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Live-OPSD: On-Policy Self-Distillation for Proactive Streaming Large Video Models

Kaixuan Du, Xin Wan, Dai Guan, Ming Chen, Xiaoxi Jiang, Guanjun Jiang

arXiv:2610.36959v1cs.LG

TL;DR

Streaming assistants must decide whether to respond while evidence is still arriving, but supervised fine-tuning does not directly train on response prefixes produced by the evolving policy. Live-OPSD uses privileged hints to guide the policy on its own continuations. On Qwen3-Omni-30B-A3B, it scores 59.64 on LiveProBench, 5.26 points above the strongest continued-SFT baseline.

  • Problem

    Streaming assistants must decide whether and when to respond as evidence arrives, while supervised fine-tuning does not directly train on response prefixes produced by the evolving policy.

    Source: §1 · p. 1

  • Method

    Live-OPSD generates continuations from streaming context, then uses the same model’s hinted distributions on those self-produced prefixes to guide the unhinted policy.

    Source: §1 · p. 1

  • Results

    59.64 average score on LiveProBench, 5.26 points above the strongest continued-SFT baseline (54.38), on Qwen3-Omni-30B-A3B.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Live-OPSD provides evidence for privileged on-policy distillation as a promising training principle for proactive streaming video models.

    Source: §7 · p. 10

    Generating continuations at recorded histories provides response-level on-policy supervision but mismatches model-generated deployment histories.

    Source: §6 · p. 9

Abstract

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Streaming multimodal assistants must make response decisions while events are still unfolding. They need to recognize when the available evidence warrants a response, produce an appropriate continuation, and remain silent otherwise. Supervised fine-tuning learns from recorded assistant turns, but does not directly train on the response prefixes produced by the evolving policy itself. We introduce Live-OPSD, an on-policy self-distillation method that uses privileged hints available only during training to supervise the policy on its own outputs. The policy first generates a continuation from the streaming context alone. The same model then re-evaluates that continuation with a hint describing the relevant evidence, and the resulting distributions guide the unhinted policy. On Qwen3-Omni-30B-A3B, Live-OPSD attains an average score of 59.64 on LiveProBench, 5.26 points above the strongest continued-SFT baseline, and stays competitive on OVO-Bench (65.84). These results indicate that guiding the policy on its own outputs with privileged hints improves both when and how a streaming assistant responds.

1 INTRODUCTION

Proactive streaming assistants must decide whether and when current evidence warrants a response, not just produce a correct answer. Live-OPSD uses privileged hints to distill the model’s own streaming continuations, improving results over continued SFT in the evaluated setting.

1 INTRODUCTION

  • Proactive streaming requires deciding whether current evidence warrants a response: speaking too early interrupts, while silence after a relevant event misses the chance to help.Evidence may still be arriving, and a standing instruction can become actionable later.Source: §1 · p. 1
  • SFT trains reference continuations rather than the policy’s own prefixes; AURA and StreamPro reweight recorded supervision but remain tied to annotated actions and prefixes (Lu et al., 2026; Li et al., 2026).Spoken responses can contribute many more training tokens than silence, leaving asymmetric supervision.Source: §1 · p. 1
  • Live-OPSD generates continuations without hints, then uses the same model with a training-time evidence hint to provide distributional targets for selected prefixes.Distillation guides the unhinted policy on text it generated itself.Source: §1 · p. 1, Figure 1 · p. 2
  • Decision-Aware Selection uses disagreements to expose errors while preserving consistent responses and silence, forming a bounded update set for reverse-KL updates.The updated policy supplies the next rollout and teacher.Source: §1 · p. 2, Figure 1 · p. 2
  • 59.64 on LiveProBench for Qwen3-Omni-30B-A3B exceeds the strongest continued-SFT baseline’s 54.38 by 5.26 points.The evaluation also compares released proactive systems on OVO-Bench and OmniMMI proactive alerting.Source: §1 · p. 2

2 RELATED WORK

Related work establishes streaming interfaces and proactive response systems, while Live-OPSD contributes a post-training objective that guides an existing policy without changing its inference mechanism. It uses privileged hints to distill token-level guidance on policy-generated continuations and evaluates whether timing-focused training preserves broad streaming capabilities.

