Rethinking Cross-Tokenizer On-Policy Distillation: From Alignment Coverage to Supervision Reliability

Bingxi Hou; Guochao Jiang; Guofeng Quan; Weiqing Li; Wenfeng Feng; Guohua Liu; Yuewei Zhang

cs.CLOct 6, 2026

Rethinking Cross-Tokenizer On-Policy Distillation: From Alignment Coverage to Supervision Reliability

Authors: Bingxi Hou, Guochao Jiang, Guofeng Quan, Weiqing Li, Wenfeng Feng, Guohua Liu, Yuewei Zhang

Organizations: Alibaba Cloud Computing

Abstract

On-Policy Distillation (OPD) trains a student on its own generations using teacher feedback. With different tokenizers, comparing teacher and student predictions requires alignment at both sequence and vocabulary levels. In this paper, we examine whether expanding this alignment coverage improves learning. Across three heterogeneous teacher--student pairs on mathematical reasoning and code generation, strict 1:1 groups already cover most student-generated tokens despite substantial vocabulary mismatch. On responses sampled from the students before distillation, the shared vocabulary retains nearly all teacher and student probability mass at strictly aligned positions on average. Restricting reverse KL to a student-selected top-16 subset of the shared vocabulary at each strict position achieves accuracy comparable to full shared-vocabulary OPD, outperforming the evaluated cross-tokenizer baselines. Adding mean squared error supervision on span log-probabilities in mismatch groups gives complete supervision coverage, yet reduces accuracy. At checkpoints from training with only the strict loss, the span gradients show weak or negative directional agreement with the strict gradients and grow in magnitude relative to them. These diagnostics may help explain the accuracy drop from adding span supervision. Our findings motivate a shift from maximizing alignment coverage to prioritizing supervision reliability: compact supervision at strict positions can be more effective than broader coverage that introduces weakly aligned or conflicting training signals.

Figures & tables

Figure 1: Three diagnostics of Cross-Tokenizer OPD for Qwen2.5-7B-Instruct $\rightarrow$ Llama-3.2-3B-Instruct. Left: The logged student-side alignment ratio remains high during Strict full training despite substantially lower static vocabulary overlap. Middle: Adding supervision on mismatch groups lowers mathematics and code performance. Right: At strictly aligned positions in student-generated responses before distillation, the shared vocabulary retains nearly all teacher and student probability mass on average, and a student-selected top-16 subset retains most of it on both sides.

Teacher $\rightarrow$ Student	$J_{\text{vocab}}$	Coverage	Training steps
Teacher $\rightarrow$ Student	$J_{\text{vocab}}$	Coverage	1–100	1–20	41–60	81–100
Qwen $\rightarrow$ Llama	64.32	$C_{1{:}1}^{\theta}$	93.56	94.63	93.20	93.43
Qwen $\rightarrow$ Llama	64.32	$C_{1{:}1}^{\mathrm{T}}$	85.91	88.65	84.90	85.36
Granite $\rightarrow$ Phi	39.49	$C_{1{:}1}^{\theta}$	96.98	96.65	96.95	97.12
Granite $\rightarrow$ Phi	39.49	$C_{1{:}1}^{\mathrm{T}}$	97.26	95.83	97.50	97.96
Granite $\rightarrow$ Qwen	64.87	$C_{1{:}1}^{\theta}$	85.57	85.23	85.06	85.88

Table 1: Static vocabulary Jaccard overlap

J_{\text{vocab}}

and strict token coverage on student trajectories from Strict full training.

C_{1{:}1}^{\theta}

and

C_{1{:}1}^{\mathrm{T}}

denote student and teacher strict token coverage over the indicated training steps.

Figure 2: Full-average accuracy (%) across mismatch weights. Dashed lines mark strict supervision (

\lambda=0

), and annotations give the decrease at

\lambda=1.5

in percentage points.

Figure 3: Probability mass retained by student-selected top-

k

subsets and the full shared vocabulary at strict positions before distillation.

