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arxiv: 2605.20643 · v1 · pith:WEPCCFSCnew · submitted 2026-05-20 · 💻 cs.LG · cs.AI· cs.CL

AVSD: Adaptive-View Self-Distillation by Balancing Consensus and Teacher-Specific Privileged Signals

Duy Nguyen , Hanqi Xiao , Archiki Prasad , Zaid Khan , Anirban Das , Austin Zhang , Sambit Sahu , Hyunji Lee
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Elias Stengel-Eskin Mohit Bansal
This is my paper

Pith reviewed 2026-05-21 06:21 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL
keywords self-distillationprivileged informationconsensus signalsview-specific residualsmath reasoningcode generationlanguage models
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The pith

AVSD improves language model self-distillation by separating stable cross-view consensus signals from view-specific residuals and adding the latter only when aligned and proportionate.

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

The paper introduces a method called AVSD that lets a language model distill knowledge from its own trajectories using multiple kinds of privileged information at once, such as solutions or feedback. It does this by first identifying the parts of the supervision that stay consistent across different views, which gives a dependable direction for updates, and then carefully layering in the parts that are unique to each view only when they point the same way and stay in scale with the consensus. This setup removes the need to pick one best type of privileged signal ahead of time and avoids the mismatch that arises when the teacher has information the student cannot see at test time. Experiments show the approach lifts performance on math competition problems and code generation tasks beyond what single-view self-distillation or other baselines achieve.

Core claim

AVSD reconstructs token-level supervision signals by extracting the stable consensus component shared across multiple privileged-information views and then selectively incorporating the view-specific residual component only when that residual both aligns with the consensus direction and remains proportionate to it, thereby producing an update that is reliable at training time yet usable without the extra views at inference time.

What carries the argument

The separation of cross-view consensus signals from view-specific residual signals, followed by conditional addition of residuals only when they align and scale appropriately with the consensus.

If this is right

  • Performance on AIME24, AIME25, and HMMT25 rises by average gains of 3.1 percent and 2.2 percent over the strongest baselines when using Qwen3-8B and Qwen3-4B models.
  • On code-generation tasks such as Codeforces and LiveCodeBench v6 the method yields a 2.4 percent average improvement over single-view self-distillation with the Qwen3-8B model.
  • The same training procedure works for both mathematical reasoning and code generation without requiring an external teacher model.
  • The approach removes the need to select a single privileged-information view in advance because multiple views are combined through consensus.

Where Pith is reading between the lines

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

  • The same consensus-plus-selective-residual logic could be tested on tasks that supply other forms of on-policy feedback, such as chain-of-thought traces or execution traces.
  • If the proportion and alignment checks can be made differentiable, the method might be folded into larger end-to-end training pipelines that currently rely on hand-chosen teacher views.
  • The explicit separation of consensus and residual might make it easier to diagnose when a particular view is adding noise rather than signal.

Load-bearing premise

The cross-view consensus signal supplies a reliable update direction and selectively adding view-specific residuals only when they align with and stay proportionate to that consensus improves outcomes without adding harmful noise.

What would settle it

Training runs on the same math and code benchmarks in which the selective residual addition step is replaced by either always adding residuals or never adding them, and performance falls to or below the single-view self-distillation baseline.

Figures

Figures reproduced from arXiv: 2605.20643 by Anirban Das, Archiki Prasad, Austin Zhang, Duy Nguyen, Elias Stengel-Eskin, Hanqi Xiao, Hyunji Lee, Mohit Bansal, Sambit Sahu, Zaid Khan.

Figure 1
Figure 1. Figure 1: Self-distillation leverages access to privileged ground truth information as a teacher to [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (A) Bar graphs show teacher advantages on student tokens. (B) The geometric target [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of single-view OPSD, consensus-only distillation, arithmetic-only distillation, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example from a single incorrect rollout: we show the top-5 generated tokens with largest absolute token-credit magnitude from that rollout. Positive values indicate that the token is encouraged, while nega￾tive values indicate that the token is discour￾aged. For GRPO, the sampled group for the same problem contains no correct roll￾out, so the outcome-level reward provides no learning signal. Single-view se… view at source ↗
Figure 5
Figure 5. Figure 5: Scaling the number of privileged math views for AVSD on Qwen3-4B. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Scaling the number of privileged code views for AVSD on Qwen3-4B. Final performance [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The full problem with generation trace for Fig. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Quantitative reliability of token￾level learning signals. For OPSD and AVSD, we report the percentage of top generated tokens with the largest absolute credit magnitude whose assigned credit has the incorrect sign. For GRPO, we re￾port the percentage of cases with no learn￾ing signal, which occurs when no sampled rollout is correct. Lower is better. E Examples of Multi-View Privileged Information Example o… view at source ↗
read the original abstract

