Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

The paper claims that a family of equally accurate concept-based models that reason through visibly different concepts can be trained in a single run, at nearly the memory cost of one model.

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

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

T0 review · deepseek-v4-flash

2026-08-03 20:27 UTC pith:DVP7OVDM

load-bearing objection Useful, memory-efficient method for building diverse concept bottleneck models; empirical claims mostly hold but abstract overstates and CIFAR-10 concept quality is a real risk. the 4 major comments →

arxiv 2511.19636 v2 pith:DVP7OVDM submitted 2025-11-24 cs.LG cs.AI

Exploring the Rashomon Set for Concept-Based Models

Shihan Feng , Cheng Zhang , Michael Xi , Ethan Hsu , Lesia Semenova , Chudi Zhong This is my paper
classification cs.LG cs.AI MSC 68T0568T07
keywords Rashomon setconcept bottleneck modelsmodel multiplicityinterpretabilityadapterslow-rank adaptationgradient checkpointingconcept diversity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to make the Rashomon set — the family of near-equally accurate models for a task — visible and usable for deep, interpretable models instead of leaving it a theoretical abstraction. Its central claim is that a diverse Rashomon slice of Concept Bottleneck Models (CBMs, which predict through human-understandable intermediate concepts) can be constructed in one training run: M models share a single frozen backbone, each carries its own lightweight adapters and its own concept-to-label head, and a min-max loss with a concept-diversity regularizer keeps every member accurate while pushing their concept representations apart. On four image datasets the resulting models match or beat baseline accuracy while agreeing far less on which concepts drive their predictions, and a model-axis checkpointing scheme keeps memory near that of a single model. If correct, this turns 'how many ways can a model be right?' into a practical audit tool: choose among equally valid reasoning styles, detect models leaning on spurious cues, and abstain when the slice disagrees.

Core claim

The core claim: a Rashomon slice of CBMs — equally accurate models that reason through distinct human-understandable concepts — can be produced in one joint training run. Each of M models has its own low-rank adapters on a shared frozen backbone, concept predictors, and classifier. Joint training minimizes the worst member's task and concept losses while subtracting a diversity term that penalizes cosine similarity between predicted concept vectors, keeping every member accurate yet spread across concept space. On four image datasets the slice matches or beats baseline accuracy while showing the lowest concept-representation and concept-usage similarity; the paper applies the slice to model

What carries the argument

The central construction is the parallel-adapter slice: one frozen backbone plus M model-specific adapter sets, each feeding its own concept heads and linear classifier, trained jointly under L_total = max_m L_pr + λ (max_m L_c − α/M Σ_m L_div), where the diversity term penalizes cosine similarity between members' predicted concept vectors. The max-operations keep every member accurate; the diversity term prevents collapse to one reasoning path; α is scheduled from gradient magnitudes. Model-axis gradient checkpointing wraps each model's full forward–backward pass in a checkpoint boundary so one model holds activations at a time, keeping memory near that of a single model rather than linear

Load-bearing premise

The claim that the models 'reason through distinct human-understandable concepts' rests on the concept labels being correct and complete, especially the CLIP-auto-generated CIFAR-10 concepts (Sec. 4.1), because all diversity metrics live in the space of those predicted concepts; noisy or superficial labels would make the measured diversity a diversity of artifacts, not of human-meaningful reasoning.

What would settle it

Zero out a member model's top SHAP concept at test time — e.g., remove 'meat' from a tiger-classifying model whose decisions are SHAP-dominated by 'meat' — and measure how much predictions and accuracy move; if they barely move, the model does not actually rely on that concept and the claimed diverse reasoning is not behaviorally real. Applying the same intervention to the auto-generated CIFAR-10 concepts would test whether the diversity survives when label quality is unverified.

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

If this is right

  • A single joint training run yields a full slice of accurate CBMs with visibly different concept reliance, so practitioners can compare and select among equally valid reasoning strategies rather than retraining many models.
  • Diversity concentrates in the adapters of the last few blocks while low-level features stay shared, giving a layer-wise account of how accuracy and diversity coexist.
  • The slice supports practical trust tools: reliable abstention when members disagree, and identification of models that lean on contextual or potentially spurious concepts such as 'jungle' or 'meat' for a tiger.
  • Memory stays near that of a single model, so the slice can grow (tested from 10 to 25 members) without exceeding GPU limits, and task accuracy remains stable as it grows.
  • The construction is backbone-agnostic, reproducing accurate, diverse slices with both ViT/LoRA and ResNet-18/Conv-Adapter instantiations.

