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REVIEW 4 major objections 4 minor 35 references

TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A distillation target that slides from the student's own distribution to the teacher's yields better language-model students than fixed-target distillation.

desk verdict A simple and genuinely useful distillation trick whose 'prevents mode collapse' theory only covers a regression toy; the empirical core is solid but lacks error bars. read the letter →

arxiv 2501.16937 v4 pith:YGH2QGBX submitted 2025-01-28 cs.LG cs.AIcs.CL

Makoto Shing , Kou Misaki , Han Bao , Sho Yokoi , Takuya Akiba This is my paper · ORCID
classification cs.LGcs.AIcs.CL
keywords temporallyadaptiveinterpolateddistillationknowledgelanguagemodelsmodecollapsecapacitygaplogitinterpolationinstructiontuningpre-training
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Knowledge distillation from a large teacher model to a much smaller student often fails because the teacher's target distribution is too far from what the student can represent, producing either oversmoothed distributions that average away rare modes or collapsed distributions that concentrate on a few common tokens. TAID attacks this by training the student against an intermediate distribution that starts as the student's own logits and gradually interpolates toward the teacher's logits, so the student first consolidates what it can already produce and only later absorbs the teacher's richer signal. The paper claims this adaptive curriculum prevents mode collapse, a behavior it supports with a theoretical analysis in a least-squares regression proxy, and empirically yields better students than KL, RKL, TVD, GKD, DistiLLM, CTKD, and DKD across instruction tuning and continued pre-training. Two released models, TAID-LLM-1.5B and TAID-VLM-2B, illustrate the practical payoff by topping their size classes.

What carries the argument

The load-bearing object is the TAID interpolated distribution --- a softmax over a convex combination of the student's detached logits and the teacher's logits --- together with the interpolation schedule that moves $t$ from $t_{\text{start}}$ to 1. The schedule is either a linear ramp or an adaptive update driven by the momentum-smoothed relative decrease of the TAID objective, bounded below by the linear ramp so $t$ never stalls. The theoretical non-collapse analysis is carried out in the Mobahi-style least-squares interpolation setting, where at each step the student must $\epsilon$-interpolate the signal $\tilde{y}_t = (1 - t/T)y_t + (t/T)y_{\text{teacher}}$, and the proof shows the singular values of the recursion keep the prediction away from zero.

What would settle it

Run TAID on an instruction-tuning pair while logging the student's KL to the interpolated target at each step; if that training loss stays far above the epsilon-interpolation level required by the proof for the entire run, the non-collapse theorem is not empirically supported in the LM regime. As a second check, compare the tail-token probability mass of the TAID student with an RKL student on the same teacher: if TAID's tail mass collapses to RKL's level, the claim that TAID balances mode collapse would be refuted.

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Extended reading notes

Core claim

The central claim is that distillation should be reimagined as a dynamic process: at training time $t$, the student minimizes KL divergence against $p_t = \mathrm{softmax}\big((1-t)\cdot \mathrm{logit}_{\text{student}} + t\cdot \mathrm{logit}_{\text{teacher}}\big)$, with the student logits detached so that only the student's own distribution is updated, and $t$ scheduled from a small start up to 1.0 either linearly or through an adaptive momentum rule that tracks the student's loss decrease. The interpolated target makes the task easier when the student is weak and gradually harder as it learns, and the paper proves in an idealized regression setting that this scheme keeps the student away from collapse for all steps provided the teacher signal is strong enough (roughly $\|y_0\| = \Omega(\sqrt{T\epsilon})$), in contrast to self-distillation which eventually collapses. The empirical sections verify that the resulting students outperform fixed-target KD baselines, show monotonic gains as teacher size grows, and preserve tail-token probability mass better than RKL while keeping focused head mass.

Load-bearing premise

The non-collapse guarantee assumes the student nearly perfectly fits each interpolated target at every step, but real language-model students are far too small to interpolate the full token distribution.

