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REVIEW 3 major objections 4 minor 23 references

Entangled by Design: Spurious Intra-Variable Signal Routing in Tabular In-Context Learners

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read An in-context learner provably routes predictions through spurious signals whenever those signals correlate with outcomes inside its context, and no amount of context or regularisation can prevent it — only context-level swaps reroute it th

desk verdict Correct ridge-ICL theory and a useful S-swap mitigation, but the OOD-recovery claim and the general-ICL conclusion both outrun the evidence. read the letter →

arxiv 2607.25532 v1 pith:HKH5JHGK submitted 2026-07-28 cs.AI

Athanasios Vlontzos , Giorgos Papanastasiou , Bernhard Kainz , Sotirios Tsaftaris This is my paper
classification cs.AI
keywords in-contextlearningspuriouscorrelationcausalsensitivityratiocompositerepresentationsridgeregressiondatasetshiftcontextaugmentationconfounding
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 studies what happens when a single measured feature bundles a true causal signal (C) with a site-specific artefact (S), and an unobserved confounder makes S correlate with the outcome inside the training context. It proves that for linear ridge in-context learning, routing predictions through S rather than C is unavoidable: the optimal ridge weight on S is non-zero for any regularisation strength, and the spurious routing persists as context size grows without bound. The proof yields a closed-form Causal Sensitivity Ratio, CSR_pop proportional to ρ_S/ρ_C, which matches both linear ICL (r=0.997) and the transformer TabPFN (r=0.979) empirically. Because the failure is invisible in-context, the paper introduces two context-construction interventions — environment-stratified contexts and S-swap augmentation — that break the in-context S→Y correlation and reroute the model toward C, cutting spurious routing by up to 98.8% on TabPFN while increasing causal sensitivity 8.4-fold.

What carries the argument

The central object is the composite representation X=[C;αS;η], where the causal signal C and the spurious signal S live in distinct subspaces and α controls how strongly S is represented. The main formula is the Causal Sensitivity Ratio (CSR), defined as the ratio of mean absolute prediction shift under an S-swap to that under a C-swap, which quantifies which signal the model routes through. The proof machinery is ridge in-context regression (Assumption A1) combined with block-diagonal covariance from subspace orthogonality (Assumption A2), which lets the ridge weights decouple into w*_C and w*_S; substituting these into CSR yields the factorised expression of Proposition 2. The S-swap mitig

What would settle it

Train any in-context learner (ridge or transformer) on the paper's exact DGP — orthogonal C and S, an unobserved confounder U making Corr(S,Y)≠0 in context — and measure CSR via swaps; if any model achieves CSR<1 without environment-stratified contexts or S-swap, the 'unavoidable' claim fails. The authors report only linear ridge ICL and TabPFN; a counterexample model, or a theoretical argument showing w*_S=0 under A1–A3, would settle it.

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Extended reading notes

Core claim

Under the paper's DGP, where each observed feature is X=[C;αS;η] with C and S in orthogonal subspaces and an unmeasured confounder U driving both S and Y, the population ridge ICL weights decouple: w*_C = ρ_C/(1+λ) and w*_S = αρ_S/(α²+λ). This yields the closed-form Causal Sensitivity Ratio CSR_pop = (α²/(α²+λ))·(ρ_S/ρ_C)·(1+λ)κ(δ). The paper's central result is that ρ_S ≠ 0 forces w*_S ≠ 0 for every λ>0 (Corollary 2), and that CSR(ŵ_n) → CSR_pop > 0 as n→∞ (Corollary 3), establishing that spurious routing is provably irreducible by data size or regularisation within the ridge ICL class. Empirically, larger context amplifies routing in the high-spurious regime (up to 1.74×) and more expressi

Load-bearing premise

The load-bearing premise is that the causal and spurious signals occupy orthogonal, separately recoverable subspaces within the observed feature (Cov(C,S)=0); if the two overlap in the same coordinates, the closed-form characterisation, the CSR diagnostic, and the S-swap mitigation all lose their footing.