Streaming perception and interaction

  • Streaming foundations preserve evolving visual history and support online interaction, but their primary contributions are not on-policy post-training objectives.Examples include VideoLLM-online, Flash-VStream, memory-based approaches, and MMDuet’s interleaved video-text turns with informative and relevance heads (Chen et al., 2024; Zhang et al., 2024; Wang et al., 2024).Source: §2 · p. 2

Proactive systems

  • Live-OPSD adds a post-training objective to an existing streaming policy, unlike proactive systems that modify inference-time gating, planning, memory, or computation.Open-source systems such as AURA, JoyAI-VL-Interaction, ROMA, and MOSS-VL-Realtime provide architectural and training comparisons distinct from the controlled objective comparison on two Qwen backbones (Lu et al., 2026; Yao et al., 2026; Tian et al., 2026; Wang et al., 2026).Source: §2 · pp. 2–3

Learning response timing

  • Live-OPSD assigns updates according to the current response decision and uses a privileged teacher distribution for token-level learning on the policy’s own continuation.This differs from sequence-level timing objectives, which optimize timing rewards but require long-stream rollouts and explicit reward definitions; examples include StreamPro’s GRPO and MMDuet2’s multi-turn reinforcement learning (Li et al., 2026; Wang et al., 2025b).Source: §2 · p. 3

Distillation with privileged information

  • Live-OPSD applies on-policy distillation to streaming decision contexts: teacher and student share parameters, but only the teacher receives a training-time hint.On-policy distillation evaluates the teacher on student-generated continuations, addressing prefixes visited by the current student; this relates to learner-induced state distributions in imitation learning (Agarwal et al., 2024; Ross et al., 2011), while privileged information supplies the teacher–student asymmetry.Source: §2 · p. 3

Evaluation of streaming behavior

  • OVO-Bench and OmniMMI assess causal stream understanding, while StreamArena extends evaluation to hour-scale open-ended streams and LiveProBench isolates response timing under standing instructions.The paper uses OVO-Bench and OmniMMI to test whether timing-oriented post-training preserves broad streaming capabilities (Li et al., 2025; Wang et al., 2025c; Zhang et al., 2026; Du et al., 2026).Source: §2 · p. 3

3 STREAMING INTERACTION

The section defines streaming interaction as decisions over a visible prefix, where utterances require responses and stream chunks allow either a response or silence. It specifies binary decision supervision with privileged hints, recorded-action SFT initialization, and on-policy continuation rollouts.

Streaming interaction

  • The visible history includes the arriving audio-visual chunk or user utterance, and the policy cannot access future observations.User utterances require a response, while stream chunks permit either a response or silence.Source: §3 · p. 3
  • Training labels whether to speak, while a privileged hint describes relevant visual or acoustic evidence and its relation to the intended behavior.The binary decision does not specify the full response; Figure 2 contrasts recorded-action SFT with hint-conditioned teacher supervision in Live-OPSD.Source: §3 · p. 3, Figure 2 · p. 4
  • Streaming SFT initializes the policy by targeting the recorded response or silence action associated with each binary decision.It supervises silent messages and the final non-silent message, excluding earlier non-silent messages whose supporting evidence may have been removed by window truncation.Source: §3 · pp. 3–4
  • The SFT objective preserves silence supervision without letting silent messages dominate, and its Live-SFT-Zero checkpoint initializes Live-OPSD.The hint is not an input or target during this stage.Source: §3 · p. 4
  • Live-OPSD generates each continuation from the current policy at a recorded context, making the response and its token prefixes on-policy without claiming earlier recorded turns were policy-generated.At deployment, earlier generated turns become part of the evolving history; the causal observation boundary applies in both training and deployment.Source: §3 · p. 4

4 LIVE-OPSD

Live-OPSD combines privileged-context distribution matching with decision-aware selection: hints condition the teacher, while supervisory decisions guide which streaming points are trained.

4.1 PRIVILEGED-CONTEXT SELF-DISTILLATION

  • From unhinted streaming context, the student generates a continuation; the current policy then scores the same generated prefixes with an offline-annotated hint to guide the student.Hints explain evidence supporting an annotated response decision. Hints are reused, but targets are recomputed after each update; their usefulness depends on annotation quality and the model’s ability to interpret them.Source: §4.1 · pp. 4–5

4.2 A DISTRIBUTIONAL OBJECTIVE

  • The default update minimizes reverse KL, D_KL(Q∥P), over selected generated continuation tokens, including silence, with gradients through student Q while teacher P and rollout prefixes remain fixed.Forward KL and symmetric Jensen–Shannon divergence are compared; the two KL directions are implemented separately rather than as JSD endpoint values.Source: §4.2 · p. 5

