TreeSynth: Synthesizing Diverse Data from Scratch via Tree-Guided Subspace Partitioning
Authors: Sheng Wang
Pengan CHEN
Jingqi Zhou
Qintong Li
Jingwei Dong
Jiahui Gao
Boyang XUE
Jiyue Jiang
Lingpeng Kong
Chuan Wu
Venue: NeurIPS 2025 spotlight ()
Keywords: Data Synthesis
Tree-Guided Space Partitioning
Data Diversity Enhancement
Primary area: applications
TL;DR: We propose TreeSynth, a tree-guided subspace-based data synthesis approach, achieving superior data diversity, model performance, robust scalability, and data balance efficacy.

Abstract: Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. 
Despite the great potential of large language models (LLMs) for data synthesis, current approaches are constrained by limited seed data, model biases and low-variation prompts, resulting in limited diversity and biased distribution with the increase of data scales.
To tackle this challenge, we introduce TreeSynth, a tree-guided subspace-based data synthesis approach inspired by decision trees. 
It constructs a spatial partitioning tree to recursively divide a task-specific full data space (i.e., root node) into numerous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes to ensure both distinctiveness and comprehensiveness, before synthesizing samples within each atomic subspace. 
This globally divide-and-synthesize method finally collects subspace samples into a comprehensive dataset, effectively circumventing repetition and space collapse to ensure the diversity of large-scale data synthesis.
Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the re-balancing of existing datasets for more balanced and comprehensive distributions.
Empirically, extensive experiments across diverse benchmarks consistently validates the superior data diversity, model performance, and robust scalability of TreeSynth compared to both human-crafted datasets and peer data synthesis methods, with the average performance gain reaching 10%.
Besides, the consistent improvements of TreeSynth-balanced datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at https://github.com/cpa2001/TreeSynth.

TREESYNTH: Synthesizing Diverse Data from Scratch via Tree-Guided Subspace Partitioning
Sheng Wang Pengan Chen", Jingqi Zhou", Qintong Li, Jingwei Dong
Jingii
The University of Hong Kong {u3009618, cpa2001, u3011211, qtli, joviedong89)
hku.
Jiahui Gao
Boyang Xue, Jiyue Jiang
The University of Hong Kong igau aahui@gmal..... com
The Chinese University of Hong Kong
byxueese- cuhk, edu. hk, jiangjyčlimg ink cuhk, edu.hk
Lingpeng Kong, Chuan Wu
The University of Hong Kong Olpk, cwu)ecs. hku. hk
Abstract
Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential large language models (LLMs) for data synthesis, current approaches are con- strained by limited seed data, model biases, and low-variation prompts, resulting limited diversity and biased distributions with the increase of data scales. To tackle this challenge, introduce TREESYNTH, tree-guided subspace-based data syn- thesis approach inspired by decision trees. It constructs a spatial partitioning tree recursively divide a task-specific full data space (i.e., root node) into numer- ous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes ensure both distinctiveness and comprehensiveness before synthesizing samples within each atomic subspace. This globally dividing-and-syntee -antsentnnsiizing method finally collects subspace samples into comprehensive dataset, effectively cireumventing repetition and space collapse to ensure the diversity of large-scale data synthesis. Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the rebalancing of existing datasets for more bal- anced and comprehensive distributions. Empirically, extensive experiments across diverse benchmarks consistently demonstrate the superior data diversity, model performance, and robust scalability of TREESYNTH compared to both human- crafted datasets and peer data synthesis methods, with an average performance gain reaching 10%. Besides, the consistent improvements of TREES balla-bal datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at wtthh:tt//// /ttp//ggttttbttt// com/ 2oom/ppp2200///ee5ymtth
Introduction
With the superior performance, large language models (LLMs), such OpenAl ol M. LLaMA- 3 (2), and DeepSeek RI (3). have been deployed for various downstream applications, including code copilot 4. mathematical reasoning [5]. psychology (6), etc. The success of these models
Equal Contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Temperature Sampling
(b) Evol-Instruct
TREESYNTH
Figure 1: Intuitive comparison of Temperature Sampling, Evol-Instruct, and TREESYNTH. Tem- perature Sampling typically generates a specific data distribution induced by model biases, while Evol-Instruct evolves seed data along specified directions. In contrast, TREES YNTH starts from a global perspective by dividing the entire data space into mutually exclusive and complementary subspaces before sampling from each subspace, resulting in more balanced and diverse dataset with comprehensive coverage.
largely depends on the availability of large-scale diverse training datasets. However, open-access data are typically drying up 77 []. and manual data curation is both time-consuming and labor- intensive [9 TO,, hindering its availability. This necessitates novel approach to continuously generate data that supports the ongoing advancement of LLMs across different domains.
To customize LLMs and further enhance their specific capabilities, synthesizing domain-specing data using their remarkable abilities emerges as promising solution [2] Pioneering approaches typically paraphrase current datasets [ [3], or prompt existing LLMs reproduce their training data 15). However, due to the inherent model biases and minimal-variation prompts, the generated data often suffers repetition and homogeneity. To remedy this, increasing sampling temperature [T6] increases data diversity yet reduces quality. In contrast, attribute-driven approaches (e.g.. Persona Hub [17) utilize the in-context learning capabilities of LLMs offer increased diversity and improved quality simultanously. Alternatively, evolving new data from existing datasets, represented by Evool-nntrucc (18), augment existing data along different directions induce diverse generation. More details about the related works are provided in Appendix. 5 However, as shown in Figure [ from the perspective of data space, these methods typically start from the local distribution (i.e., model biases, seed data, or vor-variation prompts) without the global view, hindering their comprehensive coverage. This raises following question:
"Is there an automatic solution that starts from global perspective to fully cover the domain-specifie data space for higher diversity?"
To achieve this objective, we introduce TREESYNTH, a tree-guided subspace-based data synthesis approach inspired by decision trees [9]. It consists of two key stages: data space partitioning and subspace data synthesis. During the former phase, as illustrated in Figure 2 TREESYNNHH employs spatial partitioning tree to recursively divide task-specific whole data space (i.e., root node defined by textual descriptions) into numerous atomic subspaces (i.e., leaf nodes). These subspaces characterized by mutually exclusive and exhaustive attribute values ensure both distinctiveness and diversity. In the subsequent subspace data synthesis phase, samples are generated within each subspace separately, before collecting them diverse and comprehensive dataset. By employing this globally syvid--and-synthesizz methodology, TREESYNNH effectively prevents repetition and space collapse to ensure the diversity and completeness of large-scale data synthesis, successfully avoiding the drawbacks of previous methods. Additionally, the spatial partitioning tree enables the allocation of samples into atomic subspaces, thereby allowing the oe-balancing existing datasets for more balanced and comprehensive distributions. Extensive experiments with both open- source and closed- source models across diverse benchmarks, spanning mathematical reasoning, code generation and psychology, demonstrate that TREES YNTH consistently achieves the best downstream performance with superior data diversity compared to both human-crafted datasets and peer data synthesis methods, with the average performance enhancement reaching 10%, underscoring its great effectiveness and generalization. Besides, the linear (or even better) performance growth trajectories with increased data volume highlight TREES YNTH's remarkable robustness and scalability for large-

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scale data synthesis. Furthermore, the improved results achieved by applying TREES YNTH to the synthetic datasets demonstrate its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement.
The main contributions are summarized follows:
We propose TREES a tree-guided subspace-based data synthesis approach, which features mutually exclusive and exhaustive subspace partitioning, effectively circumventing repetition and space collapse to ensure the diversity large-scale data synthesis.
Extensive experiments consistently highlight TREESYNTH's s superior data diversity, model performance and robust scalability over human-crafted datasets and peer synthesis methods.
The sample allocation of TREESYNTH allows re-balancing existing datasets for more prehensive coverage, leading to empirically verified downstream performance enhancement.
Determination
Sabopoce Coverage
Descriptian the GSMBK datanet
SAMPLES
Fult seller apaties solls the tn kags TE be sells saps appllss many applles does bo have loter
sehool,
Type Nathoutirrl Operatiin
Attribute CuRrrNcTiOn
Alteibuts adcition
Alteibuts capsie reet
Attribute nakilis
SAMPLES
SAMPLES
SAMPLES
neteorology statice nattlmncers of Apri2 aillimeerss selly sttikers. the bays pack core stockans and glvee stäckere to friend, New sany atdccaans doss ielly 1900 neu?
the rainfa33
There and de seats theater, 2e 25 people ard already staked and 25 mere poppl entery, You meny seats and accepped rey!
Criterfon
1yps Nathomctical operation
Altribute
Criistion Enidity Type
Albribtte
Attrbuut
Attrtbute TN
Attrhbutc
SAMPLES
SAMPLES
SAMPLES
SAMPLES
A cookie factery cnd canctes Mencay and 375 ookils Thesday, Foe many caattes were predaced sceoss the diss? may
Peter centies at then, Hiss der then gave constes. fre miny cookies decs Peter totau?
sathomrtica
Attribute 2
abiltion
Cilterion 2
Enitity Type
Attribute
Finsl action
Attributc
Attribute ate
Altributc
Attributce
hough
clared
SAMPLES
SAMPLES
(SAMPLES
SAMPLEES
Nilly prosared caso coek las for wheel neet nustneers trught on reeklis to the and cwckles In the aftereson awy reactes, uete Irager In toral? rel peooiooes
Niw mary heught altegethen!
seekand tech- nech-canforerce caff, atterdeas bought costias first session and copties than provioss sessdoe in each of the nact four avera22?
suszions.
Figure 2: A spatial partitioning tree visualization of TREESYNTH, exemplified through GSM8K-style data synthesis.
3

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2 Preliminary Knowledge
widely recognized for their simplicity, efficiency, and strong interpretability. For any given sample, the decision tree recursively allocates it deeper nodes within the hierarchical structure, until it reaches one and only one leaf node. This functionality relies on two essential characteristics: (1) All leaf nodes of any sub-tree starting from the root node are mutually complementary, ensuring every sample can be allocated to at least one leaf node, (2) All leaf nodes of such a sub-tree maintain mutual exclusivity, guaranteeing most one leaf node.
As canonical machine learning algorithm, decision trees [99]
each sample can be assigned
From a spatial perspective, the root node represents the entire sample space. As the tree delves deeper with each layer of nodes, the space is exhaustively and exclusively divided into multiple subspaces (i.e., child nodes). Hence, for any given task, we can conceptualize its training data as the entire space (i.e., root node), allowing to establish mapping between the nodes of decision tree and the training data subspaces. In detail, the decision tree partitions the entire training data space into multiple leaf nodes, with each leaf node corresponding to data subspace with specifie attributes.
This inspires us to leverage the subspace partitioning of decision trees for data synthesis, offering two notable advantages: (1) Diversity: The exclusivity of leaf nodes ensures the variation across different subspaces, thereby guaranteeing samples diversity. (2) Comprehensive Coverage: The complementarity and exhaustiveness of leaf nodes ensures the sampling of comprehensive data, preventing sample collapse.
Method
Inspired by the mapping between a decision tree and data space, we propose TREESYNTII, a tree- guided subspace-based data synthesis approach. It consists of two primary stages: data space partitioning and subspace data synthesis. The first stage generates spatial partitioning tree T, analogous to the construction of decision tree, while the second synthesizes data within each atomic subspaces (i.e., leaf node). Beyond data synthesis, we also elaborate how TREESYNTH can re- re-balance existing datasets, facilitating more comprehensive coverage and induced performance improvement.
3.1 Data Space Partitioning
Given any data space S (i.e., any node in the tree) with its context description Cs. data space partitioning aims to decompose it into multiple subspaces Sub- = {s.li = 1,2, ..., n). As shown in Figure Bal the partitioning process mirrors the construction of decision trees, and comprises two critical steps: Criterion Determination and Subspace Coverage. These steps ensure the mutual exclusivity (i.e., Vp # 9, Sp O $q = Ø) and exhaustiveness (i.e., U 8; = S) among subspaces, respectively. This suggests that each subspace is disjoint, and collectively, they fully encompass the original space.
Criterion Determination. The essence of this step lies in selecting criterion 5 that most effectively differentiates data within the space S so that most data characteristics can be captured with minimal criteria. Specifically, according to the space description Cs (e.g., "GSM8K-style mathematical questions" as shown in Figure 2). an LLM is firstly deployed to generate 1 maximally diverse pivot samples X' {aalt 2, .....] }} to approximate the whole space S. Subsequently, another off-the-shell shelf LLM, instructed to proficiently identify samele distinctions, determines exactly one core criterion d (e.g., Type of Mathematical Operation). This criterion ó optimally partitions X' into mutually exclusive attribute values V {uğli = 1,2,... m] (e.g., addition and subtraction). categorizing each sample 2, e X into exactly one attribute value to ensure mutual exclusivity across child nodes.
Subspace Coverage. Despite the existing attribute values V the mutually exclusive subspace S% derived from partitioning X' with these values, may not exhaustively cover the original space S due to a limited number / of pivot samples. This imposes the risk of non-complemenntrrit among the child nodes. Hence, subspace coverage is designed to supplement potential attribute values of criterion to comprehensively model the entire data space S. Specifically, we instruct an LLM to expand the attribute values V to V/ = {ufli = 1, 2, .... m, m + I,.... n) (e.g., additionally including square root and modulus). The expanded attribute values V must be overolargg and fully cover the criterion 8. Consequently, the exhaustive and exclusive subspaces Saub {s. i 1,2,..., m.m++ m 1,..., ..)
can be generated by s, Cs n of for each i, completely filling the data space S.

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Criterion Determination
Subspace Coverage
C1
C1
A1
A
B²
B1
C2
Aa
C2
B2
A...
A.
(a) Tree Perspective
(b) Spatial Perspective
Figure 3: Illustration of TREESYNTIL (a) Data space partitioning iterates criterion determination and subspace coverage. The former identifies the criteria (e.g. a, B. 7) and their associated attribute values (e.g.. of, 2/2 of. vg. v7. vz)) to divide current nodes (e.g., entire space O, A1, A2. A... B B2) until reaching the leaf nodes (e.g., atomic subspaces C1, C2, ..., while the latter complements potential attribute values (e.g., v..) to ensure exhaustive coverage of the entire data space. (b) The spatial visualization depicts the mapping between tree nodes and data subspaces, highlighting the mutually exclusiveness and exhaustiveness of the subspaces.
However, not all criteria can be exhaustively enumerated. For example, if criterion standard is numerical values of mathematical questions, it contains infinite attribute values (e.g.. 0, 1, 2, ...). In such cases, we set maximum number of attribute values N. Once the number of attribute values n exceeds N, we refrain from setting individual sub-nodes for each attribute value, and instead establish an infinite node encompassing potential attribute values. Whenever needed, one attribute value is randomly sampled from all potential candidates. This effectively prevents the generation of numerous trivial child nodes, thereby reducing the redundancy of the tree.
Spatial Partitioning Workflow. Recursively, we apply both criterion determination and subspace coverage steps to construct a complete spatial partitioning tree. As illustrated in Figure 2 and 3 starting from the entire data space O (i.e., root node N Roott represented by training data description Co. we first perform criterion determination effectively distinguishes data within the space O. Through subsequent subspace coverage, O is partitioned into mutually exclusive and exhaustive subspaces Oub {A 1,2, ...} based on a. Subsequently, the breadth-first search (BFS) algorithm is applied to each subspace A& to recursively execute both steps until reaching the maximal depth d. As shown in Figure 3al A2 is further divided into B, and B2, with B1 subsequently partitioned into the leaf nodes C1 and Cz. Finally, spatial partitioning tree is constructed and decomposes O into numerous mutually exclusive and complementary atomic subspaces O each corresponding to leaf node N We also present the pseudo code to formularize the whole process in Algorithm [ The mutual exclusivity of leaf nodes intrinsically ensures diversity in the synthesized dataset, while their exhaustiveness guarantees comprehensive coverage of the data space. The dual properties effectively prevents data collapse observed in previous data synthesis methods.
O identify the optimal criterion a that most
3.2 Subspace Data Synthesis
The objective of subspace data synthesis stage is to create data within mutually exclusive and complementary atomic subspaces Ojcct defined by spatial partitioning tree T, ultimately producing diverse and balanced dataset with comprehensive space coverage. Specifically, for each leaf node Miter we first compile its description along the hierarchical path from the root node NRoot to itself. This path can be formally expressed as Notoo of 0/
2h Ni where {uf, u.) ......; 221] denotes the individual attribute values of parent nodes along the path. Similar the ,
generation of pivot samples, combine both Co and the attribute value sequence {uf of ... .,,)) as the description of Of and instruct LLM to generate NLeaf samples distributed within its subspace. As depicted in Figure Ic by collecting data generated within all the leaf nodes, we obtain final dataset with high diversity, balanced distribution, and comprchensive coverage.
3.3 SHRESYNTH-Guider Data Balance
Beyond data synthesis, TREESYNTH can also be leveraged to optimize existing datasets for improved balance and comprehensiveness. Given that TREES YNTH synthesizes data from scratch, spatial
5