Where Pith is reading between the lines

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

  • Editorial inference: diversity is measured on predicted concept vectors, so semantically overlapping concepts (e.g., 'jungle' vs. 'bush') could inflate the reported diversity; a distance metric over concept meaning would reveal how much of it is substantive.
  • Editorial inference: the parallel-adapter recipe could transfer beyond CBMs to any architecture with an inspectable intermediate layer — for instance, hidden states of a language model — though the 'human-understandable' guarantee would then rest on that layer's interpretability.
  • Editorial inference: the layer-wise finding that deep adapters carry most of the diversity suggests a cheaper configuration the paper does not recommend — share early adapters across members and differentiate only the final blocks — which the ablation indirectly supports.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes 'Rashomon CBMs,' a framework for constructing a set of M concept bottleneck models that all achieve high task accuracy while using different concept-based reasoning. The method freezes one pretrained backbone, inserts model-specific adapters (LoRA for ViT, Conv-Adapter for ResNet), gives each model its own concept heads and label classifier, and jointly trains them with a max-loss objective plus a diversity regularizer on predicted concept vectors. A model-axis gradient checkpointing scheme is introduced to keep memory close to a single-model baseline. Experiments on CIFAR-10, AwA2, CUB, and CelebA with ViT and ResNet backbones compare against random initialization, dropout CBMs, c2y, and x2c baselines, reporting concept/task accuracy, prediction hamming, concept CKA, SHAP similarity, union size, and memory/parameter costs. The paper also includes layer-wise analyses and qualitative examples.

Significance. If the central claims held, this would be a practically useful contribution: it would give a parameter- and memory-efficient way to obtain a diverse Rashomon slice for deep concept-based models, and the model-axis checkpointing idea is interesting. The paper has clear strengths: it evaluates on four datasets and two backbones, uses several diversity metrics, includes layer-wise ablations, and its appendices disclose some limitations (e.g., the CelebA six-concept union collapse). However, the headline empirical claim that the method achieves 'better diversity than baselines' is not uniformly supported by the paper's own tables, and part of the reported diversity is by construction since the diversity loss directly optimizes cosine similarity between predicted concept vectors. The human-understandability claim is also load-bearing and rests on concept annotations that are unvalidated for CIFAR-10 and on selectively chosen qualitative examples.

major comments (4)
  1. [Abstract; §4.2 Table 1; §4.3 Table 3] The abstract's 'better diversity than baselines' and the table captions' 'consistently better' / 'on par with or better than x2c' are contradicted by the reported numbers. In Table 1 (AwA2 ViT), SHAP similarity for x2c is 0.1560 vs. 0.2046 for Rashomon CBMs, and lower is better. In Table 3 (AwA2 ResNet), concept CKA for x2c is 0.349 vs. 0.674 for Rashomon CBMs, again lower is better. Table 4 (CUB ViT) shows concept CKA 0.4698 for x2c vs. 0.6416 for Rashomon CBMs. These are not isolated small gaps; they are the primary diversity metrics in three different configurations. The central empirical claim must be qualified to 'sometimes better, sometimes worse,' and the caption wording corrected.
  2. [Eq. (1); §4.2; Figs. 2 and 8] The diversity loss in Eq. (1) directly minimizes the average pairwise cosine similarity between predicted concept vectors. The paper then reports 'concept similarity' and concept CKA trends as evidence of diversity (e.g., Fig. 2 and Fig. 8). These quantities are essentially the training objective, so observing that they change when the diversity loss is used is by construction, not a discovery about model behavior. The more meaningful evidence for behavioral diversity is SHAP similarity and union size, but those results are mixed, as noted above. To support the central claim that the models 'reason through distinct concepts,' the paper should present SHAP-based and top-concept-union diversity as the primary outcome, and should include an ablation that isolates the effect of the architecture (adapters) from the effect of L_div, e.g., training with L_div removed or with L_div but no adapte
  3. [§4.1; §4.6; Appendix D] The claim that Rashomon CBMs produce models that reason through 'distinct human-understandable concepts' depends on the correctness and completeness of the concept annotations. For CIFAR-10, concepts are auto-generated by a pretrained CLIP model (§4.1) with no validation or error analysis. If those labels are noisy or miss the features driving classification, the measured diversity is diversity over annotation artifacts rather than over human-meaningful reasoning. The qualitative support is also weak: §4.6 shows one manually chosen example, and Appendix D explicitly states that five of ten models were selected 'because they exhibit the most informative and diverse patterns.' The paper should provide a systematic validation of the CIFAR-10 concepts (e.g., human evaluation or comparison with human-annotated concept sets) and should present non-selectively chosen qualitative examples, or ex
  4. [Abstract; §5; §4] The abstract and conclusion claim that the framework 'demonstrates' trustworthy model selection, resolution of inter-class confusion, and reliable abstention. The experimental section, however, contains no experiments for abstention, no inter-class-confusion experiments, and no task other than classification with diversity metrics. These applications are only mentioned as future motivations. Either the paper should add experiments supporting these claims, or these sentences should be removed from the abstract and conclusion, since they are not demonstrated by the reported results.
minor comments (5)
  1. [§3.2.2 vs §3.2.3] The symbol α is used both for the diversity weight in Eq. (1) and for the LoRA scaling factor (α=16) in Section 3.2.3 and the implementation details. These are different quantities; rename one to avoid confusion.
  2. [Tables 1, 4, 6] Several table captions say the method 'consistently achieves better' diversity or performs 'on par with or better than x2c.' As noted, this is not true for several rows. The captions should be revised to accurately describe the direction and variability of the comparisons.
  3. [Appendix A.2] Typo: 'diferent' should be 'different.' Also in Appendix C, 'there is might be no diversity' should be 'there might be no diversity.'
  4. [§4.6] The qualitative example manually picks 15 concepts and later says 'we show 5 models out of 10.' The selection criteria for both the image and the concepts should be stated in the main text, not deferred to Appendix D, where the models are described as selected for being 'most informative and diverse.'
  5. [§3.2.2 and Eq. (1)] The description of the dynamic α schedule is brief. It would help to state whether α is annealed by the equation as written, and how the schedule interacts with the reported results across runs with different initial α values.