4.3 DECISION-AWARE SELECTION

  • DAS spends at most K scored points per update, prioritizing alternating inconsistent decisions, then consistent responses, then silence sampled across videos.Decision labels control selection rather than gradient weighting, so consistent actions can still provide a distillation signal; selection refreshes from new rollouts, and inference uses the native response interface without hints, DAS, or an extra classifier.Source: §4.3 · pp. 5–6, Figure 3 · p. 6

5 EXPERIMENTS

The experiments compare controlled training methods and released systems across proactive timing, response quality, and silence handling. Live-OPSD leads the 30B controlled LiveProBench comparison and is also evaluated on OmniMMI PA and OVO-Bench.

5.1 EXPERIMENTAL SETUP

  • The evaluation uses Qwen2.5-Omni-7B and Qwen3-Omni-30B-A3B adapted to interleaved audio-visual streaming, comparing Live-OPSD post-training with Vanilla-SFT, CB-SFT, and SSB-SFT.Live-OPSD starts from the same streaming-SFT model; training dialogues include direct questions and standing instructions requiring proactive responses.Source: §5.1 · p. 6

5.3 MAIN COMPARISONS

  • The reverse-KL Live-OPSD model in the Qwen3-Omni-30B-A3B block reports a six-task average of 59.64, exceeding Vanilla-SFT, CB-SFT, and SSB-SFT by 5.26, 6.64, and 9.05 points, respectively.Source: §5.3 · p. 8

5.2 BENCHMARKS AND METRICS

  • LiveProBench measures event triggering and silence across six task scores, while OmniMMI PA and OVO-Bench add proactive alerting, multimodal understanding, and active responding.LiveProBench’s Event Sensitivity combines alert coverage and silent-segment accuracy geometrically; window tasks score the first response within the permitted interval, and Duplicate Counting uses exact-count accuracy.Source: §5.2 · p. 7

5.3 MAIN COMPARISONS

  • Live-OPSD scores 56.50 and 59.00 on OmniMMI PA versus AURA’s 37.50, and improves OVO-Bench accuracy from 50.30 to 61.97 at 7B and 61.00 to 65.84 at 30B.The published system-level results use different inference configurations; controlled objective comparisons are reported separately on LiveProBench.Source: Table 2 · p. 7, §5.3 · p. 8, Table 3
  • 48.97 is the 7B Live-OPSD LiveProBench average, versus 48.33 for Vanilla-SFT, 44.98 for CB-SFT, and 33.78 for SSB-SFT.Live-OPSD leads Anomaly Alert; CB-SFT leads Event Sensitivity, Onset Response, and Duplicate Counting, while Vanilla-SFT leads Window Response and Sustained Silence.Source: §5.3 · p. 8

5.4 ABLATION STUDIES

  • On LiveProBench, reverse KL and JSD score 59.64 and 59.21 mean, while reverse KL leads window response (70.00 vs. 66.25) and duplicate counting (34.33 vs. 22.39).Forward KL under-triggers: its event-sensitivity and anomaly-alert scores are 43.03 and 11.34, producing a 36.10 mean. On held-out points, reverse KL leads proactive F1, false-alarm rate, and per-episode exact match for most training, with a higher event-miss rate.Source: §5.4 · p. 8, Table 4 · p. 9
  • Replacing Decision-Aware Selection with fixed-position selection lowers the JSD LiveProBench mean from 59.21 to 44.18 and reduces Duplicate Counting to 0.00.The fixed-size suffix is chosen independently of the policy while retaining each point’s preceding dialogue and media context; premature and missed timing bands also widen relative to full JSD.Source: §5.4 · pp. 8–9, Figure 4 · p. 8, Table 4 · p. 9

6 DISCUSSION AND LIMITATIONS

Live-OPSD can be adapted across streaming protocols with aligned decision supervision and conditional likelihood evaluation, but its current training uses external hints and recorded histories. Online self-training remains a future direction because the method still depends on external hints and supervised response decisions.

