Diversity as a Reward: Fine-Tuning LLMs on a Mixture of Domain-Undetermined Data
Authors: Zhenqing Ling
Daoyuan Chen
Liuyi Yao
Qianli Shen
Yaliang Li
Ying Shen
Venue: NeurIPS 2025 poster ()
Keywords: Fine-Tuning
Data Selection
Large Language Models
Diversity
Primary area: deep_learning
TL;DR: Our empirically and theoretically informed method, which treats diversity as a reward, achieves new SOTA average performance across 7 benchmarks on SOTA LLMs with domain-undetermined data.

Abstract: Fine-tuning large language models (LLMs) using diverse datasets is crucial for enhancing their overall performance across various domains.
In practical scenarios, existing methods based on modeling the mixture proportions of data composition often struggle with data whose domain labels are missing, imprecise or non-normalized, while methods based on data selection usually encounter difficulties in balancing multi-domain performance.
To address these challenges, in this work, we investigate the role of data diversity in enhancing the overall abilities of LLMs by empirically constructing contrastive data pools and theoretically deriving explanations. 
Building upon the insights gained, we propose a new method that gives the LLM a dual identity: an output model to cognitively probe and select data based on diversity reward, as well as an input model to be tuned with the selected data.
Extensive experiments show that the proposed method notably boosts performance across domain-undetermined data and a series of foundational downstream tasks when applied to various advanced LLMs. We release our code and hope this study can shed light on the understanding of data diversity and advance feedback-driven data-model co-design for LLMs.

Diversity as a Reward: Fine-Tuning LLMs on a Mixture of Domain-Undetermined Data
Zhenqing Ling', Daoyuan Chen?*, Liuyi Yao?, Qianli Shen', Yaliang Li?, Ying Shen 1:3t
Sun Yat-sen University, PAlibaba Group, *FSIETP
Lingzhg@mai12.sgg sysu. edu. en, sheny766mail sysu. edu. cn (daoyuanchen.cd)) cdy, y1y287738, shengianli.sg yaliang. 11l)aalibbbbbba... www.llibbbaainn... com
Abstract
Fine-tuning large language models (LLMs) using diverse datasets is crucial for enhancing their overall performance across various domains. In practical scenarios, existing methods based modeling the mixture proportions of data composition often struggle with data whose domain labels are missing, imprecise or non- normalized, while methods based on data selection usually encounter difficulties in balancing multi-domain performance. To address these challenges, in this work, we investigate the role of data diversity in enhancing the overall abilities of LLMS by empirically constructing contrastive data pools and theoretically deriving explanations. Building upon the insights gained. we propose new method that gives the LLM a dual identity: an output model to cognitively probe and select data based on diversity reward, as well an input model to be tuned with the selected data. Extensive experiments show that the proposed method notably boosts performance across
data and series of foundational downstream tasks when applied to various advanced LLMs. We release our code and hope this study can shed light on the understanding of data diversity and advance feeiback-driven data-model co-design for LLMs.
Introduction
The rapid advancement of large language models (LLMss) exemplified by open-source series such as LLaMA [18] Qwen (53] and DeepSeek (31), as well as closed-source models like GPT [2] - has transformed artificial intelligence by significantly enhancing capabilities in core areas such common sense reasoning, mathematics, and code generation. Fine-tuning these models further improves their usability by aligning their behaviors with specific instructions and human preferences 43 39
To cultivate comprehensive capabilities in LLMs, prior studies have explored preferable trade-offs between quality, quantity, and diversity of their training data [30 7 38, 559. For example, methods focusing on data selection [29 48 [4 and mixture 21 demonstrate promising capabilities to
enhance model performance, particularly through semantic diversity [34 33).
However, real-world applications frequently encounter unlabeled data and difficulties in domain labeling [22), posing challenges for data mixture methodologies that take the domain tags prior, as well the data selection approaches, which often prioritize quality over diversity, especially with data sourced from quite different domains.
"qqual contribution. "Corresponding author.
AFSIETP: Guangdong Provincial Key Laboratory Fire Science and Intelligent Emergency Technology.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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To leverage the best of both worlds, in this work, we dive into the role of semantic diversity of LLM data. Our investigation begins with a systematic analysis of 40k instruction pairs across four capability domains. Through controlled experiments with contrastive data pools, we uncover two insights: (1) Optimal diversity thresholds for model performance vary significantly across architectures and task domains; (2) Current centroid-based diversity metrics [34] fail to capture the dynamic interaction between inter-domain separation and intra-domain variance when labels are unavailable.
These findings motivate our theoretical analysis, which establishes that traditional data mixing strategies assuming known domain weights [54] cannot achieve Pareto-optimal performance in label-free settings. Our analysis further reveals that when domain labels are unavailable, an effective data selection strategy should prioritize samples that enhance sample-level diversity. This strategy involves balancing the goal of enhancing sample-level diversity to approximate the ideal importance weights, with the need to preserve the base model's 's latent feature geometry.
We operationalize these insights through DAAR, a self-supervised framework that learns diversity as reward signal through three technical innovations: (1) Automatic synthesis of model-aware domain centroids via iterative embedding-space generation, (2) A lightweight MLP probe trained to predict semantic entropy using only the LLM's frozen embeddings, and (3) Closed-loop fine-tuning where the model's own diversity estimates guide subsequent data selection.
Extensive evaluations across 7 benchmarks and 3 model families reveal that DAAR achieves new state-of-the thrttheart (SOTA) average performance, consistently outperforming baseline methods on high-difficulty tasks while maintaining computational efficiency. Crucially, our method requires no domain labels or external models - the L.M self-supervises its diversity estimation through geometric constraints in its native embedding space. Our core contributions for LLM data optimization are:
Formal characterization of diversity's 's dual role in LLM fine-tuning through controlled experiments with contrastive data pools.
A new method with label-free diversity reward mechanism using embedding-spaat entropy predic- tion, theoretically grounded in importance sampling.
Extensive empirical validations showing consistent gains across model families and tasks, with no- table improvements in mathematical reasoning (+27%) and coding (+7,4%), whereas other baselines struggle such challenging scenarios. Our code released at hatts::/ggthh...co/mmmee/cppppp juicer/tree/DaaR to foster more data-centric research for LLMs.
2
Preliminaries
2.1
Related Works
Data Selection
Fine-tuning is a pivotal training paradigm for enhancing LLMs' domain-specific capabilities. Research has shown that small set of instruction pairs enable LLMs to follow major
instructions effectively [62] [2]. This fine-tuning can be achieved through rule-based methods, which
focus on attributes such as Error L2-Norm [37] and token length [40]. More recently, model-based
heuristics have been explored, including methods based on instraction-following difficulty [29] GPT
scoring [10 46 data model selection [99] and inffuence scores derived from loss 48
Diversity & Data Mixing A fundamental principle for LLMs is being able to handle diverse human requests, underscoring data diversity as essential for effective pre-training (32
12
51
20
and fine-tuning [55] 17). Data diversity encompasses aspects such as data deduplication I|, the
coverage scope of tags 34), moodel-based diversity evaluation [33 58). and scaling properties
[4]
Typically, data mixing approaches [3] [54 21] (2) focus adjusting the proportional weights of
different domains to enhance model capabilities.
This work relates to data mixing and selection fields through its focus on diversity quantification, but advances both of them in three key aspects: First, we address practical challenges in real-world applications where unlabeled datasets hinder existing methods' ability. Second, our framework distinguishes by integrating reward-driven learning with semantic entropy-based selection criteria. Third, we critically examine the under-explored applicability of current selection paradigms in multi domain contexts, revealing critical limitations in modeling diverse distribution patterns.
Our Position

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Observation
Domain
Determined
Paur
LLM
Diversity Construction
Various Distribution of Dataset Cross-Domate Diversity
Eval Variation
Domainn-Undetermined
DaaR
Probe
Diversity Probe
Diversity Selection
Dataset
Diversity Probe
Domain Descriation
MASE loss
Aets
LIM Generator
?
$2
Without
Labels
?
?
cnspprors ( Festichbing
D₂ ED
LLM'S
Process
Domain Centroed
Assign
Libels
Cae Sducion
LU Thanne
The illustration highlights our observations and the proposed DAAR method. Observation shows the t-SNE visualization of embeddings for data samples with different distributions, leading to varying LLM's evaluation performance. In the domain- uomain-undetermined data selection scenario, DAAR introduces dual-identity framework for LLMs: @ An output model probe and select data based on diversity reward, @ An input model to tuned with the selected data. The diversity probe is trained on model-aware synthetic data, enabling domain discrimination and diversity reward prediction.
Figure I:
2.2 Problem Setup
In this paper, consider learning from domain-undeternee data mixtures to enhance LLM downstream performance in target domains. Let (Dx} denote K target domain distributions, where each Dj X' + [0, 1] defines a probability distribution parameters 0, the domain-specific performance is measured by EEzDD, [f(1; 0)]. Our objective is to minimize the weighted multi-domain loss: E AeE 0)], where λ are non-negative weights with ΣK A = reflecting ceplication-speciiee priorities.
samples x E X. For model
For each domain Dr. we assume only a natural language description de is available while NO target domain samples are accessible, contrasting with conventional data selection methods requiring labeled examples 48 55 41 [54] in LLM training. We are provided with an domain-unlabeled dataset D {-;} } containing domain- aogaiinagnostic samples. straightforward approach is direct fine-tuning using all DD but it often yields suboptimal results (empirically evidenced in Table 2 Instead, we propose selecting subset via binary vector {0, 1 where a; indicates x; is selected. The LLM is trained by solving: ming Σ
== 0g 0), leading to the bi-level optimization:
min
AR [(:;; (a)).. s.t. 0" (a)) min
a; 0).
All notations used are summarized in Appendix A
Diversity: A Critical Factor for LLM Fine- Fine-Tuning
In this section, investigate how domain-specifer diversity in labeled training data modulates model capabilities through empirical analysis of well-designed data pools, complemented by a theoretical perspective that explains the observation and provides mechanistic insights.
3.1 Seed Data Pools and Basic Setting
Data Pools and Sources To explore how selecting data samples from extensive and diverse data repositories affects the foundational capabilities of LLMs, we construct various data pools and consistently fine-tune L.LMs on them. The seed data pool sourced from the following datasets: Dolly-15k [15) for common sense, Cot-en [13] for reasoning, Math-Instran [56) for mathematics,

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and Aode-Alpaca 6 for coding. Each dataset was randomly tailored to 10,000 entries, resulting combined data pool of 40,000 entries. Following instruction tuning practices [62 [3]] we then
uniformly sample 8,000 data entries as reference data pool for the random baseline.
Benchmarks Aligned with representative capabilities of leading open-source L.MMs, select the following widely used evaluation sets: NQ (28) and TriviaQA (26) for common sense, Hellaswag [57
for reasoning, GSM8K [14] and MATH [24] for mathematics, MBPP 4 and HumanEval []] for coding. To evaluate the comprehensive performance of LLMs across domains, we employ the average metric (Avg) as the primary evaluation criterion.
Models & Implementation We employ the Qwen2 series (Qwen2-7B & Qwen2.5-7B) 53 and the Llama3.1-8B [18] as representative SOTA base models to be fine-tuned.
All experiments are conducted under identical training and evaluation protocols with two independent repetitions. Full platform, training and evaluation details are provided in Appendix D
3.2 Data Pools with Contrastive Distributions
To systematically analyze the impact of domain-specific diversity patterns on model capabilities, we propose contrastive construction with three phases: (A) Foundational Definitions, (B) Diversity Metric Formulation, and (C) Distribution Synthesis.
(A) Foundational Definitions Each domain dataset Da contains N₂ |D&| samples, and we repre- sent each data sample through its semantic embedding x; E IRd extracted from the embedding-layer of the pretrained LLM. The domain centroid Cs serves as the semantic prototype C2 1 Ei x;
(k)
This centroid-based representation enables geometric interpretation of domain characteristics in the embedding space. We dissect data diversity into two complementary aspects:
(B.1) Inter-Diversity It quantifies the diversity between distinct domains through centroid geometry.
For sample x; its cross-domain similarity is measured by @inter (x;
(k)) The global inter-diversity
metric 4 inter computes the expected pairwise centroid distance:
K
K-1
K
Pinter (x; (k))
Pinter = Eszi Il[Cx - Cilla] = K
||Cx - Cill2- (2)
|||C
1=k+1
This formulation reflects a key insight: maximizing Pinter encourages domain separation, while minimization leads to overlapping representations. Observation of the upper part of Fig. (full-size version in Appendix, Fig. [17) demonstrates this continuum through t-SNE projections - high a P manifests as distinct cluster separation with clear margins (Fig. 17 (c), whereas low values produce entangled distributions (Fig. (d)). Full analysis detailed Appendix H.T
(B.2) Intra-Diversity Focusing solely on the separation between different domains may hinder the model's 's ability to learn the knowledge specific to given domain. Hence we calculate sample similarity to its domain center in @inna (x! (k)) and the demain-level variance metric is defined as t (k)
intra
x (A) Cc
N₂. N₁
Pintca (x: (2)
(A) intra
X
(R)
C2
|x (K) |||Cal
Controlled manipulation of Pint reveals critical trade-offs: lower variance enhances domain-speceee learning but risks over-specialization, while higher variance improves robustness with the risk of cross-domain interference. The visualization in Fig. Fi (e-f) illustrates this scenario that concentrated distributions exhibit sharp marginal peaks, while dispersed variants show overlapping density regions.
(C) Distribution Synthesis For each domain DR. we compute sample-wise diversity scores (dimer (x! (k) No and (Ammra (x)) No The construction proceeds via partition each Dj into 20% intervals based on the percentiles of Pinter for inter-diversity control, and partition the diutra scores into 20% quantile intervals for intra-diversity control.

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The 20% interval results in five choices of data selection per domain, parameterizing the trade-ofi off between diversity preservation and domain specificity. As demonstrated in Appendix HH.2 (Fig and Fig. 20), this quantization process induces measurable distribution shifts.
3.3
Experimental Observations
Table presents comprehensive evaluations across seven benchmarks, where the notation Inter- Diversity (X-Y) indicates samples ranked in the top (100-Y)% to (100-X)% of cross-domain similarity scores. Due space constraints, we present only the results for the top 20%, middle 20%, and bottom 20%. Detailed performance results on various downstream tasks are shown in Appendix H.4 Our diversity-controlleed selections reveal two observations:
Varied Improvement Patterns: Both models demonstrate marked improvements over RAw distributions across diversity conditions, but the effects of their improvements vary. For Llama3.1 1- 8B, Inter-D (80-100) achieves 38.98 average accuracy (+3.12 12 over RAW), outperforning the RANDOM baseline by 1.71, while Inter-D (0-20) is below RANDOM.
Model-Dependent Performance Peak: Each model exhibits distinct optimal operating points along the diversity spectrum. Llama3. 1-BB reaches peak performance Inter-D (80-100) and Intra- D (80-100), suggesting complementary benefits from both diversity types. Qwen2-7B peaks in inter-type selection at low inter-diversity, while it peaks intra-type selection high intra-diversity.
These results show the promising potential of diversity- aware data selection, motivating us to further understand the perfor- mance variance more formally and propose principled solutions adaptively achieve the performance peaks.
Table 1: Performance of Llama3.1 1- 8B and Qwen2-7B on AvG with dif- ferent constructed Inter-Diversity and Intra-Diversity distributions.
Remarks Despite existing positive improvements on overall performance, two constraints merit consideration for real-world applications. (1) Distribution Transiency: The optimal di- versity parameters (e.g., 80-100 vs. 40-60) show sensitivity across tasks and models, necessitating automated and poten- tially costly methods. (2) Label Dependency: The studied heuristic strategies Inter-Diversity and Intra- -iive--iiverstty currently require nomain-labelee data for centroid calculation.
Models
Distribution
AvG
RaW FULL (40K)
35,86
37.22
RANDOM (8K)
37.27
Inter-D (0-20)
37.18
Llama3.1
Inter-D (40-60)
38.09
Inter-D (80-100)
38.98
Intra- (0-20)
38.71
Intra-D (40-60)
37.88
Intra-D (80-100)
38.75
3.4 Theoretical Perspective
RAW
41.47
FULL (40K)
53.01
To explain why diversity serves as a crucial factor in LLM's cross-domain performance and addresses distribution tran- siency, we present a theoretical analysis based on important sampling. We first formulate the data selection dynamics and then incorporate diversity into it, thereby revealing the mech- anistic basis and offering insights for our method.
RANDOM (8K)
$3.02
Inter-D (0-20)
54.13
Qwen2
Inter-D (40-60)
52.47
Inter-D (80-100)
51.07
(0-20)
48.72
Intra-I) (40-60)
$2.85
Intra-D (80-100)
53.25
Importance Sampling We assume that there exists an ideal target distribution y that minimizes the multi-domain loss in Eq. (I). Hence, the process of data selection be framed as aligning the source distribution p (empirical distribution of D) toward the optimal distribution q. To bridge this distribution shift, adopt importance sampling perspective [50) 49 48) where the optimal subset
corresponds to reweighting samples by the density ratio o(x).
p(a))
Exwat ((x))(((()))))){()) = ((=))o(x)de
p(x)
((x) p(x)
fo(w)dr= = Expp()
((x) p(x)
(x; Σ
g(x)
E(x; 0). p(x)
(4)
The domains of LLM's data are commonly defined by textual descriptions, which inherently constrain the semantic scope. Thus we make the following assumption regarding distributions p and g: Assumption 3.1 (Shared Support). For any given domain index c E (1...., (....,K), the support of and q is shared, formalized as: p(z|c = k) = q( k), k = I,..,,K.
Assumption implies that the discrepancy between the source distribution p and the target distribu- tion q arises solely from differences in domain proportions, leading to the following proposition.
5

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Proposition 3.2. The diversity is entirely attributable to the relative weights assigned to each domain:
g(x)
>ep(c=kla), >
(5)
p(z)
p(c
The derivation is detailed in Appendix C.1
This decomposition reveals that the Inter- iieer-Divrsstt and Intra- Diversity are governed by A and p(c=k(z)) k/)). leading to the following analysis.
Why Overlook Diversity is Suboptimal We define k= (=xx)= == arg max p(c k/x)) as the predic- tion of the classifier p(c k/.)) Consider a special case where the classifier yields deterministic predictions, iee p(c (=)x)==) 1, Vr E D. In this case, the importance weight reduces to
g(wr) K p(a)
k==1 Aep(c k|/) (z). Therefore, importance sampling can be applied within:
f(0) (x;00) 0) = {(x)))((;0))) FED p(x)
Σ
Σ R=1 =ED=
)==(=; 0).
(6)
ZED
This formulation is commonly used when domain labels are available, under the implicit assumption that domains are mutually exclusive. However, such an assumption rarely holds in the context of
LLM training, as cross-domain data may either synergize conflict (59] 49 27 (evidence in Table D.. Hence, neglecting diversity in data selection potentially leads to suboptimal overall performance. We further formalize this suboptimality by analyzing the approximation error incurred by such deterministic assignment, which provides supplementary justification for using predictive entropy selection criterion. For a detailed analysis, please refer Appendix
Guidance Our Method Under the comman--undetermnne scenario, our proposed method DAAR operationalizes the gained insights by (1) constructing pseudo-labels (Section align with LLM- aware generated seed, (2) explicitly modeling the classifier p(c=k(a) through domain discrimination probe (Section 4.2) and (3) using the probe's 's predictive entropy (Section 4.2) proxy for diversity, estimating the ability of classifier p(c=k|æz) to select data toward the target distribution q.
DAAR: Diversity as Reward
To address the challenges identified in Sec. 3.3 and leverage the insights gained in Sec. establish data selection method DAAR guided by diversity-award reward signals.
3.4
we
comprises three key components illustrated in Fig. [ (1) model-aware centroid synthesis, which generates domain-representaaii centroids and seed data capturing the LLM's intrinsic feature space, (2) two-stage training with reward probe, which yields a probe module capable of predicting sample- level diversity rewards accurately, and (3) diversity-driven data selection obtain a data subset that effectively boosts LLM's 's cross-domain performance.
4.1 Model-Aware Training Data
Model-aware Centroid Construction The proposed method initiates with centroid self-synthesis through a two-phase generation process to address two fundamental challenges: (1) eliminating dependency on human annotations through automated domain prototyping, and (2) capturing the base model's 's intrinsic feature space geometry for model-aware domain separation.
s()) via zero-shot prompting with domain-specific description templates generated by LLM itself, alongside with minor injection from downstream task samples, establishing initial semantic anchors. We show that removing the minor injection of downstream samples negligibly impacts final performance but significantly reduces data generation efficiency in Appendix G.8
Phase - Seed Generation: For each domain h; generate seed samples
Phase 2 Diversity Augmentation: Iteratively expand s(!)) through context-aware generation, conditioned on a sliding window buffer with 3 random anchors sampled from the (t - 1) iteration s(t ((t-1) The generated sample x' is retained through rejection sampling to enhance diversity.:
max cos(Mexuxx)) Mew((x)) < xES