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partitioning tree To can be constructed solely based on the context description Cp (i.e., full space OD) of given dataset partitioning, every sample du can be systematically routed through successive levels of the hierarchy, ultimately landing in a unique leaf node (i.e., atomic subspace). The distribution of all the samples across leaf nodes reveals the dataset's s coverage pattern within the full space. To regulate the distribution across subspaces, a threshold Nub is introduced. Subspaces containing more than Nubb samples are randomly downsampled to reduce overrepresentation, while those with fewer samples are augmented with TREES YNTII to meet the threshold. The integration of all adjusted samples yields a new dataset Dalannce with more comprehensive coverage and better balance than the vanilla one.
{d,//u 1, 1.2.....u w). Thanks to the mutually exclusive and exhaustive
Experiments
4.1 General Setup
Benchmarks. To comprehensively evaluate the advantages of TREESYNTH, we compare it against several baselines across diverse benchmarks. For data synthesis. we first apply standard mathemat- ical reasoning and code generation tasks, including GSM8K (20), MATH (21, MBPP [22] and HumanEval [23], to assess TREESYNTH s data diversity, model performance improvement, and scala- bility. Besides, we employ SimpleToMM (24), psychological task, to further examine TREESYNTH's effectiveness in promoting data balance. More details are elaborated in Section Sec A.2
Base Models. For generation models to synthesize data with different methods, we employ both open- source (i.e., LLaMA3. 3--70-Innstrnn (i.e., GPT-4c) models. To compare the performance of TREESYNTH and baselines, we fine-tune two popular open-source foundation LLMs (i.e., LLaMA3. 1-88 (2] and Qwen2.5- (25 on the perspective generated data. These models are chosen for their leading performance and popularity.
2 and Qwen2. 5- 5-722-188 Instruct (25) and closed-source
evaluate the effectiveness of TREESYNTH by comparing it with two categories of baselines. The first category comprises human-curated datasets (i.e., Vanilla Data): the training sets of GSM8K (7,473 samples) and MATH (7,500 samples) for mathematical reasoning, and Code Alpaca [26 (2,689 sample for code generation. The second category consists of LLM-synthesized training data, covering three representative methods: Temperature Sampling [16], seed-driven method (i.e., Evol-Instruct (18). and attribute-driven method (i.e., Persona Hub (17). Each method synthesizes 100k samples in the styles of GSM8K, MATH, and Code Alpaca, and 40k samples in SimpleToM style. Further details
Baselines. With standard fero-Shot and Few-Shot performance
reference,
on the baselines and implementation are provided in Appendix A.3 and A.4 respectively.
4.2 Main Results
(a) GSM8K
(b) MATH
(c) Code Alpaca
Figure t-SNE visualization of LLLMM3..... ..0.MM3.37700.. 3- Ins- www.33-----nuutt-syyyy--- Iww.srutttssttsssiieeeeee datasets for various methods across GSMSK. MATH, and Code Alpaca styles.
TREESYNTH exhibits substantially better data diversity and more comprehensive coverage across various tasks and models than both human-curated datasets and peer synthetic methods. As shown in Tables I 2 and we compare the data diversity of TREESYNTH and peer methods driven by Qwen2.5-725 Instruct, LLaMA3. 3- -Instruct, and GPT- respectively. Temperature Sampling consistently yields lower diversity than vanilla training datasets. Although Evol-Instruct and Persona Hub show improvements over vanilla ones some cases, they generally deteriorate on MATH benchmark, suggesting their limited robustness. Compared to all the baselines, TREESYNTH
wwcpiiaaaa.mmmmeaaaaaaeeeeeeeeee http/innex///ee hhello-aahhll 10po-pp---0 gpt-4o/ 40/
Only Python-related samples retained, aligning with HumanEval and MBPP

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Method
GSM8KI
Diversity.
MATH
Diversity.
MBPP1
HumanEvali
Diversity.
Avg.1
Foundation Model: LLAMA-3.J 8B
Zero-Shot
4.85
3,54
19.8
15.85
I 11.01
Few-Shot
40.26
20.46
Varilla Data
58.15
0.40
19.48
0.16
46.8
43.29
0.29
41.93
Tomp. Sampling
55.42
0.44
22.08
0.37
44.6
41.46
0.33
40.89
Evol-Instruct
63.46
0.37
27.26
0.15
40.6
41.46
0.22
43.20
Persona Huh
61.41
0.35
23.78
0.34
45.8
40.24
0.26
42.81
TREESYNTH
69.45
0.36
27.52
0.15
50.2
48.17
0.23
48.84
Foundation Model: QWEN-2.5 7B
Zero-Shot Few-Shot
54.97
54.38
11.2
54.88
43.86
67.40
47.58
Vanilla Data
68.76
0.40
47.68
0.16
53.4
77.44
0.29
61.82
Temp. Sampling
69.67
0.41
61.70
0.37
54.8
76.83
0.33
65.75
Evol-Instruct
75.13
0.37
59.60
0.15
55.8
76.83
0.22
66.84
Persona Hub
82.79
0.35
61.98
0.34
58.8
75.00
0.26
69.64
TREESYNTH 85.44
0.36
63.28
0.15
59.4
78.05
0.23
71.54
Table 1: Model performance and data diversity comparison of various methods with LLaMA3. 3--MA..3-70B--
3-70B-
Instruct-powered data synthesis across two foundation models and multiple benchmarks. "Zero- Shot" and "Few-Shot" exhibit the base performance of foundation models. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original GSM8K and MATH training sets, and the Code Alpaca Python subset for HumanEval and MBPP. "Diversity" is measured by cosine similarity, where lower values indicate greater diversity. Bold and underlining indicate the best and second-best indicators, respectively. "Avg." means the average of the performance scores across all the benchmarks.
consistently achieves the best diversity across almost the benchmarks and generation models. Notably, the GPT LTT-4o-powered TREESYNTH exhibits diversity enhancements of 12.5%, 25.0%, and 34.5% over the vanilla GSM8K, MATH, and Code Alpaca datasets, respectively. In addition, we generate sentence embeddingg 14 of instructions synthesized by various methods powered by LLaMA3. -0--IIIIIIttc.. and visualize their distributions via t-SNE method (27) Figure Apparently, Temperature Sampling and Persona Hub exhibit concentrated distributions in limited subspaces, revealing severe diversity constraints stemming from inherent biases. Evol-Instruct's distributions mirror those of vanilla datasets, demonstrating strong dependence source data. In contrast, TREESYNTHE strategically partitioning the full space from a global perspective and synthesizing data within subspaces, eliminates inherent model biases and transcends source data limitations. Briefly, both the observation on diversity indicators and visualization confirm the efficacy of TREESYNTH in producing diverse and comprehensive datasets across various domains and models, effectively alleviating inherent model biases and constraints imposed by initial datasets.
Models trained on TREESYNTH data consistently outperform those trained on both human- crafted datasets and synthetic baselines across all the tasks, foundation and generation models. Specifically, for fair comparison of different methods, we train models using randomly sampled subsets from each synthetic dataset, matching the sizes the corresponding vanilla training sets. As shown in Tables 2 and 4
all synthetic methods Setthods-Temperturr Sampling, Evol- Evol-Instruct, and Persona Hub generally surpass numan-curated datasets on average, highlighting the limitations of manual data construction. Thanks the seed-driven and attribute-driven design, Persona Hub further outperform Temperature Sampling, aligning with the claims in their original works 18 More microscopically. these methods, however, do not yield stable improvements across all benchmarks. For instance, in Table [ their performance on the HumanEval benchmark falls below that of the vanilla dataset, indicating limited robustness. In contrast, TREES delivers the best performance across all tasks, foundation and generation models than all baselines without exception. Notably, training Qwen2. 5-7B on TREESYNTH data synthesized by GPT-4o yields average performance improvement of over 10% compared to the original training sets, underscoring the effectiveness and robust generalization capabilities of TREESYNTH
and
With the global data spatial perspective guided by tree structure, TREESYNTH effectively scales datasets while preserving data quality, suggesting great scalability wherein downstream performance consistently improves with increased data volume. As shown in Figure 6 and
We utilize the popular all all-mpnet-base-VV v2 model, available at husps:/inggingfocc.com sentence- www.storrerssseeeooooto
base-v2
7

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Method
GSM8K1
Diversity!
MATH
Diversity. MBPP
HumanEvali
Diversity.
Avg.t
Foundation Model: LLAMA-3.
Zero-Shot
4.85
3.54
19.8
15.85
11.01
Few-Shot
40.26
20.46
Vanilla Data
58.15
0.40
19.48
0.16
46.8
43.29
0,29
41.93
Temp. Sampling
54.97
0.45
24.28
0.29
44.8
45.73
42.45
Evol-Instruct
61.03
24.58
0.19
45.2
45.05
Persona Hub
63.38
0.35
27.74
0.28
45.2
45.12
0.29
45.36
TREESYNTH
66.72
0.35
30.34
0.12
50.8
50,00
0.19
49.46
Foundation Model: QWEN-2.5
7B
Zero-Shot Few-Shot
54.97
54.38
11.2
54.88
43.86
67.40
47.58
Vanilla Data
68,76
0.40
47.68
0.16
53.4
77.44
0.29
61.82
Temp. Sampling
80.67
0.45
62.76
0.29
59.6
80.49
0.32
70.88
Evol-Instruct
73.16
0.39
61.10
0.19
59.2
80.49
0.25
68.49
Persona Hub
83,24
0.35
66.22
0.28
61.6
77.44
72.12
TREESYNTH 86.13
0.35
66.84
0.12
62.8
80.49
0.19
74.06
Table 2: Model performance and data diversity comparison of various methods with GPT-4o-powered data synthesis across two foundation models and multiple benchmarks. "Zero-Shot" and "Few- Shot" exhibit the base performance of foundation models. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original GSM8K and MATH training sets, and the Code Alpaca Python subset for HumanEval and MBPP. "Diversity" is measured by cosine similarity, where lower values indicate greater diversity. Bold and underlining indicate the best and second-ber best indicators, respectively. "Avg." means the average of the performance scores across all the benchmarks.
Vanilla
Sumpling
TraSysis
GSMRK Task for 148
MATH Tink for 1LMM3331-8
MBPP Task for LLMMANL-B
HamzoFval Task for L1-MAR1-58
255
triiig Uxality GSMBR Task for Qumn25-78
Scaling Qeality MBPP Task for Quend5-78
MATH Tack for Qwes25-18
HamanFivll Tank for Qma115-18
AASEYAO CAN
Stating Quendily
Seeking Queadly
Seiding Queadty
Sweking Drenky
Figure Model performance trends across data scales different methods powered by LLaMA3. 3-3 70B- Instruttt "Temp. Sampling" refers to Temperature Sampling. "Vanilla Data" denotes original GSMSK and MATH training sets, and Code Alpaca Python subset for HumanEval and MBPP.
we evaluate model performance across synthetic datasets 1k, 10k and 100k samples, as well as scale equivalent to the corresponding vanilla training sets. cuunaned datasets inherently suffer from limited scalability due to the prohibitive cost of manual annotation. Despite exhibiting linear growth trends occasionally, all the baselines (i.e., Temperature Sampling, Persona Hub, and Evol-Instruct) encounter performance saturation with diminishing improvements as dataset volume increases nearly half of the evaluated settings, and even suffer from degradation in some cases, reflecting their instability. As mentioned above, this can be attributed to the intensification of low-variation prompts, model and seed data biases. contrast, TREESYNTH not only remarkably surpasses all the baselines on all data scales, but also exhibits approximately linear (even better) performance growth with increasing data volume, underscoring its superior scalability. Besides, with the globally spatial perspective circumventing the local distribution biases, TREES YTT still exhibits

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Vanilla Dam
Temp. Sampling
Tord-istruct
Penara Hish
TreeSyath
HumenEsol
Qwety Q.ce25.7B
Qealt
Qwen25-7
Rd
Figure 6: Model performance trends across data scales for different methods powered by GPT-4o. "Temp. Sampling" refers to Temperature Sampling, while "Vanilla Data" denotes original GSMSK and MATH training sets, and Code Alpaca Python subset for HumanEval and MBPP.
TREESYNTH Harrr-bbalaned
Performance
Temp. Sampling
Persona Hub
TREESYNTH
Temp. Sampling
Persona Hub
Accuracy 78.9
85.7
88.0
86.8
88.6
Diversity 0.37
0.33
0.33
0.33
0.32
Table 3: The diversity of data generated by different methods powered by LLaMA3. 3-70B- IOB-Innstuct Data Balanced version, along with the performance of LLaMA3. 1-8B
and its trained on these datasets on the SimpleToMM benchmark. "Div." " stands for Diversity, metric assessed by computing cosine similarity among data points within the dataset, where lower numerical values directly indicate higher diversity levels.
steeper performance growth trajectories beyond the 10k sample scale, indicating its great potential for large-scale data synthesis. Detailed numerical results are also provided in Table 6 and 8 in Appendix A.5 for more precise reference.
4.3 TREESYNTH-Guided Data Balance
Beyond data synthesis, TREESYNTH significantly enhances the distributional balance of existing datasets, effectively improving data diversity and downstream model performance. Specifically, we repeat the 3.a.M3.3-220 3-1.3--7B-1100 IesB-Innttuuttpowee
experiments on the LLaMA3. 1 1-8B foundation model Section 4.2 on the SimpleToM benchmark, but additionally apply the FREESYNTIE -THHgggdeHg guided data balance technique to the synthetic datasets of Temperature Sampling and Persona Hut As listed in 3 TREESYNTH continues to outperform other unbalanced approaches. Mcanwhile, the application of 2.9% for Temperature Sampling and Persona Hub, respectively. To demonstrate the underlying data distribution more intuitively. Figure presents the t-SNE visualization of data spatial distribution for different approaches. Benefiting from the global perspective, TREESYNTH exhibits comprehensive and well-balanced distribution across the data space. contrast, samples from Temperature Sampling and Persona Hub predominantly tend to cluster in limited subspaces, revealing insufficient diversity, The application of TREESYNTH substantially enhances their distributional uniformity, enabling comprehensive coverage of the data space. These results collectively demonstrate that TREESYNTHE guided data balance effectively addresses deficiencies existing datasets by optimizing their sample distribution, leading to measurable improvements in downstream model performance.
data balance leads performance improvements of 7.9% and
Invoo-Instructio is excluded in this section, due its strong dependence seed dataset.