Scope and transfer requirements

  • Protocol adaptation requires aligned decision supervision and conditional likelihood evaluation with and without privileged context, while richer action spaces need matching supervision and selection categories.The method is defined through conditional policies and semantic actions, not a mandatory two-stage framework; adaptation can preserve a protocol’s native markers and shared backbone vocabulary.Source: §6 · p. 9

Current instantiation

  • Recorded histories enable tractable response-level on-policy supervision, but mismatch deployment histories; access only to observations at each decision is a causal constraint.External hint annotation was chosen after pilot checks found Qwen3-Omni inconsistent as its own multi-turn hint annotator; this is an implementation choice, not a backbone limitation.Source: §6 · p. 9

Toward online self-training

  • Online hint generation and trajectory-level generation could align feedback with student-generated histories, but fully self-supervised training remains future work.Model-proposed hints would need to stay grounded in the observed stream and add information beyond unassisted judgment; the current method still uses external hints and supervised response decisions.Source: §6 · p. 9

7 CONCLUSION

Live-OPSD uses privileged context to supervise a streaming policy on its own continuations, with Decision-Aware Selection allocating updates by response decisions. On Qwen3-Omni, it outperforms the strongest continued-SFT baseline on LiveProBench while remaining competitive on broader benchmarks.

7 CONCLUSION

  • 59.64 on LiveProBench, 5.26 points above the strongest continued-SFT baseline, was achieved by Live-OPSD on Qwen3-Omni.It remained competitive on broader benchmarks.Source: §7 · p. 10
  • A hinted model copy supplies token-level targets for the policy’s own continuations, while Decision-Aware Selection allocates the update budget by response decisions.The conclusion presents this as evidence for privileged on-policy distillation as a promising training principle for proactive streaming video models.Source: §7 · p. 10

AI USAGE STATEMENT

  • Generative AI tools were used for manuscript language polishing and to synthesize SFT data and offline privileged hints, but not to run training or evaluation or generate or alter measurements.The hint production procedure is described in Appendix B; the authors take full responsibility for the submitted content.Source: AI USAGE STATEMENT · p. 10

ETHICS STATEMENT

  • The study uses only publicly available video datasets, introduces no private video data, and is limited to model training and benchmark evaluation.Biases and privacy considerations inherited from source datasets and pretrained models remain applicable.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The method and comparison protocol are specified in Sections 4 and 5.1, and reported configurations are limited to details supported by retained experimental records.Appendices describe data construction, baseline objectives, selection, metrics, and settings verified from available run artifacts.Source: REPRODUCIBILITY STATEMENT · p. 10

A TRAINING DATA AND STREAMING CONTEXTS · B PRIVILEGED HINTS AND PROMPTS · C SELECTION DETAILS AND FIXED-SELECTION CONTROL

Live-OPSD trains streaming decisions on dialogue contexts as they unfold, using privileged, point-specific hints to guide the policy on its own outputs. Its data selection controls which scored points contribute to updates, while a fixed-selection control retains context without decision-dependent prioritization.

A TRAINING DATA AND STREAMING CONTEXTS

  • Each decision context contains all preceding turns and currently visible media, covering both questions and standing instructions that require silence between relevant events.Flattening dialogues changes the optimization units, not the information available in each context.Source: A TRAINING DATA AND STREAMING CONTEXTS · p. 12
  • Live-OPSD and continued-SFT use 3,712 training instances, while the preceding streaming-SFT stage uses approximately 196,000 instances.Continued-SFT trains on reference responses; points without usable teacher supervision are excluded from distillation, and training sources are checked against benchmark sources for overlap.Source: A TRAINING DATA AND STREAMING CONTEXTS · p. 12

B PRIVILEGED HINTS AND PROMPTS

  • An offline annotator uses the dialogue, reference decision, and full clip to create a hint about decision-relevant evidence, whether to respond, and why.The hint excludes the reference response and is privileged teacher context; the student’s prompt and multimodal input remain bounded by the current streaming time.Source: B PRIVILEGED HINTS AND PROMPTS · p. 12
  • The hint is teacher input rather than a sentence for the student to repeat, but the available artifact lacks the annotation-model identity and retention counts needed to reproduce hints exactly.Teacher and student share multimodal input and interaction, chat template, tokenizer, and media representation; response positions are aligned relative to each prompt’s end.Source: B PRIVILEGED HINTS AND PROMPTS · pp. 12–13