Circularity Check

1 steps flagged

Concept-similarity diversity is the training objective restated; accuracy, SHAP/CKA comparisons, and memory gains are independent.

specific steps
  1. self definitional [Eq. (1) / Sec. 3.2.2; Fig. 2 caption]
    "For each model m, a diversity loss is defined as L^{(m)}_{div} = 1− 1/(M−1) Σ_{m′≠m} sim(m, m′), where sim(·,·) is the cosine similarity between predicted concept vectors in model m and m′. ... Figure 2. Effect of varying the number of models (M) from 10 to 25 on accuracy and diversity on CIFAR-10. As M increases, concept similarity and CKA rise while concept accuracy decreases slightly, indicating mild convergence in the representation space."

    Eq. (1) directly minimizes L_div, which is literally the average pairwise cosine similarity between predicted concept vectors. The paper then reports 'concept similarity' trends (Fig. 2 and related tables) as an empirical characterization of the discovered slice. That measured quantity is the training objective itself, so reporting low concept similarity as evidence of diversity, or observing how it changes with M, restates the loss rather than constituting an independent discovery. The central claim is not wholly circular because SHAP similarity, CKA, union size, and accuracy are not directly equal to the optimized loss, and the memory/parameter comparisons are separate.

full rationale

The main circularity concern is limited to the diversity metric that coincides with the training objective: the concept-diversity regularizer in Eq. (1) is defined as cosine dissimilarity of predicted concept vectors, and the paper's headline diversity results (especially concept similarity in Fig. 2 and the related concept-CKA trends) are largely a direct readout of that objective. This is a real but partial issue: the paper also evaluates against external baselines (random init, dropout, c2y, x2c, partialx2c) on four datasets and two backbones, and reports SHAP similarity, union size, task accuracy, and memory/parameter costs that are not literally the loss terms. Those parts give the method independent empirical content. The self-citations to the Rashomon-set literature (e.g., [37], [38], [48], [51]) are definitional context rather than load-bearing uniqueness arguments, and no imported uniqueness theorem is used. The unvalidated CLIP-generated CIFAR-10 concepts are a legitimate correctness/annotation-quality risk but not a circularity. Overall, the central claim does not reduce entirely to its inputs, so score 4 rather than 6+.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim depends on several domain assumptions about concept quality and the diversity proxy, plus a few user-chosen hyperparameters. No new physical entities, forces, or particles are introduced.