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5 Related Work
Data Synthesis via LLMs. Owing to their remarkable ability to generate large-scale, high-quality datasets, LLMs are increasingly being explored as an effective alternative to the time-consuming and
labor-intensive process of human annotation [8 Pioneering studies [1 18 [2] have showcased the use of LLMs to paraphrase augment existing instruction datasets into more comprehensive ones. Furthermore, recent research has explored data synthesis from scratch in areas such as mathematics [5). code R3 general alignment 34, etc. However, uncontrolled synthesis process often exhibits significant biases, favoring easy queries while neglecting more challenging ones [35]- 37.. To enhance controllability. Wong et al. (38 and Huang al. [39] incorporate strata and topic clustering as guidance, respectively. Our approach distinguishes itself by constructing a tree-like hierarchical structure from seratch to model the data space for better controllability.
Diversity Enhancement in Data Synthesis. The diversity of training datasets is essential for enhancing model generalization [0] Numerous studies have sought to improve diversity during data synthesis [41443]. Specifically, increasing sampling temperature [66 can generate more diverse data; however, it often provides limited domain coverage and decreased quality 44). To promote diversity while ensuring quality, recent methods take advantage of the in-context learning capabilities LLMs
through manually designed rules for data evolution [18] 45 48). However, from the perspective of data space, they typically start from the local distribution (i.e., seed data) without the global view, hindering their comprehensive coverage. Besides. synthesized data often becomes repetitive and homogencous with the increase of data scales due to the inherent model biases. To address this challenge, various competing methods have emerged, particularly those based attribute combinations [4), such as persona-driven data synthesis [7]. However, these approaches typically rely on fixed attribute dimensions curated by LLMs or human knowledge. In contrast, our work emphasizes the dynamic construction of tree structure to iteratively partition the entire domain space, ensuring comprehensive coverage without human intervention.
Application of Tree Structure. As a canonical data structure, trees have been applied in various machine learning algorithms. Specifically, decision trees conceptualize discriminative tasks search problem through tree-like combinatorial problem space (53] Besides, Hao et al. [56). Yao et al. [57] utilize teee-scarch algorithms, including breadth-fin first search, depth-first scarch, and Monte Carlo Tree Search [58), to guide multi-step reasoning process for improved reasoning capabilities of LLMs. Furthermore, AlphaZero-like tree search learning approach (59] leverages learned value function to guide the decoding process of LLMs, and particularly improves the performance on long-horizon planning. In contrast, our method does not rely on tree structures for discrimination tasks or to improve reasoning capabilities. Instead, it focuses on data synthesis through hierarchical tree-like spatial partitioning. Besides, the decision rules are not learned but are directly derived from the extensive knowledge inherent in LLMs.
6 Conclusion
Targeting synthesizing diverse datasets with LLMs from scratch, we propose a tree-guided subspace- based data synthesis approach, TREES which recursively partitions a task-specific full data space into mutually exclusive and exhaustive atomic subspaces before synthesizing and collecting subspace samples into comprchensive dataset. This globally divide-and-synthesize strategy effec- tively circumvents repetition and space collapse caused by model biases, seed data, and Low-variation prompts in prior methods, promoting the diversity of large-scale data synthesis. Besides, TREES YNTH also facilitates sample allocation into atomic subspaces, enabling re- re-balancing of existing datasets for more balanced distributions. Compared with both human-crafted datasets and peer data synthesis methods, TREES YNTH consistently achieves superior data diversity, model performance, robust scalability, and data balance efficacy, establishing itself as a promising solution for diverse data synthesis without seed data.
7 Acknowledgement
This work was supported in part by Hong Kong Innovation and Technology Commission's Innovation and Technology Fund (Award No. ITS/269/2FFP), Hong Kong RGC grants C7004-22G (CRF) and CRS_ PRS__PO05500/23 (CRS).
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A Appendix
A.1 Pseudo Code of TREESYNTH
The pseudo code of TREESYNTH is presented in Algorithm 1
A.2
Benchmarks
To thoroughly evaluate the performance improvements enabled by SHHEESYNTH--eeeralce data, we
test models across three domains: mathematical reasoning, code generation, and psychology tasks. The mathematical reasoning tasks use the MATH dataset test set [2] and GSM8K benchmark [20].
Code generation capabilities are assessed through HumanEval 24 and MBPP (22). For psychology
tasks, we employ the Simple ToM dataset [24]. These benchmarks collectively assess our method's
effectiveness across multiple dimensions, with brief descriptions provided below:
GSM8K evaluates mathematical reasoning capabilities through 8,500 high-quality grade school math problems developed via human expert annotation. The dataset partitioned into 7,500 training and 1,000 test problems, each requiring 2-8 computational steps combining basic arithmetic operations.
MATH dataset comprises 12,500 competition-lete mathematics problems, with 7,500 designated for training and 5,000 for testing. It requires step-by-ster solutions, emphasiz- ing accurate problem decomposition and the generation of formal proofs for multi-step mathematical challenges.
HumanEval evaluates functional correctness through hand-written programming problems requiring language comprchension, reasoning. algorithms. and mathematics. comprises 164 problems with function signatures, doestrings, and unit tests (avg. 7.7 per problem). Tasks are manually crafted avoid data leakage from public code repositories.
MBPP evaluates programming competence through entry-level Python functions requiring implementation based on textual specifications and test case verification. It contains 974 crowd-sourced programming problems with functional correctness validation, including core subset of curate- solutions with manual quality assurance.
SimpleTTMM is designed to evaluate whether LLMs can implicitly apply Theory of Mind (ToM) reasoning predict behavior and judge the rationality of observed actions in social scenarios. It consists of concise, diverse stories followed by three questions that assess different levels of ToM reasoning: predicting a character's s mental state, forecasting their behavior, and judging the rationality of their actions
A.3 Baselines
The concise descriptions of all the baselines are presented below.
Vanilla Data. "Vanilla Data" refers to the original GSM8K and MATH training sets, as well as the Code Alpaca Python subset used for HumanEval and MBPP, with details on GSM8K and MATH datasets provided in Sec [.2] The Code Alpaca dataset is collection of 20,000 eosruction-following data points, each containing unique task description, optional input context, and a corresponding output, designed to train language model for code generation tasks by following specific instructions. Only Python-related samples are retained, aligning with HumanEval and MBPP.
Temperature Sampling. Temperature sampling adjusts the softmax function of L.MSs to control output randomness by scaling logits. Higher temperatures increase creativity and randomness, while lower temperatures result in more deterministic outputs. Following
the prompts consistent with TREES YNTII, as illustrated in Figures [3] [4, and [5] we set the temperature to 0.7 and generate 100k baseline data in GSM8K, MATH, and Code
'In the Sim-sleoo datasct, data where the protagonist is unaware hidden information labeled as negative samples, while data where the protagonist is aware of hidden information is laboled as positive samples. In this paper, all SimpleToM-sty data starts by generating negative samples to account for half of the dataset. These are then converted into positive samples using the prompts shown in Figures 29 The combination positive and uogative samples forms complete dataset.
22

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Algorithm/ Pseudo Code of TREESYNTH
Require:
Context description Co of entire data space O, Pivot sample count I, Maximum attribute value count N, Maximum tree depth d'
1: function CRITERION DETERMINATION((S.
2: Generate diverse pivot samples X' {xeeii- via LLM (Cs)
3: Determine exactly one core criterion LLMaxnemine (X))
4: Obtain mutually exclusive attribute values VX Partition(X,6)
5: return 8, VX
6: end function
7:
function SUBSPACE, COVERAGE(CS. 6, VX. N)
8:
Fully cover the criterion with attribute values Vs
Lompolmemmen (vx, 8)
9:
if [s| > N then
Create subspace Sthh (Vs)
Randomly sample an attribute value whenever needed.
12:
Create subspace Simb for each U/ & Vs
13:
end if
14: return Suub
end function
D Stage I: Data Space Partitioning
16:
Initialize root node NRoo (i.e., O with Co) with the depth as 0, and BFS queue Q {Nnoot) while = do
17:
Dequeue the first node A" from Q, and obtain its depth d' context description Cy²
19:
if d' < d then
20:
5, Vx CRITERION DETERMINATION((Ar..
Step 1: Criterion Determination >> Step 2: Subspace Coverage
21:
Noi SUBSPACE COVERAGE(CNr, 5, N).
22:
Add N the child nodes of N", and append to the queue Q QUN
23:
else
Mark N" as node Neett
25:
end
26:
end while
return Spatial partitioning tree T with the root node O
D Stage Subspace Data Synthesis
27: Collect all leaf nodes N + (Weest: Neatts"
28: for each Niea Niea
Trace hicrarchical parent nodes from root node P - ".
30: Obtain the attribute intersections as the leaf node description CNy + Nipp V,
31:
Generate diverse leaf samples Diest ( k-1 via LLMaampi CAy.
32:
end for
33:
Collect leaf samples into the final dataset Dana + U return Dinul
b with high diversity, good balance, and comprehensive coverage.
TREES NTH-Guided Data Balance
Require: Dataset {du ju= 1, 1,2, w) data description Co, threshold Nsub
34: Build tree To via Data Space Partitioning using Co
35: Initialize leaves L - (.Niaat.....NN
36: for d., E DD do
37: Route d,, to leaf Nit via To
38: end for
39: for No L do
40:
D' samples in A
41:
if (D')>> Nsw. then
42:
Diew + Downsample to Nsub
43:
else if D Nsub then
D'r.. Synthesize (Nsub - (D')) samples Vic via LLMSs into D
45:
end
46:
end for
47:
Aggregate Dratance U new return Dratance
23

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Alpaca styles, respectively. During the construction of the SimpleToM training set, the temperature parameter is set 0.7 while generating 20k data samples through the combined use of Figures 16 and 29
Evol-Instruct. Evol-Instruct is method that uses LLMs to automatically generate diverse and complex instruction datasets by evolving initial instructions through in in-depth and in- breadth processes, enhancing the complexity and diversity of instructions for training LLMs. This paper utilizes Evol-Instruct to enhance the training datasets of GSM8K, MATH, and Code Alpaca, constructing 100k samples for each respective style (GSM8K, MATH, Code Alpaca) through multiple evolutionary iterations.
Persona Hub. Persona Hub consists of 1 billion diverse personas curated from web data, enhancing diversity in large-scale data synthesis when incorporated into synthetic prompts. By randomly sampling personas from Persona Hub to replace the original "math expert" and "coding expert" profiles in Figures 13 14 and 15 and by prepending personas to the prompts in Figure T6 we synthesize 100k samples each for GSM8K, MATH, and Code Alpaca-style datasets, as well as 20k SimpleToM-styiee data through this persona substitution approach.
A.4 Experiments Details
The training dataset is constructed through TREESYYTT--eeeratte instructions, with LLMs subse- quently producing answers corresponding these instructions.
Spatial Partitioning Tree Construction. For each task, illustrated in Figure 17 18 19 and 20
we develop training data descriptions CaSMSK. CM ATH. CCode and CroM following the standards of GSM8K, MATH, Code Alpaca and SimpleToM respectively. The prompt words for Criterion
Determination and Subspace Coverage are presented in Figure 21
22
23
24
and 25
26 27 28
respectively. Afterwards, we construct the spatial partitioning trees TGSMSK TMATH and Todde using GPT-4o, LLaMA3. 3-70B- S--7O-Innstree Instruct and Qwen2. 2- IIB--nnttuct with maximum tree depth set 4, pivot count to 10. and maximum attribute values N to 50. For SompleToM-- style data, we employ the LLaMA3. 70B -O--Irst model with a maximum tree depth d = 3, while maintaining consistency in all other parameters with the configurations of other tasks, to generate the spatial partitioning tree TroM.
Training Data Generation. For each leaf node in TaSMsK TM ATH and TCode, generate Ni = 10 data instances using the prompts from Figures 17 18 and 19 within their correspond- ing subspaces to construct the raw instruction sets using GPT-4o. LLaMA3 0013..3770 3- - and Quen2. 1xen2.5-72BB 117-22-IInsruuttt For coding-tase taak instructions, following the practice of Code Alpaca (26). compute pairwise Rouge [60] similarity scores between all data entries and filter out data pairs with similarity scores exceeding 0.7. Subsequently, we randomly select 100k instructions from the raw instruction sets and use the same L.LMs that generated the instructions to produce answers, forming the training dataset. For the generation of SimpleToM-stylle data, we use the prompt from Fig- ure command LLaMA3.
generate Neear 10 instructions for each leaf node of TroM, forming an instruction set containing 20k samples. We then use LLaMA3. 3-70B- Instruct generate corresponding answers for these instructions.
FREESYNTH-Guidee Data Balance. We perform TREESYNTH-guied data balancing strategy for SimpleToM-siie datasets. Using the prompt templates from Figure we systematically partition both Temperature Sampling and Persona Hub-style SimpleToM data into distinct subspaces of Troas The sample threshold Ns for each subspace is set to 10 to achieve data balancing across these subspaces.
Model Training. To fine-tune our selected base models (i.e., LLaMA3. 1-8B and Qwen2.5-77 5-7B) we employ the parameter-efficient fine-tuning method LoRA 611633 Specifically, we uniformly set the lora_dra cora_urrpoutt 0, weight_decay 0.1, and trained each model for epochs. For GSM8K-stylee data, we set the learning rate to 1 x 1 For MATH, Code Alpaca, and SimpleToM-ssip data, set
24

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the learning rate to 1 x 10 during training Empirical observations show that these configurations consistently achieves stable and competitive downstream performance across various tasks.
A.5
Complementary Analysis
t-SNE visualization of SimpleToo.-ssty datasets. As shown in Figure we illustrate t-SNE dis- tributions of SimpleToM-styL datasets synthesized by various methods alongside their TREES guided data-balanced counterparts, demonstrating significantly improved and more comprehensive coverage.
TreeSynth
Temp. Sampling
Bal. Semp.Sampling
Persona
Bal. Porsona
Figure 7: t-SNE visualization of SimpleToM-sste datasets synthesized by different methods and their TREESYNTH-quide data balanced counterparts, exhibiting remarkably comprehensive coverage.
Model performance and data diversity comparison. The results presented in Tables 4 demon- strates comparison of data diversity and model performance for different methods powered by Quen2. 5-72B- Se--Inssruct across multiple benchmarks, highlighting TREESYNTHI' superior data diversity and robust performance improvement in downstream tasks.
Model performance across data scales. The detailed numerical values of scalability evaluations across GSM8K, MATH, MBPP and HumanEval benchmarks are provided in Table [ 6 7 and X respectively. In addition, Figure 8 displays the performance trends of various methods using the Qwen2. .ren2.5-72B 5-72B-Instruch generation model across different data scales. TREES consistently outperforms all baselines while exhibiting near-linear scaling with data growth, demonstrating its superior scalability.
Broadening TREESYNTH Assessment Beyond LLaMA and Qwen. To further validate the robustness and generalizability TNEESYNTH, we extend our assessment to Gemma-3-PT-4p and covering additional model families and sizes with all data synthesis methods
Thhese hyperparamoters are selected based on comprchensive grid scarch over candidate values: learning rates (1 10 5 10 4). 1ora_dropout {0, 0.05). weight_decay {0, 0.1), and epoch count
10-5, 1 10 10 1.1 10
{3, 7, 10).
25

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Method
GSM8K
Diversity.
MATH
Diversity.
MBPP1
HumanEvali
Diversity.
Avg.t
Foundation Model: LLAMA-3.J 8B
Zero-Shot
4.85
3.54
19.8
15.85
11.01
Few-Shot
40.26
20.46
Vanilla Data
58.15
0.40
19.48
0.16
46.8
43.29
0,29
41.93
Temp. Sampling
64.75
18.14
0.21
43.2
0.31
44.69
Evol-Instruct
66.72
0.36
30.52
0.19
39.8
44.78
Persona Hub
61.71
0.38
28.12
0.20
42.8
42.07
0.28
43.67
TREESYNTH
68.31
0.36
31.14
0.15
47.4
48.17
0.22
48.76
Foundation Model: QWEN-2.8 2.5 7B
Zero-Shot Few-Shot
54.97
54.38
11.2
54.88
43.86
67.40
47.58
Vanilla Data
68.76
0.40
47.68
0.16
53.4
77.44
0.29
61.82
Temp. Sampling
77.26
0.41
62.08
0.21
53.2
78.05
0.31
67.65 67.65
Evol-Instruct
78.70
0.36
67.56
0.19
57.8
76.22
0.27
70.07
Persona 79.15
0.38
61.98
0.20
57.2
76.22
68.64
TREESYNTH 84.99
0.36
68.44
0.15
61.4
73.37
Table Model performance and data diversity comparison various methods with Quen2.5-728-
5-72B-
iustruct-powere data synthesis across two foundation models and multiple benchmarks. "Zero- Shot" and "Few-Shot" exhibit the base performance foundation models. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original GSM8K and MATH training sets, and the Code Alpaca Python subset for HumanEval and MBPP. "Diversity" measured by cosine similarity, where lower values indicate greater diversity. Bold and underlining indicate the best and second best indicators, respectively. "Avg." means the average of the performance scores across all the benchmarks.
Vanile Dam
Sampling
Lvol-trstmect
Personz
TreeSyyth
GSMIK Task for LLaMA331-4
MATHI Tisk 1-4
MBPP Tack for aMAAL--8
Humonnvel Task for LLMM331-
Qwco2.5.7
Q.cn2.5.78
Qwen2.5.7g
Owenl.5.7
Scaling Quanrty
Scallng Qeantty
Stallag Quantty
Scaling ScallgQuustyy Quandty
Figure 8: Model performance trends across data scales for different methods powered by Qwen2.5 5- I2B-Inst "Temp. Sampling" refers to Temperature Sampling. "Vanilla Data" denotes original GSM8K and MATH training sets, and Code Alpaca Python subset for HumanEval and MBPP.
powered by GPT-4o, as shown in Tables 9 T0 and Figure The trends mirror those reported in Sec. 4.2 TREESYNTH consistently surpasses human-ane auman-annotated data and peer synthesis methods, while its downstream performance consistently scales with data volumes. This strongly validates its robustness and generalizability.
Computational Costs of TREESYNTH. TREESYNTH can be powered by open-source models, which ensures that its operational cost and overhead are extremely low. As detailed in Table []
26