Method	Qwen $\rightarrow$ Llama			Granite $\rightarrow$ Phi			Granite $\rightarrow$ Qwen
Method	Math	Code	Full	Math	Code	Full	Math	Code	Full
Base	18.32	35.60	26.96	33.06	40.04	36.55	24.61	34.51	29.56
ULD	20.51	37.74	29.12	35.24	42.01	38.63	33.36	20.87	27.12
Extended ULD	23.01	39.26	31.13	35.28	41.42	38.35	33.14	32.00	32.57
GOLD	21.21	33.10	27.16	36.22	47.29	41.75	38.26	54.84	46.55
SimCT	25.31	37.86	31.59	36.67	46.70	41.68	38.64	53.56	46.10

Table 2: Cross-tokenizer distillation accuracy (%). Base denotes the student before distillation. Bold marks the best distilled score per column.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Value
Training and optimization
Training iterations	100
Batch size	512
Dynamic batching	Disabled
Optimizer	AdamW ( Loshchilov & Hutter, 2019 )
Learning rate	$1\times 10^{-6}$

Appendix

Table 3: Training settings.

Teacher $\rightarrow$ Student	Vocabulary size			Overlap (%)
Teacher $\rightarrow$ Student	$\|\mathcal{V}_{\mathrm{T}}\|$	$\|\mathcal{V}_{\theta}\|$	$\|\mathcal{V}_{\cap}\|$	$\frac{\|\mathcal{V}_{\cap}\|}{\|\mathcal{V}_{\theta}\|}$	$\frac{\|\mathcal{V}_{\cap}\|}{\|\mathcal{V}_{\mathrm{T}}\|}$	$J_{\text{vocab}}$
Qwen $\rightarrow$ Llama	151,665	128,256	109,567	85.43	72.24	64.32
Granite $\rightarrow$ Phi	100,352	200,029	85,034	42.51	84.74	39.49
Granite $\rightarrow$ Qwen	100,352	151,665	99,163	65.38	98.82	64.87

Appendix

Table 4: Static vocabulary overlap across the three teacher–student pairs. Vocabulary counts follow the shared-vocabulary convention in Section 2 . Overlap ratios are reported as percentages.

Subset	Qwen $\rightarrow$ Llama		Granite $\rightarrow$ Phi		Granite $\rightarrow$ Qwen
Subset	Student	Teacher	Student	Teacher	Student	Teacher
$k=4$	91.74	89.81	90.08	88.12	96.58	94.53
$k=8$	93.60	92.43	92.90	91.43	97.81	96.48
$k=16$	94.55	93.92	94.68	93.54	98.44	97.67
$k=32$	95.06	94.77	95.89	95.03	98.82	98.37
$k=64$	95.35	95.29	96.75	96.14	99.07	98.82

Appendix

Table 5: Mean retained probability mass (%) at strict positions before distillation. “Shared” denotes the full shared vocabulary, and bold values mark

k=16

Step	Qwen $\rightarrow$ Llama			Granite $\rightarrow$ Phi			Granite $\rightarrow$ Qwen
Step	$c_{\mathrm{mis}}$	$c_{\mathrm{ctrl}}$	$\rho$	$c_{\mathrm{mis}}$	$c_{\mathrm{ctrl}}$	$\rho$	$c_{\mathrm{mis}}$	$c_{\mathrm{ctrl}}$	$\rho$
0	$0.030$	$0.956$	$0.294$	$0.066$	$0.986$	$0.008$	${-}0.360$	$0.977$	$0.015$
20	$0.058$	$0.671$	$1.231$	$0.008$	$0.955$	$0.021$	${-}0.129$	$0.581$	$0.113$
60	${-}0.011$	$0.296$	$1.877$	$0.044$	$0.733$	$0.100$	$0.002$	$0.049$	$0.222$
100	${-}0.021$	$0.208$	$1.942$	${-}0.004$	$0.246$	$0.233$	${-}0.001$	$0.076$	$0.269$

Appendix

Table 6: Gradient diagnostics at checkpoints from training with only the strict loss.

c_{\text{mis}}

and

c_{\text{ctrl}}

denote the mismatch–strict and split-half strict gradient cosines, respectively.