free parameters (4)
  • lambda (concept loss weight) = 1 (most datasets), 4 (CUB)
    Per-dataset hyperparameter; lambda=4 on CUB is set 'to ensure diversity', so diversity results partly depend on this choice.
  • M (number of models in slice) = 10-25
    User-specified; the paper notes that choosing M adaptively remains open (Appendix E). Diversity and accuracy vary with M.
  • LoRA hyperparameters (rank, scaling, dropout) = r=8, alpha=16, dropout=0.1
    Chosen by hand following standard LoRA defaults; not fitted to data but affects achievable diversity.
  • Diversity weight alpha schedule in Eq. (1) = initial 0.5-0.6, updated by sigma(E|grad w L_total|)
    Heuristic dynamic weight based on gradient magnitudes; no convergence or sensitivity analysis is provided.
axioms (5)
  • domain assumption Frozen pretrained backbone features are sufficient to support accurate and diverse concept encoders.
    Section 3.2.1 freezes the backbone B; if the backbone cannot represent alternative concept pathways, the achievable diversity is capped.
  • domain assumption Concept annotations, including CLIP-generated CIFAR-10 concepts, are correct and human-meaningful.
    Section 4.1 uses provided annotations for CUB/AwA2 and a CLIP pipeline for CIFAR-10; noisy or superficial concept labels would make the measured diversity meaningless.
  • ad hoc to paper Cosine similarity between predicted concept vectors is a valid proxy for reasoning diversity.
    Eq. (1) defines L_div using cosine similarity; the paper does not justify that cosine dissimilarity implies different decision logic.
  • ad hoc to paper The max-loss formulation prevents model collapse and keeps all models individually accurate.
    Eq. (1) uses max_m L_pr and max_m L_c; this is an empirical choice with no proof that it maintains accuracy for all members.
  • domain assumption Low-rank LoRA updates can capture the diversity achievable by full fine-tuning.
    Borrowed from Hu et al. (2022); not verified for the Rashomon-slice setting.

pith-pipeline@v1.3.0-alltime-deepseek · 19903 in / 13632 out tokens · 137059 ms · 2026-08-03T20:27:11.690681+00:00 · methodology

0 comments
read the original abstract

In many machine learning problems, there may exist multiple models that achieve nearly identical predictive performance while relying on fundamentally different internal logic. However, standard training procedures produce a single model, offering no practical way to explore alternatives that may better suit downstream needs. The set of these equally accurate models is known as the Rashomon set. Exploring the Rashomon set is particularly challenging in large and complex hypothesis spaces, such as Concept Bottleneck Models (CBMs), which are widely used in computer vision to make predictions through intermediate, human-understandable concepts. In this paper, we provide a method for efficiently exploring the Rashomon set of CBMs. Our framework introduces a specialized parallel adapter-based construction, combined with a checkpointing scheme and a concept diversity objective, to generate multiple equally accurate CBMs from a single training process. Empirical results show that our method finds models with better diversity than baselines while using much less memory. We further demonstrate that access to these diverse yet accurate CBMs enables trustworthy model selection, resolution of inter-class confusion, and reliable abstention in decision-making.

Figures

Figures reproduced from arXiv: 2511.19636 by Cheng Zhang, Chudi Zhong, Ethan Hsu, Lesia Semenova, Michael Xi, Shihan Feng.

Figure 1
Figure 1. Figure 1: Proposed architecture for Rashomon CBMs. (a) Overall structure: an input image passes through a frozen backbone with attached [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Layerwise eigenvector similarity on QKV matrices (left) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Layerwise ablation analysis on CIFAR-10 with a ViT [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative Analysis of Rashomon CBMs on a tiger im [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Layerwise eigenvector similarity calculated on the QKV matrices and projection matrices. Rashomon CBMs show a clear [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Layerwise ablation analysis on the CUB dataset with the ViT backbone. We switch the adapters in each layer from shared to [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Effect of varying the number of models (M) from 10 to 25 on accuracy and diversity on the CUB dataset. As M increases, [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Qualitative Analysis of Rashomon CBMs on a tiger image from AwA2 dataset (this figure is an extension of Figure [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative Analysis of Rashomon CBMs on a blue whale image from AwA2 dataset. The left heatmap shows SHAP importance [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative Analysis of Rashomon CBMs on a Lazuli Bunting image from CUB dataset. The left heatmap shows SHAP [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Task accuracy versus SHAP diversity for all methods across four datasets using the ViT backbone. Higher values on both axes [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Task accuracy versus SHAP diversity for all methods across four datasets using the ResNet-18 backbone. Higher values on [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Layerwise ablation analysis on CIFAR-10 with a ResNet-18 backbone. Adapters in each layer are switched from shared to [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Position: Explainability Research Must Prioritize Foundations over Ad-hoc Methods

    cs.LG 2026-06 conditional novelty 4.0

    Explainable AI research should prioritize definitions, properties, evaluations, and actionability over new ad-hoc methods, on evidence from 617 papers and 34 practitioners.