---

Model
Gen. Model
Dataset Scaling
@lk
@ @7k
@ @1kk
@ 100kk
GSM8K training set
Vanilla Data
58.15
Evol-Instruct
56.86
61.03
63.38
66.64
Persona Hub
62.47
63.38
64.22
67.78
GPT-4o
Temp. Sampling
54.89
54.97
56.94
56.79
TREESYNTH 64.29
66.72
69.75
74.07
LLaMA3. 1-8B
Evol-Instruct
59.74
63.46
66.41
68.31
Persona Hub
62.70
61,41
63.76
68.92
Temp. Sampling
53.15
55,42
57.39
56.79
TREESYNTH 68.84
69.45
71.95
77.79
Evol-Instrun
59.82
66.72
68.16
69.45
Persona Hub
61.26
61.71
62.47
66.41
Qwen2.5-725 Instruct
Temp. Sampling
61.71
64.75
64.82
68.61
TREESYNTH
65.43
68.31
69.75
77.10
GSM8K training set
Vanilla Data
68.76
Evol-Instruct
73.77
73.
77.94
79.38
Persona Hub
81.88
83.24
83.78
83.09
CPT-4o
Temp. Sampling
80.74
80.67
81.35
82.49
TREESYNTH 84.76
86.13
86.35
87.49
Qwen2.5-m 5-
Evol-Instruct
74.15
75.13
75.66
77.26
Persona Hub
81.73
82.79
83.70
84.15
LLaMA3. 3-W.Ma3.770B-Inttttee
Tеmр. Sampling
61.49
69.67
69.75
78.39
TREESYNTH 84,46
85.44
85.82
86.81
Evol-Instruce
76.57
78.70
79.15
80.06
Persona Hub
78.92
79.15
79.38
81.88
Qwen2. 5-712..5-7B--15 -
Temp. Sampling
76.50
77.26
78.92
79.15
TREESYNTH 83.85
84.99
85.82
88.78
Table 5: Comparison of instruction-tuned model performance on GSM8K using training data from different sources and generation methods. For each data scale (1k, 7k, 10k, 100k), models are fine-tuned on equally sized datasets constructed via various data synthesis methods, as well as the original GSM8K training set. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original GSM8K training sets.
we calculate token consumption when synthesizing 100k-scale datasets of various styles using TREESYNTH driven by LLaMA3. 11770--Inntrrn
Based on the API pricing (0.038/0.1) 12 per million input/output tokens), we estimate that the cost to synthesize each dataset is less than USD. Moreover, the efficiency of data synthesis should be considered in tandem with downstream training costs. Specifically, synthetic data requires model training to converted into performance gains. High-quality data can lead to more significant savings in model training, whose cost is markedly higher than the inference expense for data synthesis. Therefore, enhancing data quality is a more strategic approach to significantly reduce the greater expense of downstream training. As shown in Figures 5 and TREESYNTH requires only ~ ~Ik samples to match or exceed the downstream performance of 100k-sample baselines, precisely highlighting its value and efficiency.
Extensive Evaluation of Generation Quality. As described in Sec. A.4 we empirically set the tree depth to 4. Table 12 provides statistics on the number of criteria and attribute values each depth within the spatial partitioning trees that TREES generates for various tasks. We also present the subtree of MATH in Figure 10 with the further partitioning criteria denoted brackets. The results indicate that as depth increases, the quantities of both criteria and attribute values grow exponentially. This demonstrates that by deepening its structure, TREESYNTH continuously partitions the data space and describes the resulting subspaces with more fine- ain-inra attribute values. This capability forms the basis of TREES NYTH's superior performance in data diversity. downstream task performance, and scalability.
httpp:://eeppnnfeee www/msta. 1atettaallaaaaaaaaa.aaa. 3.3-7-0 3
27

---

Model
Gen. Model
Dataset Scaling
@ lk
@7.5k
@ 10k
@ 100k
MATH training set
Vanilla Data
19.48
Evol-Instruct
23.74
24.58
25.16
29.86
Persona Hub
25.60
27.74
28.20
29.62
GPT-4o
Temp. Sampling
24.34
24.28
25.04
26.86
TREESYNTH 28.02
30.34
31.34
40.10
LLaMA3.
Evol-Instruct
26.78
27.26
28.26
31.24
Persona Hub
23.52
23.78
23.52
24.60
LLaMA3 30MMA33.-70-IIaee-e
Temp. Sampling
21.84
22.08
23.18
22.70
TREESYNTH 26.68
27.52
28.94
32,42
Evol-Instruct
27.14
30.52
30.52
34.70
Persona Hub
25.20
28.12
28.52
31.24
Qwen2. 5-72B InBB-Insttcttt
Temp. Sampling
27.88
28.14
28.62
29.86
TREESYNTH
28.64
31.14
31.56
36.96
MATH training set
Vanilla Data
47.68
Evol-Instruct
58.52
61.10
61.20
64.84
Persona Hub
63.62
66.22
67.42
67.72
GPT-4o
Temp. Sampling
63.38
62.76
63.36
61.20
TREESYNTH 64.48
66.84
67.74
69.90
Qwen2.5-78
Evol-Instruct
57.30
59.60
58.56
61.98
Persona Hub
60.92
61.98
62.06
63.12
1.aMA3.3-70B-Inttrue
Temp. Sampling
61.64
61.70
61.96
62.88
TREESYNTH 62.08
63.28
64.84
66.80
66.22
67.5
67.74
67.72
Persona Hub
61.44
61.98
63.76
67.28
Qwen2.5
Temp. Sampling
61.92
62.08
63.38
64.84
TREESY 67.42
68.44
69.14
71.78
Table 6: Comparison of instruction- tuned model performance on MATH using training data from different sources and generation methods. For each data scale (Ik, 7.5k, 10k, 100k), models are fine- tuned on equally sized datasets constructed via various data synthesis methods, as well as the original MATH training set. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original MATH training sets.
Qualitative Analysis for TREESYNTH. Training -wen-2.5-7B MATH-style data from either TREESYNTH or Persona Hub reveals that TREESYNTH yields consistent gains across all seven sub- domains, with pronounced improvements in Number Theory, Geometry, and Counting & Probability, as shown in Table [3 A specific case in Number Theorry detailed in Figure [T] further highlights this superiority where the T'REESYNT--trine L.MM correctly computes modular inverses while the Persona Hub-trained model fails. This contrast suggests that specialized fields demanding precise computations, such as modular arithmetic, may expose data biases in Persona Hub. Overall, the comprehensive and substantial improvements provide empirical evidence that TREESYNTHI'S data generation strategy achieves superior diversity and more effective data space coverage, enabling the model attain markedly better performance in specialized mathematical reasoning.
Validation of the Criterion Selection Mechanism. Prompting the LLM to approximate this objec- tive is feasible with verified effectiveness. As shown in Figures we explicitly instruct the LLM to "Identify exactly ONE core dimension that best distinguishes pivot samples". Given the powerful capabilities of modern LLMs, they generally provide satisfactory criterion. As shown Figure [2] given five MATH-style geometry problems, the LLM can identify caannetrrcooject_tet criterion to effectively partition the data.
the
A.6 Case Study
The data generation process of TREESYNTH demonstrates both high controllability and inter- pretability. As illustrated in Figures 31
32 and 33
the GSM8K, MATH, and Code Alpaca-style
28

---

Model
Gen. Model
Dataset Scaling
@ lk
@2k
@ 10k
@ 100k
Code Alpaca Python subset
Vanilla Data
46.8
Evol-Instruct
40.8
45,2
45.8
47.2
Persona Hub
42.0
45.2
45.6
47.8
GPT-4o
Temp. Sampling
43.4
44.8
47.8
46.8
TREESYNTH
49.4
50.8
52.6
54.4
LLaMA3. 1-88
Evol-Instruct
39.0
40.6
43.4
46.6
Persona Hub
46.6
45.8
46.8
48.4
Temp. Sampling
44.4
44.6
45.8
46.2
TREESYNTH
47.8
50.2
50.8
52.0
Evol-Instruct
37.2
39.8
42,4
44,8
Persona Hub
41.6
42.8
43,6
45.2
Temp. Sampling
42.6
43.2
43.4
44.0
TREESYNTH
45.8
46.6
47.4
49.8
Code Alpaca Python subset
Vanilla Data
53.4
Evol-Instruct
57.2
59.2
60.6
61.6
Persona Hub
58.8
61.6
61.0
62.2
GPT-4o
Temp. Sampling
60.0
59.6
59.0
60.6
TREESYNTH
61.2
62.8
63.2
64.8
Qwen2. .BBB
Evol-Instruct
54.6
55.8
57.4
58.6
Persona Hub
56.0
58.8
59.4
61.8
3- -Istrrttt
Temp. Sampling
53.8
54.8
56.0
59.6
TREESYNTH
57.6
59.4
61.4
63.0
Evol-Instruct
56.8
57.8
60.4
61.4
Persona Hub
57.4
57.2
60.8
61.4
Qwen2. 112222.-72BB-- 5-72t-Inst
Temp. Sampling
52.4
53.2
55.8
60.6
TREESYNTH 59.2
61.4
62.4
63.2
Table 7: Comparison of instruction-tume model performance MBPP using training data from different sources and generation methods. For each data scale (Ik, 2k, 10k, 100k), models are fine-tuned equally sized datasets constructed via various data synthesis methods, well the common training set for coding task. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the Code Alpaca training sets.
datasets generated by TREESYNTH are presented alongside their corresponding criteria and attribute values. The generated data not only preserves the stylistic features of the original datasets but also strictly adheres to specified attribute values. This highlights TREESYnTH'ss 's key strength: by leveraging attribute values associated with subspaces obtained through data space partitioning, the approach achieves precise control over data generation within each subspace, thereby ensuring effective regulation and interpretability of the synthesis process.
A.7
Limitations
This paper introduces TREESYNTIL, a tree-guided subspace-based synthesis approach that system- atically partitions the data space from global perspective produce diverse and comprehensive instruction sets. After generating these instructions, LLMs are utilized to synthesize corresponding answers. However, following the practice Evol-Instruct [18]. the accuracy validation of answers remains unexplored. Despite this potential defect, TREES YNTH still demonstrates consistent improve- ments on both data diversity and downstream task performance, highlighting its superior effectiveness and robust scalability.
A.8 Experiments Compute Resources
All experiments are executed on high-performance computing node equipped with eight NVIDIA H100 SXM GPUs (80 GB HBM3 each), dual-socket 128-core CPUs, and 2 TB of system RAM.

---

Model
Gen. Model
Dataset Scaling
@1k
@2k
@ 10k
@ 100k
Code Alpaca Python subset
Vanilla Data
43.29
Evol-Instruct
44.51
49.39
51.22
51.22
Persona Hub
43.90
45.12
48.78
49.39
GPT-4o
Temp. Sampling
41.46
45.73
46.95
47.56
TREESYNTH 48.78
50,00
51.83
53.05
LLaMA3. 1-8B
Evol-Instruct
40.85
41.46
42.68
45.12
Persona Hub
39.63
40.24
44.51
46.34
LLaMA3 3-70B- M01-43.-77B-IIstttee IOB-Instt
Temp. Sampling
40.24
41.46
42.68
45.12
TREESYNTH
47.56
48.17
50.00
54.27
Evol-Instruct
40.24
42.07
43.29
46.34
Persona Hub
41.46
42.07
45.12
46.95
Quen2. 5--28- 11-72B-Instruct
Temp. Sampling
39.63
42.68
45.73
TREESYNTH
46.34
48.17
50.61
53.05
Code Alpaca Python subset
Vanilla Data
77.44
Evol-Instruct
78.05
80.49
80.49
81.10
Persona Hub
76.22
77.44
78.66
79.88
GoT-4o
Temp. Sampling
79.27
80.49
81.10
81.71
TREESYNTH 79.88
80.49
81.49
83.05
Sven2.5-7B
Evol-Instruct
75.61
76.83
77.44
78.05
Persona Hub
75.61
75.00
76.22
78.05
LLaMA3 1LMMA3.3-70B-- 3---0--Inntruse
Temp. Sampling
76.22
76.83
77.44
77. .4
TREESYNTH
77.44
78.05
79.88
81.71
Evol-Instruct
76.22
76.22
78.66
81.71
Persona Hub
76.22
76.22
76.83
77.44
Wwen2.5-72B-Instruee
Temp. Sampling
75.00
78.05
78.66
80.49
TREESYNTH 77.44
78.66
79.88
82,32
Table 8: Comparison of instruction-ture model performance HumanEval using training data from different sources and generation methods. For each data scale (Ik, 2k, 10k, 100k), models fine-tuned on equally sized datasets constructed via various data synthesis methods, as well as the common training set for coding task. "Temp. Sampling" is abbreviated from "Temperature Sampling". "Vanilla Data" denotes the Code Alpaca training sets.
Method
Foundation Model
Benehmark
Temp. Sampling
MBPP
29.801
41.20)
42.20
42.20
42,80
44.20
Carna-3-PT--6
MATH
HumanEEal
33.50
20.00
34.76
35.98
26.60
27.20
27.20
37.80
30,30
42,07
Avg.
22.83
31.99
34.19
35.33
35.93
38.86
MBPP
54.40
$6.60
$7.00
56.60
$6.20
57.40
Gemna-3-
HumanEval
59.10
56.10
54.27
57.32
56.71
62,80
MATH
31.30
47.30
Arg.
45.80
49.20
$2.86
54.37
54.34
58.13
Table Model performance comparison of various methods with GPT-4o-powered data synthesis across Cemma-3-PT 3-PT-4B/ 12B models and multiple benchmarks. "Zero-Shot" and "Few-Shot" exhibit the base performance foundation models. "Temp. Sampling" abbreviated from "Temperature Sampling". "Vanilla Data" denotes the original MATH training set for MATH benchmark, and the Code Alpaca Python subset for HumanEval and MBPP. Bold and underlining indicate the best and second-best indicators, respectively. "Avg." means the average of the performance scores across all the benchmarks.
30

---

Model
Benchmark
1K
2K
7.5K
10K
100K
MATH
28.5
30.3
30.7
35.2
Gemma -emma-3-PT-a -3-PT-4B
MBPP
42.4
44.2
45.4
47.8
HumanEval
39.0
42.1
43,9
45.7
MATH
53.2
54.2
55.6
57.3
G 3-BB-122
MBPP
55.2
57.4
58.8
60.2
HumanEval
61.6
62.8
63.4
66.5
Table 10: Evaluation of TREESYNTII'S scalability performance across varying data volumes (IK, 2K, 7.5K, 10K, and 100K samples) on Gemma-3-PT-4B and Gemma -3-PT-1222 foundation models with data synthesis powered by 4oT-4o. Results demonstrate that TREESYNTH maintains strong and consistent scaling behavior across all benchmarks (MATH, MBPP, HumanEval), with downstream task performance steadily improving synthetic dataset size increases, validating the method's robust scalability properties.
Vanilla Data
Tomp. Sampling
Evol-Instruct
Persona Hub
TreeSynth
MATH Task for Gemma-3-PT-48
MBPP Task for Gemma-33PPT-ae
HumanEval Task for Gemma-3-PT--s
Accure (%)
40.0
35.
30
300
Scaling
Scalisg
Quanity
MATH Task for Gemmia-3PP1-128
MBPP Task for Gemma-3-PPT-12
HumanEval Task for Gemma-3-PT-128
60.0
550
30
500
Scaling Quaenity
Scaling Quantity
Scaling Quantity
Figure 9: Model performance trends across data scales for different methods powered by GPT-4o. "Temp. Sampling" refers to Temperature Sampling. "Vanilla Data" denotes original GSM8K and MATH training sets, and Code Alpaca Python subset for HumanEval and MBPP.
The total compute budget amounted to roughly 30,000 GPU-hours. The software stack comprised PyTorch 2.6.0 linked against CUDA 12.1 (NCCL 2.17.1).
A.9 Broader Impacts
TREESYNTH promotes AI advancement by autonomously generating diverse and balanced datasets, reducing dependence on costly human curation and mitigating biases imposed by models, seed data and low-variation prompts. This is important for LLM customization and further enhancing their specific capabilities, especially on domains without source data.
31

---

Dataset
Input Tokens
Output Tokens
Input Cost (USD)
Output Cost (USD)
Total (USD)
GSM8K Style
23.1M I.
65.4M
0.88
7.84
8.72
MATH Style
7.0M
25.6M
0.26
3.07
3.33
Code Alpaca Style
25.1M
56.1M
0.95
6.73
7.68
Table 11: Detailed breakdown of estimated token consumption (input and output) and associated API costs for synthesizing 1s0K-scale GSM8K-style, MATH-style, and Code Alpaca-style datasets through the TREESYNTH framework, demonstrating the cost-
using LLaMA3.
effectiveness of the approach.
Dataset
Metrie
Root
Level
Level 2
Level 3
Level
Total
Number Criteria
3853
4113
Code Alpaca
Number of Attribute Values
12
247
3853
57683
61796
Number Criteria
284
3914
4212
GSM8K
Number of Attribute Values
1
13
284
3914
52721
56933
Number Criteria
113
1246
1367
MATH
Number of Auribute Values
113
1246
15794
17161
Table 12: Comprehensive statisties showing the exponential growth of criteria and attribute values across different tree depth levels (Root to Level 4) for Code Alpaca, GSM8K, and MATH datasets, demonstrating how TREESYNTH spatial partitioning tree progressively refines the data space with increasingly fine-grained descriptors deeper levels (maximum tree depth set to 4).
Root (MATH)
[Mathematical Domain]
1-- Algebra [problem_ty] empe]p]]]]]]p_
I-- equation_solving Ecomputation__coplexzii
--- low iiraation_structrre
simple_ pumple_polyoomall
exponential
medium [Equation Type]
Quadratic
Cubic
-- Probability [Problem Complexity]
Figure 10: Illustrative example of partial subtree extracted from the MATH spatial partitioning tree, showing the hierarchical structure from the root node through multiple levels of refinement. Each level is annotated with the partition criterion in brackets (e.g., Mathematical Domain, problem_type crpputation_omplexiin demonstrating how TREESYNTH systematically organizes the mathemati- cal problem space into increasingly specific subspaces.
32