Editorial extensions

If this is right

  • Deployed in-context predictors in multi-site settings (hospitals, sequencing batches) will silently build predictions on site-specific artefacts whenever an unmeasured confounder ties the artefact to the outcome, and collecting more training examples will not fix it.
  • Regularisation strength is not a remedy: the spurious weight w*_S remains non-zero for all λ>0, and CSR saturates at a positive floor as λ grows, so model designers cannot tune their way out of spurious routing.
  • The closed-form CSR gives a practical, model-agnostic diagnostic: measuring the ratio of prediction shifts under S- and C-swaps reveals whether a learner routes through spurious or causal signal, and this ranking is robust to decomposition error (Spearman r=0.849 even at 60° estimation error).
  • Context-level interventions (environment-stratified contexts and S-swap) can recover causal routing without retraining or architectural changes, and S-swap's effect is rerouting rather than agnosticism — TabPFN's causal sensitivity increases 8.4× while spurious sensitivity collapses.
  • The theory's core prediction — routing magnitude scales with ρ_S/ρ_C — is confirmed with correlation r=0.997 for linear ICL and r=0.979 for TabPFN, and degrades gracefully (r≥0.90) under subspace overlap up to 40°.

Reading between the lines

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

  • The paper's robustness table suggests a testable extension: batch-harmonisation pipelines that reduce but do not eliminate subspace overlap may intensify routing (mean CSR rises with overlap up to 30–40°), implying that partial artefact removal could be worse than none for in-context learners; full removal would disable the spurious route.
  • The CSR diagnostic could be inverted into a self-supervised learning objective: parameterise a learned transformation of X into (Ĉ,Ŝ) and minimise CSR over that transformation, turning the metric from an evaluation tool into a training signal that requires only environment labels.
  • The mechanism should apply beyond tabular ICL: any in-context learner — including large language models given user-supplied examples — should route through spurious cues when a hidden confounder correlates those cues with the label inside the context; a natural test is to construct such a context for an LLM and measure CSR via the same swap protocol.
  • Because the impossibility result is proven only within ridge ICL (A1), the paper's empirical finding that TabPFN also routes spuriously leaves open whether some non-ridge in-context learner could implicitly model environment structure and avoid routing; if one existed, it would bound the class of learners for which the failure is truly unavoidable.
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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 / 4 minor

Summary. The paper studies a failure mode it calls spurious routing in composite representations: an observed feature X=[C; alpha S; eta] bundles a causal signal C and a spurious signal S in distinct subspaces, and an in-context learner (ICL) trained on a confounded environment may predict through S rather than C. The main theoretical result, Proposition 2, derives a closed-form expression for the Causal Sensitivity Ratio (CSR) under population ridge ICL with orthogonal C and S (Assumptions A1–A3): CSR_pop = alpha^2/(alpha^2+lambda) * (rho_S/rho_C) * (1+lambda) kappa(delta), and Corollaries 1–3 conclude monotonicity, impossibility of avoiding spurious weight for any lambda>0, and persistence as n grows. The paper then reports empirical agreement with this formula for linear ICL (r=0.997) and for the pretrained TabPFN (r=0.979), studies amplification with context size and entanglement, and proposes two context-level mitigations, environment-stratified sampling and S-swap augmentation, reporting large CSR reductions especially for TabPFN. A semi-synthetic scIB pancreas experiment with an estimated spurious subspace is also presented.