\rho

is the unweighted span-to-strict norm ratio. Values are rounded to three decimals; figure growth factors use the unrounded medians.

Benchmark	Qwen $\rightarrow$ Llama		Granite $\rightarrow$ Phi		Granite $\rightarrow$ Qwen
Benchmark	Base	Teacher	Base	Teacher	Base	Teacher
MATH500	34.32	74.50	62.94	80.81	48.60	80.81
GSM8K	63.44	89.93	86.07	91.51	67.65	91.51
AIME-2024	2.29	11.88	6.35	22.71	5.10	22.71
AIME-2025	0.31	7.50	3.85	18.65	1.77	18.65
AIME-2026	0.52	7.50	4.69	12.81	2.81	12.81

Appendix

Table 7: Benchmark-level scores of the undistilled students and frozen teachers for the three main model pairs.

Benchmark	ULD	Extended ULD	GOLD	SimCT	Strict
Benchmark	ULD	Extended ULD	GOLD	SimCT	full	top-16	top-128
MATH500	40.73	47.33	41.70	50.55	52.74	52.92	52.08
GSM8K	62.11	63.96	70.00	78.20	80.21	80.26	80.08
AIME-2024	5.00	5.73	3.33	3.65	4.69	5.00	5.10
AIME-2025	0.52	1.15	0.62	1.56	1.67	1.88	1.98
AIME-2026	0.94	0.73	0.00	0.73	0.94	1.25	0.52

Appendix

Table 8: Benchmark-level comparison for Qwen2.5-7B-Instruct

\rightarrow

Llama-3.2-3B-Instruct.

Benchmark	ULD	Extended ULD	GOLD	SimCT	Strict
Benchmark	ULD	Extended ULD	GOLD	SimCT	full	top-16	top-128
MATH500	68.20	68.11	69.06	68.86	70.55	70.10	70.26
GSM8K	86.00	86.25	87.06	86.95	87.53	87.56	87.43
AIME-2024	8.85	8.33	9.48	10.73	11.25	10.83	11.46
AIME-2025	3.44	5.21	6.56	5.83	6.46	7.19	6.98
AIME-2026	5.52	6.15	6.25	6.88	7.81	7.29	6.77

Appendix

Table 9: Benchmark-level comparison for Granite-4.1-8B

\rightarrow

Phi-4-mini-instruct.

Benchmark	ULD	Extended ULD	GOLD	SimCT	Strict
Benchmark	ULD	Extended ULD	GOLD	SimCT	full	top-16	top-128
MATH500	65.84	66.16	73.31	73.73	74.91	75.25	75.31
GSM8K	85.63	83.97	88.03	87.75	88.64	88.81	88.87
AIME-2024	7.60	8.23	10.94	11.67	14.37	14.17	14.17
AIME-2025	3.85	4.38	8.33	9.06	9.27	8.75	9.69
AIME-2026	6.98	5.31	7.29	5.73	6.25	6.46	6.46

Appendix

Table 10: Benchmark-level comparison for Granite-4.1-8B

\rightarrow

Qwen2.5-7B-Base.

Benchmark	Span-MSE weight $\lambda$
Benchmark	0	0.25	0.5	0.75	1	1.25	1.5
MATH500	52.74	52.38	51.21	51.19	50.50	50.18	49.95
GSM8K	80.21	79.96	79.35	79.65	79.11	78.94	78.75
AIME-2024	4.69	5.10	5.21	5.21	4.58	4.06	5.62
AIME-2025	1.67	1.77	1.56	1.56	1.35	1.25	1.25
AIME-2026	0.94	0.42	0.62	0.31	0.42	0.52	0.21

Appendix

Table 11: Benchmark-level span-MSE weight sweep for Qwen2.5-7B-Instruct

\rightarrow

Llama-3.2-3B-Instruct.