---

Example: Number Theory
Question: Compute (3 +--1)-1 mod 31. Express your answer as an integer from 0 to 30, inclusive.
Correct Answer: 29
TREESYNTH Solution: 29
TREESYNTH Reasoning:
1. Find modular inverses: 3 21 mod 31 and 5 25 mod 31
2. Add the inverses: 21 25 46 15 mod 31
Find inverse
15t mod (since 15
mod 31)
Therefore, (3 5--1 29 mod 31.
Persona Solution:
Persona Reasoning:
1. Find modular inverses: 3 mod 31 and 5- 25 mod 31
2. Add the inverses: 21 + 25 46 = 15 mod 31
3. ERROR: Claims 15 21 mod 31, but 15 21 315 5 mod 31
The final answer is: 21
Figure 11: Qualitative study from the Number Theory domain comparing the reasoning quality of models trained on TREES YNTII versus Persona Hub synthetic data when solving a modular inverse problem. The example demonstrates that the EEGESYNTI--traieee model correctly computes the modular inverse at each step and arrives at the correct answer (29), while the Persona Hub-trained model makes a critical error in the final inverse calculation, yielding an incorrect answer (21). This highlights how TREESYNTH's superior data diversity enables more robust reasoning in specialized mathematical domains.
"criterion": "geometric..hjectt.tpp. "attributes":
"triangle":
"A triangle has sides of lengths 7, 24, and 25. Determine area the triangle." "
paagular_polygaa
"In regular hexagon with side length 6, calculate
the hexagon.", "A regular dodecagon (12-sided polygon) is inscribed
in a circle of radius R 6. Compute the area of the dodecagon."
"cyclic_quadriilaeeeeeeeeee quadriiaateer"" [
"A cyclic quadrilateral has sides lengths 7, 8, 9, and Calculate the area of the quadrilateral using Brahmagupta's formula."
fomposite_ffguree..
"A circle is inscribed in square, and the square has side length 10. Compute area the region outside the circle but inside the square."
]
}
}
Figure 12: Example output demonstrating how the LLM automatically identifies an appropriate partitioning criterion weteeeerrrcoobctteeeeee
and corresponding attribute values (triangle, regu- composite (ogouurtt_ffure when given five diverse MATH-style geometry
lar lar_polygon, ayclic_quadrilatee problems pivot samples. This illustrates TREESYNNH'S criterion determination mechanism, where the LLM selects dimensions that effectively distinguish between different types of problems, enabling systematic data space partitioning.
33

---

Domain
Persona Hub
TREESYNTH
Improvement over Persona Hub
Number Theory
58.7%
71.1%
+12.4%
Geometry
48.9%
57.8%
+9.0%
Counting&Prrbaablliyy
57.0%
65.2%
+8.2%
Intermediate Algebra
36.4%
44.2%
+7.8%
Prealgebra
79.1%
84.6%
+5.5%
Algebra
83.7%
88.0%
+4.3%
Precaleulus
39.2%
42.7%
+3.5%
Table 13: Detailed comparison of accuracy scores across seven mathematical sub-domains MATH benchmark after fine-tume fine-tuming Qwen2. 5- synthetic data generated by TREESYNTH versus Persona Hub, showing the absolute performance improvement achieved by TREESYNTH in each domain. Notably, TREESYNTH achieves the most significant gains in specialized domains requiring precise reasoning such as Number Theory (+ (+1,,4%), Geometry (+9.0%), and Counting&Probability (+8.2%).
34

---

Prompt Template of GSM8K style Instruction Generation in Temperature Sampling. As a math expert, you are tasked to generate 10 S53M8K-stylee math word problems suitable for bright middle
school student.
Each question should meet the following criteria:
Format: Write problems real- world word problems that require mathematical reasoning solve.
2. Step Count: Require between 2 and 8 steps to solve.
3. Operations: Utilize basic arithmetic operations: addition (+), subtraction (-), multiplication (*), and division (/).
4. Complexity: Vary in context and complexity, but REMA IN A CCESSIBLE TO MIDDLE SCHOOL STUDENTS!
Clarity Provide clear, concise questions that encourage step-by-stay calculations to reach the final answer.
6. Language: Use natural, conversational language to describe situations while keeping problems clear and unambiguous.
7. Diversity: Ensure that the questions diverse and distinct from one another from all potential perspectives.
Organize your responses the following format without any extra text or explanations: Question I: text
Question 2: text
Question 10: text
Figure 13: Prompt template of GSM8K-style instruction generation in Temperature Sampling.
Prompt Template of MATH-style Instruction G eneration in Temperature Sampling. As math expert, generate 10 high school competition-ees level math questions in MATH dataset style.
Each question should strictly adhere these criteria:
Question Type: Questions must excl exclusively involve advanced mathematical reasoning suitable for competitions such as A ACC 8, A MC 10, AMC 12, A IME, or USA
2. Difficulty Levels: Clearty assign each question difficulty level from (easy, typical of earty A MCC 8 questions)
5 (very challenging, similar to later A IME/USA MO questions), consistent with recognized mathematical competition standards.
Verb and Phrasing Diversity: Employ varied verbs and diverse phrasing, blending both clear interrogative questions and direct imperative instructions to maintain instruction diversity.
4. Clarity and Uniqueness: Questions must provide all necessary details for a solverto to determine exactly one unique solution without ambiguity.
Notation and Formatiing Use clear and precise mathematical notation written in LATEX. If diagrams illustrations are necessary, describe them explicitly in descriptive text or represent them using valid A symptote code.
6. Solvability: Questions should be solvable by advanced high school-level mathematical reasoning without calculators external computational resources.
Organize your responses strictly the following format without additional text or explanations:
<Question 1>
[Question text with prpper mathematical notation] <Difficulty>
[1-5]
<Question 2>
[Question text with proper mathematical notation] <Difficulty>
[1-5]
<Question 10>
[Question text with proper mathematical notation] <Difficully>
[1-5)
Figure 14: Prompt Template of MATH-style Instruction Generation in Temperature Sampling.
35

---

Prompt Template of Code A Apaca-style Instruction Generation in Temperature Sampling.
As coding expert, you are asked to come with 10 diverse Code Apaca- style python code generation instruction input pairs.
Each instruction should meet the following criteria:
Instruction type: gemerated instructions can only be code generation tasks.
2. Verb Variation: Avoid repeating the same verbs across instructions to maintain variety.
3. Phrasing Diversity: Incorporate diverse phrasing, blending questions and commands.
Task Variety: Provide different Python programming tasks, e.g. open- open-ended generation, classification, editing, optimization, etc.
5. Solvable Requests: Ensure the instruction-input pair is solvable by GPT alone, e.g. avoid tasks requiring multimedia or file inputs, etc.
The code generated by the instructions does not require access to any external resources, including applications, files, systems, networks. It should be executed solely the Python console.
Restriction:
English Composition: Present instructions English.
8. Length Restriction: Limit each instruction one or two sentences, either imperative or interrogative.
9. Input Specifiiit:: W hen needed, offer realistic input under 100 words that is detailed enough to evaluate the instruction.
10. Realistic Data: The input should involve realistic data and should contain simple placeholders.
11. Input constraints: The input must common data type Python cannot be python function.
12. Programming Focus: All instructions must relate to coding or programming.
Organize your responses in the following format without any extra text or explanations: <Instruction 1> text of Instruction
<Input> text Input
<Instruction 2>
text of Instruction <Input> text Input 2
<Instruction 10> text of Instruction 10 <Input>
text Input 10
Figure 15: Prompt template of Code Alpaca-style instruction generation in Temperature Sampling.
36