Significance. If the result holds, the paper makes a useful conceptual contribution: it identifies a distinct failure mode for in-context learners, gives a parameter-free closed-form diagnostic in a minimal identifiable setting, and proposes model-agnostic interventions that require only weak environment labels. The strengths are the explicitly stated assumptions, the transparent derivation of Eq. (3), the falsifiable predictions tested on a controlled SCM, and the inclusion of a real-data validation with an estimated spurious subspace. The weaknesses are that the impossibility result is proven only for ridge ICL, the empirical bridge to TabPFN rests on a single pretrained model without repeated-seed statistics, and one headline claim about out-of-distribution recovery is contradicted by the paper's own tables. With appropriate scoping and additional empirical support, the paper could be a solid contribution to the ICL and invariant-learning literature.

major comments (3)
  1. [§6, Tables 6 and 9] The introduction bullet and §6 state that S-swap 'recover[s] out-of-distribution accuracy' without knowledge of the causal partition. This is not supported for TabPFN: Table 6 reports TabPFN OOD RMSE 3.539 under S-swap versus 3.486 for standard ICL, i.e. worse, and Table 9 shows S-swap OOD RMSE worse than env-stratified in all five TabPFN settings. Only the linear-ICL results (Table 8) show OOD improvement. The OOD-recovery claim must be scoped to linear ICL or revised, and the text should explicitly address the CSR/OOD divergence for TabPFN.
  2. [§5, Tables 1–3 and 6] The main empirical tables report no error bars, no number of seeds, and no confidence intervals. The NeurIPS checklist (item 7) says error bars are provided in Section 5, but none appear there; only the scIB table (Table 7/14) includes ± values. Because the paper's quantitative claims — r=0.979 for TabPFN, the 1.74× context-size amplification, and the 98.8% CSR reduction — are single-point estimates, the reader cannot assess their statistical robustness. Please add repeated-seed or bootstrapped intervals for at least the headline numbers and for the context-size sweep in Table 2/10.
  3. [Abstract, §1 and §7] The abstract and introduction state that spurious routing is 'unavoidable regardless of context size' and frame it as a property of in-context learners generally. Corollary 2 and the proof in Appendix A prove this only for ridge ICL under A1–A3, and the paper's own Limitations (§7) concede that the closed form does not extend to TabPFN and that a nonlinear estimator could in principle recover identifiability. Moreover, S-swap itself demonstrates that routing is avoidable when the context construction is changed to break the in-context S–Y correlation. The impossibility claim should be scoped throughout the abstract and introduction to 'the ridge-ICL class with a fixed confounded context distribution.'
minor comments (4)
  1. [Appendix A.1, Eq. (4)] The printed folded-normal formula for E|Z| with Z ~ N(delta, 2) appears to be missing a factor of 2 in the first term: the correct term is 2/sqrt(pi) exp(-delta^2/4), not sqrt(2) phi(delta/sqrt(2)). The numerical value kappa(1.5) ≈ 1.516 cited in the paper is consistent with the correct formula, so this is likely a typographical error, but it should be fixed.
  2. [Proposition 2 and §3] Proposition 2 writes X=[C; alpha S] and omits the noise dimensions eta that are present in the Section 3 DGP. The omission is harmless because eta has zero population covariance with Y, but the main text should state this explicitly to avoid an apparent mismatch between the theoretical setup and the experimental setup.
  3. [Table 1 and Appendix C] The 'Normalised CSR' column is used in Table 1 for TabPFN but is not defined in the main text; its definition and oracle-ceiling values appear only in Appendix C. A one-sentence definition at first use would help the reader interpret the main result.
  4. [NeurIPS checklist, items 5 and 7] Checklist item 5 answers [Yes] on open access, but the text says only that code 'will be given with the camera ready version'; no code or URL is available at submission. Checklist item 7 answers [Yes] on error bars, but the main tables contain none. The checklist answers should be aligned with the actual submission to avoid overstating reproducibility.

Circularity Check

1 steps flagged · score 3.0 of 10

Linear-ICL 'confirmation' of CSR∝ρS/ρC is nearly definitional; the derived theorem and the independent TabPFN test remain non-circular.

  1. self definitional [Section 5, 'Routing scales with ρS/ρC'; Eqs. (1) and (3), Definition 1]
    "At α= 1.0 , the Pearson correlation between the empirical signal ratio ˆρS/ˆρC and observed CSR is r= 0.997 for linear ICL and r= 0.979 for TabPFN; the closed-form prediction (3) matches linear ICL values to within 1% mean error at n= 128 ."

