avoids the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Average difference between ToxiTenCompl vs. ToxiCompl predictions and original input data, by tissue. ToxiTenCompl [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Clustering of the tissue factors [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Auerbach, Ruchir R

Scott S. Auerbach, Ruchir R. Shah, Deepak Mav, Cynthia S. Smith, Nigel J. Walker, Molly K. Vallant, Gary A. Boorman, and Richard D. Irwin. 2010. Predicting the hepatocarcinogenic potential of alkenylbenzene flavoring agents using toxicogenomics and machine learning. Toxicology and Applied Pharmacology 243, 3 (March 2010), 300–314. doi:10.1016/j.taap.2009.11.021

work page doi:10.1016/j.taap.2009.11.021 2010

[2] [2]

Florian Baier, Stefan Mair, and Serafin G. Fadel. 2023. Self-supervised Siamese Autoencoders. arXiv preprint arXiv:2304.02549. http://arxiv.org/abs/2304.02549

work page Pith review arXiv 2023

[3] [3]

Dror Bank, Noam Koenigstein, and Raja Giryes. 2020. Autoencoders. arXiv preprint arXiv:2003.05991 (2020). http://arxiv.org/abs/2003. 05991

arXiv 2020

[4] [4]

Boaz Barak and Ankur Moitra. 2016. Noisy tensor completion via the sum-of-squares hierarchy. In Conference on Learning Theory (COLT). 417–445

work page 2016

[5] [5]

Minjun Chen, Min Zhang, Jürgen Borlak, and Weida Tong. 2012. A decade of toxicogenomic research and its contribution to toxicological science. Toxicological Sciences 130, 2 (Jul 2012), 217–228. doi:10.1093/toxsci/kfs223

work page doi:10.1093/toxsci/kfs223 2012

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