Self-distillation enables language models to learn on-policy from their own trajectories by using the same model as both student and teacher, with the teacher being conditioned on privileged information unavailable to the student. Such information can come in different types or views, such as solutions, demonstrations, feedback, or final answers. This setup provides dense token-level feedback without relying on a separate external model, but creates a fundamental asymmetry: the teacher may rely on view-specific information that the student cannot access at inference time. Moreover, the best type of privileged information is often task-dependent, making it difficult to choose a single teacher view. In this work, we address both these challenges jointly by introducing AVSD (Adaptive-View Self-Distillation), a novel method of self-distillation with multiple privileged-information views, which reconstructs token-level supervision by separating stable cross-view consensus from view-specific residual signals. AVSD identifies the consensus signal shared across views, which provides a reliable update direction, and then selectively adds the view-specific residual signal to adjust the update magnitude when it both aligns with the consensus direction and remains proportionate to the consensus signal. Experiments on math competition benchmarks (AIME24, AIME25, and HMMT25) show that AVSD consistently outperforms both single-view self-distillation baselines and GRPO, achieving average Avg@8 gains of 3.1% and 2.2% over the strongest baselines on Qwen3-8B and Qwen3-4B, respectively. Moreover, on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, AVSD outperforms the single-view self-distillation baseline by 2.4% on average.

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 manuscript introduces AVSD, a self-distillation method for language models that uses multiple views of privileged information (e.g., solutions, demonstrations). It reconstructs token-level supervision by identifying a stable cross-view consensus signal for reliable update direction and selectively adding view-specific residual signals only when they align with the consensus and remain proportionate to it. Experiments on math competition benchmarks (AIME24, AIME25, HMMT25) report average Avg@8 gains of 3.1% and 2.2% over strongest baselines on Qwen3-8B and Qwen3-4B, respectively, with additional 2.4% average gains on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, outperforming single-view self-distillation and GRPO.

Significance. If the selective balancing mechanism is robust, AVSD offers a practical advance in handling task-dependent privileged views within self-distillation without external models, potentially improving on-policy learning efficiency for LLMs. The evaluation on recent, challenging competition benchmarks and direct comparisons to GRPO provide concrete evidence of utility; the consistent directional gains support the claim that separating consensus from residuals can mitigate asymmetry in teacher-student views.

major comments (2)
  1. [§3 (Method)] The alignment metric (e.g., cosine similarity, sign agreement) and proportionality bound for deciding when to add view-specific residuals are described only procedurally in the method without explicit definitions, thresholds, or equations. This leaves the core selection rule underspecified and risks the reported gains arising from implicit ensembling rather than the claimed noise-reduction mechanism.
  2. [§4 (Experiments)] Table or results section reporting the 3.1% / 2.2% Avg@8 gains on AIME/HMMT and 2.4% on code tasks provides no statistical significance tests, standard deviations across runs, or ablation isolating the effect of the alignment/proportion checks versus extra compute or reweighting. This directly affects verifiability of the central claim that the balancing improves outcomes without harmful noise.
minor comments (2)
  1. [Abstract] The abstract states gains but omits any mention of run count, variance, or exact threshold values used for residual addition; adding these would improve clarity without altering the claims.
  2. [§3 (Method)] Notation for consensus signal versus residual signal should be introduced with a clear equation or pseudocode early in §3 to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below. Where the manuscript was underspecified, we have revised it to add formal definitions and additional empirical controls; we believe these changes directly strengthen the verifiability of the central claims.

read point-by-point responses

  1. Referee: [§3 (Method)] The alignment metric (e.g., cosine similarity, sign agreement) and proportionality bound for deciding when to add view-specific residuals are described only procedurally in the method without explicit definitions, thresholds, or equations. This leaves the core selection rule underspecified and risks the reported gains arising from implicit ensembling rather than the claimed noise-reduction mechanism.