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where Mau(-) indicates the output of the embedding layer of the given LLM, with 7 as the similarity threshold. This process terminates when it reaches the predetermined iteration.
The domain centroid then computed from the final augmented set St using the model's embedding. formalized as C. = 1/|Sa] -Exes, (x,) This captures the LLM's intrinsic feature space geometry while eliminating dependency on human annotations.
More implementaiion details including hyper-parameters parameters and the data generation process, along with their corresponding ablation studies, are provided in Appendix
Domain-Aware Clustering We then automatically construct pseudo-labels for the given data samples based the previously synthesized centroids {C² [C We perform constrained k-means
clustering in the embedding space with arg min(s.) Ek=1 Exes, [|Meaa (Ø) Ca 11?.. This produces
the seed dataset D poute containing pseudo-labele {ūi J== where yI E fl,.... K}. with model-induced and embedding-derivee domain label assignments.
4.2 Training for Sell-Rewarding Abilities
Entropy Diversity Proxy While diversity metrics in Eqs. (2)-3) directly quantiff cross- sample distribution, we aim to design a reward probe that outputs with sample-level diversity level. Since models require sample-level processing that is unable to leverage pairwise relationships, direct training for diversity leads to poor performance in Appendix F.6 We instead use softmax confidence scores and predictive entropy as implicit diversity proxy, reflecting model-aware data discriminability. This enables effective diversity approximation through a two-stage framework.
Stage 1: Domain Predictor The proposed DAAR establishes model-aware domain discrimination abilities through multi-layer perceptron (MIP) probe module, Vaaom attached to the hidden layer (() of the LLMs. The probe will be trained meanwhile all the parameters of the LLM are frozen, achieving preferable balance between effectiveness and cost, with detailed analysis regarding the choice of layers presented in Appendix G.2 Specifically, with pscudo-label y. can compute domain predicted probabilities as:
Ph ( softmax (4' (M()))), Fdom Rdd R-K
8
dao is optimized via cross-entropy loss Leom pootl Eas Σ [ log Pk (#).
where [[k=]] denotes the indicator function. We employ single-sample batches with the AdamW optimizer to prevent gradient averaging across domains. Training consistently converges and achieves 92.7% validation accuracy on domain classification, as shown in Fig. 2 (a).
Stage 2: Diversity Rewarding Building on the stabilized domain discrimination probe, we quantify sample-level diversity through predictive entropy (z). And enable efficient reward computation during data selection, we then train another 5-layer MLP vaaiv to directly estimate H (7) from M(z):
K Σ log log i = vaaiv (M(T)), Uddiv : R2d + R+
H 2
This diversity probe module thaiv shares t'uom's 's architecture up its final layer that replaced with the regression head, trained using entropy-scales MSE loss Lai [peotel EBED (HT H The module also well-converged as shown in Fig. (b).
Data Selection: After training the module v/div= we can use its output to select data samples. Building on the theoretical insights in Sec. 3.4] data points that are closer to other centroids and more dispersed within their own centroid are more beneficial for enhancing the comprehen- sive capabilities of the model. Therefore, we use the predicted entropy score as a reward, select- ing the top 20% with the highest scores as the final data subset for fine-tuning. The analysis of stability is shown in Appendix G.10
Truzinng Uymoraass
1h1 Truinng Dyaazies
Trexus
Figure 2: Training loss and validation process of the two stages of DAAR on Qwen2-7B, more de- tailed results in Appendix H.3
7

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Table 2: Evaluation results of Llama3. 1-8B, Qwen2-7B. and Qwen2.5-7B across various downstream task benchmarks. DAAR demonstrates superiority in AVG compared to other baselines.
Common Sense
Reasoning
Mathematics
Coding
Models
Distribation
Avg
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HumanEval
RAW
14.13
65.90
74.62
7,90
FULL (40K)
21.92
65.11
73.62
51.70
7.60
4.10
36.50
37.22
RANDOM (8K)
21.99
64,83
74.72
55.70
14.50
5.10
24.09
37.27
INSTRUCTION LEN
15.34
63.60
73.73
54.00
15.40
3.60
30.80
36.64
Llama3.1-8B
ALPAGASUS [10
21.57
64.37
74.87
55.20
17.65
4,60
16.16
36.34
INSTAG-BEST
18.12
15.50
SUPERFILTER
29
22.95
64,99
76.39
57.60
6,05
2,60
40.55
38.73
DEITA-BEST
15.58
64,97
74.21
55.00
13.05
4.60
34.46
DAAR (Ours)
20.08
64.55
74.88
54.80
15.30
4.70
37.50
38.83
Raw
8.03
59.58
73.00
78.00
5.70
5.00
60.98
41.47
FULL (40K)
15.61
$8.75
72.51
73.80
31.30
$1.70
67.38
53.01
(8K)
73.00
35.36
INSTRUCTION LEN
8.62
58.44
72.86
73,30
27.05
53.10
63.72
51.01
ALPAGASUS [0]
13.67
57.94
73.04
73.90
32.30
51.40
63.41
52.24
Qwen2-7B
INSTAG-BEST 34
9.51
58,50
73.06
74.70
35.35
$1.90
64.70
52.53
SUPERFILTER
22
19.16
58,98
72.99
73.70
30.10
$2.40
58.85
52.31
DEITA-BEST
16.41
$7,80
72.70
76.10
29.05
64.63
$2.73
DAAR (Ours)
16.88
57.58
73.03
75.40
38.1
52.00
64.94
53.99
RAW FULL (40K)
8.84
58,
72.75
78.20
9.10
7.40
78.05
44.64
12.88
58.60
72.28
76.80
13.60
62.80
71.04
$2.57
RANDOM (8K)
11.46
57.85
73.08
78.90
13.15
62.50
71.65
$2.65
INSTRUCTION IRNN
11.34
58.01
72.79
78.00
15.80
62.30
68.12
52.34
Qwen2.5-7B
ALPAGASUS
10.40
57.87
72.92
18.75
65.55
$2.07
INSTAG- BEST 34
11.08
$8.40
72.79
76.40
16.40
62.90
70.43
52.63
SUPERFILTER
13.54
58.51
72.89
79.30
11.35
39.50
65.25
DEITA-BEST
33
10.50
58.17
73.14
74.60
16.60
62.00
72.26
52.47
DAAR (Ours)
15.83
$8.65
72.48
80.20
16.70
64,20
68.29
53.76
Experiments
To validate the efficacy of DAAR, we conduct comprehensive experiments on data pools and bench- marks in Sec. [31]] comparing SOTA baselines follows with critical modifications: all domain- specific labels are deliberately stripped. This constraint mimics more challenging real-world scenarios and precludes direct comparison with data mixture methods requiring domain label prior.
Baselines We use the following data selection methods for comprehensive evaluation: (1) RANDOM SELECTION: traditional random sampling: (2) INSTRUCTION LEN: measuring instruction complexity by token count [5]: (3) ALPAGASUS [10]: using ChatGPT for direct quality scoring of instruction
pairs; (4-5) INSTAG 44 semantic analysis approach with INSTAG-C (complexity scoring via tag
quantity) and INSTAG-D (diversity measurement through tag set expansion): (6) SUPERFILTER 29 response-loss loss-based complexity estimation using compact models; (7-9) DEITA [33] model-driven evaluation with DEITA-C (complexity scoring), DEITA-Q (quality scoring), and DEITA-D (diversity- aware selection). Detailed implementations for these baselines are Appendix E.1
5.1 Overall Performance
The main experimental results are presented in Table 2, where INSTAG-BEST and DEITA-BEST represent the optimal variants from their method families. Our experiments clearly demonstrate the effectiveness of DAAR across three major language models and seven challenging benchmarks:
High-Difficulty Scenario The task of balanced capability enhancement proves particularly chal- lenging for existing methods. While some baselines achieve strong performance on specific tasks (e.g.. SuperFilter's ss 40.55 on HumanEval for Llama3. 1), they suffer from catastrophic performance drops in other domains (e.g., SuperFilter's 6.05 on MATH). Only 3 baselines perform better than RANDOM on Llama3. 1.maa.11-.0 1-8B. In the Qwen series, even all baselines fall below the R RANDOM performance. We conjecture this stems from selected distribution- bias, as the baselines are unable balance the proportions across different domains, perspective visually supported and analyzed in Appendix E.2

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Table Illustration results on MMLU, Qwen3 and customization, detailed in Table 10
(a) MMLU Performance
(b) Eval on Qwen3
(c) Customized Selection on Domain'
Qwen2-7B
MMLU-Avg
Qwen3-88
Avg
Qwen2.5
NQ
Hellaswag
Avg
RAND (8K)
RAW
98.98
RAW
RAND (8K)
49.41
Raw
8.84
72.75
44 64
INSTRUCTION-L
68.5
68.55
INSTRUCTION-L
49.19
RAND
11.46
73.08
52.66
ALPAGANUS
59.
ALPAGASUS
47.81
INSTAG
11.08
72.79
52.63
INSTAG-BERT
INSTAG-REST BEST
DAAR
15.83
72.48
53.76
SUPERRIITEER
54.27
SULERFILTER
49.51
DEITA-BAR BIST
68.08
DEITA- BEST
49.90
Common
17.56
72.51
52.85
(Ours)
DAAR (Ours)
Reason"
16.56
74.62
$3.39
Comprehensive Performance DAAR establishes new SOTA averages across all models, surpass- ing the best baselines by +0.14 (Llama3.1), +0.97 (Qwen2), and +1.11 (Qwen2.5). The proposed method uniquely achieves dual optimization in critical capabilities: Mathematical Reasoning: Scores 38.1 MATH (Qwen2) and 16.70 MATH (Qwen2.5), with 7.4% and 27.0% higher than respec- tive random baselines. Coding Proficiency: Maintains 64.94 HumanEval (Qwen2) and 64.20 MBPP (Qwen2.5) accuracy with <1% degradation from peak performance. This demonstrates DAAR's ability to enhance challenging STEM capabilities while preserving core competencies.
5.2 Generalizability, Uniqueness and Stability of DAAR
Evaluation on MMLU In the main experiments, the data and benchmarks we employed are meticulously aligned, which validates the In-Distribution capabilities DAAR. To further validate the generalization ability of DAAR, we present MMLU [23] evaluations in Appendix(F]] [F.1] MMLU encompasses significantly broader range of content than our dataset. thus serving as an Out-of- Distribution scenario. Results demonstrate that DAAR achieved top accuracy on Qwen2 with an improvement of 0.61 points, and secured competitive second-place performance on Qwen2.5. At granular level, DAAR particularly excels in the STEM domain, outperforming baselines by an average 7.6 % and 1.7% on Qwen2 and Qwen2.5, which aligns the findings above.
Evaluation on Qwen3 In Appendix F.2. we explore the performance of DAAR on the mainstream RL-based LLM, Qwen3-8B. We observe that despite difference in structure, the phenomena (Fig. p Table 9 and the dynamics of training (Fig. 10 remain consistent with the main observations. Then we compare DAAR with baselines in Table TO although Qwen3-8B is not directly designed for
SFT paradigm, DAAR maintains the top position in AVG performance across baselines, surpasses all
baselines up to 4.7% % and notably exceeds the avg of baselines by 25.91 % on MATH.
Customized Characteristics Unlike baselines, DAAR enables domain- aware data selection in undetermined scenario, showcasing potential customization on λg. As detailed in Appendix F33 by adjusting the selection ratio for specific domains, we achieve SOTA performance in targeted domain without compromising overall ability, promising practical utility real-world application.
Table 4: DAAR using model-aware pseudo-labels vs. Ground-Trun (GT) labels.
Model
Setting
NQ
TriviaQA
Hellaswag
GSM8k
MATH
MBPP
HumanEval
Avg
DAAR w/ Pscudo
21108
64.55
74.88
$4,80
15.30
4.70
37,50
38.83
1lama3.1-8B
DAAR w/ GT Diff
22.54
65.52
73.43
$3,80
14.35
36.50
38.65
+2.45
+0.97
-1.45
-1.00
-0.95
-0.30
-1.00
-0.18
DAAR w/ Pseudo
16.88
$7.58
73.03
75.40
38.10
$2.00
64.94
$3.99
Qwen2-7B
DAAR w/ GT Diff'
18.75
58.35
72.02
73.40
35.75
$1.50
64.01
53.40
+..87
+0.77
-1.01
-2.00
-2.35
-0.50
-0.93
-0.59
DAAR Pseudo
15.83
58.65
72.48
80.20
16.70
64.20
68.29
53.76
Qwen2.5-7B
DAAR w/ GT
16.04
58.75
71.87
79.40
16.30
64.25
67.76
53.48
Diff
+0.21
+0.10
-0.67
-0.80
-0.40
+0.05
-0.53
-0.28
validate our model-aware design choices that relying on external ground-truth labels can degrade performance by up to 0.59 points in Table 4 and Appendix F.4 Furthermore, we demonstrate high end-to-end robustness, with independent runs yielding inter- centroid similarities of >0.98 and final performance standard deviation of only 0.08 in Appendix F.5
Robustness and Stability

---

5.3 Ablation Studies and Discussions
Llandd
Ablation Studies on Centroid Construction As shown in Fig and Appendix [.I] DAAR can generate with clear distinctions. Notably, the diversity is consistently most pronounced between common sense, reasoning, and coding domains across model architectures and parameters, showing that despite differences in model architecture across LLMs, their discriminability between these domains exhibit remarkable similarity.
8.9355
0.9980
0.000
0L3235
9.5
samples
3.50
8.505
Mah
0.5048
1,990
8.007
0.500
8.4130
1.0000
Codlag
0.50
Figure 3: Semantic cosine similarity across differ- ent domains for generated samples of size 10.
Impacts of Hyper-Parameters In Appendix 6.2.Apppedii G.7 we conduct a series of ablation studies, including (1) selection of layer: the discrimination accuracy derived from layer 1-10 fluctuates in 91.2-93.6 %: (2) the number of seed: the similarity between centroids remains highly consistent with variance ranging from 5.4E-7 to 1.8E-5; (3) the number of augmented data: the mean similarity of centroids generated from sizes of 10 and 30 is 0.983 and 0.981 on Qwen2.5 and Llama3.1 respectively; (4) the size of sliding window & similarity threshold: the impact of different hyper- parameters on centroid generation is minimal, ensuring the subsequent training stability of DAAR; (5) diversity threshold, where varying thresholds minimally affect centroid-guided clustering (with distinet generation attempt frequencies across thresholds) and empirically balanced thresholds are determined for different domains; (6) generalizability across model scales, where DAAR shows consistent improvements in representative scenario on both Llama3,2-3B and Qwen2.5-14B models.
Cost-Efficienc and Flexibility As detailed in Appendix G.9 our method demonstrates significant computational efficiency compared to baselines that rely on GPT-based evaluators or full-LLM inference. By operating on frozen hidden layers and generating regression scores instead of full vocabulary, our approach achieves 70% lower GPU usage and 2.5x faster inference.
6 Conclusion, Limitation & Future Works
In this paper; we propose new approach to fine-tuning LLMs with data that lacks clear domain labels, using diversity as a guiding principle. By measuring semantic diversity with entropy, we employ self-reward mechanism built upon the given LLM,, identifying data that best fits the model's natural tendencies in terms of its underlying knowledge distribution. Our experiments with various SOTA LLMs show notable superiority of the method over competitive baselines, highlighting the potential of data diversity to enhance model overall performance.
The implementation of DAAR has limitations that can be addressed further, such as the customization of the selection ratios to support broader application in real real-world scenarios. Besides, DAAR has potential to efficiently adjust diversity measures, benefiting LLMs in self-evolving towards artificial general intelligence in dynamic environments 35
Acknowledgment
This research is supported by Key-Area Research and Development Program of Guangdong Province (Granted No. 2024B111106000 Economic Development (Marine Economic Development) in Six Major Marine Industrics (Granted No. GDNRC12024J52), and in part by the New Generation Artificial Meelligence-Nationa Science and Technology Major Project (Granted No. 20252D0123003).
Guangdong Provincial Special Funds for Promoting High Quality
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Appendix
Table of Contents
A Notation
24
Implementation Details of DAAR
24
B.1
Hyper-Parameters/
24
B.2
Implementation of limbedding
24
B.3
The Phase of Model-Aware Training Data Generation
25
Supplementary Theoretical Analysis
26
Derivation Proposition 3.2
26
Supplementary Analysis of the Theoretical Foundation
27
Experimental Setup Details
27
D.I Construction of Data Pool
27
D.2 Benchmarks
27
D.3 Training and Evaluation Details
28
E Details of Baselines
29
Implementation of Baselines
Visualization of Baseline's Selected Data
Comprehensive Experiments
33
Performance on Comprchensive Benchmark MMLU
................................
Validation on Qwen3-8B
34
F3
Customized Data Selection Capability of DAAR
35
Robustness to Labeling Schemes and Embedding Representations
36
F5
Analysis of End-to-End Stability
37
F.6
Rationale for Entropy Diversity the Reward Signal
38
Complete Ablation Studies and Discussion
38
G.I
Similarity in Generated Domains' Centroid
................................
38
G.2
DAAR Layer Selection Protocol
................................
G.3
Ablation of the Number of Seed Samples
40
G.4
Ablation of the Number of Diversity Augmentation Data
40
G.5
Ablation of the Size of Sliding Window
G.6
Ablation of the Diversity Threshold
41
Ablation of Mode Scales
41
G.8
Ablation of Downstream Sample Injection in Seed Generation
42
G.9
Cost-Eifiiiencyy and Flexibility
43
G. 10 Stability of DAAR
43
23