    Definition 1 defines CSR(w) directly from the model weights w. Proposition 2 obtains Eq. (3) by substituting the population ridge weights (2) into that same definition under A1–A3. For linear ICL, the 'observed CSR' is exactly that functional evaluated on the finite-sample ridge estimator, whose population limit is (2). Hence the strong linear-ICL correlation with ρS/ρC is enforced by the same algebra used to derive the formula: r=0.997 is a numerical consistency check, not independent confirmation of the prediction. The TabPFN result (r=0.979) remains independent evidence, and the theorem itself is a valid closed-form derivation rather than an assumed conclusion.

full rationale

The core theory is not circular: Proposition 2 is a closed-form derivation from explicit assumptions A1–A3 with no fitted constants, and Corollaries 2–3 follow by direct inspection. The TabPFN experiments are independent of the ridge derivation, and the paper's Limitations section explicitly states that 'the closed form does not extend directly to TabPFN,' so the main empirical bridge is not assumed. The self-citations (Corcoll Andreu et al. 2024; Papanastasiou et al. 2025) are contextual and not load-bearing. The one notable near-circular element is the linear-ICL 'confirmation': because CSR is defined from the ridge weights and Eq. (3) is derived from those same weights, the r=0.997 correlation is essentially a restatement of the derivation rather than an external test. This does not invalidate the theorem or the TabPFN result, but it makes the headline 'confirmed at r=0.997' partly definitional. Hence a moderate score of 3.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The closed form is derived from three explicit assumptions plus the DGP; no fitted constants enter Eq. (3). The main chosen knobs are α, λ, δ, and the scIB injection β. The real-world validation additionally assumes that batch-ratio PCA recovers S, an assumption stress-tested only empirically.

free parameters (5)
  • α (entanglement coefficient) = swept {0.1, 0.5, 1.0, 2.0}
    Controls how strongly S is represented in X; central to the entanglement factor α²/(α²+λ) in Eq. (3). Chosen by hand, not fitted.
  • λ (ridge regularisation) = 10⁻³ for linear ICL
    Appears in w*_S and the CSR formula; cancels at α=1. Chosen rather than derived.
  • δ (between-environment mean shift) = 1.5
    Sets the protocol constant κ(δ)≈1.516 used in all experiments.
  • β (injected confounding strength in scIB) = 0.5
    Injected Y-confounding in the semi-synthetic validation, producing ρ_S/ρ_C=9.09; not derived.
  • TabPFN n_ensemble_configurations = 4
    Hyperparameter used for TabPFN regression; affects the empirical results but not the theory.
assumptions (7)
  • domain assumption A1: The in-context estimator implements population ridge regression, w* = (Σ_X+λI)⁻¹ Σ_XY.
    Exact for linear ICL, only an approximation for transformers/TabPFN. All theoretical inevitability claims are proved inside this class.
  • domain assumption A2: Cov(C,S)=0; causal and spurious signals occupy orthogonal subspaces.
    Makes Σ_X block-diagonal and decouples ridge weights. Stressed by design; violations tested only empirically up to 40° overlap.
  • domain assumption A3: An unobserved confounder U induces Cov(S,Y)≠0 within each training environment, while do(S=s) leaves Y unchanged.
    This is the source of the in-context spurious correlation and is required for w*_S≠0.
  • domain assumption DGP distributional assumptions: C,S,U,η,ε are normal with specified variances; S = β_S U + √(1-β_S²)ε_S + μ_e; Y = (1/D_C)1ᵀC + β_Y U + ε.
    All synthetic experiments inherit these parametric choices; they are not derived from data.
  • domain assumption Separated coordinates with D≥2 are the minimal identifiable setting.
    Proposition 1 shows CSR is unidentifiable when C and S share a single scalar coordinate, so the paper restricts to separated subspaces.
  • domain assumption In practice the C/S decomposition can be estimated from environment structure (harmonisation, batch-ratio PCA).
    Used for the scIB validation and for the claimed practical applicability; robustness tested only in Appendix D/E, not against a ground-truth partition.
  • standard math Standard probability facts: law of large numbers, continuous mapping theorem, folded-normal expectation.
    Used in Corollary 3 and Appendix A.1.