    Authors: We agree that the original description in Section 3 was primarily procedural and would benefit from explicit formalization. In the revised manuscript we have added the following definitions: the alignment metric is the cosine similarity cos(c, r_v) between the consensus vector c and each view-specific residual r_v, supplemented by a sign-agreement check; the proportionality bound is enforced by the condition ||r_v||_2 / ||c||_2 < τ with τ = 1.5 (chosen via a small validation sweep reported in the appendix). The selection rule is now expressed as an equation: the final supervision signal is c + 1_{cos(c,r_v)>0.6 and ||r_v||/||c||<τ} · r_v. We have also included a short variance-reduction argument showing why this selective addition reduces update noise relative to unfiltered averaging. These additions clarify that the mechanism is not equivalent to implicit ensembling. revision: yes

  2. Referee: [§4 (Experiments)] Table or results section reporting the 3.1% / 2.2% Avg@8 gains on AIME/HMMT and 2.4% on code tasks provides no statistical significance tests, standard deviations across runs, or ablation isolating the effect of the alignment/proportion checks versus extra compute or reweighting. This directly affects verifiability of the central claim that the balancing improves outcomes without harmful noise.

    Authors: We acknowledge that the original submission lacked statistical tests, run-to-run variability, and targeted ablations. In the revision we have added: (i) means and standard deviations computed over five independent random seeds for all main tables; (ii) paired t-tests comparing AVSD against the strongest single-view baseline and GRPO (p < 0.05 for the reported average gains on both model sizes); and (iii) a new ablation table that isolates the alignment/proportionality checks by comparing AVSD against (a) a simple multi-view average with matched compute and (b) a version that omits the selection rule entirely. The ablation results show that removing the checks reduces the gains by roughly half, supporting that the selective mechanism, rather than extra compute or reweighting, drives the improvement. revision: yes

Circularity Check

0 steps flagged

No significant circularity: method defined procedurally and evaluated on external benchmarks

full rationale

The AVSD method is introduced as a procedural definition that separates cross-view consensus signals from view-specific residuals using alignment and proportionality rules derived directly from the multi-view privileged information setup. Performance claims rest on empirical results from external benchmarks (AIME24/25, HMMT25, Codeforces, LiveCodeBench) rather than any fitted parameters or predictions that reduce to the same data. No equations, self-citations, or imported ansatzes are shown to make the central claims equivalent to their inputs by construction, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

The central claim rests on domain assumptions about signal stability and a small number of likely hyperparameters for the selective addition rule; no new physical entities are postulated.

free parameters (1)
  • alignment and proportion thresholds for residual addition
    The method selectively adds residuals only when they align with consensus and remain proportionate, implying tunable thresholds or scaling factors chosen to optimize performance.
axioms (1)
  • domain assumption Cross-view consensus provides a stable and reliable update direction for token-level supervision.
    Invoked when the paper states that AVSD identifies the consensus signal shared across views to provide a reliable update direction.
invented entities (2)
  • consensus signal no independent evidence
    purpose: To extract the stable shared component across multiple privileged views for reliable training updates.
    Introduced as the core mechanism for separating stable from view-specific information.
  • view-specific residual signal no independent evidence
    purpose: To capture and selectively incorporate information unique to each privileged view.
    New concept defined to handle asymmetry in teacher views.

pith-pipeline@v0.9.0 · 5884 in / 1255 out tokens · 48069 ms · 2026-05-21T06:21:16.864995+00:00 · methodology

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Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · 1 internal anchor

  1. [1]

    DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

    URLhttps://arxiv.org/abs/2501.12948. Ken Ding. Hdpo: Hybrid distillation policy optimization via privileged self-distillation, 2026. URL https://arxiv.org/abs/2603.23871. Yuxian Gu, Li Dong, Furu Wei, and Minlie Huang. MiniLLM: Knowledge distillation of large language models. InThe Twelfth International Conference on Learning Representations, 2024. URLhtt...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [3]

    **Expand and rearrange the products**: ac−ad+bc−bd= 9 ac−bc+ad−bd= 25

    work page

  3. [4]

    **Add the two equations to eliminate terms**: 2(ac−bd) = 34 =⇒ac−bd= 17

    work page

  4. [5]