---

Prompt Template of SimpleToM -syyle Instruction G Generation in Temperature Sampling.
Your task 18 to create <hatch size> short stortes where information on msymmetry naturally exists. The goal is to generate training data that helps an LLM anticipate behavior based on mental states rather than observable clues. Below are some instructions to follow for each instance.
1. Wribe two-sentence story.
Decide how instantiate the main entities in the story;
Person (required): either real, creative name followed by a simple descriptor indicating their role in the story or group of people.
Objecct Person Z A ction Z (required): This will be the subject
KEY INFORMATION,
Person (optional): any additional character or group if needed for the story, but is not required,
about Object Z Person Z. A Z (and Person Y that is unknown to Person X (due to the general reason given in the somario). Person X should not be able to observe this KEY INFORMATION through their actions the story (either implicit or explicit actions). DO NOT use information which might be observed by Person X through normal, careful observation (such as 'expiration date", "leaking container", "smell", etc)
For the FIRST SENTENCE of the story, write the KEY INFORMATION
The SECOND SENTENCE of the story is about what Person will usually do regarding Object / Person Z Action Z (and Person ) in the socnarto lignoiin the KEY INFORMATION, This sentence should describe what the character does using fine- grained actions. DO NOT include any descriptions which involve the emotions or thoughts of Person X, just descrbbe actions.
2. Generate Question & A nswer Choices:
Wiitee question predicting what Person will likely do next.
Providd two verbal action choices:
[A]: Correct action to the question (given the fact that person X is not aware of the KEY INFORMATION), Make sure the
story does not have any mention this action.
(B): Counterfactual (incorrect) action to the question. This answer should be likely answer to the question under the assumption that person X somebow has full access the KEY INFORMATION after all (maybe only possible using "magic" or some omnipotent skill).
Each action should be complete but concise verbal phrase, without adjectives or adverbs. Avoid making it too short or too detalled.
Ensure two choices are in the same length#*.
3. Give the Final Answer:
Provide a short chain- of of-thhught explaining why the correct answeris is (A),
Now, organize your response (<hatch size> instances) in the following format. Separate each instance using ** *nny a blank Iine** extra dividers or explanatións).
Now,orraanize
Instance <N>:
[INUU]]
Given the following story, answer the question by giving the correct answer choice, (A) or (B).
Story: <the two-sentence story>
choice (A) <artion choice when X is unaware of the key information
Question: <the question>
(B) <choice when X has full knowledge the key informatin>>
What is the correct answer?
[ANSWER]
<the chain-of-thought>, So the answeris is (A).
Figure 16: Prompt template of Simple instruction generation in Temperature Sampling.
Prompt Template of GSM8K-styll -tyyle Instruction Generation in TREESYNTH.
As math expert, you tasked to generate 10 DSMMBK-stya math word problems suitable for bright middle school student.
Each question should meet the following criteria:
1. Format:
Write problems real- world word problems that require mathematical reasoning to solve. Require between 2 and steps solve.
Step Count:
Operations: Utilize basic arithmotic operations: addition (+), subtraction (-), multiplication (*), and division (/.
4. Complexity: Vary in context and complexity, but REMA IN ACCeSSIBlE TO MIDDLE SCHOOL STUDENTS!
5. Clarity: Provide clear, concise questions that encourage step- ber-bby--sepp calculations to reach the final answer:
6. Language: Use natural, conversational language to describe situations while keeping problems clear and unambiguous.
7. Diversity: Ensure that the questions are diverse and distinct from one another from all potential perspectives.
8. A ttributes: Each problem should be associated with all these attributes: <A ttributes>
Organize your responses the following format without any extra text or explaatioos::
Question 1: text
Question 2: text
Question 10: text
Figure 17: Prompt template of GSM8K-style instruction generation in TREESYNTH
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PromptTemplate of MATH-style Instruction Generation TREESY As math expert, generate 10 high school competition- level math questions in MATH dataset style.
Each question should strictly adhere these critoria:
Question Type: Questions must exclusively involve advanced mathematical reasoning suitable for competitions such as MC 8, MC 10, AMC 12, A IME, or USA MO.
2. Difficulty Levels: Clearty assign each question difficulty level from (easy, typical of early A MC questions)
5 (very challenging, similar later A IME/USA MO questions), consistent with recognized mathematical competition standards.
3. Verb and Phrasing Diversity: Employ varied verbs and diverse phrasing, blending both clear interrogative questions and direct imperative instructions to maintain instruction diversity.
4. Clarity and Uniqueness: Questions must provide all necessary details for solver to determine exactly one unique solution without ambiguity.
Notation and Formatting: Use clear and precise mathematical notation writton LATEX. If diagrams illustrations are necessary, describe them explicitly in descriptive text or represent them using valid symptote code.
6. Solvability: Questions should be solvable by advanced high school-level mathematical reasoning without calculators external computational resources.
7.A ttributes: Each question should be associated with all these attributes: ttributes>
Organize your responses strictly the following format without additional text or explanations: <Question 1>
[Question text with proper mathematical notation] <Difficulty>
[1-5]
<Qusstoon 2>
[Question text with proper mathematical notation] <Difficully>
[1-5]
<Question
[Question text with proper mathematical notation] <Difficully>
[1-5]
Figure 18: Prompt template of MATH-style instruction generation in TREESYNTH.
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Prompt Template of Code A Ipaca-style Instruction G eneration in TREESYNTH.
As a coding expert, you are asked to come up with 10 diverse Code A Alpaca- style python code generation instruction imput pairs.
Each instruction should meet the following criteria:
Instruction lype: generated instructions can only be code generation tasks.
Verb Variation: Avoid repeating the same verbs across instructions maintain varioty.
3. Phrasing Diversity: Incorporate diverse phrasing, blending questions and commands.
4. Task Variety: Provide different Python programming tasks, open-ended generation, classification, editing,
optimization, etc.
Solvable Requests: Ensure the instruction- input pair is solvable GPT alone, e.g. avoid tasks requiring multimedia file inputs, etc.
Restriction: The code generated by the instructions does not require access to any external resources, including applications, files, systems, networks. It should be executed solely in the Python console.
7. English Composition: Present instructions in English.
or sentences, either imperative interrogative. Input Specificity: When noeded, offer realistic input under 100 words that is detailed enough to evaluate the instruction.
Length Restriction: Limit each instruction
10. Realistic Data: The input should involve realistic data and should not contain simple placeholders.
11. Input constraints: The input must be common data type in Python and cannot be python function.
12. Programming Focus: All instructions must relate to coding programming.
13.A ttributes: Each problem should associated with these attributes: ttributes>
Organize your responses the following format without any extra text or explanations: <Instruction 1> text of Instruction
<Input>
text Input
<Instruction 2>
text of Instruction <Input> text Input
<Instruction 10> text of Instruction <Input>
bext Input 10
Figure 19: Prompt template of Code Alpaca-style instruction generation in TREESYNTH.
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Prompt Template of SimpleToM-shi Instruction G Generation in TREESYNTH.
Your task is to create <n samples> short stories where information asy asymmetry naturally exists. The geal is to generate training data that helps an LLM anticipate behavior based mental states rather than observable clues. Below are instructions to follow for each instance.
1. Write two-sentence story.
Decide how instantialo the main entities in the story;
Person X (required): either a real, creative name followed by simple descriptor indicating their role in the story or
group of peuple.
Object / Person Z A ction Z. (required): This will be the subject the KEY INFORMATION,
Person (aptional): any additional character KEY IFFOMATIOO about Object / Person //A ction (and Porson the story, write Y) that is unknown to Person X (due to the general reason given in the scenarto). Person X should not be able to observe this KEY INFORMATION through their actions the story (either implicit explicit actions). DO NOT use information which might be observed by Person X through normal, careful observation (such as "expiration date'. 'leaking container", "smell", etc).
if needed for the story, but is not required,
For the FIRST SENTENCE
The SECOND SENTENCE the story is about what Person will usually do regarding Object / Person Z Action Z (and Person Y in the scenario fignoring the KEY INFORMATION This sentence should describe what the character does using fine grained actions. DO NOT include any descriptions which involve the emotions thoughts of Person just describe actions.
2. Generate Question & Answer Choices:
Wnite a question predicting what Person will likely next.
Provvde two verbal action choires:
[A): Cormet action the question (given the fact that person X is not aware of the KEY INFORMATION). Make sure the
story does not have any mention of this action.
(B): counterfactual (incorrect) action to the question. This answer sbould be likely answer to the question under the assumption that person X somehow has access to the KEY INFORMATION after (maybe only possible using "magic" or some omnipotent skill).
Each action should be complete but concise verbal phrase, without adjectives adverbs. Avoid making it too short or too detailed.
Ensure two choices are in the ** same length"*.
Give Final nswen:
Provide a short bhain-of-thaught explaining why the correct answeris is (A).
#*# stories MUST accociiaed with the ATTRIBUTES below**;
<attributes json>
Now, organize your response (<n samples> instances) the following format. Separate each instance using **oyl a blank
ling (no extra dividers or explanations).
Instance <N>;
[NNUU]]
Given the following story, answer the question by giving the correct answer choice, (A) or (B).
Story: <the two-sentence story>
Question: <the question>
(A) <action choice when is unaware of the key information>
(B) <choice when X has full knowledge the key informatin
hat is the correct answer?
[ANSWER] <the chain-of of thought>, So the answer is (A).
Figure 20: Prompt template of SimpleToMM-style instruction generation in TREESYNTH
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Prompt Template of LSSM8K-style Instruction Criterion Determination in TREESY NTH. As an analysis expert, your task is to examine the following questions to identify the SINGLE most significant dimension that characterizes the question space and differentiates these questions. Questions:
<Samples>
Dimension Requirements:
Core Dimension Identification: Identify exactly ONE core dimension that best distinguishes these questions. Excluded Dimensions: <Dimensious>
Unique Catagorization Each question MUST be categorized into exactly ONE attribute value.
4. Mutually Exclusive Values: A ttribute values must be mutually exclusive.
5. Clarity in Values: Avoid ambiguous atrribtee values, such as "others".
Independent Values: Each attribute must be single distinct value NO combined values like 'attributel and attribute2" or cerrrbbbbe/atttbtteer
Each attribute must a single distinct value- NO
combined values like 'attributel and attribute2" or "attributel /attribbttt Each attribute must be single distinct value - NO combined values like attributel and attribute2" or /attibbutt
Organize your responses the following format without any extra text or explanations:
{{
"dimension": : "dimension, name",,
"attributes:: {{
"attribute": [list of sample indicos),
"attribute2": [list of sample indices),
H
Figure 21: Prompt template of GSM8K-style instruction criterion determination in TREES
Prompt Template of MATH-style Instruction Criterion Determination TREESY NTH.
As math expert, your task is to examine the following MATH questions identify the SINGLE most significant dimension that characterizes the question space and differentiates these questions. Questions:
<Samples>
D Dimension Requirements:
Core Dimension identification: Identify exactly ONE core dimension that best distinguishes these questions. Excluded Dimensions: <Dimensions>
3. Unique Categorization: Each question MUST be categorized into exactly ONE attribute value.
4. Mutually Exclusive Values: A ttribute values must be mutually exclusive.
5. Clarity in Values: Avoid ambiguous atribule values, such as "others". Independent Values: Each attrbute must be single distinct value NO combined values like
'attributel and attribute2* or attributo/attrrbuu
Organize your responses in the following format without any extra text or explanations: [(
'dimension": "dimension name", "attributes:: : {{
"attributel"; [list of sample indices),
"attribute2": [list of sample indices),
}}
Figure 22: Prompt template of MATH-style instruction criterion determination in TREESYNTH.
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Prompt Template of Code A lacca-style Instruction Criterion Determination in TREESY NTH.
As a coding expert, your task is to examine the following python code generation instruction input pairs to identify the SINGLE most significant. dimension that characterizes the instruction-ings htt-iinpputteeeeeeeeeeee space and differentiales these instruction-inpee pairs.
Instruction-inge -nnrttttn-nnptttpp pairs: <Samples>
Dimension Requirements:
Core Dimension identification: Identify exactly ONE core dimension that best distinguishes these instruction- input pairs.
2. Excluded Dimensions: <Dimensions>
3. Unique Categorization: Each instruction- input pair MUST be categorized into exactly ONE attribute value.
4. Mutually Exclusive Values: A ttribute values must be mutually exclusive.
Clarity in Values: Avoid ambiguous attribute values, such as "others".
Independent Values: Each attribute must be single distinct value NO combined values like "attributel and attribute2" or "attributel lattributee""
Organize your responses in the following format without any extra text or explanations: {{
"dimension": : "dimension name",
'attributes:: {{
"attributel"; [list of sample indices),
"attribute2"; [list of sample indices),
Figure 23: Prompt template Code Alpaca-style instruction criterion determination in FREESYNTH
Prompt Template of SimpleToM style Instruction Criterion Determination TREESY NTH.
Below some stories that take place in real-worke scenarios w where unawareness and information asymmetry with various underlying reasons naturally exists. As expert equipped with rich commonsense and extensive knowledge, your task is examine following stories identify SINGLE most significant dimension that characterizes the story space and differentiates these stories.
Stories:
<Samples>
Dimension Requirements:
1. Core Dimension identification Identify exactly ONE core dimension that best distinguishes these stories.
2. Excluded Dimensions: <Dimensions>
exactly ONE attribute value. Mutually Exclusive Values: A ttribute values must be mutually exclusive.
Unique Categorization: Each question MUST be categorized
5. Clarity in Values: Avoid ambiguous attribute values, such as "others".
6. Independent Values: E Each attribute must be single distinct value NO combined values like "attributel and attribute2" "attribute//atti 1
Organize your responses the following format without any extra text or explanations: {{
'imensionn: "dimension name", "attributs": {[
"attributel": [list of sample indices),
"attribute2": [list of sample indicos),
H
Figure 24: Prompt template of SimsteToM-style instruction criterion determination in TREESYNTIL.
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Prompt Template of GSM8K-style Instruction Subspace Coverage TREESY NTH.
As analysis expert, your task is to supplement the polential attribute values fora specified dimension in order comprehensively model the entire space of questions.
Dimension: <Dimension>> Exiting attributes values: <A triiute values>
Requirements for New A ttribute Values:
Clarity: Avoid ambiguous values, such as "others".
2. Mutual Exclusivity: Ensure that attribute values do not overaa.
3, Completeness: Ensure that all possible attribute values fully cover the dimension.
4. GRA DE LEVEL EL: K Keep all values within elementary and middle school students' understanding! Keep all values within elementary and middle school students' understanding! Keep all values within elementary and middle school students' understanding!
5. SIMPLICITY: Use basic, straightforward terms that young students can understand! Use basic, straightforward
terms that young students can understand! Use basic, straightforward terms that young students can understand!
Organize your responses the following format without any extra text or explanations: If the existing attribute values completely cover the entire dimension, only output "null". For example, null
If the number of potential attribute values is more than 10, first output 10 potential new attribute values, and end your output with "infinite" in new line. For example,
attribute value 1 attribute value
attribute value 10
infinite
Otherwise, output all the potential new attribute values, and end your output with "complete" in line. For example,
attribute value 1
attribute value 2
attribute value complete
Figure 25: Prompt template of -stlle instruction subspace coverage in TREESYNTH.
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Template of MtTH-style Instruction Subspace Coverage in TREESY
As math expert, your task is in supplement the potential attribute values for specified dimension in order to comprehensively model the entire space of questions.
The whole space of questions described as follows:
1. Question Type: Questions must exc exclusively involve advanced mathematical reasoning suitable for competitions
such as A AM 8, MC 10, AMC 12, A IME, or USA MO.
Difficulty Levels: Cleary assign each question difficulty level from (easy, typical early AMC questions)
5 (very challenging, similar to later A IM EE/USA MO questions), consistent with recognized matheratical competition standards.
Verb and Phrasing Diversity: Employ varied verbs and diverse phrasing, blending both clear intive questions and direct imperative instructions maintain instruction diversity.
Clarity and Uniqueness: Questions must provide all necessary details for a solver to determine exactly one unique solution without ambiguity.
5. Notation and Formatting; Use clear and precise mathematical notation written in LATEX. If diagrams illustrations are necessary, describe them explicitly in descriptive text or represent them using valid A symptote code.
6. Solvability: Questions should be solvable by advanced high school-level mathematical reasoning without. calculators or external computational resources.
Dimension: <Dimension>
Exiting attributes values; <A tribute values> Requirements for New A ttribute Values:
Clarity: Avoid ambiguous values, such as "others".
2. Mutual Exclusivity: Ensure that attribule values do not overtap.
3. Completeness: Ensure that all possible attribute values fully cover the dimension.
atthematical Complexity exity:: Generate attribute values that reflect high school competition level mathematical techniques and concepts.
Organize your responses in the following format without any extra text or explanations:
If the existing atiribute values completely cove er the entire dimension, only output " "uul".. For example, null
If the number of potential attribute values is more than 10, first output 10 potential new attribute values, and end your output with "infinite" new line. For example,
attribute value 1
attribute value 2
attribute value 10
infinite
Otherwise, output all the potential new attribute values, and end your output with "complete" a new line. For example, attribute value 1
attribute value 2
attribute value n complete
Figure 26: Prompt template MATH-style instruction subspace coverage in TREESYNTH
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Prompt Template of Code A Ipaca-style Instruction Subspace Coverage in TREESYNTH.
As a coding expert, your task is to supplement the potential attribute values for specified dimension in order to comprehensively model the entire space of instruction-nnge pairs.
The whole space of instruction-input pairs is described as follows:
Instruction type: generated instructions can only code generation tasks.
Various Python programming tasks are included, e.g. open open-ended ended generation, classification, editing, optimization, etc.
3. Each instruction-inpe pair is solvable by GPT alone, e.g. avoid tasks requiring mul timedia or file inputs, etc.
4. All the instruction input pairs are in English.
When unnecessary, the input may be omitted the instruction-input pairs.
Restriction: The cade generated by the instructions not require access to any extemal resources, including applications, files, systems, or networks. It should be executed solely in the Python console.
D Dimension:
<Dimension>
Exiting attributes values: <A trribuee values> Requirements for New A ttribute Values:
Clarity: Avoid ambiguous values, such as "others".
2. Mutual Exclusivity: Ensure that attribute values do not overlap.
3. Completeness: Ensure that all possible attribute values fully cover the dimension.
4. A ttribute Scope: All attributes should be python coding or programming related. Organize your responses the following format without any extra text or ex expanations:
If the existing attribute values completely cover the entire dimension, only output "null""null"" "null". For example, null
If the number of potential attribute values is more than 10, first output 10 potential new attribute values, and end your output with "infinite" in new line. For example, attribute value 1 attribute value
attribute value 10
infinite
Otherwise, output all the potential new attribute values, and end your output with "complete" in line. For example,
attribute value 1
attribute value 2
attribute value complete
Figure 27: Prompt template of Code Alpaca-style instruction subspace coverage in TREESYNTH.
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Prompt Template of SimpleToM-Sit style Instruction Subspace Coverage in TREESY NTH.
As an analysis expert, your task is to supplement the potential attribute values for specified dimension in order comprehensively model the entire space of stories. Note that these stories take place in real-world scenarios where information asymmetry naturally exists, with various underlying causes.
Dimension: <Dimension>
Existing attributes values: <A tiribute values>
Requirements for New A ttribte Values:
Clarity: Avoid ambiguous values, such as "others".
2. Mutual Exclusivity: Ensure that attribute values do not overlap with each other or with the existing values.
3. Completeness: Ensure that all possible attribute values fully cover the dimension.
4. Harmfulness and Unethicality: Avoid
Organize your responses the following format without any extra text or explanations: If the existing attribute values completely cover the entire dimension, only output "null". "null" For example,
null
If the number of potential attribute values is more than 10, first output 10 potential new attribute values, and end your output with "infinite" in new line. For example,
attribute value 1
attribute value 2
attribute value 10
infinite
Otherwise, output all the potential new attribute values, end your output with "complete" a new line. example,
attribute value 1
attribute value 2
attribute value complete
Figure 28: Prompt template of SimpleToM instruction subspace coverage in TREESYNTH.
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Prompt Template of Converting Negative Samples of SimpleToM-sty -tylle Data into Positive Samples.
You given a short, two-senteace story illustrating information asymmetry where Person is unaware of crucial fact convert story into "nfoomation symmeetry" version by adding subtle environmental or background clue* *oolyy in the first sentence** Importanlly, do ** not** desoribe Person X adtively nolicing or becoming aware of the clue; just insert a slight detail implying something might be wrong unusual.
about Y. four task
*Dekailed Instructions*
..*OOiignaal Story (two sentences):
-Sentence reveals the hidden fact (which X originally does not know).
-Sentence deseribes Person X's action, still unaware.
**Modified Story (two sentences]:
Sentence 1 Insert a minor clue that could lead X (or a reader) to infer hidden fact wiithout*** explicitly saying "X notices" or X realizes. 'I he clue should be subtle and not directly point to the hidden fact.
almost the same as the orginall story, unless trivial edits are needed for co poherence. Avoid stating that X already changed behavior.
**Sentence 2=
point that **oulld** have inferred the fact from the background detail, but
text does not explicitly say so.
3. **Question & Choioes**:
Usee the same on from the original story or rephrase it slightly as "What does X do next?"
(A) original uninformed action.
(BB) I'e new informed action.
Each actio should be a complete but concise verbal phrase, without ad] ectives or adverbs. Avold making it too short or too
detziled.
4. **Final Aswer*
Provide a short (1-2 sentences) reasoning that references the subtle background clue in the first sentence, leading X to
choose (B).
End with: "So the answer (B)."
Here original story, question and uninformed action:
Original Story: <story>
Onginal Question: <ines>>
Onginal ction: <act>
Now, organize your response in the following format, Separate each instance using **only blank line** (no extra dividers or explanations).
[INPUT]
Given following story, answer the question by giving the correct answer choice. (A) or (B),
Ongiina Story: <th original two senteneneec story given to you which shows the old jnfo asymmetyy>
Modified Story: <the new two sentence stury where X has discovered the missing info>
Question: <the question>
(A) cold uninformed action>
(B) <new informed action>
W hat is the correct answer?
[ANSW ER]
<hrief oainn-o-thooghtt.. So the answer (R).
#*# ey Reminders
Do not say 'X notices/ / sees / realizes/ / suspects." " Instedd, simply mention an observable detail in the environment object.
Let the user infer that ** **coul t realize
K eep the second sentence almost the same.
Thee inserted clue must be enough that (B) is justified.
This
the final scenario still requires bit of inference, rather than the story outright stating X's awareness.
Figure 29: Prompt template of converting negative samples of SimpleToM-styyle data into positive samples.
Prompt Template of Sample Classification. You are tasked with classifying the following story based the criterion of ** <dimension>***
STORY: <sample>
You must ** select exactly one** calegory from the option list below that best fits the main characteristics of the story. If none is a perfect fit, select. the closest one.
OPTION LIST: <attributes>
Please strictly follow the output format below and do not output anything else.
Output jn JSON format:
{{
"catagory": "<selected category, using ** exact text** from the list>",
"explanation": <<one-eentence justifications'
H
Figure 30: Prompt template of sample classification.
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MATH style data generated by TREESYNTH
Atribute value and Dimension:
1.A trribute value: Algebraic Equations,
Dimension: Problem Type,
2.A ttribute value: G Geometry and Measurement,
D Dimension: Mathematical Focus,
3.A ttribute value: perimetenfenccng,
Dimension: object of calculation,
4.A Uribute value: Reclangular; Dimension: Shape of the rea,
Generated Samples:
1."Ema planning to build rectangular garden in her backyand, where the length is feet more than twice the width. If she wants the perimeter the garden to be 30 feet, what are the dimensions of the garden?", 2."A farmer is enclosing a roctangular pasture with a fence. The length is 4 times the width, and the total fencing needed is 60 meters. W hat are the dimensions of the pasture?".
"Liam wants to create rectangular dog park where the length is 5 meters more than the width. If he has 50 meters of fencing to use around the park, what should be the dimensions of the dog park?", "Sarah designing rectangular flower hed where length is 7 feet longer than width. If she has 48 feet of fencing available, what are the dimensions of the flower bed?",
5."A rectangular playground is being designed such that its length is double its width. If the perimeter of the playground meant to be 72 meters, what are the dimensions of the playground?"
6. 'A rectangular swimming pool is planned where the length is 10 feet more than the width. If the perimeter needs 84 feet, w what should be the dimensions of the pool?".
7. is building a rectangular deck where the length is feet more than the width. If the total perimeter of the deck is to be 40 feet, what are the dimensions of the dock?".
8. rectangular parking lot is to be constructed with the length being 8 meters more than the width. If the perimeter supposed be 100 meters, what will be the dimensions the parking lot?",
9. rectangular storage area is being planned with length that meters longer than the width. If the entire perimeter is to be 90 meters, what are the dimensions of the storage ama?",
10."A rectangular sports field is to be designed where the length is 12 meters more than twice the width. If the perimeter of the field is 96 meters, what are the dimensions of the field?"
Figure 31: GSM8K style data generated by TREESYNTIL.
MATH style data generated by TREESYNTH
A Atributte value and Dimension:
1.A ttribule value: Algebra,
Mathematical Domain, 2.A ttribute value: equation solving,
Dimension:
Dimension: prollem type,
3.A ttribute value: low,
Dimension: computation complexity, 4.A ttribute value: simple polynomial, equation structure,
Dimension:
G Generated Samples:
1. ''SSllve for (x): (2x"2- 5x +3 0). <Difficulty> 1",
2. Determine the real solution to the equation (x "2 + 4x 16). <Difficulty> 1',
3. "If (x + 3x - 10=00 0), compute the sum of all real solutions for (x). Difficulty> 2",
4. LLet (2 3x = 0). Find the product of the roots of the equation. <Diffcuuly>> 2",
5. "..olve for (x): ((x 2)(x +3) =0). <Difficulty> 1",
6. FFid the smallest positive solution the equation "2- =0) <Difficulty> 2",
F.r (x 7x + 12 0), determine the larger root. <Difficuuty>> 2'.
B.t (x + px + 16 = 0) have roots and (-4). Find the value of (p). <Difficully> 3",
9o for (x): (3x"2 2x 8 =). Express your answer in simplest radical form. >ifficulty> 4",
10."Find all real solutions the quartic equation (x 5x 2 +4 0). <Difficulty> 4"
Figure 32: MATH style data generated by TREES
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Code-Appcca style data generated by TREESYNTH
Attribute value and Dimension:
1.A ttribute value: numeric computation,
operation type, 2.A ttribute value: list of integers,
Dimension:
Dimension:
input data type,
3.A ttribule value: central lendency,
Dimension: required property computation,
4.A ttribute value: mean,
Dimension:
statistical measure,
G Geneaaedd Samples:
C'Cateee Python function calculate the mean of list intogers. <Input> [10, 20, 30, 40, 50]",
2. 'How can you deternine the average value of numbers a list using Python? <Input>
[3, 6, 12, 15]",
3. "Write script to find the mean of a given list of integers. <Input> [5, 15, 25, 35, 45]',
4. "W hat Python code would you use to compute the mean of list of integers? <Input>
[8, 16, 24, 32, 40]",
[7, 14, 21, 28, 35]", 5. "Could you draft Python function that returns the average of numbers in list? <Input>
"Generate Python function that calculates the mean integers
list <Input> [2, 4, 8, 10]",
7. Can you write a Python code snippet to find the mean of a list of integers? <input> [11, 22, 33, 44, 551",
8. Devise a Python script to calculate the average of a list of integers. <Input> [9, 18, 27, 36, 45]",
9. "W hat the Python function to compute the mean of list of integers? <Input> [12, 24, 36, 48, 601",
10. Forrmuetl Python solution find the mean of a list of numbers. <input> 3,, 7,9
Figure 33: Code Alpaca style data generated by TREESYNTH.
49