Editorial extensions

If this is right

  • With TAID, distilling from a larger teacher monotonically improves the student, so the 'curse of capacity gap' (bigger teacher, worse student) disappears in the tested range.
  • TAID sits between KL and RKL on head/tail token mass: it keeps more of the teacher's rare-token distribution than RKL while still sharpening the head, balancing mode averaging and mode collapse.
  • Because TAID needs no student-generated output sampling, it trains about 2x faster than DistiLLM and 10x faster than GKD in the reported settings while scoring higher.
  • The released TAID-LLM-1.5B and TAID-VLM-2B score highest in their size categories (under 2B parameters for LLMs and up to 4B for VLMs), demonstrating the method transfers to production-scale models.

Reading between the lines

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

  • A natural extension, which the paper leaves implicit, is to combine TAID's interpolated target with on-policy student sampling: the two mechanisms target different failure modes, so the pairing might further close the train-inference gap for autoregressive LMs.
  • The same adaptive-interpolation idea should transfer to other high-entropy prediction tasks (e.g., neural machine translation or dense retrieval) where the teacher distribution has a long tail and the student is capacity-limited; the paper's ImageNet results hint that gains grow with task complexity.
  • A testable consequence of the scheduling rule is that $t$ should rise fastest when the student improves fastest; logging $t$ against held-out loss during training would show whether the schedule tracks genuine learning progress or merely reflects data ordering.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes Temporally Adaptive Interpolated Distillation (TAID), a knowledge-distillation method for language models in which the student is trained against a time-dependent interpolation of its own detached logits and the teacher logits, with an adaptive schedule for the interpolation parameter. The authors claim that this dynamic interpolation prevents mode collapse, mitigates the teacher-student capacity gap, and improves over fixed-target distillation methods. The paper presents formal non-collapse guarantees in a kernel-regression proxy setting, reports instruction-tuning and continued-pretraining experiments against several KD baselines, and demonstrates practical impact by training TAID-LLM-1.5B and TAID-VLM-2B, which outperform prior models in their size classes on LightEval and Open VLM Leaderboard, respectively.

Significance. If the central claims are upheld, TAID is a computationally attractive alternative to on-policy distillation methods: it avoids sampling from the student, is roughly 2x faster than DistiLLM and 10x faster than GKD in the reported instruction-tuning setup, and consistently improves over KL and other standard objectives in the provided experiments. The theoretical non-collapse result, though confined to an idealized regression model, is a nontrivial formal contribution that goes beyond purely empirical KD papers. The paper's experimental breadth, spanning instruction tuning, continued pretraining, capacity-gap ablations, image classification, and two released foundation models, is a clear strength. However, the load-bearing theoretical claim is broader than what the theorem actually proves, and the empirical evidence is presented as single point estimates without variance or significance information, which tempers the strength of the comparative claims.

major comments (4)
  1. [§B.2, Theorem B.1 and Corollary B.1.1] The formal non-collapse guarantee applies only when the per-mode teacher signal satisfies r0 = ||y0||/sqrt(N*epsilon) > 1, and in the multi-class extension the label vector for class c has squared norm equal to the number of training examples containing c. For low-frequency vocabulary items in the Zipfian tail, this condition fails, so the theorem is silent on exactly the rare modes that mode-collapse is most harmful for. The abstract's unqualified claim that TAID prevents mode collapse 'theoretically and empirically' is therefore stronger than what the theorem supports. The claim should either be restricted to modes with sufficiently strong teacher signal, or supplemented with empirical evidence that rare modes are preserved.
  2. [§6.3.3, Table 3] The empirical mode-collapse analysis aggregates all tokens in the 80-100th percentile into a single tail mass (39.0e-7 for TAID) and does not report a teacher row, per-token statistics, or any measure of variance. As a result, Table 3 cannot demonstrate that the rarest modes are preserved rather than merely that the aggregate tail mass of TAID is higher than that of RKL. Please report a per-token or per-frequency-bin comparison against the teacher distribution, ideally with error bars across seeds.
  3. [§4, Appendix B.2, Algorithm 2 vs Algorithm 1] The non-collapse theorem is proved for the simplified procedure in Algorithm 2, in which the interpolation parameter increases linearly as t/T and the student exactly epsilon-interpolates the regression target at every step. The actual TAID algorithm from Section 3.2 uses a momentum-based adaptive update for t, and real language-model students are capacity-limited and do not interpolate the full token distribution. No argument is provided that the adaptive schedule inherits the non-collapse bound, so the theoretical result currently applies to a simplified variant of the proposed method. Either prove the guarantee for the adaptive schedule or explicitly state that the formal result concerns the linear-schedule, interpolation-regime version.
  4. [§6.1, §6.2, Tables 1 and 2] All reported benchmark scores are single point estimates without multiple seeds, confidence intervals, or significance tests. Several comparisons are close, most notably the Table 2 average of 40.10 for TAID versus 39.91 for KL, and MT-Bench in Table 1 relies on a GPT-4 judge. Given these margins, the statement that TAID 'consistently outperforms' all baselines is not fully supported by the evidence as reported. Please provide multi-seed runs or another measure of statistical robustness, particularly for the continued-pretraining results.
minor comments (4)
  1. [References] The reference to Buciluă et al. (2006) is rendered as 'Buciluundefined' in the bibliography, and the Zhang et al. (2023b) entry contains an incomplete venue name ('ional Linguistics'). These should be corrected.
  2. [§2] The sentence 'potentially resulting in a over-smoothed and less accurate distribution' contains an article error ('a over-smoothed') and should read 'an over-smoothed'.
  3. [Appendix B.1] The multi-class extension of the regression analysis is described only verbally ('We can follow the subsequent analysis straightforwardly'). Since the paper's LM claims rely on this extension, a few lines stating the per-class label vector and the resulting per-class non-collapse condition would make the appendix self-contained.
  4. [Figure 2] The rightmost panel uses '13 14' on the vertical axis without a clear axis label; adding an explicit label such as 'LAMBADA accuracy (%)' would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: TAID's objective, theory, and benchmarks are not fitted to the claims; the only self-referential element is the detached student logits in the target, which is the method's definition rather than a hidden input.