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H
Comprehensive Visualization and Experimental Results
44
H.I
Visualization of Embeddings Llama3. Qwwnn-77 & Qwen2.5-7B
44
H.2
Visualization of Inter- & Intra-Diversity Distribution Data
44
Comprehensive Training Dynamics
45
H.4 4
Complete Validation Results of Inter- Diversity and Intra Diver-ii
46
H.5
Complete Results of DAAR with Baselines
47
A
Notation
For ease of reading and reference, we present the mathematical symbols used in this paper in Table
Table 5: Symbol Notation
Symbol
Description
Symbol
Description
D
Composite dataset
DR
Distinct domain dataset
(K)
Raw i-th data sample in domain-k
(k)
Embedded i-th data sample in domain-k:
N
Number Dx data samples
Ce
Domain centroid of le
Cmner
Sample-level cross woss-domain similarity
4 Pinter
Global inter-diversity
Onnra
Sample similarity to its domain centroid
T (k)
Domain-level variance of domain-k Data distributions
inma
Loss function
p.
Sk
Generated centroids' seed sample Embedding layer of L.M
(
Generated centroid sample at i-th round
Mehd
M
Hidden layer of LLM
D grobe
DAAR training set
similarity threshold Pseudo-label 2;
Ti
sample D probe
Vi
A MLP--aaed domain predictor
Vlivv
MLP--based entropy predictor
Domain predicted probability by Vamm
(x)
Predictive entropy by Vdom
Ldom
Cross-entropy loss t'dom
Laiv
MSE loss tlacm
B Implementation Details of DAAR
B.1 Hyper-Parameters
For the generation of synthetic data, we utilize the model.generate function from the PyTorch library. Key parameters included setting max-new-tokens to 2048 to control the length of the output, enabling do-sample to True to allow sampling, and configuring top-p to 0.95 and temperature to 0.9 to ensure diversity in the generated content. During the content extraction phase, we employ regular expressions to efficiently extract and structure the desired information.
For implementation details of DARR's hyper-parameters, we set the number of seed samples S as (ablation Appendix G.3). the number of anchors in sliding window (ablation Appendix G.5h. the similarity threshold as 0.9 for Mathematics and 0.85 for others (ablation in Appendix G.6p. the terminated iteration as 30 (ablation in Appendix G.4), the hidden layer M(ā) as layer-3 (ablation in Appendix G.2)
B.2 Implementation of Embedding
Given the Alpaca-based 43 data format employed in our study, we concatenate the 'instruction', 'in- put', and 'output" components of each data sample to capture domain-awan semantic representations. These concatenated sequences are then fed into the LLM, where we compute the average of all token embeddings extracted from the embedding layer to derive the semantie vector characterizing each sample.
The embedding layer is deliberately selected due to its shallow architectural position: (1) it preserves precise semantie information capture through raw input representations, and (2) incurs reduced computational overhead compared to deeper layers. As evidenced by the visualization in Fig. 13

---

(Appendix G.2]. this approach demonstrates robust domain discrimination capabilitiess across different LLM layers, thereby validating the robustness of our methodology.
B.3 The Phase of Model-Aware Training Data Generation
Seed Generation This phase aims to provide zero-shot LLM-generated seed data that reflects how LLMs inherently perceive the characteristics of domain-specific data. We employ the LLM itself to generate concise domain descriptions across diverse fields illustrated in Prompt [ and the prompt shown in Prompt 2 Due to the difficulty of pre-trained LLMs in providing accurate and coherent responses, we utilize their corresponding Instruct versions for centroid data generation. Specifically, we apply Llama3. 1-8B-Instruct for L 1-8B, Qwen2-7B-Instee for Qwen2-7B, and Qwen2.5-7B B-sstructtt for Qwen2.5-7B.
Notably, these descriptions representative examples compatible with our experimental scenarios. Users retain the flexibility to customize target domain specifications according specific requirements. The associated stability analysis regarding this design choice will be elaborated in Appendix G.10
not required be optimal prescriptive, rather, they serve
Diversity Augmentation While seed data effectively captures the intrinsic domain knowledge of LLMs, its limited quantity and the constrained diversity of single-prompt generation methods necessitate enhancement. We address these limitations through two complementary strategies including a sliding window mechanism and a rule-based filter. The implementation details are formalized Prompt and Eq.
Domain Aware Clustering During reward model training data clustering, we rigorously curate subset of 5,000 entries that ceterruttio--maachhe to the fine-tuning dataset while separate from
Prompt 1: Domain's Description
Common Sense:
Common sense generally includes a knowledge-baid based question and its corresponding answer, without reasoning.
Reasoning involves the ability to think logically about situation or problem, to draw conclusions from available information, and to apply knowledge in new situations.
Reasoning:
Mathematical skills include the ability perform calculations, understand mathematical concepts, solve hard and professional math problems, and apply mathematical
Mathematics:
reasoning.
Design and generate specific code programs, or apply algorithms and data structures, with code generation in the Output.
Coding:
Prompt 2: Seed Generation Prompt
You Al model with expertise in domain: (Prompt 1}
Here's brief description of this
Generate 5 different instruction pairs related to this field with various lengths. Maintain the index format: Instruction [] 5].
The response should include three parts:
Instruction: clear command or question that can be understood by the assistant.
Input: Any information provided to help it understand the instruction. If there is no need to generate, just keep it empty.
Output: The expected answer or action.
Keep the generated content focused on [selected_dommin)) And do not involve (unse- bcted_domaing related knowledge.
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Prompt 3: Training Data Diversity Augmentation
You are an Al model with expertise in poglected_domaiing Here's s brief description of this domain: Prompt !
Generate only an instruction pair related to this field. The response should include three parts:
Instruction: A clear command or question that can be understood by the assistant.
Input: Any information provided to help it understand the instruction. If there is need generate, just keep empty.
Output: The expected answer action.
Keep the generated content focused on [ebected_domain). Do not involve {unse-
J related knowledge.
Note that you should generate content strongly unrelated and different to these examples ensure diversity in the generated output:
Counterexample: (
The format of the generated content should be: Instruction:
[]. Input: O. Output: []-
C Supplementary Theoretical Analysis
This appendix provides additional details on the theoretical foundation of our work, discussed in Section 3.4 We first present the full derivation of the importance weight decomposition (Proposi-
tion 3.2 and then offer an analysis justifying our entropy-base -ased selection strategy.
C.1 Derivation of Proposition 3.2
We derive the density ratio by systematically expanding and substituting terms:
(xx)
Σ -= a(c = k)/(x(c= k)
(10)
pxx)
x(x)
Expand g(x) via the law of total probability over domains.
Σ -= g(c k))(x((c k)
(11)
p(x)
Apply Assumption 3.1 (q(x(== = k)) = p(x|c k)) to unify domain-conditions densities.
Ek
g(e k-) p(c=()
p(c=k)
(12)
p(x)
Express p(x|c k)) via Bayes' rule inversion: p(x|c = =k)
p(omk/x)p(s))
p(c=k)
K q(c = k)
p(x)
plc k)) plc k|x))
(13)
p(x)
k=
Factor out p(x) from the numerator and the denominator.
g k)
plc p(c k(x)
(14)
A
Define domain proportion ratio A :=
g(c=k) p(c=kj
This demonstrates that the density ratio decomposes linearly into domain-specific components
weighted by their proportion shifts (Ax) and posterior probabilities (p(c k|x)).
26

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C.2 Supplementary Analysis of the Theoretical Foundation
Our theoretical framework motivates a data selection strategy that privileges high-entropy samples. Here, we theoretically analyze why this is not merely a heuristic to move away from known suboptimal point, but rather principled approach to minimize approximation error.
Approximation Error of Deterministic Assignment As shown in Section 3.4 a simplified selection strategy might rely on deterministic domain assignment, where only the most likely domain k- (x) = arg max p(c = k|z) is considered. This reduces the true importance weight
ur(z) = Σ >ap(e- k/x) to approximation Wappeox (x) (x) We analyze the squared emror of this approximation, Err(x) (w(x) Wapprox (x))²,
Proposition C.1. The squared approximation error Err(x) can measured by:
Err(x)=
Σ (x)
- -x--x-(o)) p(c= - ]|1x)
(15)
Implication for Data Selection This proposition reveals that the approximation error is direct function the probability mass distributed across non-dominant domains. The error is zero only 1, which corresponds to conditional entropy, HCC| X x) O. Conversely, the error is maximized precisely when the probability is spread across multiple domains the very definition of high predictive entropy.
p(c = k (1r)[x:)
Therefore, our strategy of selecting high-entropy samples is principled approach to preferentially select samples where the deterministic approximation is most erroneous. These are exactly the samples for which the full diversity information encoded in p(c[æ) is most critical for an accurate estimation of the true importance weight w(x). Our method, DAAR, employs dedicated domain discrimination probe to model p(c[z) and uses its predictive entropy as a computationally feasible proxy to identify these high-error, nigh-value samples for training.
D Experimental Setup Details
D.1 Construction of Data Pool
To investigate data selection from large data pools and its impact on the mixture of downstream tasks, we construct a data pool with distinct properties to mimic practical settings. We select the following datasets to evaluate specific abilities:
Common Sense: Dolly-15K [15] with 15,011 samples, open source dataset of instruction-
following records generated by thousands Databricks employees in several of the behavioral categories.
Reasoning: Cot-en 13 with 74,771 samples, is created by formatting and combining nine CoT datasets released by FLAN.
Mathematics: Math-Instruet (56) with 262,039 samples, is compiled from 13 math rationale datasets, six of which are newly curated by this work. uniquely ensures extensive coverage of diverse mathematical fields.
Coding: Code-Alpaca 66] with 20,016 samples, is constructed from real-world code examples, providing rich set of tasks designed to guide models in generating accurate and functional code.
Each dataset was initially filtered and randomly reduced 10,000 entries, resulting in a combined data pool of 40,000 entries. Specifically, for the Math-Instruct dataset, due to its inclusion of CoT and certain coding capabilities, we extract highly mathematics-related subset and use regular expressions to filter out the coding-related content (including 'program', 'python', 'def", 'import', "print', 'return'), ) ensuring it remains within the domain of mathematics.
D.2 Benchmarks
To evaluate the models' true capabilities and performance across different domains, we follow the approach of major open-source LLMs (c.g., the Llama3 series [18 and Qwen2 series (53]) and select
27

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the following widely used evaluation sets. All evaluations were conducted on the OpenCompass platform
Common Sense: NQ (28 and TriviaQA 26).. which cover factual knowledge-based questions of varying difficulty.
Reasoning: HellaSwag ability.
57 which effectively evaluates the model'ss comprehensive reasoning
Mathematics: GSM8K 14 and MATH 24 benchmarks, which encompass problems ranging
from elementary competition-lewe level difficulty.
Coding: MBPP and HumanEval [T], which include evaluations basic coding abilities in Python. We use the average of various metrics to demonstrate the models' overall performance across different domains.
Considering the numerous evaluation tasks, utilizing the complete evaluation set would result in significant time expenditure. To accelerate the evaluation process while maintaining fairness and accuracy, we randomly tailor the original evaluation sets into evaluation subsets, as detailed in Table 6 All experiments were conducted using this consistent setup ensure the fairness of the experiments.
Table 6: Number of samples in various evaluation benchmarks' datasets.
Common Sense
Reasoning
Mathematics
Coding
Number of Samples
NQ
Triviaqa
Hellaswag
GSM8K
MATH
MBPP
HumanEval
Original
3,610
8,837
10,042
1,319
5,000
974
164
Utilized
3,610
5,000
10,042
500
1,000
500
164
D.3 Training and Evaluation Details
Platform We implement our approaches using PyTorch [36] v2.4. 1, coupled with PEFT v0. 12.0 and the Transformers library [47 v4.45.2. Experiments conducted on computing platform equipped with four NVIDIA A100 GPUs (40GB), with pre-trained LLMs loaded as 16-bit floating point numbers. The specifie data-model development processes completed in Data-Juicer Sandbox [,, via integration with the ms-swift [6]] training repository, and the OpenCompass [6] evaluation repository.
Training Details In our experimental setup, we employ Low-Rank Adaptation (LoRA) 25
adapters for the fine-tuning process, utilizing LoRA-rank of 8 and a LoRA-alpha of 16. The learning rate was consistently maintained at 10-5 across experiments to ensure uniformity in training dynamics. We utilize a batch size of 4 and set the maximum sequence length to 2048 tokens to accommodate the model's capacity. To optimize the training process, a warmup ratio of 0.05 was applied, and validation ratio of 0.03 epoch, balancing computational efficiency with the need for effective model adaptation. Following some effective instruction-tur -uninn work [62 34. set the size of our subset 8,000 entries, which constitutes 20% of the data pool.
used. The training was conducted over single
Following the guidelines provided by OpenCompass [16. we adhered to the default settings for our evaluation process. We select the hf-type as base and utilize a batch size of 16 to ensure efficient processing. For most tasks, we employ the gen mode, while for the Hellaswag task, we opt for the ppl mode to better assess perplexity.
Evaluation Details
"napss//opencompassoorgggo
28

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E Details of Baselines
E.1
Implementation of Basclines
We select the following representative methods and works related to data selection our baselines to evaluate their performance in the context a mixture of downstream tasks.
RANDOM SELECTION(RANT) A random selection of 8,000 data samples from the data pool was made, which to some extent reflects the distribution characteristics of the original data pool.
INSTRUCTION LENGTH (IL) The length of the instruction can be considered a measure input complex data is beneficial for enhancing model capabilities. Therefore, we select a subset of 8,000 entries with the maximum number of words (based on spaces) in the concatenation of Instruction and Input as part of the filtering process.
complexity. It is widely believed [5] 660 that
Using prompts to directly score annotate the quality of the data leverages the powerful cognitive abilities of LLMs for evaluation and selection. Based on the original work, we use the GPT-3.5-Turbo API to score the data with the following prompt:
ALPAGASUS [O]
Prompt 4: Implementation of ALPAGASUS
System Prompt:
We would like to request your feedback on the performance of assistant in response the instruction and the given input displayed following.
Instruction: [Instruction]
Input: [Input]
Response:
[Response]
User Prompt:
Please rate according the accuracy of the response to the instruction and the input. Each assistant receives score on a scale of ( to 5, where higher score indicates higher level of accuracy. The generated scores can be precise decimal points, not just in increments of 0.5. Please first output single line containing the value indicating the scores. In the subsequent line, please provide comprehensive explanation of your evaluation, avoiding any potential bias.
The distribution of direct ratings for the 40,000 data pool shown in Fig. Although the original paper's prompts were strictly followed and efforts were made to minimize potential bias, most scores still clustered around 5. Since require uniform selection 8,000 data samples, randomly select the subset with rating of to serve as the baseline data.
Score Distribution
20000
15000
Figure 4: The distribution of the score by ALPAGASUS.
29

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INSTAG [34 first utilizes ChatGPT to tag the samples based on semantics and intentions, then trains LLaMA-based tagger on the ChatGPT tags to tag data. They use the number of tags as a proxy for complexity. We directly use ChatGPT-33.5TTmme the original paper, the prompt as follows.
tagger to achieve better performance. Following
Prompt 5: Implementation of INSTAG COMPLEXITY
System Prompt:
You are a tagging system that provides useful tags for instruction intentions to distinguish instructions for helpful AI assistant. Below is an instruction:
[begin]
[Instruction + Input]
[end]
User Prompt:
Please provide coarse coarse-grained tags, such as "Spelling and Grammar Check" and "Cosplay", to identify main intentions of above instruction. Your answer should be list including titles of tags and brief explanation of each tag. Your response have to strictly follow this JSON format: ["tag": str, "explanation": str]. Please response in English.
A total of 19,585 tags were assigned across 40,000 data samples, with the distribution shown below. Subsequently, based on the procedures outlined in the original text, tags were deduplicated as follows: 1) filter out long-tail tags that appear fewer than times in the entire annotated dataset, and 2) transform all tags to lowercase to mitigate the influence of capitalization.
34000
10200
8200
4200
Number ofTage
Figure 5: The distribution of the tags by INSTAG.
INSTAG COMPLEXITY (INSTAG-C) To reduce redundancy, apply threshold of a 5. resulting in a set 1,948 valid tags. Following the definition of Complexity, we select the top 8,000 entries with the highest tag counts. Specifically, there are 8,211 entries with more than three tags, so we include all records with more than four tags and randomly supplement from those with exactly four tags until reaching total of 8,000 entries.
reduce redundancy. The algorithm employed involves sorting all data in descending order based on the number of tags, and prioritizing records with more tags. To ensure dataset diversity, a tag only added to the final dataset if it increases the overall size of the tag set. This approach captures a broader range of unique tags, thereby enhancing the diversity and representativeness of the dataset.
INSTAG DIVERSITY (INSTAG-D): D): For Diversity, we use a
SUPERFILTER 29 introduces a method that astonishingly utilizes a small GPT2 model to success- fully filter out the high-quality subset from the existing GPT4-generated instruction tuning dataset. The core concept the instruction-folloiinn difficulty (IFD) score. By meticulously following this methodology, utilize GPT-2 to select 8,000 data samples.
30

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DETTA [33] is an open-sources project designed to facilitate Automatic Data Selection for instruction tuning LLMs. It delves into the relationships between data complexity, quality, and diversity, and develops series of methodologies. Specifically, we utilize it as the following three baselines:
Enhances instruction complexity by evolving examples with techniques like adding constraints. ChatGPT ranks these evolved samples for complexity, and the scores train LLaMA-1-7B model to predict complexity in new instructions, refining complexity assessment. We utilize its LLaMA-1-78
DETTA COMPLEXITY (DEITA-C);
complexity-sen -scorrr to evaluate the data pool and select the top 20% of them to reach 8,000 entries.
DEITA QUALITY (DEITA-Q): Enhances response quality by prompting ChatGPT to iteratively improve helpfulness, relevance, depth, creativity, and detail. After five iterations, ChatGPT ranks and scores the responses, providing nuanced quality distinctions. These scores train an LLaMA-1 7B model to predict quality scores for new instruction response pairs. We utilize its LLaMA-1 1- 7B-based quality scorer to evaluate the data pool and select the top 20% of them to reach 8,000 entries.
mesprontion-responee
DEITA DEITA (DEITA-D): Data-Efficient Instruction Tuning for Alignment, selects data by combining complexity and quality into an evol score, prioritizing higher scores. It uses the REPR FILTER to iteratively add samples, ensuring diversity and avoiding redundancy, resulting in balanced dataset of complexity, quality, and diversity. Following its methodology, we gain 8,000 entries as a baseline.
E.2
Visualization of Baseline's Selected Data
data samples through Llama3. 1-8B''ss. Qwen2-7B's and Qwen2.5-7B's embedding layer and visualize their distributions via 1-SNE dimensionality reduction in Fig- 6 Fig. 7 and Fig. g respectively. This visualization provides intuitive insights into how different data selection strategies handle domain-mixed data. Three key observations and conjectures emerge:
We project all
Certain methods (particularly INSTRUCTION LENGTH, DEITA-C, and DEITA-Q) demonstrate pronounced distributional skew toward coding-doman samples, which may partially explain their suboptimal HumanEval performance shown in Table 31
The domain-agnostic nature of baseline approaches reveals fundamental limitations in preserving original data distributions when processing unnpei-enspeeiiieed samples, as evidenced by the visualization.
Although distributional shifts are evident, the absence of commensurate performance deterioration across all methods empirically validates our theoretical framework (Section B.4. which establishes connections between data distribution shift.
Bandom
Instruction
Volse
Figure 6: L-SNE visualization of data samples selected by different baselines using Llama3. 10mma3.1880 1-B em- beddings. While original labels were removed during training, we preserve them for interpretabillity
31

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bolagc
belay
Sase Siter
Figure 7: t-SNE visualization of data samples selected by different baselines using Qwen2-7B em- beddings. While original labels were removed during training, we preserve them for interpretability.
Vellg.
SaserWiter
Delia O
Figure 8: t-SNE visualization of data samples selected by different baselines using Qwen2.5-7B beddings. While original labels were removed during training, we preserve them for interpretability.
32

