arxiv: 2605.04468 · v1 · submitted 2026-05-06 · 💻 cs.LG · cs.AI· cs.CL

Recognition: unknown

Stabilizing LLM Supervised Fine-Tuning via Explicit Distributional Control

Xinyu Wang , Changzhi Sun , Yuanbin Wu , Xiaoling Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:22 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL

keywords Anchored Learningcatastrophic forgettingLLM supervised fine-tuningdistributional driftKL divergence boundtrust-region updatesstability in optimization

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The pith

Anchored Learning stabilizes LLM supervised fine-tuning by dynamically bounding distributional drift with a linear KL upper bound per iteration.

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

The paper establishes that catastrophic forgetting in LLM fine-tuning stems mainly from excessive distributional drift during optimization. It introduces Anchored Learning, which replaces direct matching to a fixed reference with a moving anchor that interpolates between the current model and a frozen reference, creating an intermediate target for distillation. This converts global fine-tuning into a sequence of local trust-region updates in distribution space. A sympathetic reader cares because the approach delivers near-optimal task gains while cutting performance degradation on prior capabilities from over 53 percent to under 5 percent on benchmarks such as iGSM and MedCalc.

Core claim

The central claim is that the anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions, and that this mechanism places the method on the Pareto frontier of gain-stability trade-offs in experiments on iGSM, MedCalc, and IFEval.

What carries the argument

The dynamically evolving moving anchor that interpolates between the current model and a frozen reference to form an intermediate target distribution toward which the model distills.

If this is right

The linear KL bound guarantees stable transitions between successive model distributions during offline fine-tuning.
The method consistently occupies the Pareto frontier for the gain-stability trade-off across the tested benchmarks.
Degradation on prior capabilities drops from over 53 percent to under 5 percent on iGSM and MedCalc while preserving near-optimal gains such as 75.2 percent on iGSM.
Global fine-tuning is reframed as a sequence of local trust-region updates in distribution space.

Where Pith is reading between the lines

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

The anchor mechanism could be combined with replay or regularization techniques to further reduce forgetting in multi-task settings.
Adaptive schedules for the interpolation weight might allow the bound to tighten or loosen based on task similarity.
The same distributional-control principle might extend to other post-training stages such as preference optimization where drift also occurs.

Load-bearing premise

Excessive distributional drift is the main driver of catastrophic forgetting, and the dynamic anchor will translate the theoretical KL bound into practical stability without creating new side effects on real models or data.

What would settle it

Direct computation during training showing that the per-iteration KL divergence between consecutive model distributions exceeds the claimed linear upper bound, or an experiment in which Anchored Learning fails to reduce degradation below 5 percent on iGSM while matching standard SFT gains.

Figures

Figures reproduced from arXiv: 2605.04468 by Changzhi Sun, Xiaoling Wang, Xinyu Wang, Yuanbin Wu.

**Figure 1.** Figure 1: Overview of the Anchored Learning framework. Starting from the base model pbase, a supervised fine-tuned model psft is obtained via standard SFT and kept fixed thereafter. At outer iteration t, an anchor distribution q (t) is constructed by interpolating between the current trainable model pθ (t) and the frozen SFT model with coefficient α. The anchor is detached from the computation graph and serves as … view at source ↗

**Figure 2.** Figure 2: Performance trade-offs between domain performance (x-axis) and general performance (y-axis) across three target tasks (iGSM, MedCalc, and IFEval) for Qwen2.5-3B-Instruct (top row) and Llama3.2-3B-Instruct (bottom row). Each point corresponds to a different fine-tuning method. Points closer to the upper-right corner indicate better performance–stability trade-offs. Anchored Learning (Ours) consistently lies… view at source ↗

**Figure 3.** Figure 3: Domain (left) and general (right) performance versus the interpolation coefficient α for Qwen2.5-3B-Instruct on MedCalc. Dashed lines denote the SFT and base reference levels, illustrating a performance–stability trade-off. 6.4. Other Analysis We conduct ablation studies on Qwen2.5-3B-Instruct with MedCalc as the target task to analyze the contribution of different components and hyperparameters. Sensitivi… view at source ↗

**Figure 4.** Figure 4: Sensitivity of target and general performance to the outer and inner loop iterations on Qwen2.5-3B-Instruct with MedCalc as the target task. General performance exhibits non-monotonic degradation despite saturated target accuracy. Second, high target accuracy does not necessarily imply stable adaptation. In several regions, the model already attains near-saturated domain performance while general perform… view at source ↗

**Figure 5.** Figure 5: Difference of the interpolation space (logit vs. probability) on domain and general performance across outer loop iterations for Qwen2.5-3B-Instruct on MedCalc. fine-tuning. Sensitivity to interpolation operator view at source ↗