full rationale

The paper's derivation chain is self-contained in the sense required here. Equation (1) defines the interpolated target from teacher logits and detached student logits, Equation (2) defines the training loss, and Theorem B.1 proves a non-collapse condition in an explicit least-squares proxy borrowed from Mobahi et al. (2020). The theorem's assumptions—near-perfect epsilon-interpolation and a strong teacher signal r0 = ||y0||/sqrt(N epsilon) > 1—are stated before the conclusion and do not include the conclusion; the proof shows that the (t/T)y0 component of the interpolated target keeps the target norm above the collapse threshold. That is a mathematical consequence of the algorithm's definition, not a fitted parameter renamed as a prediction. The empirical sections use public checkpoints and held-out benchmarks (MT-Bench, Open LLM Leaderboard, LightEval, Open VLM Leaderboard) and compare against external baselines; no reported metric is itself used as the training target or as a fitted input. The self-referential aspect noted in the reader's take—the detached student logits inside p_t—is the definition of TAID, not a circular derivation, and it is not used to generate a separate claim. There are no load-bearing self-citations; the Mobahi framework and all comparison methods are external. The long-tail limitation identified in the skeptical reading is a scope or validity concern about the regression proxy, not a circularity, because the theorem does not assume the conclusion it purports to establish. Therefore no circular step can be exhibited, and the score is 0.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

TAID introduces no new physical entity; its free parameters are training hyperparameters. The central theoretical claim imports Mobahi et al.'s regression framework and adds two strong conditions (epsilon-interpolation and large teacher signals) that are not established for real language-model distillation. The main scientific content is the new objective plus empirical comparisons.