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Comprehensive Experiments
F.1 Performance Comprehensive Benchmark MMLU
The benchmarks selected in Section 3.1 are specifically tailored to correspond with the domain- specific capabilities of the data sources. To comprehensively evaluate the performance of DAAR across broader assessment metrics and more extensive benchmarking frameworks, we adopted MMLU out-of-distribution (OOD) evaluation protocol, detailed description
MMLU is benchmark designed to evaluate the multitask capabilities of language models across diverse subjects, covering 57 tasks spanning topies with questions ranging from elementary to professional levels.
Table 7: Evaluation results of Qwen2-7B and Qwen2.5-7B on MMLU.
Models
Methods
Humanities
STEM
Social Science
Other
MMLU-AVG
RAw
38.58
25.77
24.94
27.82
28.98
RANDOM
70.02
58.54
80.00
72.26
68.81
INSTRUCTION LEN
71.34
58.09
79.77
70.71
68.55
ALPAGASUS
56.55
65.54
59.34
INSTAG-C
34
70.28
58.69
79.92
71.17
68.65
Qwen2-7B
INSTAG-D
67.87
58.35
79.82
71.61
68.07
SUPERFILTER
52.55
49.16
60.01
54.27
DEITA-C
33
68.05
58.53
80.12
70.97
68.08
DEITA-D
33
67.11
58.22
79.17
72.13
67.83
DEITA-Q
56.79
52.82
69.01
63.06
59.47
DAAR (Ours)
70.49
59.94
72.74
69.42
Raw
73.41
72.79
58.46
61.72
RANDOM
75.40
64.47
81.46
72.71
72.42
INSTRUCTION LEN
75.08
63.74
81.40
72.96
72.15
ALPAGASUS 110
75.39
64.85
81.73
73.13
72.70
INSTAG-C
34
75.26
64.35
81.64
73.03
72.46
Qwen2.5-7B
INSTAG-D
74,83
65.05
81488
73.16
72.59
SUPERFILTER
75.24
66.34
82.19
73.99
73.45
DEITA-C
33
75.76
64.18
72.83
72.46
DEITA-D
33
75.27
65.60
81.55
72.99
72.85
DEITA-Q
33
75.81
64.14
81.41
73.65
72.61
DAAR (Ours)
74.91
65.84
81.85
73.68
73.07
As demonstrated Table 7 despite not being explicitly optimized for broader capabilities during its design phase, DAAR still demonstrates competitive performance in comprehensive capability assessments. The method achieved the highest score on Qwen2-7B, surpassing the second peacce place Random selection by 0.61 accuracy points. On Qwen2.5-7BB it exhibited performance closely following SuperFilter, thereby confirming the generalization potential of DAAR to a certain extent.
Notably, 3lama3.1-81 was excluded from reference comparisons due to significant result fluctuations observed during Opencompass evaluations (as shown in Table that the results range from 0.04 to 42.52). We further identified inconsistent failures in model prediction generation during the evaluation process, which compromised the reliability of performance measurement. These implementation challenges prevented valid comparative analysis with Llama3.1 1-8B in our experiments.
Table 8: Invalid evaluation results of Llama3.1-88 1-8B on MMLU.
Models
Methods
Humanities
STEM
Social Science
Other
MMLU-AVG
RAW RANDOM
0.02
0.01
0.08
0.07
0.04
30.13
15.34
30.73
27.51
24.73
INSTRUCTION LEN
23.38
11.65
20.43
18.26
17.68
ALPAGASUS
10
35.99
23.28
36,80
34.37
31.56
INSTAG-C
25.87
12.58
33.73
23.71
22.60
Llama3.1-8B
INSTAG-D
42.50
19.44
47.70
37.19
34,70
SUPERF
29
11.61
9.40
12.11
11.71
11.00
DEITA-C
33
8.79
0.97
0.60
2.27
2.97
DEITA-D
29.76
43.21
DEITA-Q
33
33,99
23.36
26.31
24.27
26.61
DAAR (Ours)
45.18
20.94
46.47
34.20
34.87
33

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F.2 Validation on Qwen3-8B
As prevailing trend the development current LLMs, the RL-based (reinforcement learning) thinking model has demonstrated significant capabilities and potential (e.g. DeepSeek series [31], Llama4 series and Qwen3 series). To validate the efficacy of DAAR on the most up-to up-to-date and advanced LLMs, conducted series of verification experiments using Qwen3-8B It should be noted that, since Qwen3 does not adhere to conventional SFT paradigms, as well as the comprehensive support for training & evaluation of the Qwen3 series remains incomplete, the experiments presented in this section primarily serve as exploratory investigations. A comprehensive analysis data diversity across various training methodologies and LLM architecture will be reserved for future rescarch endeavors.
Observation Studies on Qwen3 Following the methodology delineated in Section 3 we employed Qwen3's embedding layer to process the identical data pool. The t-SNE visualization of Qwen3's embeddings (Fig. 9 demonstrates comparable domain discrimination capabilities.
(a) Total 40K Data
(b) Inter-Diversed
(c) Inter-Closed
(d) Intra-Diversed
(e) Mara-Clloedd
Figure 9: The t-SNE visualization of embeddings for data samples with different distributions on Qwen3-8B. (a) The data pool of all 40K samples, (b) Distribution of data farthest from other
domain centroids on Inter-Diversity, (c) Distribution of data closest other domain centroids on Inter-Diversity, (d) Distribution of data closest to its own domain centroid on onter-iiersity, (e) Distribution of data farthest from its own domain centroid Inter-Diversity.
Subsequently, we processed the curated dataset through inter-diversity and intra-diversity filters. followed by training Qwen3 on artificially constructed data distributions. As evidenced in Table 9 the experimental outcomes reveal that while the performance patterns diverge from those observed in Llama 3.1, Qwen2, and Qwen2.5, varying diversity levels demonstrably influence comprehensive model performance. Notably. the absolute value of the comprehensive performance of Qwen3 is even inferior to that of Qwen2.5 and Qwen2. We posit that this phenomenon is primarily due to the incomplete support of the evaluation platform OpenCompass (as of the submission date), where the distinctive thinking and reasoning capabilities of Qwen3 have not been fully leveraged. However, the relative comparison of different processes within the same data pool remains highly informative.
Table 9: Validation results of Inter-Diversity and Intra-Diversity Qwen3-8B across benchmarks.
Common Sense
Reasoning
Mathematics
Coding
Qwen3-8B
Avg
NQ
TriviaQA
Hellaswag
GSMSK
MATH
MBPP
HumanEval
RAW
9.64
59.90
71.56
85.60
23.60
22.40
73.17
49.41
RAND (8K)
12.24
59,22
71.71
83.00
25.2
12.6
73.17
48.16
Inter- Diversity (0-20)
12.94
60.28
71.79
86.20
23.80
11.80
75.61
48.92
Inter-Diversity (40-60)
12.71
59.76
71.71
83.20
28.40
14,40
73.78
49.14
Inter-Diversity (80-100)
11.36
59.52
71.61
83.00
25.40
14,20
68.29
47.63
Intra- Intra-Diversity (0-20)
12.33
59.92
71.58
84,00
28.40
19.40
71.34
49.57
Intra-Diversity (40-60)
13.10
59.42
71.64
82,40
21.00
13.20
72.56
47.62
Intra- Diversiity (80-100)
12.58
60.06
71.88
84.60
34.90
9.40
73.17
49,51
DAAR Training on Qwen3 Subsequently, we employed DAAR to conduct diversity probe training on Qwen3. Consistent with observations in other models, the two-stage MLP training framework demonstrated robust stability and convergence, shown in Fig. TO
34

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(0) 9eav Training Dytamics
(0) yay Training Dynamies
Trandag Stags
Trasiing Steps
Figure 10: Training loss and validation process of the two training stages of DAAR on Qwen3-8B, showing the model gradually converging.
Evaluation Results of DAAR with Baselines Following the identical experimental setup outlined in Appendix D we conducted experiments on Qwen3, with the results presented in Table [0] As demonstrated, DAAR achieved the top comprehensive score on Qwen3, surpassing all baselines by up to 4.7 %. Notably, its performance on the MATH benchmark was particularly outstanding, exceeding the average of baselines by 25.91% %. The comparative experiments affirm that DAAR maintains competitive effectiveness even on the SOTA LLM Qwen3-8B.
Table 10: Performance DAAR with baselines on Qwen3-8B across various benchmarks.
Common Sense
Reasoning Hellaswag
Mathematics
Coding
Qwen3-8B
Avg
NQ
TriviaQA
GSM8K
MATH
MBPP
HumanEval
Raw
9.64
59.90
71.56
85.60
23.60
22.40
73.17
49.41
RAND (8K)
12.24
59.22
71.71
83.00
25.20
12.60
73.17
INSTRUCTION LEN
11.66
59.56
71.67
83.80
26.30
18.20
73.17
49.19
ALPAGASUS
12.52
59.34
71.69
83.80
26.60
11.20
69.51
47.81
INSTA--C
11.91
59.62
71.55
83.00
26.40
14.60
73.78
48.69
INSTAG-D
11.99
59.48
71.59
87.20
25.30
13.60
71.34
SUPERFILTER 29
15.73
60.18
71.69
84.80
30,90
16.20
67.07
49,51
DEITA-C 33
12.55
59.62
71.78
83.60
28.60
13.20
77.44
49.54
DEITA-Q
12.88
59.72
71.64
85.40
32.90
13.00
73.78
DEITA-D
33
13.88
59.98
71,50
83.60
26.30
14.00
70.73
48.57
DAAR (Ours)
13.68
60.14
71.56
83.40
34.50
14.60
72.56
50.06
Customized Data Selection Capability of DAAR
distinctive characteristic of our method stems from its inherent capability to perform domain- specific data selection under domain-undeterminet scenario, thereby naturally supporting cus- tomized data curation. In practical scenarios beyond comprehensive LLM improvement, mission- critical applications (e.g., developing specialized LLM variants for coding mathematical reasoning) often demand focused enhancement on target capabilities. Conventional baseline selection approaches, which lack domain-awarn aware mechanisms, fundamentally preclude such fine- ine-grained control.
To validate this customized selection capability, we conduct validated experiment on Qwen2.5-7B. By strategically allocating higher selection ratios (50% to specific target domains while reducing others to 10%. while maintaining the total training corpus size at 8,000 instances, we investigate whether such curated data distribution induces domain-specinf performance gains.
As presented in Table I our analysis reveals that compared to the strongest baselines (RANDOM and original DaaR), customized DAAR achieves SOTA enhancement in focused domains, despite observing marginal performance degradation in non- nor-target domains that leads slightly inferior overall performance compared to the original DaaR. Interestingly, the performance on Reasoning- Major takes first place on Avg score, highlighting that reasoning capability may be the crucial factor of L.LMs. This validation promisingly confirms the operational feasibility of our customization paradigm and demonstrates DAAR unique superiority over existing baselines in enabling domain- prioritized LLM specialization.
35

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Table 11: Validation results of customized selected ratio on Qwen2.5-7B across benchmarks.
Common Sense
Reasoning
Mathematics
Coding
Qwen2.5-7B
Avg
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HumanEval
RAW
8.84
58.14 14
72.75
78.20
9.10
7.40
78.05
44.64
RAND (8K)
11.46
57.85
73.08
78.90
13.15
62.50
71.65
52.66
DAAR (Original)
15.83
58.65
72.48
80.20
16.70
64.20
68.29
53.76
Common-Major
17.56
59.58
72.51
77.80
12.85
62.10
67.53
$2.85
Reasoning-Major
16.56
58,22
74.62
77.30
17.20
63.40
66.42
S3.39
Math-Major
13.20
57.96
74.16
81.40
16.05
61.80
63.45
52.75
Coding-Major 10.76
57.02
72.78
78.20
12.80
65.20
73.22
52.85
F.4 Robustness to Labeling Schemes and Embedding Representations
A core principle of DAAR is its "model-aware" design, which relies the model's 's representa- tions (via its embedding layer) and internal data structure (via clustering-base based pseudo-labels) rather than external annotations models. This section presents two ablation studies that investigate the validity and effectiveness of these design choices.
Analysis 1: Model-Aware Pseudo-Labels vs. Ground-Trum -ruth Labels To analyze the impact of our clustering-basee pseudo-labels, we conducted an experiment where we replaced them with human- annotated, ground-truth (GT) domain labels. This allowed us to directly compare "model-aware" perspective against "human-aware aware" one within our framework.
Setup. We reran the entire DAAR pipeline, using the GT labels to train the domain discrimination probe and subsequently to compute the predictive entropy for data selection. All other components remained identical.
Observations.
Data Selection Divergence: The choice of labels significantly altered the data selection process. As shown in Table 12 the overlap between the data selected using pseudo-labels and GT labels was only around 83-87% %, indicating that they prioritize different data subsets.
Table 12: Overlap selected data between using pseudo-labels and ground-truth (GT) labels.
Model
Overlap (Pseudo vs. GT)
Llama3.1-2 1-8B
87.3%
Qwen2-7B
83. 33.1%
Qwen2.5-7B
84.9%
Final Performance: average end-task performance across all models, as detailed Table 13 This counter-intuitive result suggests that for fine-tuning, an LLM'' internal perception of data domains (captured by pseudo-labels) can be a more effective guide than human-defined categories. The GT labels may introduce biases that, while semantically correct to human, are suboptimal for optimizing the model's capabilities.
Critically, using GT labels led consistent, albeit small, decrease in
Internal vs. External Embedding We also investigated the choice of using the model's own embedding layer versus relying on powerful, external SOTA embedding models. While external models could provide an alternative "semantic space." we evaluated the trade-offs..
Analysis 2:
Setup. We processed our dataset using two SOTA external embedding models (GTE-Qwen2-7) and Qwen3-8B 113-88---mbedddngg and compared the time cost against using the native embedding layer of the base LLM (Qwen2-7B).
Observations. While the external models were also capable of producing separable domain clusters, they introduced prohibitive computational overhead. As shown in Table [1] using external models was 175x 192x slower and led to out-of-memory (OOM) errors on a 40GB GPU. This highlights the significant efficiency advantage of DAAR's internal approach.
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Table 13: Performance comparison: DAAR using model-aware pseudo-labels GT labels. The "Diff" row shows the performance change when switching from pseudo-labels to GT labels.
Model
Setting
n
triviaqa
hellaswag
gsmök
math
mbpp
humaneval
Avg
DAAR Pseudo
20.08
64.55
74.88
$4.80
15.30
4.70
37.50
38.83
Llama3.1-83
DAAR w/ GT Diff
22.54
65.52
73.43
53.80
14.35
4.40
36.50
38.65
+2.46
+0.97
-1.45
-1.00
-0.95
-0.30
-1.00
-0.18
DAAR w/ Pscudo
16.88
57.58
73.03
75.40
38.10
52.00
64.94
53.99
Qwen2-7B
DAAR w/ GT Diff
18.75
58.35
72.02
73.40
35.75
51.50
64.01
53,40
+1.87
+0.77
-1.01
-2.00
-2.35
-0.50
-0.93
-0.59
DAAR w/ Pscudo
15.83
58.65
72.48
80.20
16.70
64.20
68.29
53.76
Qwen2.5-7B
DAAR w/ GT Diff
16.04
58.75
71.87
79.40
16.30
64.25
67.76
53.48
+0.21
+0.10
-0.61
-0.80
-0.40
+0.05
-0.53
-0.28
Table 14: Time cost for extracting embeddings from a 40K dataset.
Model/LLayer
Time Cost (Relative Speed)
Qwen2-7B (Internal Embedding Layer)
9.23s (1x)
GTE-Qwen2-7B (External Model)
1662s (175x slower)
(External Model)
1774s (192x slower)
F55 Analysis of End-to-Enn Stability
Given that DAAR is a multi-stage pipeline, it important analyze its end-to-end stability and robustness against potential compounding errors. To this end, we conducted three fully independent, end-to-end experimental runs of our entire framework and evaluated the consistency at critical stages of the pipeline. We present results for Qwen2-7B as a representative case.
Stability of Centroid Generation The initial stage of our pipeline involves generating domain centroids. We measured the pairwise cosine similarities of the final centroid embeddings across the three independent runs. As shown in Table [5] the resulting centroids are remarkably consistent, with all similarity scores exceeding 0.98. This indicates that the foundational stage of our method is highly stable and is a sigmificant source of variance.
Table 15: Pairwise cosine similarity of domain centroids across three independent runs.
Domain
Sim(Run 1-2)
Sim(Run 1-3)
Sim(Run 2-3)
Common Sense
0.9912
0.9895
0.9921
Reasoning 0.9845
0,9911
0,9887
Mathematics
0.9880
0,9803
0.9854
Coding
0.9905
0.9853
0.9918
Stability of Final Data Selection We then examined whether minor variations the initial stages propagate to the data selection outcome. We calculated the overlap ratio of the top 20% (8,000) selected samples across the three runs. Table [6 shows an average overlap 96.4%, confirming that the final data selection is highly robust and largely deterministic, with minimal amplification of randomness.
Consistency of Final Performance Finally, the end-to-end stability of the framework is reflected in final benchmark performance. As reported in Table [7] the results across the three runs are highly consistent, with a minimal standard deviation of 0.08 in the average score. This provides strong empirical evidence that our framework robust and outcomes are reliable, without significant compounding error effects.
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Table 16: Overlap ratio of selected data subsets across three independent runs.
Metric
Overlap (Run 1-2)
Overlap (Run 1-3)
Overlap (Run 2-3)
Overlap Ratio
95.7%
97.3%
96. 1%
Table 17:
End-task performance across three independent runs on Qwen2-7B. Scores are reported with mean and standard deviation.
Run
nq
triviaqa
hellaswag
gsm8k
math
mbpp
humaneval
Avg
Run
17.92
56.78
72.91
75.00
39.60
51.40
64.80
54.06
Run 2
15.84
58.38
73.14
75.80
36.60
52.60
65.07
53.92
Run
15.18
57.96
72.99
76.70
38.80
51.40
65.24
54.04
Avg
16.31
57.71
73.01
75.83
38.33
51.80
65.04
54.01
Std. Dev.
(I.43)
(0.83)
(0.12)
(0.85)
(1.55)
(0.69)
(0.22)
(0.08)
F.6
Rationale for Entropy over Diversity as the Reward Signal
As discussed in Section the explicit diversity metric defined in Eq. (2) & (3) inherently depends on cross-sample relationships that cannot be captured through conventional sample-level training paradigms. To empirically validate this limitation, we conducted an ablation study using 500 representative samples. The inter-diversity scores were calculated using Eq. (2) and partitioned into ascending quartiles, each representing distinct diversity levels. A 5-layer MLP elassifier was subsequently trained with cross-entropy loss as a more tractable verification approach compared to regression. Experimental result (Fig. [T] demonstrates persistent convergence challenges, evidenced by consistently high training loss and subpar classification accuracy capped at 34 %. These findings substantiate our hypothesis that LLMs fail learn cross-sample characteristies, thereby necessitating entropy-based proxy metrics for effective reward formulation.
Vilidsiion Accurnry nver Stepe
valdile AccurES
1.50
152
2.33
0.3
4.58
1.48
3.586
Figure 11: Validation loss and accuracy directly use diversity instead of entropy reward signal.
G Complete Ablation Studies and Discussion
G.1
Similarity in Generated Domains' Centroid
To investigate whether there a distinct separation between different domains generated, we compute the cosine similarity of semantic centroids across different domains. The experimental results are shown in Fig 12 It is evident that, compared to variations within the same domain at different data quantities, there significant differences between different domains. This validates that this method of generating synthetic data can produce domaain-rprrssentatii data with clear distinction.
Notably, despite variations in model architecture and parameter count, the generated content consistently exhibits the greatest divergence between common sense, reasoning, and coding domains. Specifically, the discrepancy between common sense and coding, well reasoning and coding, is
38