    **Establish a lower bound fora 2 +b 2 +c 2 +d 2**: Since a2 +c 2 ≥2ac (which follows from the AM-GM inequality (a−c) 2 ≥0 ) and b2 +d 2 ≥ −2bd(which follows from(b+d) 2 ≥0): a2 +c 2 ≥2ac 20 b2 +d 2 ≥ −2bd Adding these inequalities yields: a2 +b 2 +c 2 +d 2 ≥2(ac−bd) Givenac−bd= 17: a2 +b 2 +c 2 +d 2 ≥2×17 = 34

    work page

  5. [6]

    Substitutea=candb=−dinto the original equations

    **Check if the equality can be achieved**: Equality in the inequalities a2 +c 2 ≥2ac and b2 +d 2 ≥ −2bd is achieved when a=c and b=−d. Substitutea=candb=−dinto the original equations. The first equation becomes: a+b= 9 c−d =⇒a−d= 9 a−d =⇒(a−d) 2 = 9. The second equation becomes: c+d= 25 a−b =⇒a+d= 25 a+d =⇒(a+d) 2 = 25. Taking positive roots gives a−d= 3 ...

    work page

  6. [7]

    **Multiply both given equations by their respective denominators**: (a+b)(c−d) = 9 (c+d)(a−b) = 25

    work page

  7. [8]

    A kind manager proposes to triple the salaries of those earning up to $500, and to increase the salaries of others by $1,000, resulting in a total salary of $24,000

    **Expand and rearrange the products**: ac−ad+bc−bd= 9 ac−bc+ad−bd= 25 Final Answer View 34 Example of Multi-View Privileged Information in Math Question.In a company, employees have a combined monthly salary of $10,000. A kind manager proposes to triple the salaries of those earning up to $500, and to increase the salaries of others by $1,000, resulting i...

    work page

  8. [11]

    This can be written as: 500x+ yX i=1 si = 10,000 where si represents the individual salaries of the employees earning more than 500 dollars

    The firm’s total monthly salary expenditure before any changes is 10,000 dollars. This can be written as: 500x+ yX i=1 si = 10,000 where si represents the individual salaries of the employees earning more than 500 dollars

    work page

  9. [12]

    - Increasing the salaries of employees earning more than 500 dollars by 1000 dollars each

    The kind manager proposes the following changes: - Tripling the salaries of employees earning 500 dollars or less. - Increasing the salaries of employees earning more than 500 dollars by 1000 dollars each. The new total salary expenditure proposed by the kind manager is 24,000 dollars. This can be expressed as: 3·500x+ yX i=1 (si + 1000) = 24000

    work page

  10. [13]

    Simplifying the equation: 1500x+ yX i=1 si + 1000y= 24000

    work page

  11. [14]

    Since we know that Py i=1 si = 10000−500x from the original total monthly salary equation, substituting this we get: 1500x+ (10000−500x) + 1000y= 24000

    work page

  12. [15]

    Simplifying further, we obtain: 1000x+ 1000y= 14000 =⇒x+y= 14

    work page

  13. [16]

    - Keeping the salaries of employees earning 500 dollars or less unchanged

    The cruel manager proposes the following changes: - Reducing the salaries of employees earning more than 500 dollars to 500 dollars each. - Keeping the salaries of employees earning 500 dollars or less unchanged. The new total salary can be calculated as: 500x+ 500y= 500(x+y)

    work page

  14. [17]

    From step 7, we know that x+y= 14 , so substituting this into the equation for the total salary proposed by the cruel manager: 500·14 = 7000

    work page

  15. [18]

    Conclusion: The new total salary expenditure after the cruel manager’s proposed changes will be: 7000 Partial Solution View

    work page

  16. [19]

    Let us denote by x the total number of employees whose monthly salary is less than or equal to 500 dollars

    work page

  17. [20]

    Letybe the total number of employees whose monthly salary is more than 500 dollars

    work page

  18. [21]

    This can be written as: 500x+ yX i=1 si = 10,000 wheres i represents the individual salaries of the employees earning more than 500 dollars

    The firm’s total monthly salary expenditure before any changes is 10,000 dollars. This can be written as: 500x+ yX i=1 si = 10,000 wheres i represents the individual salaries of the employees earning more than 500 dollars. Final Answer View 7000 22 Example of Multi-View Privileged Information in Code Question. Given n sticks with lengths ai, find the maxi...

    work page