Benchmark	Span-MSE weight $\lambda$
Benchmark	0	0.25	0.5	0.75	1	1.25	1.5
MATH500	70.55	71.04	70.01	70.44	69.59	70.47	70.08
GSM8K	87.53	87.64	87.31	87.57	87.09	87.31	87.46
AIME-2024	11.25	10.31	10.42	10.31	9.69	10.31	10.00
AIME-2025	6.46	6.67	6.46	6.77	7.08	6.25	6.46
AIME-2026	7.81	5.94	6.77	7.19	6.88	6.77	6.35

Appendix

Table 12: Benchmark-level span-MSE weight sweep for Granite-4.1-8B

\rightarrow

Phi-4-mini-instruct.

Benchmark	Span-MSE weight $\lambda$
Benchmark	0	0.25	0.5	0.75	1	1.25	1.5
MATH500	74.91	75.45	74.97	74.84	74.54	74.72	74.81
GSM8K	88.64	88.79	88.75	88.77	88.83	88.95	88.77
AIME-2024	14.37	15.42	13.02	14.27	12.71	12.19	12.92
AIME-2025	9.27	8.02	9.27	9.69	8.23	8.02	8.02
AIME-2026	6.25	6.15	5.94	6.15	5.83	5.83	5.52

Appendix

Table 13: Benchmark-level span-MSE weight sweep for Granite-4.1-8B

\rightarrow

Qwen2.5-7B-Base.

Benchmark	Base	Teacher
MATH500	80.81	95.88
GSM8K	91.51	94.24
AIME-2024	22.71	60.94
AIME-2025	18.65	51.98
AIME-2026	12.81	65.52
AMC23	64.53	90.00

Appendix

Table 14: Benchmark-level scores of the undistilled student and frozen teacher for Qwen3-235B-A22B-Instruct-2507

\rightarrow

Granite-4.1-8B.

Benchmark	ULD	Extended ULD	GOLD	SimCT	Strict top-16
MATH500	81.31	87.29	85.91	86.08	89.75
GSM8K	91.59	93.06	93.12	93.15	93.69
AIME-2024	23.23	37.19	35.52	37.40	43.02
AIME-2025	21.15	26.98	27.19	29.17	35.10
AIME-2026	13.33	30.10	23.02	27.29	38.44
AMC23	67.34	72.66	69.30	74.22	76.80

Appendix

Table 15: Benchmark-level distillation results for Qwen3-235B-A22B-Instruct-2507

\rightarrow

Granite-4.1-8B. Bold marks the best Math, Code, and Full averages.

Method	Seen		Unseen		Overall
Method	SR $\uparrow$	Turns $\downarrow$	SR $\uparrow$	Turns $\downarrow$	SR $\uparrow$	Turns $\downarrow$
Base	12.50	46.60	8.85	47.28	10.68	46.94
Teacher	29.69	41.07	29.43	41.22	29.56	41.15
ULD	1.56	49.61	1.30	49.74	1.43	49.68
Extended ULD	25.52	41.95	23.44	42.61	24.48	42.28
GOLD	3.65	49.30	1.56	49.58	2.61	49.44

Appendix

Table 16: ALFWorld results for Qwen3-4B-Instruct-2507

\rightarrow

Llama-3.2-3B-Instruct. Bold marks the highest SR and lowest Turns among distilled models.

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On-policy distillation (OPD) is a standard tool for transferring teacher behavior to a smaller student, but it implicitly assumes that teacher and student predictions are comparable token by token, an assumption that fails whenever the two models tokenize the same text differently. Under heterogeneous tokenizers, exact shared-token matching silently discards a large fraction of the teacher signal at precisely the positions where vocabularies disagree. We propose \textbf{\underline{Sim}ple \underline{C}ross-\underline{T}okenizer OPD (SimCT)}, which restores this signal by enlarging the supervision space: alongside shared tokens, SimCT compares teacher and student over short multi-token continuations that both tokenizers can realize, leaving the OPD loss form itself unchanged. We show that these units are the finest jointly tokenizable supervision interface, and that coarser alternatives remove teacher-student distinctions that are useful for on-policy learning. Across three heterogeneous teacher-student pairs on mathematical reasoning and code-generation benchmarks, SimCT shows consistent gains over shared-vocabulary OPD and representative cross-tokenizer baselines, with ablations confirming that the improvements come from recovering supervision discarded by exact shared-token matching. Code is available at https://github.com/sunjie279/SimCT-.

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