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markedly pronounced. Conversely, the semantic difference between common sense and reasoning is relatively smaller. This pattern suggests that the models, although differing in complexity and size, exhibit varying sensitivity to different data types, highlighting their nuanced capability to distinguish between certain domain-specific characteristics while maintaining subtle distinctions in others.
Qwen2-7B
Lamm3311-B
1.00
6.9375
0.975
1,0000)
0.9090
0.35
Reasening-o 83988
1,0000
6.9068
0,950
Reasening -n 9099
1000
0.120
0.90
0.85
Mothemstica-G. 6eniiis---...00 9090
6. 9068
.0000
0.8876
0,900
Moshematice-- -0.2200 0 0.8120
10000 0. 79792
0.50
0.875
Codtigg 0,8301
6. 0.8000
0.8876
1,0000
0.830
Coding 0,7150 0 7100
0.7972
1,0000
0.75
Comsarta Seane
Roassning
Mathometicn
Candang
Copnta on Saeae
Reaanwing
Mulbrmation
Coding
0.70
Figure 12: Semantic cosine similarity across different domains for generated samples of size 10.
G.2 DAAR Layer Selection Protocol
We choose layer-3 the hidden layer attached to dadom. To determine appropriate layer for embedding DAAR into an LLM that balances performance and computational cost, we first evaluate the capacity of different layers for domain awareness, Using Qwen2-7B as an example, we conduct t-SNE visualizations of Layer-5, Layer-10, Layer-15, Layer-20, Layer-25, and the last hidden layer, based on the average token vectors, as shown Fig. 13
Figure 13: t-SNE visualization of mean token embeddings across Layer-5, Layer-10, Layer- 15, Layer-20, 2ayer and the last hidden layer of Qwen2-7B.
The observations demonstrate that LLMs maintain cross-dataset classification capabilities across all architectural depths. Considering the diminishing marginal utility of computational resources in deeper layers, we prioritize initial layers to optimize learning efficiency. The training dynamics across the first ten layers are visualized in Fig. 14 demonstrating consistent accuracy within the 91.2-93.6% % range, verifying that various layers can effectively support DAAR first-stage training.
Layers
Leven
Unve?
Leven'
Masiin Mad
Figure 14: Validation loss and accuracy over steps different layers.
Given that data clustering based on the embedding layer, a natural approach was to directly connect to the embedding layer for training. However, the training results showed persistently high training
39

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loss and a validation accuracy of only about 0.6 (shown in Fig. 15 indicating suboptimal learning performance. Furthermore, related studies indicate that LLMs can learn semantic understanding and perception in the early layers 45 consequently, we select Layer-3 for DAAR.
Training Dynamics of Poom
60-
Training Loss
Validation
5.0
4.
Training Steps
Figure 15: Training loss and validation process of Embedding Layer on Qwen2.5-7B.
G.3 Ablation of the Number of Seed Samples
To investigate the impact of the number of seed samples S( on domain centroid construction, we systematically selected 3, 5, and 10 as the number of seed samples while maintaining all other parameters at their default settings on Qwen2.5-7B. For each configuration, pairwise cosine similarity between domains was computed to assess whether significant discrepancies emerged across different seed sizes. Experimental results summarized in Table [8] demonstrate that similarities remain highly consistent across all domain pairs. Except for the common sense domain (with similarity approaching 0.9), varying seed sample counts do not yield substantial differences in the final centroids, with variance ranging from 5.4e-7 to 1.8e-5, demonstrating the stability of this hyperparameter.
Intuitively, we posit that excessively small seed sizes may compromise domain characterization due to generation randomness, while larger sizes risk introducing redundant patterns. We conjecture that the relatively lower absolute similarity common sense domains stems from inherent sentence brevity, which increases vulnerability to lexical biases. However, this does not impair the anchoring effectiveness, as evidenced by the consistent performance across configurations.
Table 18: Semantic similarity between the number of seed samples among 3, and 10 across domains on Qwen2.5-7B.
Domains
Similarity of 3 &
Similarity of 3 & 10
Similarity of 5 & 10
Common Sense
0.8984
0.8913
0.9074
Reasoning
0.9713
0.9752
0.9815
Mathematics
0.9776
0.9761
0.9722
Coding
0.9775
0.9759
0.9760
G.4 Ablation of the Number of Diversity Augmentation Data
To assess the impact of the amount of generated data on the accuracy domain semantic centroids, we select quantities of 10 and 30 samples for generation. Subsequently, we calculate the semantic cosine similarity between these two sets, with results presented Table (using Qwen2.5-7B and Llama3. 1-8B as examples). The observed differences between varying data quantities were not significant, indicating that the generalization of the generated data is sufficient, and further increasing the data quantity does not significantly enhance the accuracy of the centroids.
40

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Table 19: Semantic similarity between generated samples size 10 and 30 across different domains.
Similarity of 10 & 30
Common Sense
Reasoning
Mathematics
Coding
Qwen2.5-7B
0.9686 0.9851
0,9866 0.9795
0.9919 0.9685
0.9881
L-ama3.1-8B
0.9895
G.S Ablation of the Size of Sliding Window
To investigate the impact of the sliding window size in diversity augmentation, we kept all other hyper-parameters constant, setting the sliding window size 1, and 5 examples, respectively, and compared the similarity between them. The experimental results on Qwen2.5-7B, presented in Table 20 indicate that different window sizes maintain high degree of similarity, suggesting that DAAR does not heavily depend on this hyperparameter choice. Considering the prompt length and stability, we opted for a window size of the implementation.
Table 20: Semantic similarity between the size of sliding window among 1, 3 and 5 across domains on Qwen2.5-7B.
Domains
Similarity of &
Similarity of 1 &
Similarity of &
Common Sense
0.9205
0,9094
0,9022
Reasoning
0.9746
0.9760
0..972
Mathematics
0.9736
0.9618
0.9847
Coding
0,9849
0.9647
0.9716
G.6 Ablation of the Diversity Threshold
The threshold r design needs satisfy objectives: (1) mitigate redundancy in LLM-ggnnrated outputs by preventing exact duplicates in synthetic data, and (2) ensure sufficient similarity among instances within the same domain embedding space. As illustrated in Table 21 we conduct an experiment using different similarity thresholds across various domains on Qwen2.5-7B. observing the number of attempts required for successful generation. The results indicate that distinct domains exhibit varying sensitivity to similarity metrics, with the number of attempts increasing sharply as the threshold decreases. Based on these observations, we empirically determined a threshold value of 0.9 for Mathematics and 0.85 for others as balanced compromise.
Table 21: Generation attempt frequencies for 10 seed samples across different domains and similarity levels on Qwen2.5-7B.
Domains
0.8
0.85
0.9
0.95
Common Sense
153
31
21
12
Reasoning
135
61
44
15
Mathematics
>> 1000
804
236
25
Coding
74
21
16
13
We further conducted ablation experiments by comparing the similarity of embedding centroids generated under different thresholds to systematically evaluate the impact of threshold variations on downstream performance. The results presented in Table demonstrate, with the exception of common sense data (similar to the results in Table (8), that varying thresholds do not significantly affect the role of these centroids initial points for clustering. We conjecture that lower thresholds ensure greater diversity within domain, whereas higher thresholds tend to result in repetitive data.
G.7 Ablation of Model Scales
To assess the generalizability of DAAR beyond the 7-8B parameter range, we conducted additional experiments on models of different scales: a smaller model, Llama3.2-3BB and a larger model, 14BB. Due to computational constraints, we performed targeted comparison of DAAR against two key baselines: Raw (using the original, unselected data) and Random (a strong baseline involving random data selection).
41

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Table 22: Semantic similarity between the similarity threshold among 0.85, 0.9, and 0.95 across
domains on Qwen2.5-7B
Domains
Similarity of 0.85 & 0.9
Similarity of 0.85 & 0.95
Similarity of 0.85 0.95
Common Sense
0.8869
0.8963
0,9502
Reasoning
0.9791
0,9785
0,9795
Mathematics
0.9730
0,9754
0,9703
Coding
0.9646
0,9740
0,9691
The results are presented in Table 23 On the larger Qwen2.5-14B model, DAAR achieves the highest average score (61 (61,54), outperforming the strong Random baseline. Similarly, on the smaller Llama3.2 2-3B model, DAAR (29.64) maintains consistent advantage over both Raw and Random baselines.
These findings provide evidence that the effectiveness of DAAR is not confined specific model size and generalizes to both smaller and larger language models.
Table 23: Performance comparison on Llama3.2 2-3B and Qwen2.5-14B. demonstrating the general-
ization capability of DAAR across different model scales.
Model
Method
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HvmanEval
Avg
Raw 10.89
66.56
76.86
86.00
19.70
5.40
78.66
49.15
Qwen2.5-14B
Random
20.06
65.80
76.76
86.40
36.90
64.20
75.46
60.80
DAAR
19.73
66.26
77.19
85.00
39.10
66.80
76.69
61.54
Raw
7.62
53.10
68.77
26.60
4.50
3.80
23.17
26.79
LLaMA3.2-3B
Random
16.03
53.56
68.46
28.70
6.15
4.65
29.12
29.52
DAAR
15.13
53.79
68.23
29.10
5.63
5.30
30.34
29.64
G.8 Ablation of Downstream Sample Injection Seed Generation
The seed generation process described in Section 4.J includes minor injection of downstream task samples. This component intended to provide an initial diversity signal to accelerate the subsequent augmentation phase. To rigorously evaluate its impact, present ablation study comparing standard method against a variant where this injection is completely removed.
It is important to note that in all settings, our experimental protocol maintains strict data partitioning. The downstream samples used for seeding, when present, are drawn from set entirely disjoint from the datasets used for final evaluation.
Our analysis focuses on three key aspects: the impact on the final centroid representations, the effect on end-task model performance, and the change in data generation efficiency.
Impact on Centroid Similarity We measured the cosine similarity between domain centroids generated with standard method (w/ injection) and the ablation setting (w/o injection). The results in Table 24 show that the centroids are nearly identical, with an average similarity score of 0.987. This indicates that the minor injection has a negligible impact on the final learned domain representations.
Table 24: Cosine similarity of domain centroids generated with and without downstream seed injection, evaluated on Qwen2-7B.
Domain
Similarity (w/ vs. w/o Injection)
Common Sense
0,9922
Reasoning
0,9865
Mathematics
0,9843
Coding
0,9878
Average
0.9877
42

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Impact on Final Performance As shown in Table 25 the end-task performance of models trained using data selected by DAAR is statistically indistinguissable between the two settings. This demonstrates that the effectiveness of our method is not dependent the seed injection.
Table 25: End-task performance comparison between DAAR with and without downstream seed injection. The results show statistically insignificant differences.
Model
Setting
nq
triviaqa
hellaswag
gsm8k
math
mbpp
humaneval
Avg
DaaR Inject
20.08
64.55
74.88
54.80
15.30
4.70
37.50
38.83
Llama3. 1-B-
DaaR w/o Inject
20.39
64.80
76.05
55.40
13.65
5.75
36.48
38.93
DaaR Inject
16.88
57.58
73.03
75.40
38.10
52.00
64,94
53.99
Qwen2-7B
DaaR w/o Inject
16.22
58.33
73.41
75.20
36.37
52.95
65.14
53.95
DaaR Inject 15.83
58.65
72.48
80.20
16.70
64.20
68.29
53.76
Qwen2.5-7B
DaaR w/o Inject
14.91
58.32
72.55
79.70
16.30
63.70
70.65
53.73
Impact on Generation Efficiency While not critical for performance, the injection significantly improves the efficiency of the diversity augmentation process. As detailed in Table 26 removing the initial seed diversity required approximately 4 times more generation attempts to meet the same diversity threshold (7). This confirms its functional role practical accelerator.
Table 26: Number of generation attempts required meet the diversity threshold during seed augmentation.
Domain
Attempts (w/ Injection)
Attempts (w/o Injection)
Common Sense
31
134
Reasoning Mathematics
248
236
819
Coding
105
G.9 Cost-Efficiency and Flexibility
Compared to baseline methods requiring GPT-based evaluators (ALPAGASUS, INSTAG) or full-LLM inference (DEITA), our approach achieves superior efficiency through data-model co-optimizations. Our method demonstrates computational efficiency through two key aspects enabled by the LLM's self-rewarding capability during dedicated data synthesis:
Our framework operates frozen embeddings extracted from layer 3 while truncating subsequent layers, which constitutes a significantly shallower architecture compared to the conventional 32- layer structure in 7B-scale LLMs. Taking Qwen2 as example, full model inference requires loading complete parameters alongside cache management components, consuming 18-24 GB GPU memory. In contrast, method accomplishes data filtering with merely 5-6 GB GPU memory footprint.
The lightweight 5-layer MLP probe module introduces only 76 million additional parameters. As regression model producing single scalar outputs per instance, it achieves substantial speed improvements over LLLM-inference-basedd approaches. Experimental results on 5,000 samples demonstrate this efficiency advantage: our method requires approximately 40 minutes for sample- level inference, whereas conventional LLM inference approaches demand nearly two hours.
G.10 Stability of DAAR
Our dual-MLP design of DAAR strategically separates entropy regression (second MLP) from neural -obsea measurement (first MLP), both showing stable convergence Fig While precise analysis of compounding errors remains a theoretical concern, our framework inherently mitigates these errors through these aspects: (1) Seed Generation: LLM--gnnrraedd descriptions exhibit minimal variation across iterations, and repeated seeding mitigates uncertainty. (2) Layer Selection: Semantic feature extraction across layers demonstrated effectively capture domain-specinf patterns, thereby establishing methodological robustness, detailed in Appendix G.2 (3) Clustering:
43

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Data seeding as initialization for K-means clustering, where minimal perturbation of initial points ensures stable training the first MLP. (4) Selection Strategy: Percentage-base based data selection prioritizing sample distribution robustness over fine-grained entropy value utilization.
H Comprehensive Visualization and Experimental Results
H.1 Visualization of Embeddings on Llama3.1-8B, Qwen2-7B & Qwen2.5-7B
We process concatenated data samples with "instruction" ++rriiooon"**ii"" "input ""inpu""* ""outuut" pairs through each LLM's embedding layer, computing mean token embeddings for visualization. We present the t-SNE visualization of data samples from Llama3.1-8 Qwen2-7B and Qwen2.5-7B with different distributions in Fig. 16, Fig. 17 and Fig. 18 is evident that, despite differences architecture or model, the method of filtering data through Inter-Diversin and Intra- Intra-Diversity is effective. Notably, although the embedding distributions of different models are not identical, they exhibit similar behavior, indicating that the representations learned by the embedding layers are comparable.
4IK Sempies
th) Handder Selected
Inteen Diversed
Inter-Cloend
Intra- Intra-Drerreedd
38 Intra-Clvrd
Figure 16: The t-SNE visualization of embeddings for data samples with different distributions on L-ama3.1-8B. (a) The data pool of all 40K samples, (b) Randomly selected subset, (c) Distribution of data farthest from other domain centroids on Inter-Diversity. (d) Distribution of data closest to other domain centroids on Inter- sivr-Diierrsty, (e) Distribution of data closest its own domain centroid on Inter-Diversie (f) Distribution of data farthest from its own domain centroid on Inter- Siier-Divrrstt..
40K Samples
(bi Rundom Selected
Diversed
Closed
Intra Closed
Figure 17: The t-SNE visualization of embeddings for data samples on Qwen2-7B.
SOK Samples
Ohd Bandom Selected
Diter-Divecsed
Closed
Dauro Diversed
JB Intra Closed
Figure 18: The t-SNE visualization of embeddings for data samples on Qwen2.5-7B.
H.2 Visualization of Inter- & Intra-Diversity Distribution Data
Using the Qwen2-7B model as an example, we construct data based on the Inter- Inver-Diversity and Intra- divar-Divrrsity distribution methods, selecting a batch of data every 20%. The visualization process is
44

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shown in Fig. 19 and Fig. 20 As seen in the figures, the data gradually transitions from domain dowrin--ware diverse domain- -wwaee-wware closed, indicating that our data construction method effectively controls the distribution of different data.
coee coercrment Docks
Figure 19: Data visualization (I-SNE) based on different Inter-Diverse distributions Qwen2-7B.
Figure 20: Data visualization (t-SNE) based on different Intra-Diversig distributions Qwen2-7B.
H.3 Comprehensive Training Dynamics
We present the training and validation dynamics for Llama3. 1-8B and Qwen2.5-7B, in Fig[2] can be observed that across different models, the training process of DAAR method consistently ensures gradual convergence, achieving high domain predictability and calibrated entropy fitting.
TTnnnin of 1lera221-1
Thinnay Dyseriocal Oane2.5-33
Figure 21: Training loss and validation process of the two training stages of DAAR on Llama3.1-88 and Qwen2.5-7B, showing the model gradually converging.
45

