From Transfer Probes to Expert Grouping: Evidence from LoRA Post-Training

Xueyang Wu

cs.LGOct 10, 2026

From Transfer Probes to Expert Grouping: Evidence from LoRA Post-Training

Authors: Xueyang Wu

Abstract

A platform that post-trains one base model for many business lines often has more lines than experts it can maintain, so lines must share experts, yet lines seldom come with a taxonomy saying which should share. We ask whether transfer probes (train on one source, measure paired changes on all sources) can discover a grouping when the standard one is unknown. To test probes against a reference, we use seven public sources that do have a label tree (five mathematics subfields and two kinds of programming, standing in for business lines) and treat the tree's grouping as a label reference that the evaluator holds and the method does not. With four LoRA experts under fixed per-source exposure and per-expert budgets, we compare a purely probe-derived grouping and an uninformed uniform default (whose tied routing serves every line from one expert) against this reference. Trained once for one interval from a shared warm-up state and routed by a rule fixed by each allocation, neither reached the prespecified practical gain of 2 percentage points, and both had lower overall utility than the reference ( $-2.43$ and $-2.54$ pp; 95% intervals below zero). In a post hoc comparison, the probe-derived grouping was indistinguishable from the uniform default ( $+0.11$ pp, $[-1.25,+1.54]$ ). In fixed-budget LoRA post-training, a grouping built from initial-state single-source probes thus did not deliver the advantage predicted from the probes once carried to a later training state, a finite budget, and specified routing.

Figures & tables

Platform aspect	Simulated	Simplified	Not covered
Lines and labels	Every request carries its line label; seven sources act as lines	Lines are public mathematics subfields and programming types with automatic verifiers	Enterprise data; noisy or changing labels; lines without automatic scoring
Expert budget	Fewer experts than lines ( $M=4<K=7$ ); LoRA experts on one shared base	Equal expert budgets and equal line exposure in every interval (Eq. 1 )	Choosing $M$ ; unequal data volumes, budgets, or hosting costs
Knowledge of the grouping	The default and probe-derived candidates use no labels; the tree’s grouping is held by the evaluator as the label reference	A tree exists, and at $M=4$ it has a single four-group cut	Platforms with no tree at all, which motivate the study but are not tested
Traffic	Per-line traffic weights in the utility (Eq. 3 )	Equal weights; other static mixes examined after the fact through linearity (Table 5 )	Drifting traffic; new or retired lines
Training	One allocation interval from a shared warm-up state W	One starting state; one training run per candidate	Repeated reallocation over many intervals; training-seed variation; later states and longer budgets
Serving	Each line served by a single expert chosen by a fixed rule	Route read off the block matrix (Eq. 2 )	Competence-calibrated routing; latency and throughput of multi-adapter serving

Table 1: The testbed against the motivating multi-line platform.

Candidate	Blocks $n$	Route $h_{\rm blk}(n)$	Role and information used
C0	$\left(\begin{smallmatrix}0&0&7&7&0&0&0\\ 7&7&0&0&0&0&0\\ 0&0&0&0&0&7&7\\ 1&1&1&1&8&1&1\end{smallmatrix}\right)$	$(1,1,0,0,3,2,2)$	Label reference: the tree’s only four-group cut, balanced onto the margins. Uses the tree; not available to a method in the label-unknown setting.
C1	$\left(\begin{smallmatrix}2&2&2&2&2&2&2\\ 2&2&2&2&2&2&2\\ 2&2&2&2&2&2&2\\ 2&2&2&2&2&2&2\end{smallmatrix}\right)$	$(0,0,0,0,0,0,0)$	Uninformed default: uses no information. Every source is a tie, so expert 0 serves all sources.
C2	$\left(\begin{smallmatrix}0&0&0&6&8&0&0\\ 0&8&2&2&0&0&2\\ 0&0&0&0&0&8&6\\ 8&0&6&0&0&0&0\end{smallmatrix}\right)$	$(3,1,3,0,0,2,2)$	Probe-derived: transportation-LP vertex for the additive proxy built from the s17 probe table. Uses the probes and the margins, not the tree.

Table 2: Candidates in the main comparison. Block matrices list experts e0–e3 as rows and sources (Integral, Differential, Abstract, Linear, Statistics, algorithmic, generic) as columns; every row sums to 14 and every column to 8. Routes are block-matrix routes (Eq. 2 ) in the same source order.

