pith. sign in

arxiv: 2606.29184 · v1 · pith:KFHT3QCYnew · submitted 2026-06-28 · 💻 cs.LG

BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning

Zhibin Duan , Yuhong Wang , Jiahong Fu , Zongsheng Yue , Bo Chen , Zongben Xu This is my paper

Pith reviewed 2026-06-30 07:52 UTC · model grok-4.3

classification 💻 cs.LG
keywords Bayesian adaptationadaptive rank allocationparameter-efficient fine-tuningLoRAuncertainty calibrationgeneralization analysissparse latent factors
0
0 comments X

The pith

BaRA uses a Bayesian global-local gate to dynamically select sparse latent factors for instance-specific effective rank in fine-tuning, with generalization governed by that joint effective rank.

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

The paper introduces BaRA to overcome the fixed-rank limitation in LoRA by allowing context-dependent adaptation capacity. It draws from probabilistic topic models to activate sparse subsets of disentangled factors via Bayesian inference. This setup provides data-driven control over capacity and leads to a theoretical result where the generalization gap is determined by the learned joint effective rank rather than the preset maximum rank. Experiments show gains in performance, robustness, and uncertainty calibration on natural language tasks.

Core claim

BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. The generalization gap depends on the learned joint effective rank induced by the global-local gate rather than the maximum rank r.

What carries the argument

The global-local gate that induces the joint effective rank from sparse subset selection of latent factors.

If this is right

  • Consistent improvements in predictive performance on diverse natural language benchmarks.
  • Better robustness and uncertainty calibration than standard LoRA and existing Bayesian LoRA variants.
  • The effective hypothesis complexity is reduced while preserving input-dependent expressiveness.
  • Mitigation of over-parameterization in low-data regimes.

Where Pith is reading between the lines

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

  • Adaptive rank selection via gates could extend to other parameter-efficient fine-tuning methods beyond LoRA.
  • Instance-wise variation in effective rank might support more efficient inference by matching compute to input needs.
  • The disentangled latent factors could be examined for alignment with specific data patterns or tasks.

Load-bearing premise

The Bayesian posterior over the sparse subset selection yields a data-driven capacity control that reduces effective hypothesis complexity without losing expressiveness.

What would settle it

A calculation or experiment showing that the generalization gap correlates more strongly with the preset maximum rank r than with the learned joint effective rank induced by the gates.

Figures

Figures reproduced from arXiv: 2606.29184 by Bo Chen, Jiahong Fu, Yuhong Wang, Zhibin Duan, Zongben Xu, Zongsheng Yue.

Figure 1
Figure 1. Figure 1: Illustration of the standard LoRA (left) and the proposed BaRA (right). Green blocks represent newly introduced trainable parameters, dashed lines [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance of test-time scaling. The results demonstrate that BaRA achieves better performance with the same sampling budget and is more efficient [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance on tasks from the OpenLLM leaderboard. The results indicate that BaRA outperforms other Bayesian LoRA, demonstrating a lower [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Layer-wise sparsity distribution of the value projection module under different rank configurations. Each subfigure shows the sparsity of the diagonal [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Token-level Sparsity visualization under the proposed BaRA method. Each subfigure corresponds to one input text from a different semantic domain. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
read the original abstract

While Low-rank adaptation (LoRA) enables highly efficient fine-tuning by constraining task-specific updates to fixed low-rank subspaces, this rigid design limits representational flexibility and often results in overconfident predictions and miscalibrated uncertainty, especially in low-data regimes. Recent Bayesian LoRA variants improve uncertainty estimation by modeling posterior distributions over adaptation parameters. However, these approaches typically rely on fixed or heuristically determined ranks, overlooking the inherently context-dependent nature of adaptation capacity. In this paper, we propose BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning. Drawing inspiration from probabilistic topic models, BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. This Bayesian formulation provides principled, data-driven capacity control, mitigating over-parameterization while preserving expressiveness. Beyond the modeling contribution, we provide a complexity-theoretic generalization analysis showing that the generalization gap of BaRA depends on the learned joint effective rank $\bar{s}_{\Phi,\theta}$ induced by the global-local gate, rather than the maximum rank $r$. This result explains why sparse adaptive rank allocation can reduce the effective hypothesis complexity while preserving input-dependent expressiveness. Extensive experiments on diverse natural language benchmarks demonstrate that BaRA consistently improves predictive performance, robustness, and uncertainty calibration compared to standard LoRA and existing Bayesian LoRA variants.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning of language models. Drawing from probabilistic topic models, it uses a global-local gate to activate sparse, context-dependent subsets of disentangled latent factors, enabling instance-wise variation in effective rank. The central theoretical claim is a complexity-theoretic generalization analysis in which the generalization gap depends on the learned joint effective rank ar{s}_{\Phi, heta} induced by the gate rather than the fixed maximum rank r. Experiments on NLP benchmarks report improved predictive performance, robustness, and uncertainty calibration relative to standard LoRA and prior Bayesian LoRA variants.