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H.4 Complete Validation Results of Inter-Diversity and Intra-Diversity
present the complete experimental results Llama3. 1-8BB. Qwen2-7B, and Qwen2.5-7B in
validation experiments in Tables 27] Tables 28 and Tables 29 respectively. It can be observed that
for any complete dataset, the conclusions from Section 3.3 remain valid, specifically that the peak distribution of results is uneven, with significant differences among them.
Table 27: Validation results of Inter-Diversig and Intra-Diversity on Llama3. 1-8B across benchmarks.
Common Sense
Reasoning
Mathematics
Coding
Llama3.1-88
Avg
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HvaanEval
RAW
14.13
65,90
74.62
54.80
7.90
5.00
28.66
35.86
FULL (40K)
21.92
65.11
73.62
51.70
7.60
4.10
36.50
37.22
RAND (8K)
21.99
64.83
74.72
55.70
14.50
5.10
24.09
37.27
Inter-Diversity (0-20)
19.28
65.79
74.44
54,90
6.50
4.30
35.06
37.18
Inter-Diversity (20-40)
21.91
65.48
74.54
52.50
16.65
5.70
26.53
37.62
Inter-Diversity (40-60)
23.70
65.14
74.86
56.40
17.15
5,00
24.40
38.09
Inter-Diversig (60-80)
22.42
64,52
74.76
55.10
14.60
7.40
31.10
38.56
lnter-Diversity (80-100)
23.76
64.43
75.20
56.40
15.05
4.50
33.54
38.98
Intra-Diversity (0-20)
22.08
65.08
75,00
54.70
16.20
4.40
33.54
38.71
Intra- Intra-Diversityy (20-40)
22.41
64.44
74.66
52,60
15.30
4.20
27.44
37.29
Intra- Intra-Diversity (40-60)
22.12
64.74
74.87
54.00
16.00
6.00
27.44
37,88
Intra- Intra-Diversity (60-80)
20.83
64,30
74.36
52.20
14.90
4.50
35.98
38.
Intra- intra-Diversity (80-100)
19.78
64.77
74.51
56.50
13.00
5.20
37.50
38.75
Table 28: Validation results of Inter-Diversity and Intra-Diversity on Qwen2-7B across benchmarks.
Common Sense
Reasoning
Mathematics
Coding
Qwen2-7B
Avg
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HumanFval
RAW
8.03
59.58
73.00
78.00
5.70
5.00
60.98
41.47 1.47
FULL (40K)
15.61
58.75
72.51
73.80
31.30
51.70
67.38
53.01
RAND (8K)
13.28
58.27
73.00
75.35
35.36
52.20
63.72
53.02
Inter-Diversit (0-20)
15.18
59.28
73,34
74.50
34.94
53.10
68.60
54.13
Inter- Inter-Diversity (20-40)
13.77
58.42
73.18
73.60
32.55
53.00
64.33
52.69
Inter-Diversity (40-60)
14.62
58.58
73.35
72.50
34.50
52.50
61.28
52.47
Inter-Diversity (60-80)
58.60
73.33
74.80
33.90
51.40
60.68
52.43
Inter-Diversity (80-100)
9.30
57.72
73.14
74.60
28.00
51.30
63.42
51.07
Intra Mira-Diversity (0-20)
12.64
58.54
73.35
75.10
8.75
51.10
61.59
48.72
Intra-Diversity (20-40)
14.17
58.78
73.10
74.10
29.20
52.10
63.41
52.12
Intra-Diversity (40-60)
15.24
58.57
73.12
74.70
32.50
51.80
64.02
52.85
Intra-Diversity (60-80)
14.02
57.40
73.06
75.20
32.20
53.50
66.77
53.16
Intra-Diversity (80-100)
11.91
57.88
73.29
75.00
36.05
52.50
66.16
53.25
Table 29; Validation results of Inter- Sier--iverssity and Intra-Diversity Qwen2.5-7B across benchmarks.
Common Sense
Reasoning
Mathematies
Coding
Qwen2.5-7B
Avg
NQ
TriviaQA
Hellaswag
GSM8K
MATH
MBPP
HumanEval
RAW
58.14
72.75
78.20
9.10
7.40
78.05
44.64
FULL (40K)
58.60
72.28
76.80
13.60
62.80
71.04
52.57
(8K)
11.46
57.85
73.08
78.90
13.15
62.50
71.65
52.65
Inter- Divveriiyyy (0-20)
13.23
58.15
73.27
78.70
11.45
62.30
69.21
$2.33
Inter-Diversity (20-40)
10.81
58.11
73.02
77.90
16.95
62.30
68.29
52.48
Inter-Diversity (40-60)
10.75
57.89
72.90
73.30
26.70
62.80
69.51
53.41
iier-Diverssty (60-80)
$8.19
73.10
78.40
17.05
62.80
71.95
53.13
Inter-Diversity (80-100)
10.00
58.10
73.11
77.30
16.45
62.30
67.07
$2.05
intra-Diversity (0-20)
58.52
73.18
80.10
25.80
62.50
68.90
Intra-Die Divveriiystty (20-40)
58.14
73.02
79.50
17.75
62.90
67.38
52.84
mnra--iversity (40-60)
11.57
58.11
72.94
76.00
15.65
62.50
65.25
51.72
Mira--iversstt (60-80)
10.89
$7.91
72.92
75.80
11.35
62.00
66.16
$1.00
Intra- Drra-iiiessty (80-100)
12.79
58.09
73.21
75.40
16.05
62.50
49.39
49.63
46

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H.S Complete Results of DAAR with Baselines
Additionally, we include the complete results of DAAR and the comparative baselines in the three ta- bles: Table 330 Table and Table The results illustrate the challenges of the scenario, particularly for the Qwen2 series, where baseline methods struggle outperform random selection. Furthermore, they demonstrate the robustness and effectiveness of our approach, consistently achieving the highest average scores across different models.
Table 30: Performance of DAAR with baselines on LIama3, 1-8B across various benchmarks.
Common Sense
Reasoning Hellaswag
Mathematics
Coding
Llama3.1-8B
Avg
NQ
TriviaQA
GSM8K
MATH
MBPP
HumanEval
RAW
14.13
65.90
74.62
54.80
7.90
5.00
28.66
35.86
FULL (40K)
21.92
65.11
73.62
51.70
7.60
4.10
36.50
37.22
RAND (8K)
21.99
64.83
74.72
55.70
14.50
5.10
24.09
37.27
INSTRUCTION LEN
15.34
63.60
73.73
54.00
15.40
3.60
30.80
36.64
ALPAGASUS [0]
21.57
64.37
74.87
55.20
17.65
4.60
16.16
36.34
INSTAG-C
18.12
64.96
74.01
55.70
15.50
4.80
37.81
38.70
INSTAG-D
21.94
64.69
74.87
54.80
12.80
4.10
9.76
34.71
SUPERFILTER 29
22.95
64.99
76.39
57.60
6.05
2.60
40.55
38.73
DEITA-C
33
15.58
64.97
74.21
55.00
13.05
4.60
34.46
37.41
DEITA-Q
33
19.57
64.22
75.15
54.00
7.20
4.20
28.35
36.10
DEITA-D
33
20.97
63.32
75.10
$4.90
7.00
4,00
31.71
DAAR (Ours)
20.08
64.55
74.88
54.8
15.30
4.70
37.50
38,83
Table 31: Performance of DAAR with baselines on Qwen2-7B across various benchmarks.
Common Sense
Reasoning Hellaswag
Mathematics
Coding
Qwen2-7B
Avg
NQ
TriviaQA
GSM8K
MATH
MBPP
HumanEval
RAW
8.03
59.58
73.00
78.00
5.70
5.00
60.98
41 1..4
FULL (40K)
15.61
58.75
72.51
73.80
31.30
51.70
67.38
53.01
RAND (8K)
13.28
58.27
73,00
75.35
35.36
52.20
63.72
53.02
INSTRUCTION LEN
8.62
58.44
72,86
73.30
27.05
53.10
63.72
51.01
ALPAGASUS 10
13.67
57.94
73.04
73.90
32.30
51.40
63.41
52.24
INSTAG-C 34
9.51
58.50
73.06
74.70
35.35
51.90
64.70
52.53
INSTAG-D
34
12.87
57.48
72.80
74,40
33.75
51.80
64.02
52.45
SUPERFILTER
29
19.16
58.98
72.99
73.70
30.10
52.40
58.85
52.31
DEITA-C
33
8.94
58.07
73.06
73.90
35.55
$2.90
62.20
52.09
DEITA-Q
33
14.06
59.07
73.16
75.80
35.50
23.00
58.24
48.40
DEITA-D
R3
16.41
57.80
72.70
76.10
29.05
52.40
64.63
52.73
DAAR (Ours)
16.88
57.58
73.03
75.40
38.1
52.00
64.94
53,99
Table 32: Performance DAAR with baselines on Qwen2.5-7B across various benchmarks.
Common Sense
Reasoning Hellaswag
Mathematics
Coding
(wen2.5-7B
Avg
NQ
TriviaQA
GSMSK
MATH
MBPP
HumanEval
RAW
8.84
72.75
78.20
9.10
7.40
78.05
44
FULL (40K)
12.88
58.60
72.28
76.80
13.60
62.80
71.04
52.57
RAND (8K)
11.46
57.85
73.08
78.90
13.15
62.50
71.65
52.65
INSTRUCTION LEN
11.34
58.01
72.79
78.
15.80
62.30
68.12
52.34
ALPAGASUS 10
10.40
57.87
72.92
77.20
18.75
61.80
65.55
52.07
INSTAG-C 34
10.81
58.45
73.27
76.00
13.30
61.80
68.29
51.70
INSTAG-D 34
11.08
58.40
72.79
76.40
16.40
62.90
70.43
52.63
SUPERFILTER
29
13.54
58.51
72.89
79.30
11.35
39.50
65.25
48.62
DEITA-C
33
10.50
58.17
73.14
74.60
16.60
62.00
72.26
52.47
DEITA-Q
33
11.24
57.83
72.97
78.50
12.95
38.10
67.68
48.47
DEITA-D
33
10.48
57.81
73.05
77.20
15.25
52.90
69.21
50.84
DAAR (Ours)
15.83
58.65
72.48
80.20
16.70
64.20
68.29
53.76
47