Link	State	Data	What it answers, and what it does not
1. Probes	$S_{0}$ : base model with a fresh adapter ( $B=0$ )	Training split, one source, 16 blocks; audit split, 80 problems per source (OpenCodeInstruct for both code sources); shuffles s17 (7/7 rows) and s23 (6/7 rows), sharing problems and initial predictions	Whether training on source $k$ moves accuracy on source $j$ at $S_{0}$ , as paired flips. Not: effects at W, under mixed-source training, or at other doses.
2. Candidate construction (development)	No training; uses the $S_{0}$ probe table	C0: label tree and margins. C1: margins only. C2: s17 table, margins, and the additive proxy with competence routing. No test data and no data from W	Which allocations to train. Not: how they perform. C3, an edit of C0, is described in Appendix D .
3. Training at W	W: shared warm-up, one uniform interval (two blocks per expert per source)	Training split; one interval of 56 blocks per candidate, with identical tokens per source across candidates; one run per candidate	What each allocation produces from W in one interval. Not: training-seed variation, other starting states, or longer budgets.
4. Fixed-routing test	W plus one candidate interval	Test split, first 400 problems per source (algorithmic: 376 MBPP+ and 24 OpenCodeInstruct problems), two samples each (seeds 2001 and 2002); route by Eq. 2	$U_{\rm all}$ , $U_{\rm LS}$ , $U_{\rm other5}$ , and per-source accuracy of allocation and route together, with intervals for test sampling. Not: performance under competence-calibrated routing; for algorithmic programming, performance on the benchmark that was probed.

Table 3: State and evidence along the chain from probes to scores.

	When specified	$U_{\rm all}$	$U_{\rm LS}$	$U_{\rm other5}$
C0 (label reference)	—	0.5036	0.5019	0.5042
C1 (uninformed default)	—	0.4782	0.4888	0.4740
C2 (probe-derived)	—	0.4793	0.4906	0.4747
		$\Delta U_{\rm all}$	$\Delta U_{\rm LS}$	$\Delta U_{\rm other5}$
C1 $-$ C0	before the run	$-2.54$ $[-4.04,-1.12]$	$-1.31$ $[-4.19,+1.50]$	$-3.02$ $[-4.70,-1.42]$
C2 $-$ C0	before the run	$-2.43$ $[-3.84,-1.14]$	$-1.13$ $[-3.88,+1.38]$	$-2.95$ $[-4.50,-1.40]$

Table 4: Candidate comparison at W. Top: routed utilities (mean accuracy; 400 test problems per source, two samples each). Bottom: paired differences in percentage points with 95% joint paired bootstrap intervals.

U_{\rm LS}

averages Linear Algebra and Statistics;

U_{\rm other5}

averages the other five sources.

	C1 $-$ C0		C2 $-$ C0
Source	$\Delta_{j}$	Simultaneous 95%	$\Delta_{j}$	Simultaneous 95%
Integral Calculus	$-4.500$	$[-10.42,+1.42]$	$-3.250$	$[-8.87,+2.37]$
Differential Calculus	$-4.250$	$[-10.02,+1.52]$	$-4.625$	$[-10.14,+0.89]$
Abstract Algebra	$+0.875$	$[-4.87,+6.62]$	$-0.125$	$[-5.73,+5.48]$
Linear Algebra	$-1.250$	$[-7.57,+5.07]$	$-3.125$	$[-8.85,+2.60]$
Statistics	$-1.375$	$[-7.10,+4.35]$	$+0.875$	$[-4.70,+6.45]$

Table 5: Other traffic mixes and single sources, relative to the label reference (percentage points).

\Delta_{j}

is the per-source accuracy difference. Because utility is linear in the traffic weights,

\Delta U_{w}=\sum_{j}w_{j}\Delta_{j}

lies in

[\min_{j}\Delta_{j},\max_{j}\Delta_{j}]

for every

w

. Intervals are simultaneous 95% intervals (max-

|t|

bootstrap, critical value 3.025).

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Cell	$+g/-l$	$p$	$+g/-l$	$p$
	s17 (7 rows)		s23 (6 rows)
Linear $\to$ Statistics	$+16/-3$	0.004	$+14/-4$	0.031
Statistics $\to$ Statistics	$+18/-4$	0.004	$+13/-6$	0.167
Linear $\to$ Integral	$+21/-6$	0.006	$+17/-10$	0.248
Statistics $\to$ Linear	$+22/-8$	0.016	$+19/-8$	0.052
Abstract $\to$ Abstract	$+21/-9$	0.043	$+20/-15$	0.500

Appendix

Table 6: Probe cells with nominal

p<0.05

in either shuffle, plus the boundary case Integral

\to

Abstract. Two-sided exact McNemar

p

; the Bonferroni-adjusted value is

p_{\rm Bonf}=\min(1,49p)

over the 49-cell family; † marks the only cell with

p_{\rm Bonf}<0.05

(

p_{\rm Bonf}=0.00103

). The two shuffles share audit items and initial predictions.

Reading	Tensor	C1 $-$ C0	C2 $-$ C0	C3 $-$ C0	C3 $\Delta U_{\rm LS}$
Block-matrix routing	s17	$-2.23$	$+2.01$	$+1.22$	$+4.57$
	s23*	$-1.92$	$+0.67$	$+0.74$	$+2.27$
Competence routing	s17	$-3.90$	$+0.90$	$+0.58$	$+0.94$
	s23*	$-3.67$	$+1.06$	$+0.40$	$+1.64$
Zero transfer	s17	$-3.73$	$+0.02$	$-0.02$	$-0.55$
	s23*	$-2.98$	$-0.10$	$-0.02$	$-0.27$

Appendix

Table 7: Model-predicted and measured differences from C0 (pp); post hoc. The two rightmost columns concern the candidate outside the setting (Appendix D ). Model rows use the

S_{0}

audit tensors; the measured row uses state W, 400 test items per source, and two samples per item.