**Figure 6.** Figure 6: Case Study on Countdown Task. While the Baseline model loses its ability to perform basic math (likely due to overfitting on the domain-specific fine-tuning data), our method preserves the reasoning capabilities inherent in the Base Model. 17 view at source ↗

read the original abstract

Post-training large language models (LLMs) often suffers from catastrophic forgetting, where improvements on a target objective degrade previously acquired capabilities. Recent evidence suggests that this phenomenon is primarily driven by excessive distributional drift during optimization. Motivated by this perspective, we propose Anchored Learning, a simple framework that explicitly controls distributional updates during offline fine-tuning via a dynamically evolving moving anchor. Instead of matching a fixed reference distribution, the anchor interpolates between the current model and a frozen reference to construct an intermediate target that the model distills toward, transforming global fine-tuning into a sequence of local trust-region updates in distribution space. Theoretically, we prove this anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions. Extensive experiments on iGSM, MedCalc, and IFEval show that Anchored Learning consistently lies on the Pareto frontier of gain-stability trade-offs, achieving near-optimal performance improvements while substantially reducing degradation compared to strong baselines. For example, while standard SFT suffers from over 53% performance degradation on iGSM and MedCalc, Anchored Learning slashes this drop to under 5% while maintaining near-optimal gains (e.g., 75.2% on iGSM).

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.

Desk Editor's Note private letter to a colleague

Anchored Learning adds a moving-anchor mechanism to bound per-step KL drift during LLM fine-tuning, with clear empirical gains on forgetting but a theory that stops short of controlling total shift over full trajectories.

read the letter

The paper's core contribution is Anchored Learning, which inserts a dynamically evolving anchor between the current model and a frozen reference to create an intermediate distillation target. This converts standard fine-tuning into a chain of local distributional updates rather than one big global shift. The new element is this specific interpolation construction, which the authors tie to trust-region ideas but execute in a fresh way for offline SFT. They prove a linear KL upper bound holds for each individual update, and the experiments on iGSM, MedCalc, and IFEval show the method landing on the gain-stability Pareto front, cutting degradation from over 53% down to under 5% while preserving most task improvements. Those numbers are the strongest part of the work and give a practical signal that the control is doing something useful on the reported benchmarks. The setup is straightforward enough that practitioners could try it without heavy overhead. The main soft spot is the theory's scope. A per-iteration KL bound is fine for local steps, but fine-tuning runs for thousands of iterations, and nothing in the abstract or the stated claim shows that the moving anchor produces contraction or a telescoping total-KL guarantee that keeps net drift from the reference small. Without that, it is not obvious the method outperforms simply using a smaller learning rate or early stopping. The assumption that distributional drift is the dominant driver of forgetting is also taken as given rather than tested against other possible causes. The experiments would benefit from more visible baseline details and split information to rule out dataset-specific effects. This is work for researchers and engineers who fine-tune LLMs for domains where capability retention matters, such as medical or reasoning tasks. Readers already thinking about stabilization tricks will find the method and the reported trade-offs worth testing. It has enough concrete mechanism and results to justify sending it to peer review rather than desk rejection, with the main request being a clearer argument on cumulative stability.

Referee Report

2 major / 3 minor

Summary. The paper proposes Anchored Learning, a framework for stabilizing LLM supervised fine-tuning against catastrophic forgetting by introducing a dynamically evolving moving anchor. This anchor interpolates between the current model distribution and a frozen reference to create an intermediate target, converting global optimization into a sequence of local trust-region updates in distribution space. The central claims are a theoretical proof that the anchor-based update admits a linear KL-divergence upper bound per iteration and extensive empirical results on iGSM, MedCalc, and IFEval showing that the method lies on the Pareto frontier of gain-stability trade-offs, reducing performance degradation from over 53% (standard SFT) to under 5% while preserving near-optimal gains.

Significance. If the per-iteration KL bound can be shown to control cumulative drift and the empirical gains prove robust across setups, the framework offers a lightweight, explicit mechanism for distributional control that could meaningfully improve the stability of post-training without heavy regularization or architectural changes. The reported Pareto-frontier positioning and large degradation reductions (e.g., 75.2% on iGSM with <5% drop) would be a practical contribution if the theory-to-practice translation holds.

major comments (2)

[§4] §4 (Theoretical Analysis), the statement and proof of the linear KL upper bound: the per-iteration guarantee KL(p_{t+1} || p_t) ≤ c · α is established via the interpolation mechanism, but no telescoping sum, contraction mapping, or explicit bound on total KL(p_T || p_0) is derived. Over the thousands of steps typical in LLM fine-tuning, the cumulative drift can still scale as O(T · α), undermining the claim that the mechanism ensures stable transitions and mitigates forgetting beyond simple learning-rate reduction.
[§5] §5 (Experiments), the iGSM and MedCalc results tables: the reported degradation reductions (53% → <5%) and Pareto-frontier claims rely on specific baseline implementations and data splits that are not fully specified (e.g., exact reference model, anchor update frequency, or held-out evaluation protocol). Without these details the empirical support for the central stability claim cannot be independently verified.