Significance. If the generalization result is correct and the Bayesian capacity control is shown to be non-circular, the work would supply a principled mechanism for data-driven rank allocation in PEFT, with direct implications for uncertainty calibration in low-data regimes. The explicit link between adaptive effective rank and hypothesis complexity is a potentially valuable contribution to the theory of parameter-efficient methods.

major comments (2)
  1. [Generalization analysis] Generalization analysis (abstract and corresponding section): the claim that the generalization gap depends on the learned joint effective rank ar{s}_{\Phi, heta} induced by the global-local gate rather than the maximum rank r is load-bearing for the theoretical contribution. Because ar{s}_{\Phi, heta} is itself produced by the fitted model, the argument risks circularity unless an independent derivation is supplied; the abstract provides neither the definition of the gate nor the supporting lemmas or proof steps.
  2. [Method] Method (Bayesian formulation): the assumption that the posterior over sparse subset selection yields data-driven capacity control that reduces effective hypothesis complexity without loss of expressiveness is central to both the modeling and generalization claims. Explicit definitions of the disentangled latent factors, the global-local gate, and how the posterior enforces the claimed complexity reduction are required to verify this step.
minor comments (2)
  1. [Abstract] Abstract: the description of the global-local gate is compressed; a single additional sentence clarifying its input/output would improve readability for readers unfamiliar with topic-model analogies.
  2. [Experiments] Experiments: confirm that all reported improvements include error bars across multiple random seeds and that calibration metrics are compared against the same set of Bayesian LoRA baselines used in the theoretical discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address the two major comments point-by-point below, clarifying the theoretical and methodological elements already present in the manuscript while agreeing to improve exposition where helpful.

read point-by-point responses

  1. Referee: [Generalization analysis] Generalization analysis (abstract and corresponding section): the claim that the generalization gap depends on the learned joint effective rank ar{s}_{\Phi,\theta} induced by the global-local gate rather than the maximum rank r is load-bearing for the theoretical contribution. Because ar{s}_{\Phi,\theta} is itself produced by the fitted model, the argument risks circularity unless an independent derivation is supplied; the abstract provides neither the definition of the gate nor the supporting lemmas or proof steps.

    Authors: The abstract is concise by design, but the full paper supplies the requested elements. Section 3.1 defines the global-local gate as a hierarchical model with global parameters \Phi and instance-specific parameters \theta that induce a binary activation matrix over the latent factors. Theorem 4.1 states the generalization bound explicitly in terms of the posterior expectation of the joint effective rank \bar{s}_{\Phi,\theta}; the complete proof appears in Appendix B and proceeds from a PAC-Bayesian argument that treats the posterior over the gate as fixed after training, yielding a non-circular capacity term. We will revise the abstract to include a one-sentence reference to the gate definition and Theorem 4.1. revision: partial

  2. Referee: [Method] Method (Bayesian formulation): the assumption that the posterior over sparse subset selection yields data-driven capacity control that reduces effective hypothesis complexity without loss of expressiveness is central to both the modeling and generalization claims. Explicit definitions of the disentangled latent factors, the global-local gate, and how the posterior enforces the claimed complexity reduction are required to verify this step.

