A helps B while B hurts A: directed transfer in instruction-tuning mixture

Nima H. Siboni; Vahid Rostami

cs.AISep 30, 2026

A helps B while B hurts A: directed transfer in instruction-tuning mixture

Authors: Nima H. Siboni, Vahid Rostami

Organizations: Juna.ai, Kastanienallee 32, 10435 Berlin, Germany · Computational Systems Neuroscience, Institute of Zoology, University of Cologne, Germany

Abstract

Adapting a language model to a specialized corpus means choosing which instruction-tuning tasks to train on under a fixed budget, and testing one choice costs a fine-tuning run. Common heuristics add more source tasks or pick sources similar to the target. The first assumes transfer is never negative; the second, that it is symmetric. We show that both assumptions fail: task $A$ can help task $B$ while $B$ hurts $A$ , so helpfulness is a signed property of ordered source--target pairs. We introduce the transfer map, a signed estimate of how much each source helps or hurts each held-out target. We fit the map in hundreds of fine-tuning runs on Qwen3 and Mistral models from 0.6B to 32B parameters, with all sources drawn from one corpus and no training examples from the target. The map predicts a held-out target's accuracy on unseen mixtures: recorded before those runs, its predictions have less than half the error of a mixture-agnostic baseline. The map is specific to its target and corpus but transfers across model scale: a mixture selected in advance at one size beats training on all source tasks at every other size we tested. Transfer is thus a property of the data. The map selects the tasks that help and drops the one that interferes: accuracy on the reasoning targets (causal explanation, multi-hop questions and methodological critique) rises by up to 14 percentage points over training on all source tasks.

Figures & tables

Figure 1: Probe, map, predict. (a) Balanced mixtures over one corpus, each withholding a target, give a signed, directed map whose predictions for unseen mixtures are recorded before the runs that test them. (b) Source identity predicts an unseen mixture and mixture size predicts little (within-target

R^{2}

, Table 6 ). (c) The two directions of a task pair differ. (d) Recorded predictions against realized effects in the eight cells of Section 5 : filled markers are three-seed means (

\pm 1

standard error), open markers single seeds.

Figure 2: The transfer map is signed, directed, and stable across model size. Effect of each source (rows) on each withheld reasoning target (columns), in pp relative to an average source. Left five panels: Qwen3 at five sizes; $r$ is the mean per-target correlation with the $32$ B map (Section 7 ). Mistral-24B on the same corpus keeps the map; Qwen3-32B on PubMed (faded), with about a tenth of the evaluation items, agrees less, but err remains mhop ’s most negative source. For these two panels, $r$ pools the $18$ entries from sources other than match , which scores near ceiling (Appendix F ).

Condition	Target	Interferer	Uniform	Single-best	Skill-It	TaskShop	Embed-sim
Qwen3-32B	why	mc-mc	$+1.21$	$-2.37$	$-1.45$	$+0.00$	$-0.53$
Qwen3-32B	mhop	err	$+13.19$	$-1.41^{\dagger}$	$+2.43^{\dagger}$	$+2.73$	$+3.11$
Qwen3-32B	err	mhop	$+8.64$	$+2.11^{\dagger}$	$-0.20$	$+0.64$	$+8.10$
Mistral-24B	why	err	$+2.18$	$-2.13$	$-1.31$	$-0.34$	$+1.36$
Mistral-24B	mhop	err	$+17.23$	$+0.44^{\dagger}$	$+7.59$	$-0.15$	$+9.68$
Mistral-24B	err	mhop	$+7.76$	$+1.42$	$+7.91$	$+0.10$	$+7.47$

Table 1: Map-selected mixture minus competitor on the withheld target, at each competitor’s mixture size

d

and at one training seed; positive favours the map. “Interferer” is the target’s most negative measured source.

\dagger

marks a run whose generations tripped a degeneration check (Appendix F ).

\ddagger

marks the vacuous cell: every uncentered coefficient there is positive, so the rule keeps all seven sources and we print no interferer; its two runs train the same mixture at the same seed, so their

+1.69\,\mathrm{pp}

gap is one replicate difference. Full sweep in Appendix D .

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Predictor	MAE (pp)	Pearson $r$	Origin slope
Recorded map prediction	$\mathbf{2.31}$	$0.865$	$1.054$
Zero effect	$6.20$	—	—
Best constant, fitted post hoc	$4.80$	—	$1.037$
Count, linear	$9.31$	$0.731$	$-0.371$
Count, quadratic	$9.20$	$0.362$	$-0.730$

Appendix

Table 2: Calibration on the same eight cells. The constant oracle is fitted on the values it is scored against, so it lower-bounds any constant predictor.