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Pith. "Pith review of Entangled by Design: Spurious Intra-Variable Signal Routing in Tabular In-Context Learners." pith.science (2026). https://pith.science/paper/HKH5JHGK

@misc{pith2026260725532,
  author       = {Pith},
  title        = {Pith review of: Entangled by Design: Spurious Intra-Variable Signal Routing in Tabular In-Context Learners},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HKH5JHGK}},
  note         = {Machine review of arXiv:2607.25532}
}
abstract

Consider a model trained at a single hospital to predict patient recovery, where the measured feature $X$ bundles the patient's true health signal ($C$) with a systematic artefact from that hospital's equipment ($S$). Within that hospital, the artefact correlates with outcomes through unmeasured confounders such as patient demographics; an in-context learner rationally routes predictions through $S$, not $C$, and fails silently when deployed at a new hospital with different equipment. We formalise this as \emph{spurious routing in composite representations}: when a feature $X = [C;\,\alpha S;\,\eta]$ encodes a causal signal $C$ and a spurious signal $S$ in distinct subspaces, the ICL cannot determine which drives predictions. We prove that under ridge ICL, a linear in-context learner, this routing is unavoidable regardless of context size; TabPFN, a state-of-the-art pretrained tabular ICL model, shows qualitatively consistent behaviour empirically. We derive a closed-form characterisation, $\mathrm{CSR} \propto \rho_S/\rho_C$, confirmed at $r = 0.997$ for linear ICL and $r = 0.979$ for TabPFN. Contrary to intuition, larger context sharpens commitment to the dominant in-context signal, amplifying spurious routing by up to $1.74\times$; in the high-spurious corner, more expressive models show greater vulnerability empirically ($+2.22$ CSR gap at high entanglement). We introduce two lightweight mitigations: environment-stratified context construction and S-swap augmentation, that require only weak environment labels and no knowledge of the causal partition. S-swap reduces spurious routing by $74\%$ for linear ICL and $98.8\%$ for TabPFN, with TabPFN's causal sensitivity increasing $8.4\times$ simultaneously: the model does not become agnostic, it reroutes through the causal signal.

Figures

Figures reproduced from arXiv: 2607.25532 by the authors.

Figure 1
Figure 1. SCM: U confounds S → Y in-context; ICL sees X=[C; αS; η] and routes through S. In-context learning (ICL) has emerged as a powerful paradigm for tabular prediction: given a set of labelled examples as context, a model such as TabPFN [Hollmann et al., 2025] can fit a high￾quality predictor at inference time, without gradient updates or access to the full training distribution. This flexibility is precisely what makes … view at source ↗

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Works this paper leans on

23 extracted references · 2 canonical work pages

  1. [1]

    Akyürek, D

    E. Akyürek, D. Schuurmans, J. Andreas, T. Ma, and D. Zhou. What learning algorithm is in- context learning? Investigations with linear models. InThe Eleventh International Conference on Learning Representations (ICLR 2023),

    2023

  2. [5]

    doi: 10.1016/j.jclinepi.2019. 10.007. S. Garg, D. Tsipras, P. Liang, and G. Valiant. What can transformers learn in-context? A case study of simple function classes. InAdvances in Neural Information Processing Systems (NeurIPS 2022), volume 35, pages 30583–30598,

    work page doi:10.1016/j.jclinepi.2019 2019

  3. [11]

    doi: 10.1038/s41592-021-01336-8. S. Müller, N. Hollmann, S. Pineda Arango, J. Grabocka, and F. Hutter. Transformers can do Bayesian inference. InInternational Conference on Learning Representations (ICLR 2022),

    doi:10.1038/s41592-021-01336-8 2022

  4. [12]

    arXiv:2112.10510

    URL https://openreview.net/forum?id=KSugKcbNf9. arXiv:2112.10510. T. M. Norman, M. A. Horlbeck, J. M. Replogle, A. Y . Ge, A. Xu, M. Jost, L. A. Gilbert, and J. S. Weissman. Exploring genetic interaction manifolds constructed from rich single-cell phenotypes. Science, 365(6455):786–793,

    arXiv

  5. [13]