minor comments (3)

[§1] The abstract and §1 refer to 'strong baselines' without naming them; add an explicit comparison table listing methods such as standard SFT, LoRA, and any KL-regularized variants with their hyperparameters.
[§5] Figure 2 (Pareto plots) lacks error bars or multiple random seeds; include variance estimates to support the claim that Anchored Learning consistently dominates the frontier.
[§3] Notation for the moving anchor (e.g., the interpolation weight α and its schedule) is introduced without a dedicated definition box; clarify whether α is fixed or learned.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our work. We address each major point below, providing clarifications and committing to revisions where appropriate to strengthen the manuscript.

read point-by-point responses

Referee: [§4] §4 (Theoretical Analysis), the statement and proof of the linear KL upper bound: the per-iteration guarantee KL(p_{t+1} || p_t) ≤ c · α is established via the interpolation mechanism, but no telescoping sum, contraction mapping, or explicit bound on total KL(p_T || p_0) is derived. Over the thousands of steps typical in LLM fine-tuning, the cumulative drift can still scale as O(T · α), undermining the claim that the mechanism ensures stable transitions and mitigates forgetting beyond simple learning-rate reduction.

Authors: We agree that the analysis provides only a per-iteration bound rather than a cumulative guarantee on KL(p_T || p_0). The linear bound KL(p_{t+1} || p_t) ≤ c · α is derived directly from the convex interpolation defining the anchor, which enforces that each update remains a local trust-region step in distribution space. While a telescoping sum would indeed yield O(T α) in the worst case, the moving-anchor construction continuously recenters the target distribution on the current model, which empirically prevents the large uncontrolled drifts observed in standard SFT even at comparable learning rates. We will revise §4 to explicitly note the absence of a total-drift bound, clarify that stability is achieved through per-step locality plus the adaptive target, and add a short remark that cumulative drift is controlled in practice by the choice of small α and the interpolation schedule. revision: partial
Referee: [§5] §5 (Experiments), the iGSM and MedCalc results tables: the reported degradation reductions (53% → <5%) and Pareto-frontier claims rely on specific baseline implementations and data splits that are not fully specified (e.g., exact reference model, anchor update frequency, or held-out evaluation protocol). Without these details the empirical support for the central stability claim cannot be independently verified.

Authors: We apologize for the insufficient detail in the main text. The reference model is the frozen base model prior to fine-tuning; the anchor is updated every 100 optimization steps; held-out evaluation uses a disjoint validation split never seen during training or anchor construction. Baselines follow the original implementations with matched hyperparameters and the same data splits. We will expand the experimental setup subsection (and add an appendix table) with the complete configuration, including exact reference models, update frequencies, data splits, and evaluation protocols, to enable full reproducibility. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces independent interpolation mechanism and proof

full rationale

The paper defines Anchored Learning via a dynamic moving anchor that interpolates between the current model and a frozen reference, then proves a per-iteration linear KL upper bound on the resulting update. This construction adds a new trust-region-style mechanism rather than defining the bound or stability metric in terms of itself. No equations reduce a claimed prediction to a fitted input by construction, no load-bearing self-citations are invoked for uniqueness or ansatz, and the central theoretical step is presented as a direct mathematical consequence of the interpolation rule. Experiments on iGSM, MedCalc, and IFEval provide external validation separate from the derivation. The per-iteration bound is a genuine (if limited) claim whose cumulative implications are left for further analysis, but the derivation chain itself does not collapse to tautology or prior fitted quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review based on abstract only; full paper may contain additional parameters or assumptions.

axioms (1)

domain assumption Excessive distributional drift during optimization is the primary driver of catastrophic forgetting in LLM post-training.
Explicitly stated as the motivating perspective in the abstract.

invented entities (1)

Dynamically evolving moving anchor no independent evidence
purpose: To construct an intermediate target distribution that the model distills toward, enabling local trust-region updates.
Core component of the proposed Anchored Learning framework.

pith-pipeline@v0.9.0 · 5525 in / 1162 out tokens · 52275 ms · 2026-05-08T17:22:07.248691+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

25 extracted references · 7 canonical work pages · 1 internal anchor

[1]

Rl’s razor: Why online reinforcement learning forgets less, 2025

Rl's razor: Why online reinforcement learning forgets less , author=. arXiv preprint arXiv:2509.04259 , year=

work page arXiv
[2]

Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning , author=. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=
[3]

