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+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0068", "section": "OVERVIEW OF APPENDIX", "page_start": 14, "page_end": 14, "type": "ListGroup", "text": "Appendix A: The Use of LLMs Appendix B: Baselines Appendix C: Training Details Appendix D: Detailed BM25 and ReasonIR Results on BRIGHT Appendix E: Evaluation on BEIR Appendix F: Analysis of the Hyperparameter \\alpha Appendix G: Different Backbone Models Appendix H: Analysis of the Length Control Instruction for Distillation Appendix I: Out-of-Domain Generalization on R2MED Appendix J: Rubrics of Rubric-based Relevance Scoring Appendix K: Analysis of the Necessity of Reasoning Appendix L: Task Relevance Definitions for Different Benchmarks Appendix M: Reasoning Examples", "source": "marker_v2", "marker_block_id": "/page/13/ListGroup/132"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0069", "section": "A THE USE OF LLMS", "page_start": 14, "page_end": 14, "type": "Text", "text": "We used the LLMs to assist with writing. Specifically, their use included grammar checking, rephrasing for clarity, and textual polishing. Additionally, we utilized the LLMs to help draft Python codes for plotting figures. The LLMs used for these purposes include Gemini 2.5 Pro<sup>2</sup>, ChatGPT<sup>3</sup>, DeepSeek-V3.1<sup>4</sup>.", "source": "marker_v2", "marker_block_id": "/page/13/Text/16"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0070", "section": "B BASELINES", "page_start": 14, "page_end": 14, "type": "Text", "text": "This section provides additional details for each of the baseline models used in our comparative analysis. As outlined in the experimental setup 4.1, we categorize these models into two groups: non-reasoning and reasoning-enhanced approaches. For each baseline listed below, we describe its core methodology and implementation details:", "source": "marker_v2", "marker_block_id": "/page/13/Text/18"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0071", "section": "B BASELINES", "page_start": 14, "page_end": 14, "type": "ListGroup", "text": "RankLLaMA: A pointwise re-ranking model that jointly encodes the query and document, generating a scalar relevance score by projecting the representation of the end-of-sequence token through a linear layer. The model is trained with a contrastive loss. RankZephyr: A listwise re-ranking model that takes a query and a set of candidate documents as input and outputs their relative ranking order. It employs a sliding window strategy to to handle large lists of candidates. The model is trained on MS MARCO (Bajaj et al., 2016) dataset via knowledge distillation from GPT-3.5 (Ouyang et al., 2022) and GPT-4 (Achiam et al., 2023). JudgeRank : A zero-shot, reasoning-enhanced pointwise re-ranking method. It utilizes carefully designed prompts to guide LLMs through explicit reasoning steps before producing the final relevance judgment (\"yes\" or \"no\"). Rank1: A reasoning-enhanced pointwise re-ranking model. For each query-document pair, the model generates a reasoning process and outputs a binary relevance judgment (\"yes\" or \"no\"). Rank1 is trained on reasoning trajectories generated by DeepSeek-R1 (Guo et al., 2025) on the MS MARCO dataset. Rank-R1: A reasoning-enhanced setwise (Zhuang et al., 2024) re-ranking model. Given a query and a candidate set, the model selects the most relevant document and applies a heap-sort procedure to obtain top-k results. The model is trained on the MS MARCO dataset with the GRPO algorithm.", "source": "marker_v2", "marker_block_id": "/page/13/ListGroup/133"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0072", "section": "B BASELINES", "page_start": 14, "page_end": 14, "type": "Footnote", "text": "2", "source": "marker_v2", "marker_block_id": "/page/13/Footnote/24"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0073", "section": "B BASELINES", "page_start": 14, "page_end": 14, "type": "Footnote", "text": "3", "source": "marker_v2", "marker_block_id": "/page/13/Footnote/25"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0074", "section": "B BASELINES", "page_start": 14, "page_end": 14, "type": "Footnote", "text": "4", "source": "marker_v2", "marker_block_id": "/page/13/Footnote/26"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0075", "section": "B BASELINES", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 4: Hyperparameters for the SFT stage. Learning Epochs WarmUp LR Batch Size Gradient Rate Ratio Scheduler Per-Device Accumulation 10^{-5} 1 0.1 cosine 1 8 Table 5: Hyperparameters