Scale: agreement with 32B map		Transport: between conditions
Qwen3-0.6B	$0.780$	Qwen $\leftrightarrow$ Mistral	$0.880$
Qwen3-1.7B	$0.876$	Qwen $\leftrightarrow$ PubMed	$0.545$
Qwen3-4B	$0.918$	Mistral $\leftrightarrow$ PubMed	$0.279$
Qwen3-8B	$0.757$
Out-of-fold gain over the widest mixture of the left-out design (pp)
Qwen3-32B, full probe	$+5.03$	Qwen3-32B, $24$ runs	$+4.83$

Appendix

Table 3: Where the map holds. Scale agreement is the mean per-target centered correlation with the Qwen3-32B map; transport agreement is the centered correlation between conditions over the

18

non- match source-to-reasoning entries. An out-of-fold gain refits the map without one design’s mixtures, lets it pick among that design’s trained mixtures, and compares the pick with that design’s widest mixture; the

24

-run rows refit on

24

runs drawn at random from the same fitting runs, averaged over

60

draws. The last block trains the recorded

32

B selection against the uniform mixture at each size, averaged over the three targets (Table 4 gives every cell).

Size	Target	Recorded	Realized	95% CI	$d$	Realized	95% CI
		Transported $32$ B selection			Refit at this size
0.6B	why	$+2.64$	$+1.39$	$[-2.41,+5.19]$	$4$	$+7.15$	$[+5.20,+9.11]$
0.6B	mhop	$+9.92$	$+5.04$	$[+4.38,+5.71]$	$3$	$+6.60$	$[+5.41,+7.79]$
0.6B	err	$+3.53$	$+6.60$	$[+4.77,+8.43]$	$3$	$+6.88$	$[+4.97,+8.78]$
1.7B	why	$+2.64$	$+1.49$	$[-0.07,+3.04]$	$4$	$+6.10$	$[+5.50,+6.71]$
1.7B	mhop	$+9.92$	$+7.69$	$[+5.02,+10.36]$	$4$	$+8.42$	$[+7.19,+9.65]$

Appendix

Table 4: The second test of recorded predictions, cell by cell. Transported : the mixture the Qwen3-32B map selected for each target, recorded before any other size ran, minus the uniform mixture; it keeps the Qwen3-32B sources of Table 5 ( why : clz , def , err , mhop ; mhop : clz , def , match , why ; err : def , match , sc-mc , why ), and Recorded is the

32

B map’s prediction. Refit : the mixture that the map refitted at that size selects, with

d

sources, minus the uniform mixture. Effects are paired over three data-order seeds, with

t

intervals over the seed-paired differences. No run in these cells trips the degeneration check on the withheld target except in the refit 1.7B/ mhop cell.

Condition	Target	Sources kept	$d$	Recorded	Realized	95% CI
Qwen3-32B	why	clz , def , err , mhop	$4$	$+2.64$	$-0.90$	$[-4.73,+2.92]$
Qwen3-32B	mhop	clz , def , match , why	$4$	$+9.92$	$+11.89$	$[+6.99,+16.79]$
Qwen3-32B	err	def , match , sc-mc , why	$4$	$+3.53$	$+7.96$	$[+6.76,+9.16]$
Mistral-24B	why	clz , def , mc-mc , mhop , sc-mc	$5$	$+3.79$	$+2.49$	$[+1.16,+3.81]$
Mistral-24B	mhop	clz , def , mc-mc	$3$	$+14.86$	$+13.76$	$[+3.78,+23.73]$
Mistral-24B	err	all but mhop	$6$	$+4.95$	$+8.56$	$[+6.65,+10.48]$

Appendix

Table 5: Every predicted cell, recorded prediction against realized effect: selected mixture minus uniform default, paired over three data-order seeds, with

t

intervals over the seed-paired differences.

d

is the number of sources the rule keeps, against seven in the uniform default, so a smaller

d

also means more examples per source. The PubMed err cell is excluded from the primary

n=8

: every uncentered coefficient there is positive, the rule drops nothing, and the predicted effect is exactly zero. The probe already trains the selected mixture of Mistral/ mhop , Mistral/ err and PubMed/ mhop ; refitting without those runs moves their predictions by at most

0.22\,\mathrm{pp}

Figure 3: The effects on an absolute scale. Untuned base, the uniform mixture and the map-selected mixture on each withheld target, for Qwen3-32B and Mistral-24B, without the PubMed control. Where uniform already captures most of the available gain ( why ) the map adds little; where uniform barely improves on the untuned model ( mhop , err ) it adds the most.