C SELECTION DETAILS AND FIXED-SELECTION CONTROL

  • Selection caps inconsistent points at q = max{1, ⌊αK⌋}, relaxing the quota to K when consistent silence is insufficient, then fills slots with responses before round-robin silence points.Inconsistent directions are randomized and interleaved; selection changes sample composition, not Equation 6’s weights.Source: C SELECTION DETAILS AND… · p. 13
  • The consistent-silence scoring subset is selected independently of current response probabilities, and only scored points enter the effective set.The scoring fraction, quota, and effective contributing-point count jointly determine update composition and cost; the artifacts retain the selected budget but not the other two values.Source: C SELECTION DETAILS AND… · p. 13
  • The w/o DAS control selects a fixed 128-point batch of per-video decision-point suffixes before training, without decision-dependent prioritization or teacher admission.Earlier turns and media remain in each retained point’s context, validation and test streams keep full schedules, and matching update budgets does not equalize computation because the full method generates extra candidates.Source: C SELECTION DETAILS AND… · p. 13

D TRAINING PROCEDURE · E SUPERVISED BASELINE OBJECTIVES

Live-OPSD refreshes rollout, teacher scoring, and selection at each update, while its supervised baselines share data representation, continuations, initialization, and schedule but vary token supervision and weighting.

D TRAINING PROCEDURE

E SUPERVISED BASELINE OBJECTIVES

  • The supervised baselines share the streaming representation, reference continuations, initialization checkpoint, and schedule, differing only in supervised tokens and their weights.Source: E SUPERVISED BASELINE OBJECTIVES · p. 13
  • Vanilla-SFT gives equal weight to all target tokens in retained reference assistant messages.Source: E SUPERVISED BASELINE OBJECTIVES · p. 13
  • SSB-SFT retains silent messages and the final non-silent message, masking earlier non-silent messages and weighting silent-message tokens by 1/Nsil.Nsil counts silent messages per training instance; the retained non-silent message's tokens receive unit weight.Source: E SUPERVISED BASELINE OBJECTIVES · p. 13
  • Decision-aware selection scores inconsistent decisions, correct responses, and sampled correct silences, then selects up to K points for the policy update.Inconsistent decisions are prioritized subject to a quota, followed by correct responses and sampled correct silences.Source: E SUPERVISED BASELINE OBJECTIVES · p. 14
  • CB-SFT reweights silence-versus-response decision positions by class and scales response-text tokens with λtext, using only supervised training.The baseline omits StreamPro's subsequent policy-optimization stage; its run artifacts do not preserve β or λtext values.Source: E SUPERVISED BASELINE OBJECTIVES · p. 14

F EXPERIMENTAL CONFIGURATION

The configuration represents streams as ordered one-second audio-visual chunks and uses compact, hint-conditioned teacher targets to train on student rollouts. It also specifies response-position masking and omits unverified run details rather than inferring them.

Data format and preprocessing

  • Streams use one-second chunks with two frames at 2 fps, 16 kHz mono audio, and a 65,536-token context window.Frames are rescaled to at most 448×448 pixels; chunks are encoded as separate image and audio inputs, with instructions, user turns, and assistant decisions interleaved in streaming order. Qwen2.5-Omni is extended to the same context window with YaRN (Peng et al., 2024).Source: F EXPERIMENTAL CONFIGURATION · p. 15

Configuration limitations

  • The available artifacts lack a complete run manifest for the 7B model and supervised baselines, so unverified identifiers, seeds, hardware time, and coefficients are omitted.Baseline-specific coefficients are not inferred from script defaults.Source: F EXPERIMENTAL CONFIGURATION · p. 15

Compact teacher targets

  • Teacher targets use the k highest-probability tokens under the hint-bearing context, with teacher and student distributions restricted to the shared support and renormalized.For a response of length Lt, retained targets require O(kLt) probability values and token identities rather than O(|V|Lt); this reduces storage and transfer, not the computation needed to obtain probabilities. Targets and support identities stay fixed during each student update, and the updated student is synchronized for subsequent generation and scoring.Source: F EXPERIMENTAL CONFIGURATION · p. 15

Loss implementation

  • Loss aggregation includes only valid response positions with scored targets, while all divergence variants use the same support, normalization, and token mask.Padding, prompt positions, and absent teacher targets are excluded; any numerical floor or clipping is reported in Table 5 because it can alter the objective at extreme probabilities.Source: F EXPERIMENTAL CONFIGURATION · p. 15

G EVALUATION DETAILS … I.2 FROM ON-POLICY DISTILLATION TO RESPONSE DECISIONS

The evaluation reports Live-OPSD’s comparative standing on StreamingBench and OVO-Bench, while the case study shows its responses landing within annotated windows where SFT baselines are silent or premature. The decision-level analysis explains how privileged hints can resolve ambiguity and how on-policy distillation can transfer decision quality, subject to coverage and truncation limits.