Reference graph

Works this paper leans on

51 extracted references · 13 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Advancing vision-language models with adapter ensemble strategies

    Yue Bai, Handong Zhao, Zhe Lin, Ajinkya Kale, Jiuxi- ang Gu, Tong Yu, Sungchul Kim, and Yun Fu. Advancing vision-language models with adapter ensemble strategies. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 15702–15720, 2024. 3

    2024

  2. [2]

    Model multiplicity: Opportunities, concerns, and solutions

    Emily Black, Manish Raghavan, and Solon Barocas. Model multiplicity: Opportunities, concerns, and solutions. In2022 ACM Conference on Fairness, Accountability, and Trans- parency, pages 850–863, 2022. 2

    2022

  3. [3]

    Using noise to infer aspects of simplicity without learning.Advances in Neural Information Process- ing Systems, 37:131824–131858, 2024

    Zachery Boner, Harry Chen, Lesia Semenova, Ronald Parr, and Cynthia Rudin. Using noise to infer aspects of simplicity without learning.Advances in Neural Information Process- ing Systems, 37:131824–131858, 2024. 2

    2024

  4. [4]

    Statistical modeling: The two cultures (with comments and a rejoinder by the author).Statistical science, 16(3):199–231, 2001

    Leo Breiman. Statistical modeling: The two cultures (with comments and a rejoinder by the author).Statistical science, 16(3):199–231, 2001. 2

    2001

  5. [5]

    Hao Chen, Ran Tao, Han Zhang, Yidong Wang, Weirong Ye, Jindong Wang, Guosheng Hu, and Marios Savvides. Conv- adapter: Exploring parameter efficient transfer learning for convnets.2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 1551– 1561, 2022. 2, 6

    2024

  6. [6]

    Adaptformer: Adapting vision transformers for scalable visual recognition

    Shoufa Chen, Chongjian Ge, Zhan Tong, Jiangliu Wang, Yibing Song, Jue Wang, and Ping Luo. Adaptformer: Adapting vision transformers for scalable visual recognition. ArXiv, abs/2205.13535, 2022. 2

    Pith/arXiv arXiv 2022

  7. [7]

    Concept whitening for interpretable image recognition.Nature Machine Intelli- gence, 2(12):772–782, 2020

    Zhi Chen, Yijie Bei, and Cynthia Rudin. Concept whitening for interpretable image recognition.Nature Machine Intelli- gence, 2(12):772–782, 2020. 2

    2020

  8. [8]

    Zhe Chen, Yuchen Duan, Wenhai Wang, Junjun He, Tong Lu, Jifeng Dai, and Y . Qiao. Vision transformer adapter for dense predictions.ArXiv, abs/2205.08534, 2022. 2

    Pith/arXiv arXiv 2022

  9. [9]

    Diversifying deep ensembles: A saliency map approach for enhanced ood detection, calibration, and accuracy

    Stanislav Dereka, Ivan Karpukhin, Maksim Zhdanov, and Sergey Kolesnikov. Diversifying deep ensembles: A saliency map approach for enhanced ood detection, calibration, and accuracy. In2024 IEEE International Conference on Image Processing (ICIP), pages 437–443, 2024. 2

    2024

  10. [10]

    Exploring the cloud of vari- able importance for the set of all good models.Nature Ma- chine Intelligence, 2(12):810–824, 2020

    Jiayun Dong and Cynthia Rudin. Exploring the cloud of vari- able importance for the set of all good models.Nature Ma- chine Intelligence, 2(12):810–824, 2020. 2

    2020

  11. [11]

    Rashomon sets for prototypical-part networks: Editing interpretable models in real-time

    Jon Donnelly, Zhicheng Guo, Alina Jade Barnett, Hayden McTavish, Chaofan Chen, and Cynthia Rudin. Rashomon sets for prototypical-part networks: Editing interpretable models in real-time. InProceedings of the Computer Vi- sion and Pattern Recognition Conference, pages 4528–4538,

  12. [12]

    Underspecification presents challenges for credibility in modern machine learning.Journal of Machine Learning Research, 2020