	Qwen3-32B		Mistral-24B		PubMed
Model of the mixture	$R^{2}$	MAE	$R^{2}$	MAE	$R^{2}$	MAE
Size, linear	$0.114$	$4.66$	$0.003$	$3.92$	$0.153$	$2.52$
Size, quadratic	$0.085$	$4.75$	$-0.027$	$3.96$	$0.121$	$2.57$
Size, categorical	$-0.019$	$5.04$	$-0.130$	$4.19$	$0.037$	$2.67$
Source presence	$0.768$	$2.44$	$0.746$	$1.82$	$\mathbf{0.557}$	$1.95$
Presence $+$ share	$0.744$	$2.29$	$0.702$	$1.80$	$0.523$	$1.98$

Appendix

Table 6: Leave-one-mixture-out prediction of the withheld target, between-target variance removed (Section 4.2 ). MAE is against a per-target constant scoring

5.16/4.05/2.81\,\mathrm{pp}

. Mixture size gets every advantage: linear, quadratic, and a free indicator per size. Share adds each source’s share of the training examples,

z_{S}/d

. Pairwise adds all

21

products

z_{S}z_{S^{\prime}}

29

parameters against

52

training mixtures per fold.

Condition	Target	Accuracy at $d=1$ / … / $6$	Slope in $d$	$\overline{\beta}$	Diff.
Qwen3-32B	why	$21.3$ / $24.0$ / $28.5$ / $30.5$ / $32.5$ / $36.4$	$+2.91$	$+2.40$	$+0.51$
Qwen3-32B	mhop	$24.7$ / $24.9$ / $26.2$ / $28.2$ / $28.2$ / $32.1$	$+1.15$	$-0.17$	$+1.32$
Qwen3-32B	err	$8.8$ / $9.9$ / $10.2$ / $11.9$ / $12.4$ / $14.6$	$+0.96$	$+0.40$	$+0.56$
Qwen3-32B	def	$32.0$ / $31.4$ / $30.6$ / $29.5$ / $28.8$ / $29.0$	$-0.80$	$-0.68$	$-0.13$
Mistral-24B	why	$28.2$ / $30.1$ / $33.1$ / $33.3$ / $34.4$ / $35.1$	$+1.50$	$+1.29$	$+0.21$
Mistral-24B	mhop	$31.2$ / $30.9$ / $31.1$ / $31.1$ / $30.9$ / $33.7$	$+0.06$	$-1.26$	$+1.32$

Appendix

Table 7: The dose response is the mean source effect. The slope in

d

is OLS over the unique mixtures that withhold the target;

\overline{\beta}

averages the presence-model coefficients from the same fit. Across all

12

cells they agree at

r=0.898

, mean absolute difference

0.46\,\mathrm{pp}

, maximum

1.32\,\mathrm{pp}

. def is included to show the slope is target-specific and can be negative.

Figure 4: Lemma 1 as a measurement. (a) Withheld-target accuracy against mixture size. It rises for the reasoning targets except Mistral/ mhop , which is flat, and falls for def in both neuroscience conditions. (b) Each cell’s OLS slope in

d

against the mean source coefficient of the presence fit for the same cell. The points lie near the identity line: the quantity one would report as a breadth bonus is the average source effect.

				Opposite signs
Condition	$r(B,B^{\mathsf{T}})$	Skew	Directional	Estimates	Diff. CI	Both CIs
Qwen3-32B	$+0.304$ $[+0.177,+0.409]$	$0.590$	$14/28$	$10/28$	$7/28$	$3/28$
Mistral-24B	$+0.290$ $[+0.167,+0.381]$	$0.596$	$13/28$	$15/28$	$10/28$	$4/28$
PubMed	$+0.262$ $[+0.052,+0.393]$	$0.607$	$9/28$	$10/28$	$3/28$	$0/28$

Appendix

Table 8: Asymmetry of the transfer map.

r(B,B^{\mathsf{T}})

1

for symmetric transfer and is computed over the

56

off-diagonal entries, that is,

28

pairs in both orientations. The skew fraction,

\lVert(B-B^{\mathsf{T}})/2\rVert_{F}/\lVert B\rVert_{F}

over the off-diagonal entries, equals

\sqrt{(1-r)/2}

here, so it restates

r

; independent noise sits near

0.707

. Directional counts pairs whose difference interval excludes zero. The last three columns count pairs whose two directions have opposite signs: as point estimates, with the difference interval also excluding zero, and with each direction’s own interval excluding zero (the count Section 4.1 reports).