G EVALUATION DETAILS

  • LiveProBench’s headline is the arithmetic mean of six task scores, with ES scored as √uv and OR, WR, AA, and SS scored by first-response timing.DC uses final-total exact-count accuracy, not timing at individual completions. An empty output or standalone silence marker denotes silence under the explicit protocol, and comparisons require complete runs over the same examples.Source: G EVALUATION DETAILS · p. 16
  • On StreamingBench, the 30B variant leads overall, RTVU, and OSU, while on OVO-Bench Live-OPSD leads RTVP and BT but trails the strongest released system on FAR.Table 6 reports the StreamingBench system-level comparison with audio enabled; Table 7 reports OVO-Bench with video only. The supplied passages do not give the underlying score values.Source: Table 6 · p. 16, G EVALUATION DETAILS · p. 16, Table 7 · p. 17

H CASE STUDY

  • Live-OPSD responds inside the valid window in every illustrated case, whereas streaming-SFT baselines are silent or premature.The six LiveProBench tasks cover evidence-triggered alerts (ES), onset-anchored responses (OR), broad response windows (WR), ambiguous anomalies (AA), long-prefix silence (SS), and final-total duplicate counting (DC).Source: H CASE STUDY · p. 17, Figure 7 · p. 19

I DECISION-LEVEL ANALYSIS OF LIVE-OPSD

  • Live-OPSD uses privileged context to construct a teaching signal, on-policy distillation to transfer it, and DAS to select where it is applied.The analysis studies how these operations can support better response decisions by relating hint information, teacher–student discrepancy, and disagreement-based selection to decision risk.Source: I DECISION-LEVEL ANALYSIS OF LIVE-OPSD · p. 20

I.1 PRIVILEGED CONTEXT AND DECISION AMBIGUITY

  • Privileged hints can lower optimal decision risk when they split supervisory outcomes that remain ambiguous from visible context alone.The inequality is strict when the hint-conditioned response probability falls on both sides of 1/2 with positive conditional probability; a deterministic hint adds no information, though it may clarify evidence use for a finite model.Source: §I.1 · p. 20

I.2 FROM ON-POLICY DISTILLATION TO RESPONSE DECISIONS

  • On-policy reverse-KL discrepancies along student-generated prefixes bound response-decision disagreement, with a resolving-prefix bound charging only positions before the decision is settled.The prefix distribution is the student’s own, and the guarantee concerns continuations at recorded contexts—not full model-generated interaction histories. Under the explicit silence protocol, the resolving prefix is short relative to a full response.Source: §I.2 · pp. 21–22
  • A teacher’s decision advantage transfers only when residual discrepancy is sufficiently small; exact agreement may be unattainable when hints reveal information unavailable to the student.Connecting the sufficient distribution-level condition to training requires coverage of relevant contexts, prefixes, and vocabulary. Retained-support bounds account for discarded probability mass, while implementation also uses selected fixed samples and global token-mean normalization.Source: §I.2 · pp. 22–23

I.3 WHICH CONTEXTS DECISION-AWARE SELECTION EMPHASIZES

Decision-aware selection enriches the inconsistent context pool, but its value for distillation depends on whether the teacher has an advantage on those contexts. The analysis also characterizes an idealized quota while distinguishing it from the implemented selection procedure.

I.3 WHICH CONTEXTS DECISION-AWARE SELECTION EMPHASIZES

  • Selecting contexts after sampled disagreement raises fresh-continuation disagreement on average, strictly when disagreement probability varies across contexts.This enrichment describes the candidate pool before direction balancing and adding consistent points.Source: §I.3 · p. 23
  • The inconsistent pool has greater mean teacher advantage only when disagreement probability and teacher advantage have positive covariance.If the student and hinted model struggle on the same contexts, disagreement alone need not identify a stronger teaching signal; student improvement also depends on transfer fidelity.Source: §I.3 · pp. 23–24
  • When covariance is positive, an idealized mixture exceeds the baseline mean teacher advantage exactly when its inconsistent share λ exceeds the current disagreement rate ēθ.Setting λ = ēθ reproduces the original context distribution.Source: §I.3 · p. 24
  • The quota analysis is an approximation: run artifacts cannot establish that the implemented inconsistent share exceeds ēθ at every update.Implemented DAS caps inconsistent points at q = max{1, ⌊αK⌋}, fills remaining groups by deterministic priority, and changes context weighting as the policy changes.Source: §I.3 · p. 24
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