    Alexander D’Amour, Katherine Heller, Dan Moldovan, Ben Adlam, Babak Alipanahi, Alex Beutel, Christina Chen, Jonathan Deaton, Jacob Eisenstein, Matthew D Hoffman, et al. Underspecification presents challenges for credibility in modern machine learning.Journal of Machine Learning Research, 2020. 2

    2020

  13. [13]

    Concept embedding mod- els: Beyond the accuracy-explainability trade-off.Advances in neural information processing systems, 35:21400–21413,

    Mateo Espinosa Zarlenga, Pietro Barbiero, Gabriele Ciravegna, Giuseppe Marra, Francesco Giannini, Michelan- gelo Diligenti, Zohreh Shams, Frederic Precioso, Stefano Melacci, Adrian Weller, et al. Concept embedding mod- els: Beyond the accuracy-explainability trade-off.Advances in neural information processing systems, 35:21400–21413,

  14. [14]

    Aaron Fisher, Cynthia Rudin, and Francesca Dominici. All models are wrong, but many are useful: Learning a variable’s importance by studying an entire class of prediction models simultaneously.Journal of Machine Learning Research, 20 (177):1–81, 2019. 2

    2019

  15. [15]

    Deep ensembles: A loss landscape perspective.ArXiv, abs/1912.02757, 2019

    Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape perspective.ArXiv, abs/1912.02757, 2019. 2

    Pith/arXiv arXiv 1912

  16. [16]

    The curi- ous case of arbitrariness in machine learning.arXiv preprint arXiv:2501.14959, 2025

    Prakhar Ganesh, Afaf Taik, and Golnoosh Farnadi. The curi- ous case of arbitrariness in machine learning.arXiv preprint arXiv:2501.14959, 2025. 2

    Pith/arXiv arXiv 2025

  17. [17]

    Merging experts into one: Improv- ing computational efficiency of mixture of experts.ArXiv, abs/2310.09832, 2023

    Shwai He, Run-Ze Fan, Liang Ding, Li Shen, Tianyi Zhou, and Dacheng Tao. Merging experts into one: Improv- ing computational efficiency of mixture of experts.ArXiv, abs/2310.09832, 2023. 7

    Pith/arXiv arXiv 2023

  18. [18]

    Parameter-efficient transfer learning for NLP

    Neil Houlsby, Andrei Giurgiu, Stanislaw Jastrzebski, Bri- anna Morrone, Quentin De Laroussilhe, Andrea Gesmundo, Mona Attariyan, and Sylvain Gelly. Parameter-efficient transfer learning for NLP. InInternational Conference on Machine Learning (ICML), 2019. 2

    2019

  19. [19]

    Rashomon capacity: A met- ric for predictive multiplicity in classification

    Hsiang Hsu and Flavio Calmon. Rashomon capacity: A met- ric for predictive multiplicity in classification. InNeural Information Processing Systems (NeurIPS), pages 28988– 29000, 2022. 1, 2

    2022

  20. [20]

    Dropout-based rashomon set exploration for efficient predic- tive multiplicity estimation

    Hsiang Hsu, Guihong Li, Shaohan Hu, and Chun-Fu Chen. Dropout-based rashomon set exploration for efficient predic- tive multiplicity estimation. InInternational Conference on Representation Learning, pages 33104–33144, 2024. 5

    2024

  21. [21]

    Lora: Low- rank adaptation of large language models

    Edward J Hu, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low- rank adaptation of large language models. InInternational Conference on Learning Representations, 2022. 2, 4

    2022

  22. [22]

    Probabilistic concept bottleneck models

    Eunji Kim, Dahuin Jung, Sangha Park, Siwon Kim, and Sun- groh Yoon. Probabilistic concept bottleneck models. InPro- ceedings of the 40th International Conference on Machine Learning (ICML). JMLR.org, 2023. 2, 3 9

    2023

  23. [23]

    Eq-cbm: A probabilistic concept bottle- neck with energy-based models and quantized vectors, 2024

    Sangwon Kim, Dasom Ahn, Byoung Chul Ko, In su Jang, and Kwang-Ju Kim. Eq-cbm: A probabilistic concept bottle- neck with energy-based models and quantized vectors, 2024. 2

    2024

  24. [24]

    Concept bottleneck models

    Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, and Percy Liang. Concept bottleneck models. InInternational conference on machine learning, pages 5338–5348. PMLR, 2020. 1, 2

    2020

  25. [25]