free parameters (6)
  • alpha (step size for interpolation parameter t) = 5e-4 for instruction tuning and VLM; 5e-5 for TAID-LLM-1.5B
    Hyperparameter controlling how quickly t increases; chosen per experiment and affects final accuracy.
  • beta (momentum coefficient) = 0.99
    Smooths the relative objective-decrease signal used in the adaptive t update; set by authors across experiments.
  • t_start = 0.2 to 0.4
    Initial interpolation weight, selected based on assumed initial student-teacher similarity.
  • t_end = 1.0
    Final interpolation weight, forcing the target to converge to the teacher distribution.
  • epsilon (small constant in delta_n) = Not reported
    Prevents division by zero in the adaptive update; exact value omitted.
  • Top-50 teacher probabilities for TAID-LLM-1.5B = 50
    Storage-saving truncation of teacher distribution; may affect distillation quality and is a design choice.
assumptions (5)
  • domain assumption Least-squares interpolation regression (Eq. 3) is a valid proxy for token-level KL distillation in language models.
    Invoked in Appendix B.1 to import Mobahi et al. analysis; the paper acknowledges this 'obviously deviates' from the LM objective.
  • domain assumption At every distillation step the student achieves near-perfect epsilon-interpolation of the current training signal.
    Algorithm 2 and Theorem B.1 assume the variational solution with lambda from Eq. (9) solves the constrained problem; real finite-capacity LMs do not interpolate the teacher's full distribution.
  • domain assumption Teacher signal strength satisfies ||y0|| = Omega(sqrt(T epsilon)), so r0 = ||y0||/sqrt(N epsilon) is large enough.
    The non-collapse conditions in Theorem B.1 and Corollary B.1.1 require sufficiently strong initial teacher signals; otherwise the guarantee is vacuous.
  • standard math The closed-form solution (7)-(8) of the variational problem, taken from Mobahi et al. (2020), is correct and G is positive definite.
    The proof relies entirely on this external analytical solution and spectral decomposition.
  • domain assumption Distilling against an interpolated distribution that contains the detached student's own logits is a stable training target.
    This is the core design assumption of TAID; the theoretical analysis covers only its regression analogue, not the logit-interpolation KL objective.

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Cite this review

Pith. "Pith review of TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models." pith.science (2026). https://pith.science/paper/YGH2QGBX

@misc{pith2026250116937,
  author       = {Pith},
  title        = {Pith review of: TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YGH2QGBX}},
  note         = {Machine review of arXiv:2501.16937}
}
abstract

Causal language models have demonstrated remarkable capabilities, but their size poses significant challenges for deployment in resource-constrained environments. Knowledge distillation, a widely-used technique for transferring knowledge from a large teacher model to a small student model, presents a promising approach for model compression. A significant remaining issue lies in the major differences between teacher and student models, namely the substantial capacity gap, mode averaging, and mode collapse, which pose barriers during distillation. To address these issues, we introduce $\textit{Temporally Adaptive Interpolated Distillation (TAID)}$, a novel knowledge distillation approach that dynamically interpolates student and teacher distributions through an adaptive intermediate distribution, gradually shifting from the student's initial distribution towards the teacher's distribution. We provide a theoretical analysis demonstrating TAID's ability to prevent mode collapse and empirically show its effectiveness in addressing the capacity gap while balancing mode averaging and mode collapse. Our comprehensive experiments demonstrate TAID's superior performance across various model sizes and architectures in both instruction tuning and pre-training scenarios. Furthermore, we showcase TAID's practical impact by developing two state-of-the-art compact foundation models: $\texttt{TAID-LLM-1.5B}$ for language tasks and $\texttt{TAID-VLM-2B}$ for vision-language tasks. These results demonstrate TAID's effectiveness in creating high-performing and efficient models, advancing the development of more accessible AI technologies.

Figures

Figures reproduced from arXiv: 2501.16937 by the authors.

Figure 1
Figure 1. Comparison of standard KD and TAID. (Left) Standard KD methods typically employ direct optimization towards a fixed teacher distribution. (Right) TAID creates a dynamic bridge through adaptive, time-dependent intermediate teacher distributions (green dashed lines), enabling gradual optimization of the student. This approach facilitates a flexible transition from the student’s initial distribution towards the teacher… view at source ↗
Figure 2
Figure 2. Analysis of TAID’s behavior and performance. (Left) Interpolation parameter t be￾havior: Higher α values lead to faster initial growth compared to linear increase, allowing for more aggressive knowledge transfer in early stages when the capacity gap is small. (Middle) Objective value comparison: TAID exhibits a more stable objective value with lower variance compared to standard KL divergence throughout training, in… view at source ↗
Figure 3
Figure 3. Comparison between im￾age classification and language mod￾eling tasks. Language modeling (GPT-2) exhibits significantly higher entropy and lower target-class proba￾bilities compared to image classifica￾tion (ResNet-56). These fundamental differences highlight the unique chal￾lenges in language model distillation. Our experiments revealed that KD methods developed for image classification, such as CTKD (Li et al., 20… view at source ↗

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Reference graph

Works this paper leans on

35 extracted references · 15 canonical work pages

  1. [1]