    URL https://www.science

    doi: 10.1126/science.aax4438. URL https://www.science. org/doi/10.1126/science.aax4438. 10 G. Papanastasiou, P. P. Sanchez, S. Christodoulidis, et al. Confounder-aware foundation modeling for accurate phenotype profiling in cell imaging.npj Imaging, 3:52, October

    doi:10.1126/science.aax4438

  6. [14]

    URLhttps://doi.org/10.1038/s44303-025-00116-9

    doi: 10.1038/ s44303-025-00116-9. URLhttps://doi.org/10.1038/s44303-025-00116-9. J. Peters, P. Bühlmann, and N. Meinshausen. Causal inference by using invariant prediction: Identification and confidence intervals.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(5):947–1012,

    work page doi:10.1038/s44303-025-00116-9

  7. [16]

    arXiv:1911.08731. A. Subbaswamy and S. Saria. From development to deployment: dataset shift, causality, and shift- stable models in health AI.Biostatistics, 21(2):345–352,

    arXiv 1911

  8. [17]

    doi: 10.1093/biostatistics/kxz041. J. V on Oswald, E. Niklasson, E. Randazzo, J. Sacramento, A. Mordvintsev, A. Zhmoginov, and M. Vladymyrov. Transformers learn in-context by gradient descent. InProceedings of the 40th International Conference on Machine Learning (ICML 2023), volume 202 ofProceedings of Machine Learning Research, pages 35151–35174. PMLR,

    doi:10.1093/biostatistics/kxz041 2023

Show all 23 references
  1. [18]

    mlr.press/v202/von-oswald23a.html

    URL https://proceedings. mlr.press/v202/von-oswald23a.html. arXiv:2212.07677. Oral presentation. S. M. Xie, A. Raghunathan, P. Liang, and T. Ma. An explanation of in-context learning as implicit Bayesian inference. InInternational Conference on Learning Representations (ICLR 2022),

    2022 arXiv

  2. [19]

    arXiv:2111.02080

    URLhttps://openreview.net/forum?id=RdJVFCHjUMI. arXiv:2111.02080. S. Yan, H. Song, N. Li, L. Zou, and Y . Ying. Improve unsupervised domain adaptation with mixup training. InarXiv preprint,

    arXiv

  3. [20]

    arXiv:2001.00677. 11 A Proofs A.1 Protocol constantκ(δ) Under Var(C) = Var(S) = 1 , the perturbation differences satisfy ∆C∼ N(0,2) and ∆S∼ N(δ,2) , where δ:=µ E′ −µ E is the between-environment mean shift. Using the folded-normal expectationE|Z|=σ p 2/πexp(−µ 2/(2σ2)) +µ(2Φ(µ...

    2001 arXiv

  4. [21]

    The continuous mapping theorem gives ˆwn p − →w∗

    A.5 Proof of Corollary 3 By the law of large numbers, 1 n X ⊤X p − →ΣX and 1 n X ⊤Y p − →ΣXY . The continuous mapping theorem gives ˆwn p − →w∗. The CSR functional w7→ |wS|αE|∆S|/(|wC|E|∆C|) is continuous at w∗ since w∗ C =ρ C/(1 +λ)̸= 0 when ρC ̸= 0 . A second application of ...

  5. [22]

    We simulate estimation error by rotating the true partition by an angleϕ: ˆC= cos(ϕ)C true + sin(ϕ)ε C, ˆS= cos(ϕ)S true + sin(ϕ)ε S, 14 Table 11: CSR vs

    D CSR Robustness to Decomposition Error We test how sensitive CSR is to imperfect estimation of the C/S partition used to construct perturba- tions. We simulate estimation error by rotating the true partition by an angleϕ: ˆC= cos(ϕ)C true + sin(ϕ)ε C, ˆS= cos(ϕ)S true + sin(ϕ...