for the RL stage with GRPO.", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/82"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0076", "section": "B BASELINES", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "\\alpha \\mid \\tau \\mid N Learning Rate Epochs Batch Size Mini Batch Size Micro Batch Size Per-Device KL Coefficient Temperature 0.75 20 8 10^{-6} 1 256 256 8 0.005 1.0 Table 6: Detailed nDCG@10 results for Retro* on the BRIGHT benchmark. Retro* re-ranks the top-100 documents retrieved by either BM25 or ReasonIR. The retrieval stage utilized a GPT-4 reasoning query, while the re-ranking stage utilized the original query.", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/83"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0077", "section": "B BASELINES", "page_start": 15, "page_end": 15, "type": "Table", "text": "Models Avg. Stack Exch ange Coc ling Th ieorem-ba ased Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BM25 27.0 53.6 54.1 24.3 38.7 18.9 27.7 26.3 19.3 17.6 3.9 19.2 20.8 Retro* (7B) 35.3 56.4 56.1 30.8 46.4 31.6 36.7 39.8 22.7 28.2 7.3 27.6 40.4 Retro* (32B) 36.6 61.6 59.4 35.9 47.8 33.6 35.6 43.2 18.8 29.2 6.6 28.1 39.3 , , Test- Time S caling ( Mean-So ore@ 16) Retro* (7B) 37.0 60.7 59.0 31.9 48.2 32.1 34.9 40.8 25.2 33.2 8.5 29.8 40.1 Retro* (32B) 38.5 64.0 61.6 36.9 50.1 33.9 37.7 45.2 19.9 32.3 8.5 30.6 41.5 ReasonIR 30.6 43.4 43.0 33.1 39.6 20.9 31.0 27.0 31.6 19.5 7.4 33.9 36.9 Retro* (7B) 36.8 54.7 54.5 33.5 47.7 32.5 40.1 41.2 22.7 28.9 8.3 34.1 43.7 Retro* (32B) 37.4 60.7 56.1 37.6 47.7 31.3 38.6 45.7 19.0 27.3 9.0 33.0 43.2 Test- Time S caling ( Mean-So ore@ 16) Retro* (7B) 38.4 60.4 57.4 34.8 48.2 31.6 37.9 41.9 24.9 32.1 9.0 38.1 44.0 Retro* (32B) 39.5 64.7 57.5 38.5 49.7 31.7 42.6 47.3 19.4 30.2 10.0 37.8 44.8", "source": "marker_v2", "marker_block_id": "/page/14/Table/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0078", "section": "B BASELINES", "page_start": 15, "page_end": 15, "type": "Text", "text": "• ReasonRank : A reasoning-enhanced listwise re-ranking model. It introduces an automated data synthesis framework to generate high-quality reasoning-intensive training data. The model is trained on this synthesized dataset in two stages: SFT with reasoning trajectories distilled from DeepSeek-R1, followed by GRPO with a multi-view re-ranking reward.", "source": "marker_v2", "marker_block_id": "/page/14/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0079", "section": "C Training Detials", "page_start": 15, "page_end": 15, "type": "Text", "text": "For the SFT stage, we use the LLaMA-Factory framework (Zheng et al., 2024b), fine-tuning both the 7B and 32B models on a single node equipped with 8 NVIDIA H100 GPUs. For the RL stage, we employ the GRPO algorithm through the VeRL framework (Sheng et al., 2025). In our main experiments, we set the hyperparameter \\alpha to 0.75 and \\tau to 20, as 20 represents a meaningful interval between relevance levels in our rubrics 3.1.1. An ablation study on the impact of different \\alpha values is presented in Appendix F. The 7B model is trained on a single node, while the 32B model is trained across two nodes. Detailed hyperparameters for the SFT and RL stages are provided in Table 4 and Table 5, respectively.", "source": "marker_v2", "marker_block_id": "/page/14/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0080", "section": "D Detailed BM25 and ReasonIR Results on BRIGHT", "page_start": 15, "page_end": 15, "type": "Text", "text": "This section provides the complete, per-dataset results on the BRIGHT benchmark, corresponding to the summarized analysis in the main body. Table 6 details the nDCG@10 scores of Retro* when re-ranking the top-100 documents retrieved by two different first-stage retrievers: BM25 and ReasonIR. The results highlight the model's robust and consistent performance across various domains, regardless of the initial retrieval method.", "source": "marker_v2", "marker_block_id": "/page/14/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0081", "section": "D Detailed BM25 and ReasonIR Results on BRIGHT", "page_start": 15, "page_end": 15, "type": "Text", "text": "ReasonIR further introduces a zero-shot re-ranking method (QwenRerank) based on Qwen2.5-Instruct-32B, and we conduct a detailed comparison between this method and Retro*. However, QwenRerank computes its final ranking scores by fusing normalized retriever and re-ranker outputs with 0.5 \\times s_{\\rm reranker} + 0.5 \\times s_{\\rm retriever} , meaning that its reported performance reflects the joint effect of", "source": "marker_v2", "marker_block_id": "/page/14/Text/12"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0082", "section": "D Detailed BM25 and ReasonIR Results on BRIGHT", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 7: Comparison of Retro* with QwenRerank from ReasonIR under two evaluation settings, where all methods re-rank the top-100 documents retrieved by ReasonIR. Retro* consistently achieves higher performance in both settings. Results marked with † are reported by ReasonIR. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. ReasonIR 30.6 43.4 43.0 33.1 39.6 20.9 31.0 27.0 31.6 19.5 7.4 33.9 36.9 Re-ranking w/o Score Fusion QwenRerank† (32B) 30.3 50.2 47.5 23.6 35.8 24.7 28.1 29.9 30.3 26.5 5.5 20.7 40.8 Retro* (7B) 36.8 54.7 54.5 33.5 47.7 32.5 40.1 41.2 22.7 28.9 8.3 34.1 43.7 Retro* (32B) 37.4 60.7 56.1 37.6 47.7 31.3 38.6 45.7 19.0 27.3 9.0 33.0 43.2 Retro* (7B, Mean-Score@16) 38.4 60.4 57.4 34.8 48.2 31.6 37.9 41.9 24.9 32.1 9.0 38.1 44.0 Retro* (32B, Mean-Score@16) 39.5 64.7 57.5 38.5 49.7 31.7 42.6 47.3 19.4 30.2 10.0 37.8 44.8 Re-ranking w/ Score Fusion QwenRerank† (32B) 36.9 58.2 53.2 32.0 43.6 28.8 37.6 36.0 33.2 34.8 7.9 32.6 45.0 Retro* (7B) 38.4 54.2 55.9 35.0 49.7 32.4 40.2 41.7 26.1 32.7 10.9 36.9 45.0 Retro* (32B) 39.6 60.0 58.2 38.4 51.1 31.4 39.2 45.3 25.0 33.4 10.5 37.0 45.4 Retro* (7B, Mean-Score@16) 39.0 56.8 57.1 36.0 49.8 31.7 38.2 42.3 27.1 34.1 10.4 39.2 44.9 Retro* (32B, Mean-Score@16) 40.2 60.1 58.4 38.5 51.4 32.1 41.5 46.3 25.2 33.3 11.1 38.4 46.2 Table 8: nDCG@10 results on the BEIR benchmark, where all methods re-rank the top-100 documents retrieved by BM25 provided by Lin et al. (2021) . The retrieval stage and the re-ranking stage both utilize the original query. Results marked with † are reported by ReasonRank.", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/235"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0083", "section": "D Detailed BM25 and ReasonIR Results on BRIGHT", "page_start": 16, "page_end": 16, "type": "Table", "text": "Models Methods Avg. TREC-COVID DBPedia SciFact NFCorpus Signal-1M Robust04 TREC-NEWS BM25 Retriever 43.7 59.5 31.8 67.9 33.8 33.0 40.7 39.5 Non-Reasoning Re-Ranking Baselines RankZephyr† (7B) Listwise 54.1 82.9 44.4 75.4 38.3 31.4 53.7 52.8 Reasoning-Enhanced Re-Ranking Baselines Rank1† (7B) Pointwise 50.7 79.0 35.8 73.3 37.5 25.4 57.1 47.7 Rank1† (32B) Pointwise 51.0 80.6 34.8 74.8 37.3 25.6 58.3 45.6 Rank-R1† (7B) Setwise 53.6 83.7 42.3 72.2 38.9 33.1 54.5 50.6 Rank-R1† (14B) Setwise 54.6 84.6 44.1 76.0 38.6 33.0 56.9 49.2 ReasonRank† (7B) Listwise 54.4 82.0 46.0 75.6 39.6 31.4 55.4 50.5 ReasonRank† (32B) Listwise 55.4 83.2 45.7 77.2 40.0 31.1 58.7 52.2 Retro* (7B) Pointwise 55.8 84.7 45.9 77.1 37.1 31.2 64.7 49.7 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 56.8 85.4 46.7 78.5 38.1 32.1 65.8 51.0", "source": "marker_v2", "marker_block_id": "/page/15/Table/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0084", "section": "D Detailed BM25 and ReasonIR Results on BRIGHT", "page_start": 16, "page_end": 16, "type": "Text", "text": "both retriever and re-ranker rather than its standalone re-ranking capability. To ensure a fair comparison, we compare both models under the same evaluation settings. As shown in Table 7, Retro* consistently outperforms QwenRerank across all evaluation settings, indicating substantially stronger re-ranking ability. These results suggest that most of the gains attributed to QwenRerank largely come from the strong retriever ReasonIR, whereas Retro* achieves higher performance purely from its re-ranking capability.", "source": "marker_v2", "marker_block_id": "/page/15/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0085", "section": "E EVALUATION ON BEIR", "page_start": 16, "page_end": 16, "type": "Text", "text": "To assess the generalizability of our model, we further evaluate its performance in traditional retrieval scenarios. Following ReasonRank (Liu et al., 2025) , we select seven datasets from the BEIR benchmark (Thakur et al., 2021) , for their relatively small number of queries. In the retrieval stage, BM25 is applied with the original query to obtain candidate documents, after which all re-ranking methods re-rank the top-100 BM25 results. We report nDCG@10 as the performance metric.", "source": "marker_v2", "marker_block_id": "/page/15/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0086", "section": "E EVALUATION ON BEIR", "page_start": 16, "page_end": 16, "type": "Text", "text": "In this scenario, we utilize the MS