    Phi-3 technical re- port: A highly capable language model locally on your phone

    Marah Abdin, Sam Ade Jacobs, Ammar Ahmad Awan, Jyoti Aneja, Ahmed Awadallah, Hany Awadalla, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, et al. Phi-3 technical re- port: A highly capable language model locally on your phone. arXiv preprint arXiv:2404.14219,

    arXiv

  2. [4]

    Model compression

    11 Published as a conference paper at ICLR 2025 Cristian Buciluundefined, Rich Caruana, and Alexandru Niculescu-Mizil. Model compression. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 535–541. Association for Computing Machinery,

    work page 2025

  3. [5]

    A survey of large language models for healthcare: from data, technology, and applications to accountability and ethics

    Kai He, Rui Mao, Qika Lin, Yucheng Ruan, Xiang Lan, Mengling Feng, and Erik Cambria. A survey of large language models for healthcare: from data, technology, and applications to accountability and ethics. arXiv preprint arXiv:2310.05694,

    arXiv

  4. [7]

    Scaling laws for neural language models

    Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361,

    arXiv 2001

  5. [8]

    Learning multiple layers of features from tiny images

    12 Published as a conference paper at ICLR 2025 Alex Krizhevsky. Learning multiple layers of features from tiny images. Master’s thesis, Depart- ment of Computer Science, University of Toronto,

    work page 2025

  6. [9]

    Textbooks are all you need ii: phi-1.5 technical report

    Yuanzhi Li, S´ebastien Bubeck, Ronen Eldan, Allie Del Giorno, Suriya Gunasekar, and Yin Tat Lee. Textbooks are all you need ii: phi-1.5 technical report. arXiv preprint arXiv:2309.05463, 2023a. Zheng Li, Xiang Li, Lingfeng Yang, Borui Zhao, Renjie Song, Lei Luo, Jun Li, and Jian Yang. Curriculum temperature for knowledge distillation. In Proceedings of th...

    arXiv

  7. [11]

    Gpt-4 technical report

    OpenAI, Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Floren- cia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774,

    arXiv

  8. [13]

    github.io/blog/qwen2.5/

    URLhttps://qwenlm. github.io/blog/qwen2.5/. 13 Published as a conference paper at ICLR 2025 Alec Radford, Jeff Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI blog,

    work page 2025

Show all 35 references
  1. [15]

    Omkar Thawakar, Ashmal Vayani, Salman Khan, Hisham Cholakal, Rao M

    URL https://huggingface.co/ stabilityai/stablelm-zephyr-3b. Omkar Thawakar, Ashmal Vayani, Salman Khan, Hisham Cholakal, Rao M. Anwer, Michael Fels- berg, Tim Baldwin, and Eric P. Xing. Mobillama: Towards accurate and lightweight fully trans- parent gpt. arXiv preprint arXiv:2...

    arXiv

  2. [16]

    Llama 2: Open founda- tion and fine-tuned chat models

    Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Niko- lay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open founda- tion and fine-tuned chat models. arXiv preprint arXiv:2307.09288,

    arXiv

  3. [17]

    Efficient large language models: A survey

    Zhongwei Wan, Xin Wang, Che Liu, Samiul Alam, Yu Zheng, et al. Efficient large language models: A survey. arXiv preprint arXiv:2312.03863,

    arXiv

  4. [18]

    Bloomberggpt: A large language model for finance

    Shijie Wu, Ozan Irsoy, Steven Lu, Vadim Dabravolski, Mark Dredze, Sebastian Gehrmann, Prab- hanjan Kambadur, and David Rosenberg. Bloomberggpt: A large language model for finance. arXiv preprint arXiv:2303.17564,

    arXiv

  5. [19]

    Rethinking kullback-leibler divergence in knowledge distillation for large language models

    Taiqiang Wu, Chaofan Tao, Jiahao Wang, and Zhe Zhao. Rethinking kullback-leibler divergence in knowledge distillation for large language models. arXiv preprint arXiv:2404.02657,

    arXiv

  6. [20]

    A survey on knowledge distillation of large language models

    Xiaohan Xu, Ming Li, Chongyang Tao, Tao Shen, Reynold Cheng, Jinyang Li, Can Xu, and Dacheng Tao. A survey on knowledge distillation of large language models. arXiv preprint arXiv:2402.13116,

    arXiv

  7. [21]