    Similarity of neural network represen- tations revisited

    Simon Kornblith, Mohammad Norouzi, Honglak Lee, and Geoffrey Hinton. Similarity of neural network represen- tations revisited. InInternational conference on machine learning, pages 3519–3529. PMlR, 2019. 5

    2019

  26. [26]

    Learning multiple layers of features from tiny images

    Alex Krizhevsky. Learning multiple layers of features from tiny images. Technical Report TR-2009, University of Toronto, 2009. 4

    2009

  27. [27]

    Simple and scalable predictive uncertainty esti- mation using deep ensembles

    Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty esti- mation using deep ensembles. InNeural Information Pro- cessing Systems, 2016. 2

    2016

  28. [28]

    Ensembles of low-rank expert adapters.arXiv preprint arXiv:2502.00089, 2025

    Yinghao Li, Vianne Gao, Chao Zhang, and MohamadAli Torkamani. Ensembles of low-rank expert adapters.arXiv preprint arXiv:2502.00089, 2025. 3

    Pith/arXiv arXiv 2025

  29. [29]

    Dora: Weight-decomposed low-rank adaptation.ArXiv, abs/2402.09353, 2024

    Shih-Yang Liu, Chien-Yi Wang, Hongxu Yin, Pavlo Molchanov, Yu-Chiang Frank Wang, Kwang-Ting Cheng, and Min-Hung Chen. Dora: Weight-decomposed low-rank adaptation.ArXiv, abs/2402.09353, 2024. 2

    Pith/arXiv arXiv 2024

  30. [30]

    Deep learning face attributes in the wild

    Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. InProceedings of International Conference on Computer Vision (ICCV), 2015. 4

    2015

  31. [31]

    A unified approach to interpreting model predictions.Advances in neural informa- tion processing systems, 30, 2017

    Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions.Advances in neural informa- tion processing systems, 30, 2017. 6

    2017

  32. [32]

    Predictive multiplicity in classification

    Charles Marx, Flavio Calmon, and Berk Ustun. Predictive multiplicity in classification. InProceedings of the Inter- national Conference on Machine Learning (ICML), pages 6765–6774, 2020. 2

    2020

  33. [33]

    Lora-ensemble: Efficient uncertainty modelling for self-attention networks

    Dominik J M ¨uhlematter, Michelle Halbheer, Alexan- der Becker, Dominik Narnhofer, Helge Aasen, Konrad Schindler, and Mehmet Ozgur Turkoglu. Lora-ensemble: Efficient uncertainty modelling for self-attention networks. arXiv preprint arXiv:2405.14438, 2024. 3, 7

    arXiv 2024

  34. [34]

    Oikarinen, Subhro Das, Lam M

    Tuomas P. Oikarinen, Subhro Das, Lam M. Nguyen, and Tsui-Wei Weng. Label-free concept bottleneck models. ArXiv, abs/2304.06129, 2023. 4

    Pith/arXiv arXiv 2023

  35. [35]

    Learning multiple visual domains with residual adapters

    Sylvestre-Alvise Rebuffi, Hakan Bilen, and Andrea Vedaldi. Learning multiple visual domains with residual adapters. InAdvances in Neural Information Processing Systems (NeurIPS), 2017. 2

    2017

  36. [36]

    Melora: Mini-ensemble low-rank adapters for parameter-efficient fine-tuning.arXiv preprint arXiv:2402.17263, 2024

    Pengjie Ren, Chengshun Shi, Shiguang Wu, Mengqi Zhang, Zhaochun Ren, Maarten de Rijke, Zhumin Chen, and Jiahuan Pei. Melora: Mini-ensemble low-rank adapters for parameter-efficient fine-tuning.arXiv preprint arXiv:2402.17263, 2024. 3

    Pith/arXiv arXiv 2024

  37. [37]

    Amazing things come from having many good models

    Cynthia Rudin, Chudi Zhong, Lesia Semenova, Margo Seltzer, Ronald Parr, Jiachang Liu, Srikar Katta, Jon Don- nelly, Harry Chen, and Zachery Boner. Amazing things come from having many good models. InProceedings of the Inter- national Conference on Machine Learning (ICML), 2024. 1, 2

    2024

  38. [38]

    On the ex- istence of simpler machine learning models

    Lesia Semenova, Cynthia Rudin, and Ronald Parr. On the ex- istence of simpler machine learning models. InACM Confer- ence on Fairness, Accountability, and Transparency (ACM FAccT), 2022. 1, 2