		C1 $-$ C0		C2 $-$ C0
Reading	Tensor	$\Delta U_{\rm LS}$	$\Delta U_{\rm other5}$	$\Delta U_{\rm LS}$	$\Delta U_{\rm other5}$
Block-matrix routing	s17	$+0.23$	$-3.22$	$+4.92$	$+0.84$
	s23*	$-1.48$	$-2.09$	$+1.95$	$+0.16$
Competence routing	s17	$-3.40$	$-4.09$	$+1.29$	$+0.75$
	s23*	$-3.75$	$-3.64$	$+3.12$	$+0.23$
Zero transfer	s17	$-4.45$	$-3.44$	$-0.23$	$+0.13$

Appendix

Table 8: Model-predicted and measured differences from C0 on the Linear–Statistics lines (

\Delta U_{\rm LS}

) and the other five lines (

\Delta U_{\rm other5}

), pp; post hoc.

Source	Disagreeing items	$\sigma_{d}^{2}$	$\sigma_{t}^{2}$	$\sigma_{b}^{2}$	Decoding share
Integral	22/80	0.138	0.252	0.115	54%
Differential	27/80	0.169	0.253	0.084	67%
Abstract	25/80	0.156	0.248	0.092	63%
Linear	23/80	0.144	0.252	0.108	57%
Statistics	20/80	0.125	0.237	0.112	53%
algorithmic	17/80	0.106	0.250	0.144	42%

Appendix

Table 9: Decoding-variance decomposition used to choose

k

: two independent samples of one model on 80 items per source. The 80 algorithmic items are MBPP+ problems.

	$\Delta U_{\rm all}$	$\Delta U_{\rm LS}$	$\Delta U_{\rm other5}$
C3 $-$ C0	$-1.54$ $[-2.89,-0.20]$	$-3.56$ $[-6.25,-0.88]$	$-0.72$ $[-2.30,+0.83]$
C3 $-$ C1	$+1.00$ $[-0.37,+2.45]$	$-2.25$ $[-5.00,+0.50]$	$+2.30$ $[+0.67,+4.02]$

Appendix

Table 10: The candidate outside the setting, C3: differences in pp with 95% jointly paired bootstrap intervals. The comparison with C0 was specified before the run; the comparison with C1 was added after observing results and is not adjusted for multiplicity.

Line	Difference	Marginal 95%	Simultaneous 95%
Integral	$-3.625$	$[-7.500,+0.375]$	$[-9.43,+2.18]$
Differential	$-0.875$	$[-4.625,+2.875]$	$[-6.78,+5.03]$
Abstract	$+1.500$	$[-2.125,+5.000]$	$[-4.15,+7.15]$
Linear	$-4.750$	$[-8.625,-0.875]$	$[-10.64,+1.14]$
Statistics	$-2.375$	$[-6.125,+1.125]$	$[-7.80,+3.05]$
algorithmic	$+0.875$	$[-2.125,+3.875]$	$[-3.75,+5.50]$

Appendix

Table 11: Per-line differences C3

-

C0 (pp). Point estimates are exact multiples of 0.125 pp. Marginal 95% intervals come from the analysis specified before the run; simultaneous 95% intervals (max-

|t|

bootstrap over all 21 executed per-line comparisons,

q=3.025

; Appendix A ) were added after observing results.

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Linear Probes Transfer from Base to Distilled Language Models despite Rotation

Marios Tsatsos

Independent researcher

Language Model Probing LLM Safety Monitoring Language Model Safety Evaluation

Open paper AskPDF arXiv

Linear probes, classifiers that read a language model's internal activations, are widely used to detect harmful requests. They are cheap to train and run, and an auditor who has trained one would like to reuse it when the model is replaced by a successor rather than retrain it for every release. We test how well probes can be reused. For four base models (Qwen2.5-Math-7B, Llama-3.1-8B, Qwen2.5-14B, Qwen2.5-32B) we train a probe on the base model with the XSTest prompt set and apply it, unchanged, to two successors of that base: the DeepSeek-R1 distilled reasoning model and the developer's instruction-tuned chat model. We find that the successors rotate the direction separating unsafe from safe prompts by 17

^\circ

to 35

^\circ

, yet on XSTest the transferred probe's AUC changes by only

-0.011

+0.027

, and on an independent OR-Bench evaluation, never used for training, by

-0.015

+0.053

. On XSTest, whose safe prompts deliberately contain alarming words, the probes beat a classifier that sees only the prompt text by 0.15 to 0.20 AUC. On the OR-Bench prompts that margin shrinks to 0.03 to 0.20, and the probes flag 29% to 42% of prompts that sound harmful but are benign, so part of what they read is the appearance of harm rather than harm itself. A probe trained on a base model can thus be reused, in these families, after distillation and after instruction tuning; how much it reads beyond textual cues depends on the test set.

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