    Qwen2 technical report

    An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, et al. Qwen2 technical report. arXiv preprint arXiv:2407.10671,

    arXiv

  8. [22]

    Minicpm-v: A gpt-4v level mllm on your phone

    Yuan Yao, Tianyu Yu, Ao Zhang, Chongyi Wang, Junbo Cui, Hongji Zhu, Tianchi Cai, Haoyu Li, Weilin Zhao, Zhihui He, et al. Minicpm-v: A gpt-4v level mllm on your phone. arXiv preprint arXiv:2408.01800,

    arXiv

  9. [23]

    One small step for gen- erative ai, one giant leap for agi: A complete survey on chatgpt in aigc era

    Chaoning Zhang, Chenshuang Zhang, Chenghao Li, Yu Qiao, Sheng Zheng, Sumit Kumar Dam, Mengchun Zhang, Jung Uk Kim, Seong Tae Kim, Jinwoo Choi, et al. One small step for gen- erative ai, one giant leap for agi: A complete survey on chatgpt in aigc era. arXiv preprint arXiv:2304...

    2025 arXiv

  10. [24]

    A TAID TRAINING ALGORITHM Algorithm 1 provides a detailed description of the TAID training procedure, including the adap- tive update mechanism for the interpolation parameter t. The TAID algorithm utilizes several key Algorithm 1 TAID training algorithm 1: Input: Learning rat...

    2020

  11. [25]

    Thus, it is crucial to investigate when and whether the non-collapse condition ∥y∥2 > N ϵis satisfied to ensure that our hypothesis learns meaningful signals

    Such a collapse may happen particularly in the self-distillation paradigm because the teacher signals are (partially) given by our hypothesis itself. Thus, it is crucial to investigate when and whether the non-collapse condition ∥y∥2 > N ϵis satisfied to ensure that our hypoth...

    2025

  12. [26]

    be the condition number of G. The prediction vector yt+1 does not collapse, namely yt+1 = 0 cannot be a solution to the interpolation problem (3), if for some γ ∈ [0, 1], either of the following holds: t <min 1 γ + κ (r0 − γ) + o(1), γ r0 T or 1 r0 T < t, (10) where r0 := ∥y0∥...

    2025

  13. [27]

    tY τ =0 1 − t − τ T # ·

    than self-distillation by a constant factor. Specifically, TAID and self-distillation have critical steps of collapse t = O(r0/(γ + κ)) and t = O(r0/κ), respectively. To ensure that TAID learns meaningful features in the early phase, γ should be reasonably bounded away from 0,...

    2025

  14. [28]

    20 Published as a conference paper at ICLR 2025 Table 6: Performance comparison between TAID and Skew KL across different teacher sizes

    The last lower bound can be asymptotically (in large r0) expressed as follows: t ≥ γ+o(1) γ+κ+o(1) γ+o(1) (r0−γ)(1+o(1)) = 1 γ + κ (r0 − γ) + o(1). 20 Published as a conference paper at ICLR 2025 Table 6: Performance comparison between TAID and Skew KL across different teacher...

    2025

  15. [29]

    By solving this quadratic inequality, we can verify the statement

    + o(1) ≥ 1 r0 T suffices for yt not being collapsed for any t. By solving this quadratic inequality, we can verify the statement. C D ETAILED COMPARISON WITH SKEW KL We provide a detailed comparison between TAID and Skew KL to highlight their fundamental differ- ences, focusin...

  16. [31]

    The final value of t (tend) was set to 1.0 for all experiments

    72.19 74.11 77 .08 76 .63 75 .35 75 .18 (Ours) TAID 72.25 73.51 74.85 75.81 74.51 74.38 Phi-3-mini-4k-instruct pair and 0.2 for the other two pairs. The final value of t (tend) was set to 1.0 for all experiments. Regarding baseline methods, we implemented GKD using Generalized...

    2009

  17. [33]

    However, the gains are modest compared to state-of-the-art methods specifically designed for image classification, such as MLKD

    71.90 73.01 (Ours) TAID 72.10 72.71 As shown in Table 7, TAID performs competitively on CIFAR-100, consistently outperforming KL divergence across all model pairs. However, the gains are modest compared to state-of-the-art methods specifically designed for image classification...