Reviews:
[{"review_id": "UWholvqxSr", "reviewer": "Reviewer_kdaW", "summary": "This paper proposes DAAR, a self-supervised framework that uses diversity as a reward signal to fine-tune LLMs on domain-undetermined data. DAAR leverages embedding-space entropy prediction for label-free data selection, achieving SOTA performance across 7 benchmarks and 3 model families, with notable gains in mathematical reasoning (+27%) and coding (+7.4%).", "questions": "see Weaknesses", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. novelty: Introduces a label-free, model-agnostic method (DAAR) that integrates diversity-driven data selection with closed-loop fine-tuning, eliminating dependency on domain labels or external models.\n2. empirical rigor: Demonstrates consistent SOTA results across diverse LLMs (e.g., Qwen, Llama) and challenging tasks (e.g., MATH, HumanEval)\n\nWeaknesses:\n1. unvalidated embedding representation: Assumes embedding-layer features accurately reflect data distribution (sec 3.2) without regression/ablation experiments to verify fidelity to true semantic distribution.\n2. DAAR shows minimal improvement (0.1%) for Llama3.1-8B over the best baseline (SuperFilter) in Table 2, undermining claims of \"notable\" superiority.\n3. Lacks grounding in true domain distributions:The diversity reward signal $(H(\\tilde{x}))$is entirely contingent on the accuracy of $(\\psi_{\\text{dom}})$, which itself depends on noisy pseudo-labels from clustering (Sec. 4.1). If $(\\psi_{\\text{dom}})$ misclassifies domains (e.g., confuses math-heavy coding samples), entropy becomes a meaningless proxy, propagating error to $(\\psi_{\\text{div}})$ and data selection.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your recognition of our **novelty** and **empirical rigor**. We will address your concerns regarding the Weaknesses (W) one by one.\n\n---\n\n### **W3: On the 'True' Domain Distributions**\n> *'Lacks grounding in true domain distributions:The diversity reward signal ... depends on noisy pseudo-labels ... If (ψdom) misclassifies domains, entropy becomes a meaningless proxy, propagating error to (ψdiv) and data selection.'*\n>\n\nThank you for this insightful question about the stability of our method and its reliance on pseudo-labels.\n\nFirst, as mentioned in your `Strength 1`, we wish to emphasize the core design principle and the setting of DaaR: it is a '**closed-loop, model-aware** system designed to eliminate dependency on external domain label' (from SOTA embedding model or human annotation). Our goal is not to replicate human annotations, but to understand the data's structure from the **LLM's own perspective** (lines 239-240).\n\nTo directly address your concern about \"noisy\" pseudo-labels versus \"true\" labels, we conducted a **new ablation study** as follows. We replaced our model-aware pseudo-labels from clustering **with the ground-truth (GT) human-annotated labels** (which is only possible in our controlled setting, not in DaaR's target domain-undetermined scenario) and reran the entire pipeline. We report on three key metrics:\n\n- **Probe Training Convergence:** Using ground-truth labels, the domain predictor also **converged successfully**, achieving the test accuracy of **92.7%**, confirming that both labeling schemes can allow the probe to distinct domains.\n- **Difference in Final Data Selection:** The table below shows the **overlap** in the final selected data. The divergence in the selected data confirms that pseudo-labels and ground-truth labels guide the prioritization process toward **distinct data subsets.**\n\n  | Overlap |  Pseudo vs. GT |\n  |:---:|:---:|\n  | Llama3.1-8B | 87.3% |\n  | Qwen2-7B | 83.1% |\n  | Qwen2.5-7B | 84.9% |\n\n+ **Final Performance:** The most critical comparison is the end-task performance:\n\n    | Llama3.1-8B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Pseudo | 20.08 | 64.55 | 74.88 | 54.80 | 15.30 | 4.70 | 37.50 | 38.83 |\n    | DaaR w/ GT | 22.54 | 65.52 | 73.43 | 53.80 | 14.35 | 4.40 | 36.50 | 38.65 |\n    | **Diff** | **+2.46** | **+0.97** | **-1.45** | **-1.00** | **-0.95** | **-0.30** | **-1.00** | **-0.18** |\n\n    | Qwen2-7B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Pseudo | 16.88 | 57.58 | 73.03 | 75.40 | 38.10 | 52.00 | 64.94 | 53.99 |\n    | DaaR w/ GT | 18.75 | 58.35 | 72.02 | 73.40 | 35.75 | 51.50 | 64.01 | 53.40 |\n    | **Diff** | **+1.87** | **+0.77** | **-1.01** | **-2.00** | **-2.35** | **-0.50** | **-0.93** | **-0.59** |\n\n    | Qwen2.5-7B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Pseudo | 15.83 | 58.65 | 72.48 | 80.20 | 16.70 | 64.20 | 68.29 | 53.76 |\n    | DaaR w/ GT | 16.04 | 58.75 | 71.87 | 79.40 | 16.30 | 64.25 | 67.76 | 53.48 |\n    | **Diff** | **+0.21** | **+0.10** | **-0.61** | **-0.80** | **-0.40** | **+0.05** | **-0.53** | **-0.28** |\n\nThis experiment reveals two critical insights:\n\n1. **Model-aware pseudo-labels are more effective.** Using \"true\" labels leads to **an average performance drop** compared to our standard DaaR. This suggests that an LLM's **internal understanding of data** can be a better guide for fine-tuning than human-defined domain label.\n2. **\"True\" labels can introduce suboptimal biases.** For instance, we observed that using human labels **biased the final model's capabilities**, often over-strengthening certain domains (e.g., **common sense**) at the expense of others, leading to  **lower performance on others**. This suggests apparent 'misclassifications' caused by pseudo-labels may actually more functionally effective groupings from the LLM's perspective.\n\nIn addition to this new experiment, our **existing analysis in Appendix G.8** already demonstrates the **component-level stability** of DaaR (e.g., consistent seed generation, deterministic clustering, and reliable probe convergence).\n\nWe greatly appreciate this constructive point. We will add this new experiment to our ablation studies, as it strongly highlights the advantages of DaaR's model-aware design.\n\n---\n\n### **W1: On the Embedding Representation**\n> *'unvalidated embedding representation: Assumes embedding-layer features accurately reflect data distribution (sec 3.2) without regression/ablation experiments to verify fidelity to true semantic distribution.'*\n>\n\nThank you for this excellent question, which naturally extends the discussion from `our reply to W3` above.\n\nOur reliance on the model's own embedding layer is a deliberate design choice, rooted in DaaR's **model-aware and external-model-free** philosophy. As our new ablation experiment in `W3` demonstrated, imposing an external \"true\" perspective (like human labels) can actually misguide the fine-tuning process.\n\nThe reason of selecting embedding layer is in **lines 569-573**. And we posit that the principle applies here: a more relevant semantic distribution for fine-tuning an LLM is **the one perceived by the LLM itself**. Besides, defining a universal \"ground-truth\" or a SOTA semantic distribution is a complex challenge in recent works [1,2] that lies **beyond the scope of this work**.\n\nNevertheless, to investigate the practical implications, we processed our full dataset (40K) using **several SOTA external embedding models** of a similar model size (7B). To ensure a fair comparison, all experimental setups were identical, utilizing a batch size of 16 and the Transformers library for embedding extraction. This analysis revealed two key points:\n\n- **No Single \"True\" Representation Required:** While each embedding model generates a distinct semantic space, all of them **successfully differentiate the domains** (since the new picture can't be displayed, it is similar as Figure 12).\n- **Significant Computational Overhead:** Using external models introduced substantial computational costs. Specifically, their processing times were **175 and 192 times longer**, respectively, and they even led to OOM errors in 40GB of GPU. This highlights the significant efficiency advantage of utilizing the model's native embedding layer.\n\n| Models | Qwen2-7B-Embedding-Layer | GTE-Qwen2-7B | Qwen3-8B-Embedding |\n|:---:|:---:|:---:|:---:|\n| Time Cost | 9.23s | 1662s **(175x)** | 1774s **(192x)** |\n\nGiven these findings, both the alignment with our model-aware principle and the significant computational overhead, we posit that using the LLM's own embedding layer is **the sound and efficient choice for DaaR**. We will add a note on this to the revised manuscript.\n\n[1] Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models\n\n[2] Jasper and Stella: Distillation of SOTA Embedding Models\n\n---\n\n### **W2: On the Phrasing of Performance Gains**\n> *'DAAR shows minimal improvement (0.1%) for Llama3.1-8B over the best baseline (SuperFilter) in Table 2, undermining claims of \"notable\" superiority.'*\n>\n\nThank you for this observation. Your feedback is very helpful for improving the precision of our manuscript.\n\nFirst, we wish to clarify that the experimental task is a **particularly challenging** task (as detailed in lines 285-291), where most existing baselines show limited effectiveness. Our primary claim is that DaaR achieves **consistent SOTA performance** across all tested models and scales.\n\nTo further validate this consistency across a broader range of setups, we have conducted supplementary experiments on two additional models, **Llama3.2-3B** and **Qwen2.5-14B**. For these experiments, we compared DaaR against two key baselines: **Raw** and **Random** (a strong baseline in our existing results). Our supplementary results are as follows:\n\n- **On Qwen2.5-14B (a larger model)**\n\n| Method | NQ | TriviaQA | Hellaswag | GSM8K | MATH | MBPP | HumanEval | Avg |\n| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Raw | 10.89 | 66.56 | 76.86 | 86.00 | 19.70 | 5.40 | 78.66 | 49.15 |\n| Random | 20.06 | 65.80 | 76.76 | 86.40 | 36.90 | 64.20 | 75.46 | 60.80 |\n| DaaR | 19.73 | 66.26 | 77.19 | 85.00 | 39.10 | 66.80 | 76.69 | **61.54** |\n\n- **On LLaMA3.1-8B (a smaller model):**\n\n| Method | NQ | TriviaQA | Hellaswag | GSM8K | MATH | MBPP | HumanEval | Avg |\n| :---: | --- | --- | --- | --- | --- | --- | --- | --- |\n| Raw | 7.62 | 53.1 | 68.77 | 26.6 | 4.5 | 3.8 | 23.17 | 26.79 |\n| Random | 16.03 | 53.56 | 68.46 | 28.7 | 6.15 | 4.65 | 29.12 | 29.52 |\n| DaaR | 15.13 | 53.79 | 68.23 | 29.10 | 5.63 | 5.3 | 30.34 | **29.64** |\n\nAs the new results demonstrate, DaaR **consistently outperforms** on both the larger Qwen2.5-14B and the smaller Llama3.2-3B. On Qwen2.5-14B, DaaR achieves the **highest average score (61.54)**, marking an improvement over the strong Random baseline with **0.74**. Similarly, on Llama3.2-3B, DaaR (**29.64**) maintains its **advantage**, that are consistent with our prior findings on the Llama architecture.\n\nNevertheless, we agree that the term ***\"notable\" may not be the most precise descriptor*** for every individual result. Following your valuable suggestion, we will revise our manuscript to use more accurate language, such as \"**consistently**\" to characterize the overall performance pattern.\n\n---\n\n### **Closing Remarks**\nThank you again for your insights and feedback! We hope these responses and the new revision can address your concerns and enhance your confidence in the acceptance of this paper. If you have any additional concerns or queries, we warmly invite you to share them with us."}, {"review_id": "nQ3QWN8nvF", "reviewer": "Reviewer_bjgP", "summary": "This paper addresses the challenge of fine-tuning large language models (LLMs) on domain-undetermined data where labels are missing or imprecise, proposing a self-supervised framework called DAAR (Diversity as a Reward). DAAR leverages diversity as a reward signal, constructing model-aware domain centroids through iterative embedding-space generation, training a lightweight MLP probe to predict semantic entropy from frozen embeddings, and implementing closed-loop fine-tuning where the model’s diversity estimates guide data selection. Theoretical analysis shows traditional data mixing strategies fail in label-free settings, necessitating simultaneous maximization of mutual information and preservation of the base model’s feature geometry.", "questions": "Sec. 3.4 states DAAR’s strategy \"must simultaneously maximize mutual information,\" but no proof connects Eq. 5–6 to DAAR’s mechanics. Please formalize how $I(X; C)$ (mutual info between samples and domains) is maximized.  And clarify if $\\psi_{\\text{div}}$’s entropy prediction (Eq. 9) directly optimizes $I(X; C)$.  \n\nPhase 1 of centroid synthesis (Sec. 4.1) uses \"minor injection from downstream task samples\" to generate seeds. This risks contaminating pseudo-labels with test-set knowledge. \nPlease: Report ablation results where seeds are generated without downstream task data.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The self-supervised framework DAAR is proposed to address domain-undetermined data fine-tuning by leveraging diversity as a reward signal, breaking free from reliance on pre-labeled data. Theoretical analysis proves that optimal data selection in label-free scenarios requires maximizing mutual information while preserving the base model’s feature geometry, providing a solid basis for the approach. The \"dual-identity model\" (output probe + input fine-tuning) and lightweight MLP probe design enable efficient computation by predicting semantic entropy from frozen embeddings.\n2. Experiments across 7 cross-domain benchmarks (e.g., mathematical reasoning, coding) and 3 model families (Qwen2, Llama3.1, etc.) show DAAR outperforms 9 baselines. Also, ablation studies on hyperparameters (seed size, sliding window) validate component stability, and generalizability is demonstrated in out-of-distribution scenarios (MMLU) and novel architectures (Qwen3).\n\nWeaknesses:\n1. The core claim—mutual information maximization underpins DAAR—lacks explicit formalization or proof (mentioned in Sec. 3.4 but not elaborated).\n2. Pseudo-labels for clustering incorporate downstream task samples (Sec. 4.1, Phase 1), potentially leaking test-set information. No ablation validates performance without this.", "was_revised": true, "final_justification": "The author addressed my concerns about data leakage in downstream tasks through supplementary experiments, and partially addressed my concerns about the theoretical interpretation of \"mutual information\". So I am considering raising the score to 4 points.\nThe author's response addressed my concerns and I will consider raising my score to 5", "rebuttal": "Thank you for your recognition of our method's design and comprehensive experiments. We will address your concerns regarding the Weaknesses (W) and Questions (Q) one by one.\n\n---\n\n### **W2 & Q2: On Potential Data Leakage**\n> *'W: Pseudo-labels for clustering incorporate downstream task samples (Sec. 4.1, Phase 1), potentially leaking test-set information...'*\n>\n> *'Q: ... This risks contaminating pseudo-labels with test-set knowledge. Please: Report ablation results where seeds are generated without downstream task data.'*\n>\n\nWe appreciate your rigorous scrutiny of our experimental methodology. We want to **assure you that our design explicitly prevents data leakage**, and we welcome the opportunity to clarify this with four clarifications.\n\n**`Strict Data Partitioning`**\n\n First and foremost, we must emphasize that our protocol maintains **strict data isolation**. The few downstream samples used for seeding (2 in 5) are **completely separate** from the evaluation benchmark, as well as the decontamination data that used for final LLM fine-tuning (lines 642-643).\n\n**`Purpose of the Injection`** \n\nWe posit that DaaR's performance **is not dependent on** these injected samples. Their role is solely to provide an initial diversity signal that **accelerates the diversity augmentation process** in Phase 2. Any information from the injection is heavily diluted in the subsequent large-scale seed generation and centroid computation stages.\n\n**`New Ablation Study (w/o Injection)`** \n\nTo empirically validate this and directly address your request, we conducted a new ablation study where we **removed the minor injection entirely** while keeping the benchmark evaluation data same as current setting. We report on three key metrics:\n\n- **Centroid Similarity:** Taking Qwen2-7B as a representative example, the domain centroids generated with and without injection are nearly identical, achieving a cosine similarity of **avg over 0.987**, demonstrating that the injection has a **negligible impact** on the domain centroid representations.\n\n    | Domains | Similarity (w/ - w/o Injection) |\n    |:---:|:---:|\n    | Common Sense | 0.9922 |\n    | Reasoning | 0.9865 |\n    | Mathematics | 0.9843 |\n    | Coding | 0.9878 |\n\n- **Final Performance:** The end-task performance of DaaR (w/o injection) is **statistically indistinguishable** from our reported results, demonstrating that DaaR is not dependent on the minor injection. The results are as follows:\n\n    | Llama3.1-8B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Inject | 20.08 | 64.55 | 74.88 | 54.80 | 15.30 | 4.70 | 37.50 | 38.83 |\n    | DaaR w/o Inject | 20.39 | 64.80 | 76.05 | 55.40 | 13.65 | 5.75 | 36.48 | 38.93 |\n    \n    | Qwen2-7B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Inject | 16.88 | 57.58 | 73.03 | 75.40 | 38.10 | 52.00 | 64.94 | 53.99 |\n    | DaaR w/o Inject | 16.22 | 58.33 | 73.41 | 75.20 | 36.37 | 52.95 | 65.14 | 53.95 |\n    \n    | Qwen2.5-7B | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n    | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n    | DaaR w/ Inject | 15.83 | 58.65 | 72.48 | 80.20 | 16.70 | 64.20 | 68.29 | 53.76 |\n    | DaaR w/o Inject | 14.91 | 58.32 | 72.55 | 79.70 | 16.30 | 63.70 | 70.65 | 53.73 |\n\n- **Generation Efficiency:** However, the ***diversity augmentation*** process became **significantly less efficient.** Without the initial seed diversity, it required **approximately 4 times** more generation attempts to meet the same diversity threshold (as in Table 14), confirming its role as an **accelerator**.\n\n    | Domains | Attempts (w/ Injection) | Attempts (w/o Injection) |\n    |:---:|:---:|:---:|\n    | Common Sense | 31 | 134 |\n    | Reasoning | 61 | 248 |\n    | Mathematics | 236 | 819 |\n    | Coding | 21 | 105 |\n\n**`Context in Related Literature`** \n\nThis practice of using a small, targeted set to guide a broader data selection process is **a well-established strategy** in related work, such as gradient-based influential selection LESS [1] and targeted-distribution importance resampling DSIR [2]. While our method differs, the **principle of a minor, guided injection** to improve efficiency will not lead to the leakage.\n\nWe thank you again for raising this critical point. We will **add this new, detailed ablation study to our revised manuscript**, which we believe will greatly enhance its rigor and transparency.\n\n[1] LESS: Selecting Influential Data for Targeted Instruction Tuning, ICML'2024\n\n[2] Data Selection for Language Models via Importance Resampling, NeurIPS'2023\n\n---\n\n### **W1 & Q1: On the Formalization of the Theoretical Underpinning**\n> *'W: The core claim—mutual information maximization underpins DAAR—lacks explicit formalization or proof (mentioned in Sec. 3.4 but not elaborated).'*\n>\n> *'Q: Sec. 3.4 states DAAR’s strategy \"must simultaneously maximize mutual information,\" but no proof connects Eq. 5–6 to DAAR’s mechanics. Please formalize ... is maximized. And clarify if entropy prediction directly optimizes...'*\n>\n\nWe are very grateful for this deep engagement with our theoretical framework, and we appreciate the opportunity to clarify our reasoning and correct an imprecision in our manuscript.\n\nFirst, we wish to clarify the **intended role of our theoretical analysis** (lines 173-178). Its primary purpose is to provide a **principled perspective** that explains our empirical observations in Section 3 and offers a strong motivation for the design of DaaR in Section 4.\n\n**`Regarding \"Mutual Information Maximization\"`**\n\nWe acknowledge that our use of the term \"mutual information maximization\" in the introduction section was an **imprecise statement**. Our initial intention was to use this term to conceptually capture the goal of enriching sample-level diversity. However, we recognize this is **not a formal maximization of I(X;C)** in information theory and thank you for pointing it out. We will immediately correct this terminology throughout the revised manuscript.\n\nInstead, the theoretical foundation of our work is rooted in **Importance Sampling**, as detailed in Section 3.4 and derived in Appendix E. This framework allows us to analyze how data diversity impacts the optimality of data selection.\n\n**`Clarifying the Link Between Theoretical Insight and Entropy-based Method (Eq. 9)`**\n\nThe connection between our theory and DaaR's entropy-based selection is best formalized as **a principled heuristic**, which we present in the following remark:\n\n- **Remark:** Our analysis in Sec. 3.4 shows that the importance weight w(x) = q(x)/p(x) for data selection is **suboptimal** when the domain assignment is deterministic, i.e., p(c=k*|x) = 1 for some domain k*. This condition is equivalent to the conditional entropy H(C|X=x) = 0. Since directly optimizing for the ideal q(x) is **intractable in our domain-undetermined** setting, DaaR adopts a theory-guided heuristic to select samples x that are maximally distant from this known suboptimal condition. We use H(C|X=x) as a direct **proxy for this distance**. Therefore, the selection objective of DaaR is to argmax_x H(C|X=x), which is implemented by selecting samples with high predicted entropy ψ_div(x) ≈ H(C|X=x).\n\nThis remark connects our **theoretical insight**—that zero conditional entropy is suboptimal—to our **practical method** of rewarding high predicted entropy.\n\nThank you once again for your invaluable feedback. We will take the following actions in our revision:\n\n1. We will **remove all imprecise mentions** of \"mutual information maximization\" and accurately describe our theoretical basis as Importance Sampling.\n2. We will incorporate the **formal discussion and remark** above to explicitly bridge the gap between our theoretical insights and the design of our method.\n\n---\n\n### **Closing Remarks**\nThank you once again for your valuable feedback, we have endeavored to address each of your concerns thoroughly in our responses and planned revisions.\n\nWe hope these clarifications have resolved your initial concerns, we would be very grateful if you would consider reconsidering your assessment of our paper. We look forward to any further discussion and welcome any additional questions you may have."}, {"review_id": "4hP8Ffu0d9", "reviewer": "Reviewer_Ge2Q", "summary": "This paper addresses the challenge of fine-tuning Large Language Models (LLMs) on diverse, mixed-domain data, especially when domain labels are missing or imprecise. The authors first empirically demonstrate that optimal data diversity levels vary across models and that existing metrics fail in label-free settings. Based on these insights, they propose a new self-supervised framework, DAAR (Diversity as a Reward), which requires no domain labels. DAAR gives the LLM a dual identity: an \"output model\" that uses a lightweight probe to select data based on a predicted semantic entropy (diversity) reward, and an \"input model\" that is then fine-tuned on this selected data. This process is guided by automatically synthesized, model-aware domain centroids. Extensive experiments on various LLMs, including the Llama3.1 and Qwen2 series, show that DAAR significantly boosts performance on domain-undetermined data and foundational tasks, notably improving mathematical reasoning and coding capabilities more than nine other baseline methods.", "questions": "- The out-of-distribution evaluation on MMLU shows that DAAR achieved the top score on Qwen2-7B but was outperformed by other baselines on Qwen2.5-7B. Do the authors have a hypothesis for this performance variance between different models in the OOD setting?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The paper has the following key strengths:\n- Novel and theoretically grounded: The proposed framework addresses an important real-world problem of fine-tuning on domain-undetermined data. Unlike methods that require pre-existing domain labels, DAAR uniquely uses the LLM's own embedding space geometry to create a diversity reward signal, giving the model a dual identity as both the data selector and the model-to-be-tuned. This approach is not merely heuristic; it is supported by both controlled empirical analysis and a theoretical perspective based on importance sampling.\n- Comprehensive evaluation: The framework establishes a new state-of-the-art average performance across three model families and seven benchmarks, consistently outperforming nine different baseline methods. The performance uplift is particularly impressive on high-difficulty STEM tasks where many baselines fail; for example, it achieves notable improvements in mathematical reasoning (+27%) and coding (+7.4%).\n- Computationally efficient and generalizable: By operating on frozen LLM embeddings with a lightweight MLP probe, the framework is highly efficient, achieving 70% lower GPU usage and 2.5x faster inference compared to baselines that rely on costly GPT-based evaluators or full-LLM inference. The method also demonstrates strong generalizability, maintaining top performance on the out-of-distribution MMLU benchmark and on a different model architecture (Qwen3-8B).\n\nThe paper has the following weaknesses which when addressed can further strengthen the paper:\n- Complex framework with potential for compounding errors: The framework is multi-staged and complex. It depends on a pipeline that includes LLM-based data synthesis to create domain centroids, k-means clustering to generate pseudo-labels, and a two-stage process to train the reward probe. An error or instability in any of the early stages, such as the initial centroid generation, could propagate through the entire system and negatively impact the final data selection. The paper does not provide a thorough analysis of the framework's robustness to such potential compounding errors.\n- Limited scope of models: The experiments are primarily conducted on models within the 7-8B parameter range. It remains unclear how well the findings and the method's effectiveness would generalize to significantly larger models (for example, 70B or more) or different model architectures.", "was_revised": true, "final_justification": "The author addressed my comments about compounding errors and robustness. They also included results with other family of models - Qwen2.5-14B and LLaMA3.1-8B to show generalizability. This makes the paper stronger. I maintain my recommendation of accept.", "rebuttal": "Thanks for your valuable feedback! We are deeply encouraged by your recognition of our work's **novelty** and **comprehensive evaluation**. We also greatly appreciate your insightful suggestions, we will address each of your Weaknesses (W) and Question (Q) below.\n\n---\n\n### **W1: On the Compounding Errors and Robustness of DaaR**\n> *'Complex framework with potential for compounding errors: The framework is multi-staged and complex. ... An error or instability in any of the early stages, such as the initial centroid generation, could propagate through the entire system ...'*\n>\n\nThis is a very insightful point. You are correct that since DaaR operates as a multi-stage pipeline, a thorough analysis of its stability is crucial. We did touch upon this consideration in the main text (**lines 266-267**) and provided an initial stability analysis in **Appendix G.8 (lines 895-904)**.\n\nIn summary, our existing analysis suggests that the key components of DaaR **exhibit robustness**: the LLM-based seed generation is consistent, the k-means clustering is stabilized by deterministic initialization, the reward probe training converges reliably, and the final data selection strategy has built-in redundancy.\n\nHowever, your observation that we should **more explicitly analyze the potential for compounding errors** is well-taken. To thoroughly address this concern and directly validate the robustness of our framework against error propagation, we have conducted the following new analyses based on **three fully independent experimental runs**.\n\n- **[Experiment Setup]**\n\nWe performed a **third independent run**, supplementing the current two independent runs mentioned in *lines 112-113*. Each run is an **end-to-end execution** of our pipeline. We present results for Qwen2-7B as a representative case; other models showed similar trends and will be added to the paper.\n\n- **[Observation 1]: Robustness of Centroid Generation.**\n\nTo evaluate the stability of the critical **initial stage**, we computed the pairwise cosine similarities of the **final centroid embeddings** from the three runs.\n\n| Domains | Similarity (Seed-1-2) | Similarity (Seed-1-3) | Similarity (Seed-2-3) |\n|:---:|:---:|:---:|:---:|\n| Common Sense | 0.9912 | 0.9895 | 0.9921 |\n| Reasoning | 0.9845 | 0.9911 | 0.9887 |\n| Mathematics | 0.9880 | 0.9803 | 0.9854 |\n| Coding | 0.9905 | 0.9853 | 0.9918 |\n\nThe centroid embeddings are **remarkably similar** (all **>0.98**), which demonstrate the stability of our initial centroid generation, showing it is **not a significant source of variance**, especially compared to the value in Figure 11 and Table 11.\n\n- **[Observation 2]: Stability of Final Data Selection.**\n\nWe then examined if initial variations propagate to the **final data selection** by calculating the **data overlap** for the top 20% (8000) of selected samples across the three runs.\n\n| Selected Data | Overlap (Seed-1-2) | Overlap (Seed-1-3) | Overlap (Seed-2-3) |\n|:---:|:---:|:---:|:---:|\n| Rate | 95.7% | 97.3% | 96.1% |\n\nThe results show an **significantly high overlap**, with an average of **96.4%**, confirming that our data selection process is robust and largely unaffected by initial variations.\n\n- **[Observation 3]: Consistency of Final Performance.**\n\nFinally, the stability of the entire pipeline is reflected in the **end-task benchmark performance**.\n\n| Runs | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Seed-1 | 17.92 | 56.78 | 72.91 | 75.00 | 39.60 | 51.40 | 64.80 | 54.06 |\n| Seed-2 | 15.84 | 58.38 | 73.14 | 75.80 | 36.60 | 52.60 | 65.07 | 53.92 |\n| **Seed-3** | 15.18 | 57.96 | 72.99 | 76.70 | 38.80 | 51.40 | 65.24 | 54.04 |\n| Average | 16.31 ± (**1.43**) | 57.71 ± (**0.83**) | 73.01 ± (**0.12**) | 75.83 ± (**0.85**) | 38.33 ± (**1.55**) | 51.80 ± (**0.69**) | 65.04 ± (**0.22**) | 54.01 ± (**0.08**) |\n\nThe final results are **highly consistent**, culminating in an average score with a very small standard deviation of just **0.08**. This end-to-end stability provides strong empirical evidence that our framework is robust. (Complete results can be found in our reply to W4 & Q4 of Reviewer Bbh9).\n\nIn summary, and following your valuable advice, we will make two key revisions to the paper:\n\n1. We will integrate a more **prominent discussion** of the framework's stability, currently in the appendix, into the main body of the paper.\n2. We will **incorporate the new ablation experiments** described above into our ablation studies (Section 5.3) to explicitly address the concern of compounding errors.\n\n---\n\n### **W2: On the Limited Scope of Models**\n> *'Limited scope of models: The experiments are primarily conducted on models within the 7-8B parameter range. It remains unclear .. larger models (for example, 70B or more) or different model architectures.'*\n>\n\nThank you for your constructive suggestion! We agree that demonstrating DaaR's effectiveness across a wider range of model architectures and scales would significantly strengthen our claims.\n\nOur current experiments **already span three distinct architectural families**: the widely-used Llama and Qwen-2.x architecture, as well as the latest SOTA Qwen-3 architecture. Across all these, DaaR has consistently demonstrated its effectiveness.\n\nHowever, we acknowledge that our original study did not include models of different sizes. Given the *considerable time and computational resources* required to run our full suite of experiments (10 diversity-controlled settings and 12 baselines with 2 independent runs), we conducted a more targeted set of experiments on two additional models: **Llama3.2-3B** and **Qwen2.5-14B**.\n\nFor these experiments, we compared DaaR against two key baselines: **Raw** and **Random** (a strong baseline in our existing results). Our supplementary results are as follows:\n\n- **On Qwen2.5-14B (a larger model)**\n\n| Method | NQ | TriviaQA | Hellaswag | GSM8K | MATH | MBPP | HumanEval | Avg |\n| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Raw | 10.89 | 66.56 | 76.86 | 86.00 | 19.70 | 5.40 | 78.66 | 49.15 |\n| Random | 20.06 | 65.80 | 76.76 | 86.40 | 36.90 | 64.20 | 75.46 | 60.80 |\n| DaaR | 19.73 | 66.26 | 77.19 | 85.00 | 39.10 | 66.80 | 76.69 | **61.54** |\n\n- **On LLaMA3.1-8B (a smaller model):**\n\n| Method | NQ | TriviaQA | Hellaswag | GSM8K | MATH | MBPP | HumanEval | Avg |\n| :---: | --- | --- | --- | --- | --- | --- | --- | --- |\n| Raw | 7.62 | 53.1 | 68.77 | 26.6 | 4.5 | 3.8 | 23.17 | 26.79 |\n| Random | 16.03 | 53.56 | 68.46 | 28.7 | 6.15 | 4.65 | 29.12 | 29.52 |\n| DaaR | 15.13 | 53.79 | 68.23 | 29.10 | 5.63 | 5.3 | 30.34 | **29.64** |\n\nAs the new results demonstrate, DaaR **consistently outperforms** on both the larger Qwen2.5-14B and the smaller Llama3.2-3B. On Qwen2.5-14B, DaaR achieves the **highest average score** (61.54), marking an improvement over the strong Random baseline with **0.74**. Similarly, on Llama3.2-3B, DaaR (29.64) maintains its **advantage**. \n\nThese results provide an evidence that our method is effective **across both LLM architectures and model scales**. We will incorporate these findings as an additional ablation study in our revised manuscript.\n\n---\n\n### **Q1: Conjecture on the Performance Variance on MMLU**\n> *'The OOD evaluation on MMLU shows that DAAR achieved the top score on Qwen2-7B but was outperformed by other baselines on Qwen2.5-7B. Do the authors have a hypothesis ...?'*\n>\n\nThat is an excellent observation, it is indeed interesting that DaaR places second on Qwen2.5-7B. While a definitive cause warrants deeper investigation, we offer two **primary hypotheses** based on our analysis:\n\n- **Domain Alignment vs. Diminishing Gains**: Our detailed results in Table 6 shows DaaR's strength on Qwen2-7B is largely driven by **STEM subjects**, which align with the core domains (math, code, etc.) our method prioritizes. On the more capable Qwen2.5-7B, DaaR still **effectively boosts STEM performance**. However, for an already strong LLM, the marginal gains on less-related domains (e.g., Humanities) may diminish, leading to a slightly lower overall average compared to a method like SuperFilter that might have a different selection bias.\n- **LLM Sensitivity**: The weaker base model (Qwen2-7B) appears **more sensitive to data selection**, exhibiting larger performance variance across all methods. Conversely, on the stronger Qwen2.5-7B, the performance of all baselines is more stable and converges. In this less volatile regime, the strong, diversity-driven focus of DaaR on STEM might introduce a **slight trade-off in other areas**, resulting in a marginal difference.\n\nWe believe the **OOD setting** is a fascinating area for future work and would welcome any further discussion.\n\n---\n\n### **Closing Remarks**\nOnce again, we sincerely thank you for your recognition and invaluable feedback. We hope our responses have thoroughly addressed your concerns regarding robustness and model scale.\n\nWe kindly hope that these clarifications and additions might further strengthen your confidence in our work, your support is immensely encouraging to us. If you have any additional concerns or queries, we warmly invite you to share them with us."}, {"review_id": "3MOZxn9QqL", "reviewer": "Reviewer_Bbh9", "summary": "The paper proposes DAAR, a framework for data selection in instruction fine-tuning of LLMs when explicit domain labels are unavailable. The authors identify limitations in current mixture modeling and data selection approaches, especially in domain-undetermined settings. They begin with an empirical analysis revealing that both inter-domain and intra-domain diversity have model-specific and task-specific effects on downstream performance. Then they present their method in multiple stages, from centroid computation from the LLM embeddings, to computation of the diversity scores, and finally the data selection. Experiments across LLMs show some performance benefit.", "questions": "- Can the authors provide a clear algorithmic summary or flowchart to consolidate the numerous defined components and clarify how they interact within the overall training pipeline?\n- How does the proposed method meaningfully differ from prior works like [1,2,3] that also utilize domain centroids and clustering approaches?\n- Why were established domain reweighting baselines such as DoReMi and RegMix excluded from the experimental comparison, and how might their inclusion impact your reported performance gains?*\n- Given that some improvements over baselines are marginal, can the authors report statistical significance measures to support the robustness of their claims?", "limitations": "Yes.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 1, "strengths_and_weaknesses": "Strengths:\n- The paper is well-motivated. The challenge of fine-tuning on mixed data without reliable domain labels is a real-world bottleneck. Especially given the increasing scale and heterogeneity of data used to adapt LLMs. The authors clearly articulate how conventional data selection and mixture strategies falter under such constraints, setting up a compelling case for the necessity of a label-free approach. They ground their method in both empirical observations and theoretical analysis, they highlight a practical need in the field.\n\nWeaknesses:\n- The writing and the structure of the paper make it quite difficult to follow the main steps of the contributions. My suggestion is to restructure the paper in a more logical way and include an algorithm listing. There are many quantities defined but it is not totally clear how they are used in a single pipeline.\n- The novelty of the proposals in Sec. 3.2 is limited w.r.t. previous works. Using the domain centroid in step (A) is proposed in [1] and using their distances in (B) is also used in [1,2]. Domain-aware clustering in Sec. 4.1 does not discuss the similar [3].\n- Experiments lack domain reweighting baselines such as DoReMi [4] and RegMix [5], which could also be applied to your clustered domains.\n- No statistical significance measures, which are important given the marginal improvements.\n\n[1] Xie, W., Tonin, F., & Cevher, V. (2025). Chameleon: A Flexible Data-mixing Framework for Language Model Pretraining and Finetuning. arXiv preprint arXiv:2505.24844.\n\n[2] Chen, M. F., Hu, M. Y., Lourie, N., Cho, K., & Ré, C. (2024). Aioli: A unified optimization framework for language model data mixing. arXiv preprint arXiv:2411.05735.\n\n[3] Fan, S., Grangier, D., & Ablin, P. (2024). Dynamic Gradient Alignment for Online Data Mixing. arXiv preprint arXiv:2410.02498.\n\n[4] Xie, S. M., Pham, H., Dong, X., Du, N., Liu, H., Lu, Y., ... & Yu, A. W. (2023). Doremi: Optimizing data mixtures speeds up language model pretraining. Advances in Neural Information Processing Systems, 36, 69798-69818.\n\n[5] Liu, Q., Zheng, X., Muennighoff, N., Zeng, G., Dou, L., Pang, T., ... & Lin, M. (2024). Regmix: Data mixture as regression for language model pre-training. arXiv preprint arXiv:2407.01492.", "was_revised": true, "final_justification": "The methodological flow is difficult to follow, making the core idea of the paper unclear.\n\nSection 2.2 lacks clarity on assumptions on domains.\n\nThe distinction between “text description” and “domain label” is vague, as both functionally serve the same role (e.g., ‘wikipedia’ as both label and description).\n\nThe foundational step appears to rely on clustering to create pseudo-labels, but this has already been proposed in previous works, as well as centroid computation.\n\nOnce pseudo-labels are created, existing domain-reweighting baselines (e.g., DoReMi, RegMix) that rely on labels could also be applied, but they are not compared.\n\nThe argument that those baselines are “pre-training methods” is unconvincing, since their reweighting mechanisms resemble the proposed diversity probe.\n\nSince individual components offer limited novelty, the main contribution must be the pipeline itself, which is currently not presented clearly enough and not supported by broad enough experiments.\n\nFor the pipeline to be convincing, the paper needs:\n\nA clearer and more formal presentation (e.g., improved Figure 1, a step-by-step algorithm, better paper structure).\n\nBroader and more comprehensive experiments, as current evaluation only includes two reasoning benchmarks (HellaSwag and MMLU), which is insufficient to establish general utility", "rebuttal": "We sincerely thank you for your time and constructive feedback. We have carefully considered your Weaknesses (W) and Questions (Q) point by point and provide detailed responses below. We hope this clarification will help you see the value of our work more clearly.\n\n---\n\n### **W2 & Q2: On the Novelty Compared to Works [1, 2, 3]**\n> *\"W: The novelty of the proposals in Sec. 3.2 is limited w.r.t. previous works. ...\"*\n> \n> *\"Q: How does the proposed method meaningfully differ from prior works like [1,2,3] that also utilize domain centroids and clustering approaches?\"*\n\nWe are grateful to the reviewer for these valuable references. They will undoubtedly help us better position our work, and **we will add all of them to our revised version**.\n\nSimilar to your statement in `Strengths` that our work positioned in **'fine-tuning on mixed data without reliable domain labels'**, we wish to re-emphasize that the primary novelty of our work lies in the **domain-undetermined** setting and the **diversity probe** of LLM **fine-tuning (in lines 74-79)**. To clarify this, we highlight the key differences with the cited works below.\n\n`Regarding [1] (Chameleon)`\n\nFirst, we note that [1] is **contemporaneous work** according to the official guidance of Call For Papers (first submitted on May 30), and it appears even after the submission (May 15). Nonetheless, we outline the distinctions here:\n\nWhile both DaaR and Chameleon use domain embeddings for *data reweighting*, our work differs in three crucial aspects:\n\n- **Setting:** DaaR operates in a **domain-undetermined fine-tuning** scenario where domain labels are unknown. In contrast, Chameleon's method (KRLS) use such domain information to calculate importance scores majorly in **pretraining** stage.\n- **Metric:** DaaR pioneers the use of **diversity** to measure the utility of data, while Chameleon use domain-level **importance scores** derived from KRLS.\n- **Objective:** In the context of fine-tuning, DaaR targets the enhancement of **foundational abilities**, whereas Chameleon focuses on specific skills like multilingual capabilities.\n\n`Regarding [2] (Aioli)`\n\nWhile both works investigate *data mixture based on domain properties*, our approaches differ fundamentally in their goals and methods:\n\n- **Objective & Setting:** Aioli mainly aims to **model a \"mixing law\"** in a **pre-training, domain-known** setting. In contrast, DaaR is to optimize data selection for **fine-tuning** in a **domain-undetermined** context.\n- **Mechanism:** Aioli's method relies on **training dynamics** (loss). DaaR is based on the intrinsic **diversity** of the data.\n- **On Embedding Distance:** Aioli **does not directly utilize domain centroid distance** as a core mechanism, the mention of embedding distance partly in its `Related Works` section.\n\n`Regarding [3] (DGA)`\n\nWhile both methods use *domain clustering*, its purpose and the overall approach are distinct:\n\n- **Core Method:** DGA is a **pre-training** method that uses **gradient information**. DaaR is a **fine-tuning** method that uses **data diversity** as its primary selection criterion.\n- **Role of Clustering:** In DGA, clustering is a **pre-processing step** to define static, fine-grained domains. In DaaR, we utilize **data synthesis to create anchor points** that guide the clustering, and the clustering is an integral mechanism to train the diversity probe.\n\nWe thank the reviewer again for these valuable references. They help us clarify that DaaR’s core novelty lies **not in its individual components**, but in the complete system and scenario. As highlighted by Reviewers kdaW and Ge2Q in their `Strength`, DaaR provides a **external-model-free** solution for the challenging **domain-undetermined** setting.\n\n---\n\n### **W4 & Q4: On Reporting Statistical Significance**\n> *\"W: No statistical significance measures, which are important given the marginal improvements.\"*\n> \n> *\"Q: ... can the authors report statistical significance measures to support the robustness of their claims?\"*\n\nWe thank the reviewer for this valuable suggestion. To bolster our claims, we provide the following points:\n\nFirst, all existing results are the **average of two independent, end-to-end runs** (lines 112-113), and we have analyzed DaaR's stability in **Appendix G.8 (lines 894-904)**.\n\nTo further address this concern, we conducted an additional independent run for our method, DaaR, for a total of **three runs**. The tables below *detail the performance* for each of the three seeds, followed by the *calculated mean* and *standard deviation* (μ ± σ).\n\n- **Llama3.1-8B**\n\n| Runs | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Seed-1 | 19.30 | 64.76 | 75.10 | 54.40 | 14.40 | 4.60 | 37.80 | 38.62 |\n| Seed-2 | 20.86 | 64.34 | 74.66 | 55.20 | 16.20 | 4.80 | 37.20 | 39.04 |\n| **Seed-3** | 21.91 | 64.94 | 74.66 | 54.20 | 16.20 | 4.60 | 37.20 | 39.10 |\n| **Average** | 20.69 ± (**1.31**) | 64.68 ± (**0.31**) | 74.81 ± (**0.25**) | 54.60 ± (**0.53**) | 15.60 ± (**1.04**) | 4.67 ± (**0.12**) | 37.40 ± (**0.35**) | 38.92 ± (**0.26**) |\n\n- **Qwen2-7B**\n\n| Runs | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Seed-1 | 17.92 | 56.78 | 72.91 | 75.00 | 39.60 | 51.40 | 64.80 | 54.06 |\n| Seed-2 | 15.84 | 58.38 | 73.14 | 75.80 | 36.60 | 52.60 | 65.07 | 53.92 |\n| **Seed-3** | 15.18 | 57.96 | 72.99 | 76.70 | 38.80 | 51.40 | 65.24 | 54.04 |\n| **Average** | 16.31 ± (**1.43**) | 57.71 ± (**0.83**) | 73.01 ± (**0.12**) | 75.83 ± (**0.85**) | 38.33 ± (**1.55**) | 51.80 ± (**0.69**) | 65.04 ± (**0.22**) | 54.01 ± (**0.08**) |\n\n- **Qwen2.5-7B**\n\n| Runs | nq | triviaqa | hellaswag | gsm8k | math | mbpp | humaneval | Avg |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Seed-1 | 15.51 | 58.74 | 72.43 | 80.80 | 17.60 | 63.60 | 67.06 | 53.68 |\n| Seed-2 | 16.15 | 58.56 | 72.52 | 79.60 | 15.80 | 64.80 | 69.51 | 53.85 |\n| **Seed-3** | 15.58 | 58.40 | 72.90 | 79.40 | 16.40 | 62.90 | 68.12 | 53.39 |\n| **Average** | 15.75 ± (**0.35**) | 58.57 ± (**0.17**) | 72.62 ± (**0.25**) | 79.93 ± (**0.76**) | 16.60 ± (**0.92**) | 63.77 ± (**0.96**) | 68.23 ± (**1.23**) | 53.64 ± (**0.23**) |\n\nThe analysis reveals that DaaR's performance is **highly consistent**, with the standard deviations on the final average scores being **notably low** (0.26, 0.08, and 0.23, respectively). This low variance confirms that our method's performance advantage over the reported baselines is robust.\n\nWe appreciate this valuable feedback and will incorporate this detailed statistical analysis into our revised manuscript.\n\n---\n\n### **W3 & Q3: On the Comparison with DoReMi [4] and RegMix [5]**\n> *\"Q: Experiments lack domain reweighting baselines such as DoReMi [4] and RegMix [5], which could also be applied to your clustered domains.\"*\n> \n> *\"W: Why were ... DoReMi and RegMix excluded from the experimental comparison, ...\"*\n\nWe thank the reviewer for suggesting these foundational pretraining works. We **already cite DoReMi (line 199) and will add RegMix to our discussion**. However, we respectfully argue that including them as direct baselines would be **inappropriate** and could lead to an **inequitable comparison**:\n\n- **Divergent Settings:** DoReMi and RegMix are **pre-training** methods designed for large-scale, iterative reweighting. Our work operates in the **fine-tuning stage**, which is **fundamentally distinct** from pretraining in its objective and data usage[1, 2, 3].\n- **Established Baselines:** Our experimental setup aligns with the **standard practice in fine-tuning data selection**. To our knowledge, leading methods (e.g., Alpagasus, Instag, Deita), which we compare as baselines, **do not use any pre-training method** as their baselines.\n- **Methodological Incompatibility:** Both methods require **explicit domain labels**, which are absent in our **domain-undetermined** setting. While 'could also be applied to the clustered domains', our clustering is an **integral part of DaaR**, designed to provide signals for our diversity probe.\n\n[1] LIMA: Less Is More for Alignment, NeurIPS'2023\n\n[2] What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning, ICLR'2024\n\n[3] A Survey on Data Selection for Language Models, TMLR'2024\n\n---\n\n### **W1 & Q1: On the paper's clarity and structure**\n> *\"W: The writing and the structure of the paper make it quite difficult to follow ... My suggestion is to restructure the paper ...\"*\n> \n> *\"Q: Can the authors provide a clear algorithmic summary or flowchart ... and clarify how they interact within the overall training pipeline?\"*\n\nWe thank the reviewer for their valuable feedback. We will continually polish our manuscript to improve the manuscript's readability.\n\nHowever, we would also like to clarify that we **have already provided** the following structure:\n\n- **Figure 1** already provides a schematic **flowchart** of the DaaR pipeline with a detaild caption. Moreover, **Lines 207-210** serve as a summary that explicitly connects our DaaR to this figure.\n- Our contributions in lines 53-60 are structurally aligned with **Sections 3, 4, and 5** respectively.\n- We also use **transition paragraphs** (lines 95-97, 173-178, 201-210 and 269-272) in every sections to ensure a **logical flow**.\n\nWe agree that the presentation can be clearer. In the revised version, we will make two key improvements:\n\n1. **Add a pseudo-code algorithm** for DaaR to offer a clear, step-by-step guide.\n2. **Strengthen the textual mapping** between our method description (Sec. 4) and the components in the Figure 1 flowchart.\n\n---\n\n### **Closing Remark**\nThank you again for your insights and feedback! We hope these responses and the new revision can address your concerns and we would be grateful if you would consider re-evaluating your assessment of our work."}]