    Authors: These definitions are already explicit in the manuscript. The disentangled latent factors are the rank-1 components of the low-rank update matrices, each equipped with independent Gaussian priors (Section 2.3). The global-local gate is introduced in Section 3.1 as a hierarchical Beta-Bernoulli construction (inspired by topic models) that produces a sparse binary mask; the posterior over this mask is approximated by mean-field variational inference. The resulting sparsity directly controls the number of active factors per instance, which is then bounded in the generalization analysis. Should the referee still find the presentation insufficiently clear, we will add a short algorithmic box summarizing the gate sampling and variational update steps. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided text (abstract and reader's summary) asserts a complexity-theoretic generalization result in which the gap depends on the learned joint effective rank induced by the global-local gate rather than maximum rank r. No derivation, lemmas, or equations are supplied that would allow exhibition of a specific reduction (e.g., the bound equaling a fitted quantity by construction). The modeling description of sparse context-dependent rank allocation is presented as an independent contribution drawing from topic models, with no self-citation load-bearing steps or ansatz smuggling visible. Per the rules, absence of quotable reduction steps requires score 0.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Abstract-only; ledger populated from stated claims only. The method introduces latent factors and a global-local gate whose independence and sparsity properties are taken as given.

free parameters (1)
  • maximum rank r
    Fixed upper bound on adaptation rank; value chosen per experiment but not derived.
axioms (1)
  • domain assumption The posterior over sparse subset selection yields instance-wise effective rank variation that preserves expressiveness.
    Invoked to justify dynamic allocation without increasing parameter count.
invented entities (1)
  • disentangled latent factors with global-local gate no independent evidence
    purpose: Enable sparse context-dependent rank allocation
    New modeling construct introduced to achieve adaptive capacity; no independent evidence supplied in abstract.

pith-pipeline@v0.9.1-grok · 5789 in / 1360 out tokens · 24636 ms · 2026-06-30T07:52:56.716838+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

62 extracted references · 32 canonical work pages · 16 internal anchors

  1. [1]

    Language Models are Few-Shot Learners

    T. B. Brown, “Language models are few-shot learners,”arXiv preprint arXiv:2005.14165, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  2. [2]

    Scaling Laws for Neural Language Models

    J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Radford, J. Wu, and D. Amodei, “Scaling laws for neural language models,”arXiv preprint arXiv:2001.08361, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  3. [3]

    Parameter-efficient transfer learning for nlp,

    N. Houlsby, A. Giurgiu, S. Jastrzebski, B. Morrone, Q. De Laroussilhe, A. Gesmundo, M. Attariyan, and S. Gelly, “Parameter-efficient transfer learning for nlp,” inInternational conference on machine learning. PMLR, 2019, pp. 2790–2799

    2019

  4. [4]

    Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey

    Z. Han, C. Gao, J. Liu, J. Zhang, and S. Q. Zhang, “Parameter-efficient fine-tuning for large models: A comprehensive survey,”arXiv preprint arXiv:2403.14608, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  5. [5]

    Lora: Low-rank adaptation of large language models

    E. J. Hu, Y . Shen, P. Wallis, Z. Allen-Zhu, Y . Li, S. Wang, L. Wang, W. Chenet al., “Lora: Low-rank adaptation of large language models.” ICLR, vol. 1, no. 2, p. 3, 2022

    2022

  6. [6]

    Measuring the Intrinsic Dimension of Objective Landscapes

    C. Li, H. Farkhoor, R. Liu, and J. Yosinski, “Measuring the intrinsic dimension of objective landscapes,”arXiv preprint arXiv:1804.08838, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    Intrinsic dimensionality explains the effectiveness of language model fine-tuning,

    A. Aghajanyan, S. Gupta, and L. Zettlemoyer, “Intrinsic dimensionality explains the effectiveness of language model fine-tuning,” inProceedings of the 59th annual meeting of the association for computational linguistics and the 11th international joint conference on natural language processing (volume 1: long papers), 2021, pp. 7319–7328

    2021

  8. [8]

    On calibration of modern neural networks,

    C. Guo, G. Pleiss, Y . Sun, and K. Q. Weinberger, “On calibration of modern neural networks,” inInternational conference on machine learning. PMLR, 2017, pp. 1321–1330

    2017

  9. [9]

    (2023).Do Large Language Models Know What They Don’t Know?arXiv:2305.18153

    Z. Yin, Q. Sun, Q. Guo, J. Wu, X. Qiu, and X. Huang, “Do large language models know what they don’t know?”arXiv preprint arXiv:2305.18153, 2023

    work page arXiv 2023

  10. [10]

    Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs

    M. Xiong, Z. Hu, X. Lu, Y . Li, J. Fu, J. He, and B. Hooi, “Can llms express their uncertainty? an empirical evaluation of confidence elicitation in llms,”arXiv preprint arXiv:2306.13063, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  11. [11]

    Knowledge entropy decay during language model pretraining hinders new knowledge acquisition,

    J. Kim, H. Lee, H. Cho, J. Jang, H. Hwang, S. Won, Y . Ahn, D. Lee, and M. Seo, “Knowledge entropy decay during language model pretraining hinders new knowledge acquisition,”arXiv preprint arXiv:2410.01380, 2024

    work page arXiv 2024

  12. [12]

    Bayesian reward models for llm alignment,

    A. X. Yang, M. Robeyns, T. Coste, Z. Shi, J. Wang, H. Bou-Ammar, and L. Aitchison, “Bayesian reward models for llm alignment,”arXiv preprint arXiv:2402.13210, 2024

    work page arXiv 2024

  13. [13]

    Uncertainty quantification and confidence calibration in large language models: A survey,

    X. Liu, T. Chen, L. Da, C. Chen, Z. Lin, and H. Wei, “Uncertainty quantification and confidence calibration in large language models: A survey,” inProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V . 2, 2025, pp. 6107–6117

    2025

  14. [14]

    Towards bayesian deep learning: A framework and some existing methods,

    H. Wang and D.-Y . Yeung, “Towards bayesian deep learning: A framework and some existing methods,”IEEE Transactions on Knowledge and Data Engineering, vol. 28, no. 12, pp. 3395–3408, 2016

    2016

  15. [15]

    Simple and scalable predictive uncertainty estimation using deep ensembles,

    B. Lakshminarayanan, A. Pritzel, and C. Blundell, “Simple and scalable predictive uncertainty estimation using deep ensembles,”Advances in neural information processing systems, vol. 30, 2017

    2017

  16. [16]

    Ensemble of low-rank adapters for large language model fine-tuning,

    X. Wang, L. Aitchison, and M. Rudolph, “Ensemble of low-rank adapters for large language model fine-tuning,” inNeurIPS Workshop on Efficient Natural Language and Speech Processing, 2023. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 15

    2023

  17. [17]

    Bayesian low-rank adaptation for large language models,

    A. X. Yang, M. Robeyns, X. Wang, and L. Aitchison, “Bayesian low-rank adaptation for large language models,”arXiv preprint arXiv:2308.13111, 2023

    work page arXiv 2023

  18. [18]

    Blob: Bayesian low- rank adaptation by backpropagation for large language models,

    Y . Wang, H. Shi, L. Han, D. Metaxas, and H. Wang, “Blob: Bayesian low- rank adaptation by backpropagation for large language models,”Advances in Neural Information Processing Systems, vol. 37, pp. 67 758–67 794, 2024

    2024

  19. [19]

    Scalable bayesian low-rank adaptation of large language models via stochastic variational subspace inference,

    C. Samplawski, A. D. Cobb, M. Acharya, R. Kaur, and S. Jha, “Scalable bayesian low-rank adaptation of large language models via stochastic variational subspace inference,”arXiv preprint arXiv:2506.21408, 2025

    work page arXiv 2025

  20. [20]

    Latent space factorization in lora,

    S. Kumar, Y . Kaloga, J. Mitros, P. Motlicek, and I. Kodrasi, “Latent space factorization in lora,”arXiv preprint arXiv:2510.19640, 2025

    work page arXiv 2025

  21. [21]

    How transferable are features in deep neural networks?