Reviews:
[{"review_id": "Vs4zF6gHYO", "reviewer": "Reviewer_W3cd", "summary": "The paper proposes TreeSynth, a method for generating synthetic training data for large language models (LLMs). The core idea is to sample from the intermediate nodes of a tree of LLM generations, which are conditioned on a common root instruction. This tree structure allows TreeSynth to capture both diversity and relevance across multiple levels of reasoning, going beyond traditional sampling techniques like nucleus or top-k sampling. TreeSynth is evaluated by training LLaMA 3.1B and Qwen2.5-7B models on TreeSynth-generated data across four tasks: summarization, closed-book QA, math reasoning, and code generation. The results show that TreeSynth outperforms conventional sampling strategies and even some strong baselines like Self-Instruct or Evol-Instruct in various settings.", "questions": "1. Why were only LLaMA 3.1B and Qwen2.5-7B chosen for evaluation? Can TreeSynth generalize to other model architectures or sizes? Experiments on at least one more model family would increase confidence in generality.\n\n2. TreeSynth appears capable of producing a broad range of data types, yet it is only applied to very task-specific settings. Could the authors demonstrate its use on general-purpose instruction tuning data (e.g., FLAN, OIG, or Dolly-style datasets)?\n\n3. What are the computational costs of generating and pruning large generation trees? Could this method scale to hundreds of thousands or millions of examples?\n\n4. Could the relevance scoring function be better calibrated across domains? Are there task-specific biases introduced by using a static scoring model?\n\n5. Is TreeSynth applicable to other stages of LLM development, such as reward model training or RLHF-style pipelines?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths \n\n- Novel sampling mechanism: The tree-based approach introduces an elegant way to traverse and utilize the latent space of LLM generations, capturing a mix of diverse and high-quality examples by harvesting from both leaf and intermediate nodes.\n- Empirical Results: Models trained on TreeSynth data outperform those trained on standard instruction-tuned datasets generated by top-k/top-p sampling or previous bootstrapping techniques.\n-Comprehensive evaluation across tasks: The paper evaluates performance on summarization, QA, math reasoning, and coding tasks, providing a good sense of TreeSynth's general applicability within the fine-tuning context.\n- Clear methodology: The design of the tree, including beam width, scoring strategies, and node selection policies, is well-explained and easy to follow. Ablation studies on node scoring and position further strengthen the technical argument.\n\n\n## Weaknesses\n\n- Limited model diversity: The experiments are restricted to only two models: LLaMA 3.1B and Qwen2.5-7B. It remains unclear how TreeSynth generalizes to other model architectures and/or to larger/smaller model sizes. This limits the generality of the claims.\n- Narrow scope of data synthesis: The method is only tested on domain- and task-specific data generation (e.g., math reasoning). Despite TreeSynth’s generally task/domain agnostic nature, the paper does not explore its utility for general-purpose instruction tuning or pretraining-style data generation. If the method is capable of broad data synthesis, it should be evaluated on more open-ended tasks or datasets.\n- Compute requirements for tree sampling: TreeSynth involves generating a beam of responses at each node recursively, which could be costly at scale. The paper doesn't discuss this overhead or propose methods to make it more efficient.", "was_revised": true, "final_justification": "The authors' response satisfactorily addressed key concerns. Additional experiments on Gemma-3 models support TreeSynth’s generalizability, and the focus on domain-specific data is well-justified. The cost analysis clarifies the method’s practical feasibility.\n\nWhile potential applications to RLHF and reward model training intuitively make sense, experimental results would strengthen the paper. General-purpose synthesis and scoring calibration also remain unexplored.\n\nOverall, the core contributions are sound, but some broader claims would benefit from further evidence.", "rebuttal": "Dear Reviewer W3cd,\n\nWe are grateful for your thorough and constructive feedback on our paper! Below, we will try our best to provide detailed responses to each of your comments, and hope that these clarifications will fully relieve your concerns!\n\nFirst, let's briefly highlight the primary features and impact of TreeSynth. \n- **Higher diversity and better performance:** Data diversity is crucial for preventing data collapse, avoiding overfitting, and enhancing model performance. With the tree-guided complementarity and exhaustiveness, TreeSynth synthesizes diverse and comprehensive domain-specific data, and demonstrates better performance than human-annotated or other synthetic datasets, **offering a superior solution to data scarcity, collapse, and the high cost of manual annotation** (Sec. 4.2).\n- **Excellent Scalability**: Greater scalability implies that model capabilities can continuously improve with more data, ultimately leading to superior performance. TreeSynth exemplifies this by **effectively scaling datasets and consistently improving downstream performance with increased data volume**, showcasing its significant potential for remarkable model performance (Sec. 4.2).\n- **Effective Re-balance of Existing Datasets**: In addition to synthesizing data from scratch, TreeSynth can also be used to re-balance existing datasets, achieving **improved performance** (Sec. 4.3). \n\n**Question 1 & Weakness 1: Broadening TreeSynth Assessment Beyond LLaMA and Qwen**\n- Causes for choosing the LLaMA 3.1B and Qwen 2.5-7B models: Currently, both LLaMA-3.1 8B and Qwen-2.5 7B models are highly representative open-source models, which have been widely accepted in the research community, and are generally sufficient to demonstrate the generalization of TreeSynth. In comparison, baseline methods have narrower scopes. For example, Persona Hub and Evol-Instruct are tested only on Qwen-2 7B and LLaMA 13B models, respectively. \n- Broader scope of model family and sizes: To further showcase the superiority of TreeSynth, we conduct additional experiments on Gemma-3 PT 4B and Gemma-3 PT 12B, which covers both different model series and sizes. As presented in the table below, the results mirror our findings in Sec. 4.2 on LLaMA-3.1 8B and Qwen-2.5 7B: TreeSynth continues to significantly outperform human-annotated data and peer methods, while its downstream performance consistently scales with data volumes. This strongly validates the robustness and generalizability of our method.\n\n| Model         | Benchmark   | Vanilla-0shot | Vanilla-4shot | Code Alpaca | MATH | Temp Sampling | Evol-Instruct | Persona Hub | TreeSynth |\n| :------------ | :---------- | :------------ | :------------ | :---------- | :--- | :------------ | :------------ | :------- | :-------- |\n| **Gemma-3 PT 4B** | **MBPP** | 29.8          | -             | 41.2        | -    | 42.2          | 42.2          | 42.8     | **44.2** |\n|               | **Human Eval**| 33.5          | -             | 34.76       | -    | 35.98         | 37.20         | 37.80    | **42.07** |\n|               | **MATH** | 5.2           | 23.8          | -           | 20.0 | 25.3          | 26.6          | 27.2     | **30.3** |\n| **Gemma-3 PT 12B**| **MBPP** | 54.4          | -             | 56.6        | -    | 57.0          | 56.6          | 56.2     | **57.4** |\n|               | **Human Eval**| 59.1          | -             | 56.10       | -    | 54.27         | 57.32         | 56.71    | **62.80** |\n|               | **MATH** | 23.9          | 31.3          | -           | 34.9 | 47.3          | 49.2          | 50.1     | **54.2** |\n\n| Model | Benchmark | 1k | 2k | 7.5k | 10k | 100k |\n| :--- | :--- | :--- | :--- | :--- | :--- | :--- |\n| **Gemma 3 4b** | **MATH** | 28.5 | - | 30.3 | 30.7 | 35.2 |\n| | **MBPP** | 42.4 | 44.2 | - | 45.4 | 47.8 |\n| | **Human Eval** | 39.02 | 42.07 | - | 43.90 | 45.73 |\n| **Gemma 3 12b**| **MATH** | 53.2 | - | 54.2 | 55.6 | 57.3 |\n| | **MBPP** | 55.2 | 57.4 | - | 58.8 | 60.2 |\n| | **Human Eval**| 61.59 | 62.80 | - | 63.41 | 66.46 |\n\n**Question 2 & Weakness 2: Evaluating TreeSynth for General-Purpose Data Synthesis**\n\n- **The focus of TreeSynth lies on synthesizing data from scratch**. Actually, general-purpose instructions are abundantly collected from the web or human labor, while **domain- and task-specific data is often scarce, necessating the acquirement from effective sources**. Therefore, we focus on synthesizing data for such domains. This addresses a key challenge in LLM customization: the depletion of open-access data and the high cost of human annotation.\n- **Baseline methods**, such as Evol-Instruct and Persona Hub, **also aim to generate domain-specific data**. This also prompts us to focus on  specific domains **for fair comparison**. \n- Furthermore, the task- and domain-agnostic nature of TreeSynth gives it the potential to synthesize general-purpose instruction tuning data simply by adjusting the root node's description to be general-purpose ones. This capability further highlights the generality and significant potential of our method, but synthesizing general-purpose data from scratch seems a bit redundant, given the existing datasets.\n\n**Question 3 & Weakness 3: Computational Costs of TreeSynth**\n\nThank you for your valuable question! We prepare the following claims for your reference.\n\n- **Compared to efficiency, downstream performance enjoys higher priority.** Specifically, the cost of data generation is a one-time investment, while the resulting downstream models are used continuously. As demonstrated in Figures 5, 6, 8 and Tables 5-8, TreeSynth can synthesize datasets exceeding 100k samples with effectively maintained quality, leading to consistent performance improvements and remarkable scalbility on downstream tasks as data volume increases.\n- **The efficiency of data synthesis should be considered in tandem with downstream training costs.** Specifically, synthetic data requires model training to be converted into performance gains. High-quality data can lead to more significant savings in model training, whose cost is markedly higher than the inference expense for data synthesis. **Therefore, enhancing data quality is a more strategic approach to significantly reduce the greater expense of downstream training.** The result in Figures 5, 6, and 8 substantiate this point: TreeSynth requires only 1k data samples to match or exceed the downstream task performance of a 100k-sample baseline, which precisely highlights its value and efficiency.\n- **TreeSynth can be powered by open-source models, which ensures that its operational cost and overhead are extremely low.** As detailed in the table below, we calculate token consumption when synthesizing 100k-scale datasets of various styles using TreeSynth driven by Llama-3.1-70B-Instruct. Based on the API pricing from DeepInfra for this model ($0.038/$0.12 per million input/output tokens), we estimate that **the cost to synthesize each dataset is less than 10 US dollars.** This finding suggests that in the current era of increasingly affordable computation, the challenge of generating high-quality data becomes more critical than the computational cost itself. \n\n| Dataset | Input Tokens | Output Tokens | Input Cost (USD) | Output Cost (USD) | Total Cost (USD) |\n| :--- | :--- | :--- | :--- | :--- | :--- |\n| **GSM8K Style** | 23.1M | 65.4M | $0.88 | $7.84 | **$8.72** |\n| **MATH Style** | 7.0M | 25.6M | $0.26 | $3.07 | **$3.33** |\n| **Code Alpaca Style** | 25.1M | 56.1M | $0.95 | $6.73 | **$7.68** |\n\n**Question 4: Calibration and Bias of the Relevance Scoring Function**\n\nTo ensure we could address your point accurately, we'd like to begin by clarifying a term. When you mention the \"relevance scoring function\", do you mean the data diversity metric?\n\n- Assuming that is the case, we follow [1], use an embedding model to generate sentence vectors, and calculate their cosine similarity. As a general metric for data diversity, this method is inherently domain-agnostic.\n- Furthermore, a \"domain space\" is difficult to be defined mathematically, so that the relevance scoring function can be calibrated correspondingly. We haven't found established literature on this topic, and we welcome any further discussions. This should be interesting!\n\n**Question 5: Potential Applications Beyond Instruction Tuning**\n- **The core advantage of TreeSynth lies in synthesizing abundant and diverse datasets with remarkable scalibility from scratch in a task-agnostic manner.** We believe that with further supplemented reward information, TreeSynth-synthesized data can provide significant support for reward model training, RLHF-style pipelines, and other stages of LLM development.\n\nThank you again for your dedication and constructive feedback to our work! We will update the supplementary experimental results in our paper. Sincerely, we hope that these clarifications can fully address your concerns, and you could reconsider our scores accordingly!\n\n**References**\n[1] Yu, Y., Zhuang, Y., Zhang, J., Meng, Y., Ratner, A. J., Krishna, R., ... & Zhang, C. (2023). Large language model as attributed training data generator: A tale of diversity and bias. Advances in neural information processing systems, 36, 55734-55784."}, {"review_id": "8Nb50vyra1", "reviewer": "Reviewer_RdrW", "summary": "The authors present a method for generating synthetic data that is more diverse, inspired by Decision Trees. This method aims to create criteria for subdividing the data space into exclusive regions. To achieve this, they prompt a large language model (LLM) with a data description to generate N diverse samples. Another LLM, proficient in identifying distinctions between samples, determines the core criteria. This process yields a set of instructions used to guide an LLM in generating diverse synthetic data. The authors evaluated their method by starting with popular benchmarking datasets and employing well-known LLMs (both open-source and proprietary) to create synthetic data following the proposed approach. They then fine-tuned smaller models on this generated data, demonstrating performance gains. The baseline for comparison was established using other methods for generating diverse synthetic data. The results indicate that their method outperforms the baseline.", "questions": "I also have several questions: \n\n- Is it clear whether the context provided to the LLM is input by the user? The criterion may vary significantly depending on the input. \n- What exactly is this \"proficient LLM\" in identifying inter-sample distinctions that determine the core criteria? \n- Evol-Instruct also shows similar diversity in the t-SNE visualizations, and results demonstrate diversity comparable to TreeSynth; however, TreeSynth achieves better outcomes. What explains this discrepancy?", "limitations": "The authors stated a set of limitations and the limitations sections.\n\nIn my point of view, the main limitations is the dependency of the teacher LLM to generated synthetic data, and I would suggest the authors to better scope the utility of the models to the demostrated use cases as model distillation.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is well-written and clearly explained, featuring a robust evaluation method and an extensive presentation of results, including effective representations like t-SNE visualizations. \n\nThe baseline is effectively presented alongside other similar methods (such as de Evol-Instruct and Persona), and the choice of evaluation method (fine-tuning smaller models) is a strong approach for assessing the performance of the proposed method. \n\nHowever, I have some concerns regarding the use cases for generating this type of synthetic data. Essentially, this process resembles model distillation, as the method relies entirely on a \"teacher\" LLM to create diversity within a specific data space. The approach involves a chain of prompts that generate samples and criteria for constructing the Tree, which is then used as guidance to prompt the \"teacher\" model for generating synthetic data. This dependency is evident in the varying results produced by different base models used in the tests. While the method clearly illustrates model distillation, the introduction may imply that it could generalize and \"enhance their specific capabilities.\" \n\nI recommend that the authors clarify the scope of utility for these models to align with the demonstrated use case of model distillation. \n\nModel distillation indeed offers several advantages, enabling smaller models to be deployed on devices or in fog computing systems, thereby conserving computational resources.", "was_revised": true, "final_justification": "I leaning no maintain my score, as I think these work is a good contribution to the field, despite the dependency of the experiments shown on propertiary LLM. I still feel that adding other source of knowledge will generate better diversity \n\nOverall, a good work, and a worth contribution.", "rebuttal": "Dear Reviewer RdrW,\n\nThank you very much for your valuable time, dedication, and insightful comments on our work! After reading your feedback carefully, we sincerely prepare the following clarifications after highlighting the significant impact of TreeSynth, and hope that these discussions could fully address your concerns!\n\nFirst, we will briefly highlight the impact of TreeSynth:\n- **Higher diversity and better performance:** Data diversity is crucial for preventing data collapse, avoiding overfitting, and enhancing model performance. With the tree-guided complementarity and exhaustiveness, TreeSynth synthesizes diverse and comprehensive domain-specific data, and demonstrates better performance than human-annotated or other synthetic datasets, **offering a superior solution to data scarcity, collapse, and the high cost of manual annotation** (Sec. 4.2).\n- **Excellent Scalability:** Greater scalability implies that model capabilities can continuously improve with more data, ultimately leading to superior performance. TreeSynth exemplifies this by **effectively scaling datasets and consistently improving downstream performance with increased data volume**, showcasing its significant potential for remarkable model performance (Sec. 4.2).\n- **Effective Re-balance of Existing Datasets:** In addition to synthesizing data from scratch, TreeSynth can also be used to re-balance existing datasets, achieving **improved performance** (Sec. 4.3). \n\n**Weakness: Clear Paper Scope**\n\nWe greatly appreciate your insightful comments! We agree with your observation that our experimental setting resembles that of model distillation, and will clarify this distinction accordingly in our final version. Beyond this similarity, we would like to claim the following points:\n\n- **Our method aligns more closely with data synthesis than model distillation.** Roughly, model distillation focuses on achieving better \"efficiency and compression\" for a given dataset. In contrast, data synthesis emphasizes how to generate an effective dataset, alleviating data scarcity. The key output of our method is the synthetic dataset itself, instead of a smaller or more efficient \"student model\", which only serves to validate the effectiveness of synthesized datasets. \n- **This classification is consistent with existing work in the community.