Support or Magnitude? Characterizing Neuron Relevance for Instruction Data Selection

Yifan Le

cs.CLOct 12, 2026

Support or Magnitude? Characterizing Neuron Relevance for Instruction Data Selection

Authors: Yifan Le

Organizations: Independent Researcher

Abstract

Model-internal signals, such as neuron activations and gradients, have been used for instruction data selection, yet how neuron relevance should be characterized remains underexplored. In particular, should selection prioritize the magnitude of relevance or how broadly it is distributed across neurons? To investigate this question, we construct sample-level relevance profiles using AttnLRP-guided attribution and introduce two complementary criteria: Effective Relevance Support (ERS), which measures the effective support of positive relevance, and Positive Relevance Magnitude (PRM), which captures its average strength. Our analyses reveal that these characterizations produce distinct sample rankings and selection preferences despite sharing the same underlying relevance profiles. On Qwen2 models, PRM exhibits stronger associations with activation-based selection, whereas ERS produces substantially different rankings. These differences extend to task composition, within-task sample preferences, and semantic selection patterns, with varying degrees of agreement across backbones. Experiments across three language models and five downstream benchmarks demonstrate the practical value of relevance-guided selection, with ERS achieving the best overall average performance rank among the evaluated methods. Our findings highlight that how neuron relevance is distributed and characterized, rather than its magnitude alone, matters for instruction data selection.

Figures & tables

Figure 1: Overview of the proposed neuron relevance-based instruction data selection framework. We first compute neuron-level relevance profiles using AttnLRP for candidate instruction examples. Two complementary selection criteria are introduced: Effective Relevance Support (ERS), which captures the breadth of positive relevance, and Positive Relevance Magnitude (PRM), which measures its magnitude. Examples are ranked and selected for supervised fine-tuning, followed by evaluation on five downstream benchmarks.

Backbone	Method	ARC-C	CSQA	Meta-GSM8K	IFEval	WinoGrande	Avg. Rank $\downarrow$
Llama-3.2-1B	Base	39.68	52.01	6.75	10.54	60.30	–
	Random	40.87	49.63	18.14 1	16.64 1	63.77 1	2.40 2
	Activation	40.44	50.86 1	13.08	16.45 2	63.22 3	3.40
	Gradient	41.72 2	49.55	13.08	16.64 1	62.75	3.40
	NAIT	41.21	50.20 3	15.19 3	11.83	63.77 1	3.00 3
	PRM	42.24 1	50.61 2	16.46 2	13.86 3	63.22 3	2.20 1

Table 1: Maximum downstream performance (%) across three training-epoch checkpoints for each benchmark. Superscripts

1

2

, and

3

denote the top three selection methods, with the best highlighted in bold. Avg. Rank is averaged across five benchmarks (lower is better). Base is excluded from ranking.

Method	Qwen0.5	Qwen1.5	Llama1B	Overall Max $\downarrow$	Overall Mean $\downarrow$
Random	2.20	3.60	2.40	2.73	2.87
Activation	4.00	3.40	3.40	3.60	3.73
Gradient	3.40	2.80	3.40	3.20	4.00
NAIT	4.20	3.00	3.00	3.40	3.93
PRM	3.60	2.40	2.20	2.73	3.07
ERS	1.80	2.80	2.20	2.27	2.73

Table 2: Average ranks across five downstream benchmarks (lower is better). For each backbone and benchmark, the six selection methods are ranked by either their maximum (Max) or mean (Mean) performance over three training epochs. Backbone-specific columns report Max-based average ranks. Overall Max and Overall Mean further average the corresponding backbone-specific ranks across all three models. Bold indicates the best result in each column, including ties.

Figure 2: Joint semantic proximity and downstream performance changes relative to Random across 15 backbone–benchmark combinations. Purple denotes improvements in both metrics; blue and orange indicate improvements only in semantic proximity or downstream performance, respectively; gray indicates neither. Downstream performance is measured using Max scores.

Figure 3: Relationship between changes in Benchmark-to-Training Top-5 semantic proximity and downstream performance gains relative to Random. Each benchmark contains 15 observations. Colors indicate selection methods and markers indicate scoring backbones. Performance gains are measured in percentage points using Max scores. Spearman rank correlations are reported for each benchmark.

Qwen2-0.5B
Signal Pair	Raw $\rho$	Strat. $\rho$	Overlap (%)
ERS / Activation	-0.169	0.123	22.05
ERS / Gradient	-0.402	-0.032	18.58
ERS / PRM	-0.088	-0.009	25.41
PRM / Activation	0.612	0.412	72.17
PRM / Gradient	0.440	0.140	60.57

Table 3: Ranking correlations and selection overlap between relevance-based and baseline methods. Raw

\rho

denotes Spearman rank correlation over jointly valid examples. Stratified

\rho

is the residual rank correlation after centering global ranks within joint strata defined by task type, answer length, and answer perplexity. Top-

K

overlap is

|S_{A}\cap S_{B}|/\min(|S_{A}|,|S_{B}|)

, computed over deduplicated valid selections.