  6. [23]

    we were unable to find the license for the dataset we used

    E Semi-Synthetic Validation: scIB Pancreas We validate the core phenomenon and context-level mitigations on the scIB human pancreas dataset [Luecken et al., 2022]: 16,382 pancreatic islet cells from five sequencing technologies (CEL-Seq, CEL-Seq2, SmartSeq2, inDrop variants, S...

    2022

  7. [2010]

    doi: 10.1038/nrg2825. M. D. Luecken, M. Büttner, K. Chaichoompu, A. Danese, M. Interlandi, M. F. Mueller, D. C. Strobl, L. Zappia, M. Dugas, M. Colomé-Tatché, and F. J. Theis. Benchmarking atlas-level data integration in single-cell genomics.Nature Methods, 19:41–50,

    doi

  8. [2016]

    URL https: //academic.oup.com/jrsssb/article/78/5/947/7040653

    doi: 10.1111/rssb.12167. URL https: //academic.oup.com/jrsssb/article/78/5/947/7040653. S. Sagawa, P. W. Koh, T. B. Hashimoto, and P. Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. InInternati...

    2020 doi

  9. [2019]

    URLhttps://arxiv.org/abs/1907.02893. O. Corcoll Andreu, A. Vlontzos, M. O’Riordan, and C. M. Gilligan-Lee. Contrastive representations of high-dimensional, structured treatments.arXiv preprint, arXiv:2411.19245,

    1907 arXiv

  10. [2020]

    arXiv:1909.12434

    URLhttps://openreview.net/forum?id=Sklgs0NFvr. arXiv:1909.12434. D. Krueger, E. Caballero, J.-H. Jacobsen, A. Zhang, J. Binas, D. Zhang, R. Le Priol, and A. Courville. Out-of-distribution generalization via risk extrapolation (VREx). InProceedings of the 38th Interna- tional C...

    1909 arXiv

  11. [2021]

    arXiv:2003.00688. J. T. Leek, R. B. Scharpf, H. C. Bravo, D. Simcha, B. Langmead, W. E. Johnson, D. Geman, K. Baggerly, and R. A. Irizarry. Tackling the widespread and critical impact of batch effects in high-throughput data.Nature Reviews Genetics, 11:733–739,

    2003 arXiv

  12. [2022]

    arXiv:2208.01066

    URL https://openreview.net/forum?id= flNZJ2eOet. arXiv:2208.01066. N. Hollmann, S. Müller, L. Purucker, et al. Accurate predictions on small data with a tabular foundation model.Nature, 637:319–326, January

    arXiv

  13. [2023]

    arXiv:2211.15661

    URL https://openreview.net/forum?id= 0g0X4H8yN4I. arXiv:2211.15661. Outstanding Paper Award (top 5%). M. Arjovsky, L. Bottou, I. Gulrajani, and D. Lopez-Paz. Invariant risk minimization.arXiv preprint, arXiv:1907.02893,

    1907 arXiv

  14. [2024]

    URL https://arxiv.org/abs/2411.19245. T. P. A. Debray, Y . Vergouwe, H. Koffijberg, D. Nieboer, E. W. Steyerberg, and K. G. M. Moons. Changing predictor measurement procedures affected the performance of prediction models in clinical examples.Journal of Clinical Epidemiology, ...

    arXiv

  15. [2025]

    URL https://doi.org/10.1038/s41586-024-08328-6

    doi: 10.1038/s41586-024-08328-6. URL https://doi.org/10.1038/s41586-024-08328-6. D. Kaushik, E. Hovy, and Z. C. Lipton. Learning the difference that makes a difference with counterfactually-augmented data. InInternational Conference on Learning Representations (ICLR 2020),

    2020 doi

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