    2022

  39. [39]

    A path to simpler models starts with noise.Ad- vances in neural information processing systems, 36:3362– 3401, 2023

    Lesia Semenova, Harry Chen, Ronald Parr, and Cynthia Rudin. A path to simpler models starts with noise.Ad- vances in neural information processing systems, 36:3362– 3401, 2023. 2

    2023

  40. [40]

    Diversity regularization in deep ensembles.ArXiv, abs/1802.07881, 2018

    Changjian Shui, Azadeh Sadat Mozafari, Jonathan Marek, Ihsen Hedhli, and Christian Gagn ´e. Diversity regularization in deep ensembles.ArXiv, abs/1802.07881, 2018. 2

    Pith/arXiv arXiv 2018

  41. [41]

    Diverse ensembles improve calibration.ArXiv, abs/2007.04206, 2020

    Asa Cooper Stickland and Iain Murray. Diverse ensembles improve calibration.ArXiv, abs/2007.04206, 2020. 2

    Pith/arXiv arXiv 2007

  42. [42]

    El- liCE: Efficient and provably robust algorithmic recourse via the rashomon sets

    Bohdan Turbal, Iryna V oitsitska, and Lesia Semenova. El- liCE: Efficient and provably robust algorithmic recourse via the rashomon sets. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025. 2

    2025

  43. [43]

    Moritz Vandenhirtz, Sonia Laguna, Ricards Marcinkevics, and Julia E. V ogt. Stochastic concept bottleneck models. ArXiv, abs/2406.19272, 2024. 2

    Pith/arXiv arXiv 2024

  44. [44]

    C. Wah, S. Branson, P. Welinder, P. Perona, and S. Belongie. Caltech-ucsd-birds-200-2011. Technical Report CNS-TR- 2011-001, California Institute of Technology, 2011. 4

    2011

  45. [45]

    Predictive multiplicity in probabilistic classification

    Jamelle Watson-Daniels, David C Parkes, and Berk Ustun. Predictive multiplicity in probabilistic classification. InPro- ceedings of the AAAI Conference on Artificial Intelligence, pages 10306–10314, 2023. 2

    2023

  46. [46]

    Decor- relating structure via adapters makes ensemble learning practical for semi-supervised learning.arXiv preprint arXiv:2408.04150, 2024

    Jiaqi Wu, Junbiao Pang, and Qingming Huang. Decor- relating structure via adapters makes ensemble learning practical for semi-supervised learning.arXiv preprint arXiv:2408.04150, 2024. 3

    Pith/arXiv arXiv 2024

  47. [47]

    Lampert, Bernt Schiele, and Zeynep Akata

    Yongqin Xian, Christoph H. Lampert, Bernt Schiele, and Zeynep Akata. Zero-shot learning—a comprehensive eval- uation of the good, the bad and the ugly.IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(9):2251– 2265, 2019. 4

    2019

  48. [48]

    Exploring the whole rashomon set of sparse decision trees.Advances in neural information processing systems, 35:14071–14084, 2022

    Rui Xin, Chudi Zhong, Zhi Chen, Takuya Takagi, Margo Seltzer, and Cynthia Rudin. Exploring the whole rashomon set of sparse decision trees.Advances in neural information processing systems, 35:14071–14084, 2022. 1, 2

    2022

  49. [49]

    Energy-based concept bottleneck models: Unifying predic- tion, concept intervention, and probabilistic interpretations

    Xin-Chao Xu, Yi Qin, Lu Mi, Hao Wang, and Xiaomeng Li. Energy-based concept bottleneck models: Unifying predic- tion, concept intervention, and probabilistic interpretations. InInternational Conference on Learning Representations,

  50. [50]

    The diversified ensemble neural network

    Shaofeng Zhang, Meng Liu, and Junchi Yan. The diversified ensemble neural network. InProceedings of the 34th Confer- ence on Neural Information Processing Systems (NeurIPS), Red Hook, NY , USA, 2020. Curran Associates Inc. 2, 3, 5

    2020

  51. [51]

    stripes” and “stalker

    Chudi Zhong, Zhi Chen, Jiachang Liu, Margo Seltzer, and Cynthia Rudin. Exploring and interacting with the set of good sparse generalized additive models. InNeural Infor- mation Processing Systems (NeurIPS), 2023. 1, 2 10 Appendix A. Additional results comparing Rashomon CBMs to baselines In this section, we provide more results on model performance compar...

    arXiv 2023