    J. Yosinski, J. Clune, Y . Bengio, and H. Lipson, “How transferable are features in deep neural networks?”Advances in neural information processing systems, vol. 27, 2014

    2014

  22. [22]

    Lisa: Layerwise importance sampling for memory-efficient large language model fine-tuning,

    R. Pan, X. Liu, S. Diao, R. Pi, J. Zhang, C. Han, and T. Zhang, “Lisa: Layerwise importance sampling for memory-efficient large language model fine-tuning,”Advances in Neural Information Processing Systems, vol. 37, pp. 57 018–57 049, 2024

    2024

  23. [23]

    Not all adapters matter: Selective adapter freezing for memory-efficient fine-tuning of language models,

    H. Son, Y . Son, C. Kim, and Y . G. Kim, “Not all adapters matter: Selective adapter freezing for memory-efficient fine-tuning of language models,” inProceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), 2025, pp. 9479–9496

    2025

  24. [24]

    Deja vu: Contextual sparsity for efficient llms at inference time,

    Z. Liu, J. Wang, T. Dao, T. Zhou, B. Yuan, Z. Song, A. Shrivastava, C. Zhang, Y . Tian, C. Reet al., “Deja vu: Contextual sparsity for efficient llms at inference time,” inInternational Conference on Machine Learning. PMLR, 2023, pp. 22 137–22 176

    2023

  25. [25]

    AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning

    Q. Zhang, M. Chen, A. Bukharin, N. Karampatziakis, P. He, Y . Cheng, W. Chen, and T. Zhao, “Adalora: Adaptive budget allocation for parameter- efficient fine-tuning,”arXiv preprint arXiv:2303.10512, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  26. [26]

    Sparse low-rank adaptation of pre-trained language models,

    N. Ding, X. Lv, Q. Wang, Y . Chen, B. Zhou, Z. Liu, and M. Sun, “Sparse low-rank adaptation of pre-trained language models,”arXiv preprint arXiv:2311.11696, 2023

    work page arXiv 2023

  27. [27]

    Fine-tuning can distort pretrained features and underperform out-of-distribution,

    A. Kumar, A. Raghunathan, R. Jones, T. Ma, and P. Liang, “Fine-tuning can distort pretrained features and underperform out-of-distribution,” arXiv preprint arXiv:2202.10054, 2022

    work page arXiv 2022

  28. [28]

    M., and Raghunathan, A

    S. Kotha, J. M. Springer, and A. Raghunathan, “Understanding catas- trophic forgetting in language models via implicit inference,”arXiv preprint arXiv:2309.10105, 2023

    work page arXiv 2023

  29. [29]

    Sparse bayesian learning for basis selection,

    D. P. Wipf and B. D. Rao, “Sparse bayesian learning for basis selection,” IEEE Transactions on Signal processing, vol. 52, no. 8, pp. 2153–2164, 2004

    2004

  30. [30]

    Latent variable bayesian models for promoting sparsity,

    D. P. Wipf, B. D. Rao, and S. Nagarajan, “Latent variable bayesian models for promoting sparsity,”IEEE Transactions on Information Theory, vol. 57, no. 9, pp. 6236–6255, 2011

    2011

  31. [31]

    Latent dirichlet allocation,

    D. M. Blei, A. Y . Ng, and M. I. Jordan, “Latent dirichlet allocation,” Journal of machine Learning research, vol. 3, no. Jan, pp. 993–1022, 2003

    2003

  32. [32]

    Beta-negative binomial process and poisson factor analysis,

    M. Zhou, L. Hannah, D. Dunson, and L. Carin, “Beta-negative binomial process and poisson factor analysis,” inArtificial Intelligence and Statistics. PMLR, 2012, pp. 1462–1471

    2012

  33. [33]

    What uncertainties do we need in bayesian deep learning for computer vision?

    A. Kendall and Y . Gal, “What uncertainties do we need in bayesian deep learning for computer vision?”Advances in neural information processing systems, vol. 30, 2017

    2017

  34. [34]

    Auto-Encoding Variational Bayes

    D. P. Kingma and M. Welling, “Auto-encoding variational bayes,”arXiv preprint arXiv:1312.6114, 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  35. [35]

    arXiv preprint arXiv:2310.11454 , year=

    D. J. Kopiczko, T. Blankevoort, and Y . M. Asano, “Vera: Vector-based random matrix adaptation,”arXiv preprint arXiv:2310.11454, 2023

    work page arXiv 2023

  36. [36]

    Sparseadapter: An easy approach for improving the parameter-efficiency of adapters,

    S. He, L. Ding, D. Dong, J. Zhang, and D. Tao, “Sparseadapter: An easy approach for improving the parameter-efficiency of adapters,” in Findings of the Association for Computational Linguistics: EMNLP 2022, 2022, pp. 2184–2190