    2024

  18. [34]

    41.15 0.68 58.41 76.01 66.40 40.00 59.35 48.86Phi-1.5B(Li et al., 2023a) 35.92 6.06 60.53 75.62 60.72 46.00 67.88 50.39StableLM-2-1.6B(Bellagente et al., 2024)36.21 29.59 53.57 76.77 66.60 37.20 58.72 51.24SmolLM-1.7B(Allal et al.,

    2024

  19. [35]

    This demonstrates the effectiveness of our distillation approach in creating a compact model that maintains high performance across a diverse range of language tasks

    As shown in Table 9, TAID-LLM-1.5B achieves competitive or superior performance across all tasks, with particularly strong results in PIQA and Hellaswag. This demonstrates the effectiveness of our distillation approach in creating a compact model that maintains high performanc...

    2024

  20. [64]

    To select the best checkpoint for evaluation, we calculated the ROUGE-L score on the validation set after each epoch and chose the checkpoint with the highest score

    We employed the AdamW optimizer with a learning rate of 1e−4 and a cosine learning rate scheduler. To select the best checkpoint for evaluation, we calculated the ROUGE-L score on the validation set after each epoch and chose the checkpoint with the highest score. For our prop...

    2025

  21. [640]

    The TAID-specific parameters for the pre-training experiments were kept consistent with those used in the Phi-3- mini-4k-instruct pair in the instruction tuning experiments

    We used the AdamW optimizer with a learning rate of 1e−4 and a cosine learning rate scheduler. The TAID-specific parameters for the pre-training experiments were kept consistent with those used in the Phi-3- mini-4k-instruct pair in the instruction tuning experiments. Also, th...

    2025

  22. [1991]

    Mobile edge intelligence for large language models: A contemporary survey

    Guanqiao Qu, Qiyuan Chen, Wei Wei, Zheng Lin, and Xianhao Chen. Mobile edge intelligence for large language models: A contemporary survey. arXiv preprint arXiv:2407.18921,

    arXiv

  23. [2010]

    Gemma 2: Improving open language models at a practical size

    Gemma Team, Morgane Riviere, Shreya Pathak, Pier Giuseppe Sessa, Cassidy Hardin, Surya Bhu- patiraju, L´eonard Hussenot, Thomas Mesnard, Bobak Shahriari, Alexandre Ram ´e, et al. Gemma 2: Improving open language models at a practical size. arXiv preprint arXiv:2408.00118,

    arXiv

  24. [2020]

    Compact language models via pruning and knowledge distillation.arXiv preprint arXiv:2407.14679,

    Saurav Muralidharan, Sharath Turuvekere Sreenivas, Raviraj Joshi, Marcin Chochowski, Mostofa Patwary, Mohammad Shoeybi, Bryan Catanzaro, Jan Kautz, and Pavlo Molchanov. Compact language models via pruning and knowledge distillation.arXiv preprint arXiv:2407.14679,

    arXiv

  25. [2022]

    Mantis: Interleaved multi-image instruction tuning

    Dongfu Jiang, Xuan He, Huaye Zeng, Cong Wei, Max Ku, and Qian Liu. Mantis: Interleaved multi-image instruction tuning. arXiv preprint arXiv:2405.01483,

    arXiv

  26. [2023]

    Stable lm 2 1.6 b technical report

    Marco Bellagente, Jonathan Tow, Dakota Mahan, Duy Phung, Maksym Zhuravinskyi, Reshinth Adithyan, James Baicoianu, Ben Brooks, Nathan Cooper, Ashish Datta, et al. Stable lm 2 1.6 b technical report. arXiv preprint arXiv:2402.17834,

    arXiv

  27. [2024]

    URL https://huggingface.co/datasets/ HuggingFaceTB/smollm-corpus. Lucas Beyer, Andreas Steiner, Andr´e Susano Pinto, Alexander Kolesnikov, Xiao Wang, Daniel Salz, Maxim Neumann, Ibrahim Alabdulmohsin, Michael Tschannen, Emanuele Bugliarello, et al. Paligemma: A versatile 3b vl...

    arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.