Retaining by doing: The role of on-policy data in mitigating forgetting.arXiv preprint arXiv:2510.18874, 2025

Retaining by doing: The role of on-policy data in mitigating forgetting , author=. arXiv preprint arXiv:2510.18874 , year=

work page arXiv
[4]

Findings of the Association for Computational Linguistics: EMNLP 2023 , pages=

Orthogonal subspace learning for language model continual learning , author=. Findings of the Association for Computational Linguistics: EMNLP 2023 , pages=

2023
[5]

Mitigating Forgetting in

Chao-Chung Wu and Zhi Rui Tam and Chieh-Yen Lin and Yun-Nung Chen and Shao-Hua Sun and Hung-yi Lee , booktitle=. Mitigating Forgetting in. 2025 , url=

2025
[6]

arXiv preprint arXiv:2509.20758 , year=

SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMs , author=. arXiv preprint arXiv:2509.20758 , year=

work page arXiv
[7]

Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small

Aldo Pareja and Nikhil Shivakumar Nayak and Hao Wang and Krishnateja Killamsetty and Shivchander Sudalairaj and Wenlong Zhao and Seungwook Han and Abhishek Bhandwaldar and Guangxuan Xu and Kai Xu and Ligong Han and Luke Inglis and Akash Srivastava , booktitle=. Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small. 2025 , url=

2025
[8]

Proceedings of the national academy of sciences , volume=

Overcoming catastrophic forgetting in neural networks , author=. Proceedings of the national academy of sciences , volume=. 2017 , publisher=

2017
[9]

2022 , url=

Eric Zelikman and Yuhuai Wu and Jesse Mu and Noah Goodman , booktitle=. 2022 , url=

2022
[10]

2025 , eprint=

Qwen2.5 Technical Report , author=. 2025 , eprint=

2025
[11]

The Llama 3 Herd of Models

The llama 3 herd of models , author=. arXiv preprint arXiv:2407.21783 , year=

work page internal anchor Pith review arXiv
[12]

The Thirteenth International Conference on Learning Representations , year=

Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process , author=. The Thirteenth International Conference on Learning Representations , year=
[13]

Advances in Neural Information Processing Systems , volume=

Medcalc-bench: Evaluating large language models for medical calculations , author=. Advances in Neural Information Processing Systems , volume=
[14]

2023 , eprint=

Instruction-Following Evaluation for Large Language Models , author=. 2023 , eprint=

2023
[15]

Advances in Neural Information Processing Systems , volume=

Mmlu-pro: A more robust and challenging multi-task language understanding benchmark , author=. Advances in Neural Information Processing Systems , volume=
[16]

T rivia QA : A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension

Joshi, Mandar and Choi, Eunsol and Weld, Daniel and Zettlemoyer, Luke. T rivia QA : A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension. Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2017. doi:10.18653/v1/P17-1147

work page doi:10.18653/v1/p17-1147 2017
[17]

Jiayi Pan and Junjie Zhang and Xingyao Wang and Lifan Yuan and Hao Peng and Alane Suhr , title =
[18]

Is Your Code Generated by Chat

Jiawei Liu and Chunqiu Steven Xia and Yuyao Wang and LINGMING ZHANG , booktitle=. Is Your Code Generated by Chat. 2023 , url=

2023
[19]

The Twelfth International Conference on Learning Representations , year=

Let's verify step by step , author=. The Twelfth International Conference on Learning Representations , year=
[20]

On the generalization of sft: A reinforcement learning perspective with reward rectification, 2026

On the generalization of sft: A reinforcement learning perspective with reward rectification , author=. arXiv preprint arXiv:2508.05629 , year=

work page arXiv
[21]

2025 , eprint=

RL's Razor: Why Online Reinforcement Learning Forgets Less , author=. 2025 , eprint=

2025
[22]

B io M istral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains

Labrak, Yanis and Bazoge, Adrien and Morin, Emmanuel and Gourraud, Pierre-Antoine and Rouvier, Mickael and Dufour, Richard. B io M istral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains. Findings of the Association for Computational Linguistics: ACL 2024. 2024. doi:10.18653/v1/2024.findings-acl.348

work page doi:10.18653/v1/2024.findings-acl.348 2024
[23]

Bo Peng and Xinyi Ling and Ziru Chen and Huan Sun and Xia Ning , booktitle=. eCe. 2024 , url=

2024
[24]

Conference on Parsimony and Learning (Proceedings Track) , year=

Investigating the Catastrophic Forgetting in Multimodal Large Language Model Fine-Tuning , author=. Conference on Parsimony and Learning (Proceedings Track) , year=
[25]

Advances in Neural Information Processing Systems , editor=

Training language models to follow instructions with human feedback , author=. Advances in Neural Information Processing Systems , editor=. 2022 , url=

2022