    2022

  37. [37]

    LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning

    L. Zhang, L. Zhang, S. Shi, X. Chu, and B. Li, “Lora-fa: Memory- efficient low-rank adaptation for large language models fine-tuning,” arXiv preprint arXiv:2308.03303, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  38. [38]

    Dylora: Parameter-efficient tuning of pre-trained models using dynamic search- free low-rank adaptation,

    M. Valipour, M. Rezagholizadeh, I. Kobyzev, and A. Ghodsi, “Dylora: Parameter-efficient tuning of pre-trained models using dynamic search- free low-rank adaptation,” inProceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, 2023, pp. 3274–3287

    2023

  39. [39]

    arXiv preprint arXiv:2307.05695 , year=

    V . Lialin, N. Shivagunde, S. Muckatira, and A. Rumshisky, “Relora: High- rank training through low-rank updates,”arXiv preprint arXiv:2307.05695, 2023

    work page arXiv 2023

  40. [40]

    Autolora: Automati- cally tuning matrix ranks in low-rank adaptation based on meta learning,

    R. Zhang, R. Qiang, S. A. Somayajula, and P. Xie, “Autolora: Automati- cally tuning matrix ranks in low-rank adaptation based on meta learning,” arXiv preprint arXiv:2403.09113, 2024

    work page arXiv 2024

  41. [41]

    Roselora: Row and column-wise sparse low-rank adaptation of pre-trained language model for knowledge editing and fine-tuning,

    H. Wang, T. Liu, R. Li, M. X. Cheng, T. Zhao, and J. Gao, “Roselora: Row and column-wise sparse low-rank adaptation of pre-trained language model for knowledge editing and fine-tuning,” inProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, 2024, pp. 996–1008

    2024

  42. [42]

    Dropout as a bayesian approximation: Representing model uncertainty in deep learning,

    Y . Gal and Z. Ghahramani, “Dropout as a bayesian approximation: Representing model uncertainty in deep learning,” ininternational conference on machine learning. PMLR, 2016, pp. 1050–1059

    2016

  43. [43]

    Gaussian stochastic weight averaging for bayesian low-rank adaptation of large language models,

    E. Onal, K. Flöge, E. Caldwell, A. Sheverdin, and V . Fortuin, “Gaussian stochastic weight averaging for bayesian low-rank adaptation of large language models,”arXiv preprint arXiv:2405.03425, 2024

    work page arXiv 2024

  44. [44]

    Lora ensembles for large language model fine-tuning,

    X. Wang, L. Aitchison, and M. Rudolph, “Lora ensembles for large language model fine-tuning,”arXiv preprint arXiv:2310.00035, 2023

    work page arXiv 2023

  45. [45]

    Blob: Bayesian low-rank adaptation by backpropagation for large language models,

    Y . Wang, H. Shi, L. Han, D. Metaxas, and H. Wang, “Blob: Bayesian low-rank adaptation by backpropagation for large language models,” inAdvances in Neural Information Processing Systems, A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, Eds., vol. 37. Curran Associates, Inc., 2024, pp. 67 758–67 794

    2024

  46. [46]

    C-lora: Contextual low-rank adaptation for uncertainty estimation in large language models,

    A. H. Rahmati, S. Jantre, W. Zhang, Y . Wang, B.-J. Yoon, N. M. Urban, and X. Qian, “C-lora: Contextual low-rank adaptation for uncertainty estimation in large language models,”arXiv preprint arXiv:2505.17773, 2025

    work page arXiv 2025

  47. [47]

    The generalized reparameter- ization gradient,

    F. R. Ruiz, T. R. AUEB, D. Bleiet al., “The generalized reparameter- ization gradient,”Advances in neural information processing systems, vol. 29, 2016

    2016

  48. [48]

    Reparameterization gradients through acceptance-rejection sampling algorithms,

    C. Naesseth, F. Ruiz, S. Linderman, and D. Blei, “Reparameterization gradients through acceptance-rejection sampling algorithms,” inArtificial Intelligence and Statistics. PMLR, 2017, pp. 489–498

    2017

  49. [49]

    Deep autoencoding topic model with scalable hybrid bayesian inference,

    H. Zhang, B. Chen, Y . Cong, D. Guo, H. Liu, and M. Zhou, “Deep autoencoding topic model with scalable hybrid bayesian inference,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 12, pp. 4306–4322, 2020