Figure 4: Task-conditioned selection overlap among different methods on Qwen2-1.5B. Each cell reports the overlap between two methods within a task category, normalized by the smaller selected subset. Cells with fewer than 50 selected examples in either subset are masked. Results for Qwen2-0.5B and Llama-3.2-1B are provided in Appendix D .

Figure 5: Semantic-region selection enrichment on Qwen2-1.5B. All methods share the same UMAP projection. Red and blue indicate over-selection and under-selection relative to the full candidate pool, respectively. Markers denote examples from the five downstream benchmarks. Corresponding results for Qwen2-0.5B and Llama-3.2-1B are provided in Appendix E .

Method	Q0.5/Q1.5	Q0.5/L1	Q1.5/L1
Random	100.00%	100.00%	100.00%
Activation	89.49%	58.99%	55.92%
Gradient	93.00%	87.77%	86.78%
NAIT	53.25%	54.05%	39.74%
PRM	79.91%	51.90%	54.43%
ERS	53.20%	30.74%	34.66%

Table 4: Cross-backbone selection overlap. Q0.5, Q1.5, and L1 denote Qwen2-0.5B, Qwen2-1.5B, and Llama-3.2-1B. Overlap is computed over deduplicated valid selections after excluding the assistant_identity category, using

|S_{A}\cap S_{B}|/\min(|S_{A}|,|S_{B}|)

. Random uses the same random selection across backbones.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Training Configuration
Configuration	Qwen2-0.5B	Qwen2-1.5B	Llama-3.2-1B
Training framework	LLaMA-Factory
Fine-tuning strategy	Full-parameter SFT
Candidate pool size	$\sim$ 100K
Selected training examples	30K
Optimizer	AdamW

Appendix

Table 5: Training and data-scoring configurations for the three pretrained backbones. Unless otherwise specified, configurations are shared across models and selection methods.

Figure 6: Answer NLL distributions of training examples selected by different methods on Qwen2-0.5B. The Full Pool distribution is included as a reference.

Figure 7: Answer NLL distributions of training examples selected by different methods on Qwen2-1.5B. The Full Pool distribution is included as a reference.

Figure 8: Answer NLL distributions of training examples selected by different methods on Llama-3.2-1B. The Full Pool distribution is included as a reference.

Figure 9: Capability composition of training subsets selected by different methods on Qwen2-0.5B. Each stacked bar represents the relative proportions of nine capability categories within the selected training subset.

Figure 10: Capability composition of training subsets selected by different methods on Qwen2-1.5B. Each stacked bar represents the relative proportions of nine capability categories within the selected training subset.

Figure 11: Capability composition of training subsets selected by different methods on Llama-3.2-1B. Each stacked bar represents the relative proportions of nine capability categories within the selected training subset.

Figure 12: Semantic-region selection enrichment on Qwen2-0.5B.

Figure 13: Semantic-region selection enrichment on Llama-3.2-1B.

Figure 14: Distribution of capability categories in the candidate training pool. Instruction examples are categorized according to their source datasets. Proportions are calculated after excluding the assistant_identity category from task-level analysis.

Figure 15: Task-conditioned selection overlap among different methods on Qwen2-0.5B. Overlap is normalized by the smaller selected subset within each task category. Cells with fewer than 50 selected examples in either subset are masked.

Figure 16: Task-conditioned selection overlap among different methods on Llama-3.2-1B. Overlap is normalized by the smaller selected subset within each task category. Cells with fewer than 50 selected examples in either subset are masked.

Task Type	Random	Activation	Gradient	NAIT	ERS	PRM
Math Reasoning	1.00	0.16	0.08	1.69	1.82	0.77
Coding	1.00	0.77	0.75	0.50	0.57	1.06
Instruction Following	1.01	0.90	0.92	0.41	0.20	0.50
General Chat	1.01	0.41	0.48	0.52	0.52	0.33
General Multitask	1.01	2.79	3.21	1.65	1.29	2.29
Multilingual	0.99	2.36	2.06	0.42	0.76	2.13

Appendix

Table 6: Task-type enrichment of selected data on Qwen2-1.5B. Values indicate the ratio between the proportion of a task category in the selected subset and its proportion in the full candidate pool. Values above one indicate over-representation.

Backbone	Method	ARC-C	CSQA	Meta-GSM8K	IFEval	WinoGrande	Avg. Rank $\downarrow$
Llama-3.2-1B	Base	39.68	52.01	6.75	10.54	60.30	–
	Random	40.22	49.39	14.77 1	16.14 1	63.56 2	2.80 1
	Activation	40.13	50.18 3	10.97	15.47 3	62.83	4.40 3
	Gradient	40.59 3	48.95	10.97	15.77 2	62.75	4.60
	NAIT	40.36	49.74	13.64 3	10.60	63.59 1	3.60 2
	PRM	41.61 1	50.34 2	13.78 2	13.62	62.88	2.80 1

Appendix

Table 7: Mean downstream performance (%) across three backbones and five benchmarks over three training epochs. Superscripts

1

2

, and

3

indicate the top three methods, with the best highlighted in bold. Avg. Rank is computed across the five benchmarks (lower is better). Base is excluded from ranking.

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