Pair $(A,B)$	First	95% CI	Second	95% CI	Difference	95% CI
why , mhop	$+2.55$	$[+1.20,+4.02]$	$+10.71$	$[+8.65,+12.52]$	$-8.16$	$[-10.51,-5.71]$
mhop , def ∗	$-1.24$	$[-1.68,-0.75]$	$+5.27$	$[+3.55,+6.84]$	$-6.51$	$[-8.17,-4.74]$
err , mhop	$-9.72$	$[-11.29,-7.93]$	$-3.85$	$[-4.81,-2.89]$	$-5.88$	$[-7.77,-3.82]$
err , why ∗	$-2.37$	$[-4.18,-0.61]$	$+3.11$	$[+2.35,+3.90]$	$-5.48$	$[-7.59,-3.58]$
why , def ∗	$-2.25$	$[-2.69,-1.79]$	$+2.49$	$[+0.32,+4.48]$	$-4.73$	$[-6.77,-2.61]$
why , mc-mc	$-0.29$	$[-0.54,-0.06]$	$-3.72$	$[-5.56,-1.86]$	$+3.43$	$[+1.50,+5.29]$

Appendix

Table 9: Qwen3-32B: every task pair

(A,B)

, both directions. First is

\beta_{A\to B}

and second is

\beta_{B\to A}

, as centered substitution effects in pp; the difference is first minus second. All intervals are

95\%

percentile bootstrap intervals over distinct mixtures. ∗ marks the pairs whose two directions have opposite signs with each direction’s interval excluding zero.

Figure 5: The similarity selector loses where selection matters. (a) Map-selected minus competitor accuracy on the withheld target, each competitor at its own mixture size

d

. (b) Accuracy on the target against the non-target macro (the mean over the six scored tasks other than the target and match ): the map-selected mixture sits between the uniform mixture and the single best source.

Cond.	Target	Competitor	$d$	Interferer in mix	target	other-6
Qwen	why	uniform	$7$	yes ( mc-mc )	$+1.21$	$-0.75$
Qwen	why	single_best	$1$	no	$-2.37$	$+1.25$
Qwen	why	skillit	$4$	no	$-1.45$	$+1.41$
Qwen	why	taskshop_k3	$3$	no	$-1.36$	$+0.04$
Qwen	why	taskshop	$4$	no	$+0.00$	$+0.00$
Qwen	why	taskshop_k5	$5$	no	$-2.13$	$-0.53$

Appendix

Table 10: Map minus competitor, on the withheld target and on the non-target macro.

Pair	Size	Sources	Target	Predicted	Realized [95% CI]	Last vs shuffled [95% CI]	Status
P1 at three model sizes
P1	4B	def + err	mhop	$+8.32$	$\mathbf{+9.55}$ $[+6.89,+12.21]$	$+7.75$ $[+4.48,+11.02]$	confirmed
P1r17	1.7B	def + err	mhop	$+7.71$	$\mathbf{+8.21}$ $[+7.11,+9.30]$	$+4.72$ $[+2.91,+6.53]$	confirmed
P1r8	8B	def + err	mhop	$+7.24$	$\mathbf{+9.62}$ $[+2.17,+17.07]$	$+7.04$ $[+3.36,+10.72]$	confirmed
Other recorded pairs
P2	4B	mhop + sc-mc	why	$+4.57$	$\mathbf{-0.66}$ $[-1.74,+0.42]$	$+0.97$ $[-1.72,+3.66]$	covers $0$

Appendix

Table 11: Order effect on the target for every pair, in percentage points. Realized is the seed-paired accuracy of the run that trains the better source last minus that of the run that trains it first. Predicted is half the transfer differential, the difference between the two sources’ map effects on the target; for the placebos it was computed after the predictions were recorded. Confirmed means the interval excludes zero in the predicted direction, and reversed that it excludes zero against it. Last vs shuffled is the run that trains the better source last minus the run that trains the same examples shuffled together, over the same three seeds. The verdict in the text counts the seven rows of the first two blocks.

Task	Capability	Items	Ref. words	Scoring
def	definition with ontology fields	$2{,}166$	$32.2$	Eq. 1
clz	fill-in-the-blank span	$1{,}265$	$1.4$	normalized exact match
sc-mc	one correct option	$2{,}148$	$7.8$	option match
mc-mc	multiple correct options	$2{,}032$	$25.2$	option-set match
match	term–definition pairing	$852$	$7.9$	pair-set match
mhop	two-evidence reasoning	$2{,}055$	$34.9$	Eq. 1

Appendix

Table 12: Neuroscience evaluation inventory (

14{,}618

items). The PubMed condition uses the same task set over

1{,}464

items.

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