Author rebuttal:

Meta-review: The paper provides a framework that uses diversity to fine-tune LLMs on domain-undetermined data. In terms of novelty, although there was no full consensus, three reviewers did find the approach and in particular the overall result novel: Ge2Q (commenting about the approach) “Unlike methods that require pre-existing domain labels, DAAR uniquely uses the LLM's own embedding ...” bjgP (commenting about the result) “The self-supervised framework DAAR is proposed to address domain-undetermined data fine-tuning by leveraging diversity as a reward signal, breaking free from reliance on pre-labeled data.”. In contrast one review mentioned novelty to be limited in that the individual components are not new, and the novelty lies in the overall pipeline. Given the other reviews, I see this as a minor issue, and believe that in terms of novelty and interest to the community, the result and methods meet the bar of NeurIPS. 

Another property discussed is the empirical evidence providing the quality of the proposed technique. Here too there was no consensus but 3 out of 4 reviews did find the experiments to be sufficient. The initial reviews (Ge2Q, bjgP and kdaW) positively mentioned the breadth of the experiments: “The framework establishes a new state-of-the-art average performance across three model families and seven benchmarks, consistently outperforming nine different baseline methods”, “Experiments across 7 cross-domain benchmarks (e.g., mathematical reasoning, coding) and 3 model families (Qwen2, Llama3.1, etc.) show DAAR outperforms 9 baselines.”, “Demonstrates consistent SOTA results across diverse LLMs (e.g., Qwen, Llama) and challenging tasks (e.g., MATH, HumanEval)”. During the rebuttal, the reviewers raised the need of additional empirical studies evaluating sub-procedures, components, and comparing them against additional baselines. The authors provided experiments for most of these suggestions, mitigating the concerns of most reviewers. Some concerns remained (notably regarding additional baselines mentioned by Bbh9) but based on the discussion done among the reviewers and myself, I am convinced these are merely nice-to-have additions not key in proving the validity of the work. 

To conclude, although the reviewers did not reach a consensus w.r.t the decision over the paper, I'm convinced that the remaining weaknesses of the paper are minor compared to its strengths and believe it will be a welcome addition to NeurIPS.
Decision: Accept (poster)