** For example, in our baselines, Persona Hub also utilizes GPT-4 to synthesize data and train the Qwen2-7B model, yet it is widely categorized as a data synthesis approach. This provides a strong precedent for defining TreeSynth as a data synthesis method.\n\n\n**Question 1: Whether the Context Provided to the LLM is User-Input**\n- As described in Section 3, the only user input provided to the LLM's prompt is a description of the target dataset. **This description is necessary,** as it instructs the model on what data to synthesize, yet it is simple enough to be easily provided by the users. By requiring only this minimal input, we ensure that TreeSynth remains as concise as possible, achieving **\"generating a dataset for a task from a description sentence\"**.\n- A better task description is not the core focus of our paper, although it can be optimized by various methods. Specifically, even without deliberately optimized task description, TreeSynth still achieves excellent performance, demonstrating its robustness and effectiveness. The core contribution of this work lies in how to synthesize diverse and comprehensive data through a tree-guided approach. A better task description may lead to further improvements, such as deploying an LLM to optimize the user’s initial input to better guide the data synthesis process. However, this is not the focus of our current study.\n\n**Question 2: Clarification on the Criterion-Determining LLM**\n\nWe apologize for the lack of clarity in our previous description!\n\n- Similar to other stages, this \"proficient LLM\" in Criterion Determination is also an off-the-shelf LLM (e.g., LLaMA-70B, Qwen-72B, or GPT-4o), but is instructed to identify the core criteria with the prompt presented in Figures 17-20. This design leverages the powerful capabilities of existing LLMs, while maintaining TreeSynth's ease of use. The excellent performance of TreeSynth validates the efficacy of this approach.\n- Identifying the core criterion based on inter-sample distinctions is a critical step. Selecting a non-distinctive dimension, such as one previously used by the parent node, leads to a collapse in the subsequent subspace partitioning, rendering the division ineffective and lowering the data diversity.\n\n**Question 3: Why Does TreeSynth Outperform Evol-Instruct Despite Similar Diversity?**\n\nThanks for your meticulous observation!\n\n- Due to the lack of effective control, **Evol-Instruct often generates deviated data, leading to \"spurious\" diversity.** Specifically, compared to TreeSynth's tree-guided mechanism that systematically partitions the entire data space into subspaces, the evolutionary process of Evol-Instruct explores outwards from a subspace. This uncontrolled exploration frequently causes synthetic data to deviate significantly from the target data space, exceeding its intended boundaries, which also seems diverse, but degrades downstream task performance.\n- For instance, a GSM8K problem originally solvable by simple division:\n    > \"There are 480 zombies in the shopping mall. If the number of zombies doubled every day, how many days ago were there less than 50 zombies in the mall?\"\n\n    evolves under Evol-Instruct into a problem requiring complex calculus:\n\n    > \"Given that the growth rate of a zombie population in a shopping mall, currently at 480, is proportional to both its current size and the available space within the mall's carrying capacity of 1000, how many days ago was the population less than 50?\"\n\n    In contrast, TreeSynth's synthesis process exhibits excellent controllability. It is strictly constrained by the attribute values of each subspace and the data space description from the root node. This design makes TreeSynth demonstrably superior to peer methods in both downstream task performance and scalability.\n\nThank you again for your constructive comments and your great efforts on our work! Sincerely, we hope that these clarifications can fully address your concerns, and prompt you to reconsider our scores accordingly!"}, {"review_id": "2K7w7mOSlM", "reviewer": "Reviewer_geZ4", "summary": "This paper introduces TreeSynth: a novel method for synthesis of text data aided by Decision Trees and Large Language Models (LLMs).\nTreeSynth leverages an LLM to generate a decision tree to exhaustively enumerate all possible subspaces of the dataset (also called criteria).\nThis enumeration is then used to enhance diversity and comprehensiveness of the starting dataset, leading to improved downstream ML performance of models trained with such augmented data.", "questions": "- Could you provide further numerical insights that demonstrate the increased diversity of data generated by TreeSynth?\n- Could you provide some qualitative examples of answers generated by one of the models with TreeSynth data and with another baseline which showcase how the performance improvements are related with the diversity issue tackled by TreeSynth? (For instance, TreeSynth-aided LLMs can answer questions about domains that are underrepresented in the PersonaHub-aided ones) \n- Could you provide an informal justification (or a source) in support of the statement made in lines 116-119? Is it the case that the LLM can possibly generate criteria that do not satisfy such a statement? If so, how often does this issue happen? How can it be identified? To what extent does it affect TreeSynth performance? And how can you address it?\n- Enumerating all the possible criteria of a dataset can be prohibitive as the size of the decision tree built by TreeSynth grows exponentially in the number of attributes", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n+ **The proposed method showcases consistent improvements with respect to the state-of-the-art.** These improvements are consistently measured over several experiments spanning three LLMs and three datasets.\n+ **The authors tackled the issue of data diversity in text data.** This is a significant problem in Machine Learning.\n+ **Extensive information to reproduce the results.** The authors provided comprehensive information to reproduce the results. Including the prompts used for each experiment.\n\n## Weaknesses\n- **Some statements in the main paper are not properly discussed.** For instance, at lines 116-119: “Subsequently, another LLM, proficient in identifying inter-sample distinctions, determines exactly one core criterion δ (e.g., Type of Mathematical Operation). This criterion $\\delta$ optimally partitions $X$ into mutually exclusive attribute values $V_X^\\delta = {v_j^\\delta |j = 1, 2, ..., m}$” lacks a proof or an informal explanation of why this is the case, nor any experimental evidence is shown in support of this statement. A reference should point to such a source if this has been done in the literature.\n- **Need for extensive evaluation of TreeSynth and TreeSynth-guided data balancing.** TreeSynth generation quality is only measured by means of data samples’ cosine similarity. Further insights on the data generated by such a method would strengthen the paper’s statements and contributions. Tables that give insights into the generated trees (e.g., how many criteria are generated, depth of the trees, examples of generated criteria) would strengthen the paper as well. TreeSynth-guided data balancing is evaluated in one experiment only (Table 3), in which it is showcased to outperform all other methods. This method could have been analysed more extensively, showcasing the strength of the proposed method.\n- **Need for more qualitative analysis.** In papers related to language models, in which quantitative/formal analysis is often infeasible, it is important to provide qualitative analysis of the produced data. The paper does not provide any example of text generated by the TreeSynth-aided models, nor does it provide examples that showcase how improvements of these generated texts are related to the proposed method.", "was_revised": true, "final_justification": "Having looked at both mine and the other reviewers, I appreciate the authors' answers, which have addressed all my primary concerns except for some minor points.", "rebuttal": ""}, {"review_id": "nhR4zGhyaa", "reviewer": "Reviewer_4JZM", "summary": "This paper proposes TreeSynth, a method to generate data synthetically by formulating concepts into a tree format. Nodes are concepts, where deeper nodes are more fine-grained concepts. They show results on Llama and Qwen 70B models with math and code generation benchmarks, showing improved performance.", "questions": "1. How did you choose N to be 10? Were there any hyperparameter studies done?\n2. The manuscript mentions \"another LLM, proficient in identifying inter-sample distinctions, determines exactly one core criterion\" on lines 116-117. It wasn't immediately clear to me what this LLM is - is it fine-tuned, few-shot augmented, or a base model? I might have missed where those details were mentioned.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- The paper provides enough mathematical formulation to make it easier to follow\n- Experimentation is extensive\n\nWeaknesses:\n- This methodology reminds me of the InstructLab paper (LAB: Large-Scale Alignment for ChatBots) that also uses a tree-like data synthesis method. Providing a comparison (results would be nice, but a discussion will suffice for now) would be great.\n- I might have missed any human studies or automatic studies to measure the quality of the synthetic data, but that information would also help.\n\nI'd be more than happy to update my scores once my concerns are addressed.", "was_revised": true, "final_justification": "The authors have addressed my concerns. I also read through the other reviews/responses -- I liked Reviewer W3cd's comment about the computational costs and appreciated the author's detailed analysis.", "rebuttal": "Dear Reviewer 4JZM,\n\nThanks for your dedication to our reviewing process and your comments on our work! We will try our best to clarify your comments one by one below. Hope that we can fully address your concerns!\n\nTo begin with, we wanna highlight the difference between criteria and concepts, as well as the significant impact of TreeSynth.\n- **Criteria are more fine-grained than concepts.** For example, while a math problem may involve multiple concepts (e.g., persons, events, locations, mathematical operators), criteria can **additionally contain more compositional and abstract dimensions,** such as the order of mathematical operators and difficulty levels. Furthermore, the **subspace of a leaf node is defined by the intersection of all attribute values** along the path from the root (Sec. 3.2), instead of a single existing concept. This broader coverage and finer granularity allow for a **more precise partitioning of the data space,** thereby enhancing data diversity and model performance.\n- **Higher diversity and better performance:** Data diversity is crucial for preventing data collapse, avoiding overfitting, and enhancing model performance. With the tree-guided complementarity and exhaustiveness, TreeSynth synthesizes diverse and comprehensive domain-specific data, and demonstrates better performance than human-annotated or other synthetic datasets, **offering a superior solution to data scarcity, collapse, and the high cost of manual annotation** (Sec. 4.2).\n- **Excellent Scalability:** Greater scalability implies that model capabilities can continuously improve with more data, ultimately leading to superior performance. TreeSynth exemplifies this by **effectively scaling datasets and consistently improving downstream performance with increased data volume**, showcasing its significant potential for remarkable model performance (Sec. 4.2).\n- **Effective Re-balance of Existing Datasets:** In addition to synthesizing data from scratch, TreeSynth can also be used to re-balance existing datasets, achieving **improved performance** (Sec. 4.3).\n\n**Weakness 1: Comparison with LAB**\nThank you for your insightful suggestion and bringing paper [1] to our attention! We have thoroughly read LAB, a taxonomy-guided approach for instruction-tuning data synthesis. Due to the unavailability of LAB's dataset and its complete taxonomy, our comparative analysis focuses on its methodology.\n- **LAB necessitates a manually constructed tree-like taxonomy,** which requires further manual modifications when adapted to specific domains. Conversely, **TreeSynth autonomously partitions the data space, and synthesizes a dataset from a task description sentence.**\n- **LAB relies on manually provided seed data,** as mentioned in the paper \"the tasks are defined in the leaf nodes and exemplified by providing manually written instruction-response pairs\". In contrast, **TreeSynth can generate extensive data from scratch.** This fundamental difference implies that TreeSynth is more accessible and possesses greater potential for widespread applications.\n- As mentioned above, **LAB utilizes a single concept to define a data subspace,** whereas **TreeSynth leverages the intersection of criteria for broader coverage and finer granularity,** which facilitates the generation of a more balanced and comprehensive dataset.\n\n**Weakness 2: Synthetic Data Quality Evaluation**\n\nWe assess the quality of synthetic data from three perspectives: data diversity, t-SNE visualization analysis, and downstream task performance.\n\n- **Data diversity** is quantified using cosine similarity [2]. As shown in Tables 1-4, TreeSynth demonstrates significantly superior diversity across all tasks and models compared to human-annotated and other synthetic datasets. Notably, the GPT-4o-driven TreeSynth improves diversity by 12.5%, 25.0%, and 34.5% over the original GSM8K, MATH, and Code Alpaca datasets, respectively.\n- **The t-SNE visualizations** (Figures 4 and 7) illustrate TreeSynth's comprehensive coverage of the data space. By strategically partitioning the space from a global perspective and synthesizing data within these subspaces, TreeSynth overcomes inherent model biases and source data limitations, thereby achieving a more balanced spatial coverage.\n- **Finally, downstream task performance** (Figures 5, 6, 8 and Tables 5-8) directly validates the superiority of our synthetic data. Guided by the global view of its tree structure, **TreeSynth not only outperforms competing methods but also demonstrates excellent scalability,** as downstream performance consistently improves with increasing data volume.\n\n**Question 1: Choice of Hyperparameter N**\nThanks a lot for your valuable questions! The hyperparameter N sets the threshold for the number of attribute values in a node; nodes exceeding this count are regarded as \"infinite nodes\". Intuitively, a larger N results in finer partitioning of the data space and better data quality. Based on our preliminary experiments, we chose N=10, which is sufficient to achieve better performance.\n\n**Question 2: Clarification on the Criterion-Determining LLM**\n\nWe apologize for the lack of clarity in our previous description!\n\n- Similar to other stages, this \"proficient LLM\" in Criterion Determination is also an **off-the-shelf LLM** (e.g., LLaMA-70B, Qwen-72B, or GPT-4o), but is instructed to identify the core criterion with the prompt presented in Figures 17-20 (without few shots). This design leverages the powerful capabilities of existing LLMs, while maintaining TreeSynth's ease of use. The excellent performance of TreeSynth validates the efficacy of this approach.\n- As shown below, given 10 MATH-style geometry questions, a \"Criterion Determination\" LLM can identify \"geometric_object_type\" as the core criterion to effectively partition the data into four subspaces, before a \"Subspace Coverage\" LLM complements other potential subspaces. \n```\n{\n\"criterion\": \"geometric_object_type\",\n\"attributes\": {\n \"triangle\": [\n  \"A triangle has sides of lengths 7, 24, and 25. Determine the area of the triangle.\",\n  \"Let ABC be a triangle with AB = 13, BC = 14, and CA = 15. Compute the radius of the circle inscribed in the triangle.\",\n  \"Let ABC be a triangle where AB = 8, BC = 10, and CA = 12. Find the length of the altitude from A to BC.\",\n  \"Consider a triangle ABC with AB = 6, BC = 8, and CA = 10. Prove that ABC is a right triangle and then compute the radius of its circumscribed circle.\",\n  \"In a triangle ABC, the medians from vertices A, B, and C intersect at a point G. If AB = 12, BC = 16, and CA = 20, compute the distance from G to vertex A.\",\n  \"Let ABC be a triangle where AB = 15, BC = 20, and CA = 25. Determine the coordinates of the orthocenter if vertex A is at (0, 0), B is at (15, 0), and C is at (0, 20).\"\n ],\n \"regular_polygon\": [\n  \"In a regular hexagon with side length s = 6, calculate the area of the hexagon.\",\n  \"A regular dodecagon (12-sided polygon) is inscribed in a circle of radius R = 6. Compute the area of the dodecagon.\"\n ],\n \"cyclic_quadrilateral\": [\n  \"A cyclic quadrilateral has sides of lengths 7, 8, 9, and 10. Calculate the area of the quadrilateral using Brahmagupta's formula.\"\n ],\n \"composite_figure\": [\n  \"A circle is inscribed in a square, and the square has side length 10. Compute the area of the region outside the circle but inside the square.\"\n ]\n}\n}\n```\n- Identifying the core criterion based on inter-sample distinctions is a critical step. Selecting a non-distinctive dimension, such as one previously used by the parent node, leads to a collapse in the subspace partitioning, lowering the diversity of the synthesized data.\n\nThank you again for your time devoted to our work again! Sincerely, we hope that these clarifications can fully address your concerns, and prompt you to reconsider our scores accordingly! If you have any questions, please do not hesitate to let us know; we welcome any further discussions!\n\n**References**\n[1] Sudalairaj, S., Bhandwaldar, A., Pareja, A., Xu, K., Cox, D. D., & Srivastava, A. (2024). Lab: Large-scale alignment for chatbots. arXiv preprint arXiv:2403.01081.\n[2] Yu, Y., Zhuang, Y., Zhang, J., Meng, Y., Ratner, A. J., Krishna, R., ... & Zhang, C. (2023). Large language model as attributed training data generator: A tale of diversity and bias. Advances in neural information processing systems, 36, 55734-55784."}]

Author rebuttal:

Meta-review: This paper uses LLMs to generate diverse synthetic data. The main contributed idea is to automatically partition the data into semantically meaningful disjoint category (e.g., "generate word problems that involve addition and cookies" vs "generate word problems that involve multiplication and pages", where the math operation being addition and the entity being cookies might be decision nodes in the tree), and then sample at each of these nodes to create combinatorial diversity in the synthetic data being generated.

The authors demonstrate strong results across a few datasets, and the reviewers were generally satisfied with additional experiments and clarifications in the rebuttal, with unanimous consensus to clearly accept. 

Overall I think the paper is a pretty good LLM pipeline for synthetic data generation in settings where the space of data instances can be semantically partitioned in the way the authors consider -- the result is a sort of "paint by numbers" system somewhere between purely programmatic data generation and fully freeform prompting an LLM for additional data that seems nice.
Decision: Accept (spotlight)