    2020

  50. [50]

    Adam: A Method for Stochastic Optimization

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, Y . Bengio and Y . LeCun, Eds., 2015. [Online]. Available: http://arxiv.org/abs/1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  51. [51]

    Qwen2 Technical Report

    A. Yang, B. Yang, B. Hui, B. Zheng, B. Yu, C. Zhou, C. Li, C. Li, D. Liu, F. Huanget al., “Qwen2 technical report,”arXiv preprint arXiv:2407.10671, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  52. [52]

    Winogrande: An adversarial winograd schema challenge at scale,

    K. Sakaguchi, R. L. Bras, C. Bhagavatula, and Y . Choi, “Winogrande: An adversarial winograd schema challenge at scale,”Communications of the ACM, vol. 64, no. 9, pp. 99–106, 2021

    2021

  53. [53]

    Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge

    P. Clark, I. Cowhey, O. Etzioni, T. Khot, A. Sabharwal, C. Schoenick, and O. Tafjord, “Think you have solved question answering? try arc, the ai2 reasoning challenge,”arXiv preprint arXiv:1803.05457, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  54. [54]

    Can a suit of armor conduct electricity? a new dataset for open book question answering,

    T. Mihaylov, P. Clark, T. Khot, and A. Sabharwal, “Can a suit of armor conduct electricity? a new dataset for open book question answering,”

  55. [55]

    Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering

    [Online]. Available: https://arxiv.org/abs/1809.02789

    work page internal anchor Pith review Pith/arXiv arXiv

  56. [56]

    BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions

    C. Clark, K. Lee, M.-W. Chang, T. Kwiatkowski, M. Collins, and K. Toutanova, “Boolq: Exploring the surprising difficulty of natural yes/no questions,”arXiv preprint arXiv:1905.10044, 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1905

  57. [57]

    Measuring Massive Multitask Language Understanding

    D. Hendrycks, C. Burns, S. Basart, A. Zou, M. Mazeika, D. Song, and J. Steinhardt, “Measuring massive multitask language understanding,” arXiv preprint arXiv:2009.03300, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  58. [58]

    UltraFeedback: Boosting Language Models with Scaled AI Feedback

    G. Cui, L. Yuan, N. Ding, G. Yao, B. He, W. Zhu, Y . Ni, G. Xie, R. Xie, Y . Linet al., “Ultrafeedback: Boosting language models with scaled ai feedback,”arXiv preprint arXiv:2310.01377, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  59. [59]

    Preserving diversity in supervised fine-tuning of large language models,

    Z. Li, C. Chen, T. Xu, Z. Qin, J. Xiao, Z.-Q. Luo, and R. Sun, “Preserving diversity in supervised fine-tuning of large language models,”arXiv preprint arXiv:2408.16673, 2024

    work page arXiv 2024

  60. [60]

    Alpacaeval: An automatic evaluator of instruction- following models,

    X. Li, T. Zhang, Y . Dubois, R. Taori, I. Gulrajani, C. Guestrin, P. Liang, and T. B. Hashimoto, “Alpacaeval: An automatic evaluator of instruction- following models,” 2023

    2023

  61. [61]

    Rewardbench: Evaluating reward models for language modeling,

    N. Lambert, V . Pyatkin, J. Morrison, L. J. V . Miranda, B. Y . Lin, K. Chandu, N. Dziri, S. Kumar, T. Zick, Y . Choiet al., “Rewardbench: Evaluating reward models for language modeling,” inFindings of the Association for Computational Linguistics: NAACL 2025, 2025, pp. 1755– 1797

    2025

  62. [62]

    Evaluating Large Language Models Trained on Code

    M. Chen, “Evaluating large language models trained on code,”arXiv preprint arXiv:2107.03374, 2021. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 16 APPENDIXA: PROOF OFCOMPLEXITY-BASED GENERALIZATIONBOUND APPENDIXA PROOF OFCOMPLEXITY-BASEDGENERALIZATIONBOUND In this appendix, we provide the detailed proof of Theorem 1. The proof is based on emp...

    work page internal anchor Pith review Pith/arXiv arXiv 2021