MARCO dataset as our training data. Specifically, we construct 24,000 query-document pairs for both SFT and RL training. The RL stage is trained for 3 epochs, while the other training settings are consistent with Section 4.1.", "source": "marker_v2", "marker_block_id": "/page/15/Text/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0087", "section": "E EVALUATION ON BEIR", "page_start": 16, "page_end": 16, "type": "Text", "text": "The evaluation results on BEIR, as shown in Table 8, demonstrate the strong generalizability of Retro* to traditional re-ranking tasks. The Retro* (7B) model achieves an average nDCG@10 of 55.8, outperforming all non-reasoning and reasoning-enhanced baselines. These results confirm", "source": "marker_v2", "marker_block_id": "/page/15/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0088", "section": "E EVALUATION ON BEIR", "page_start": 17, "page_end": 17, "type": "TableGroup", "text": "Table 9: nDCG@10 results on the BRIGHT benchmark with models trained using varying α values. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 15.7 20.6 7.9 27.9 36.6 + SFT + RL (α = 0.00) 30.8 43.6 48.7 30.8 36.7 25.6 28.5 37.7 13.1 28.6 5.6 30.6 40.6 + SFT + RL (α = 1.00) 33.2 49.4 51.8 29.9 44.2 27.6 33.4 36.4 20.1 23.3 8.6 32.0 41.3 + SFT + RL (α = 0.25) 36.1 53.0 55.1 33.3 46.3 34.3 36.2 40.3 17.3 29.3 7.0 35.2 45.8 + SFT + RL (α = 0.50) 35.8 51.3 54.3 32.7 47.4 31.7 35.0 39.3 20.7 29.2 8.2 34.6 44.6 + SFT + RL (α = 0.75) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0", "source": "marker_v2", "marker_block_id": "/page/16/TableGroup/272"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0089", "section": "E EVALUATION ON BEIR", "page_start": 17, "page_end": 17, "type": "Text", "text": "that our reasoning-enhanced pointwise approach is general-purpose and suitable for both reasoningintensive and traditional retrieval scenarios. Moreover, by integrating over 16 sampling scores, the model achieves a final nDCG@10 of 56.8, indicating the effectiveness of test-time scaling even on traditional benchmarks, as illustrated in Figure 6.", "source": "marker_v2", "marker_block_id": "/page/16/Text/3"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0090", "section": "F ANALYSIS OF THE HYPERPARAMETER α", "page_start": 17, "page_end": 17, "type": "Text", "text": "Table 9 reports the performance of training with different weights α for the composite rewards. When α = 0 or α = 1, the model degenerates into using only one of the composite rewards, resulting in suboptimal performance. In particular, training with only the intra-document reward (α = 1) clearly outperforms training with only the inter-document reward (α = 0), suggesting that the intra-reward provides a stronger optimization signal for model learning. This observation aligns with its role in stabilizing training by encouraging more consistent reasoning trajectories within a document.", "source": "marker_v2", "marker_block_id": "/page/16/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0091", "section": "F ANALYSIS OF THE HYPERPARAMETER α", "page_start": 17, "page_end": 17, "type": "Text", "text": "However, despite its dominance, the intra-reward alone still underperforms any weighted combination of the two rewards. Across all α ∈ (0, 1), we observe consistent performance gains over using either reward alone, demonstrating that the intra- and inter-document rewards serve complementary purposes. While the intra-reward promotes stable and learnable ranking behavior, the inter-reward introduces document-level discrimination that further enhances final ranking performance.", "source": "marker_v2", "marker_block_id": "/page/16/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0092", "section": "F ANALYSIS OF THE HYPERPARAMETER α", "page_start": 17, "page_end": 17, "type": "Text", "text": "These results indicate that effective reward balancing enables the model to simultaneously exploit stable intra-document ranking signals and informative inter-document comparisons. Notably, performance peaks when α is biased toward the intra-reward (e.g., α = 0.75), highlighting that the intra-reward should dominate training dynamics, while the inter-reward acts as an essential complementary signal that enhances ranking performance.", "source": "marker_v2", "marker_block_id": "/page/16/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0093", "section": "G DIFFERENT BACKBONE MODELS", "page_start": 17, "page_end": 17, "type": "Text", "text": "To demonstrate the generalizability and effectiveness of our Retro*, we conducted experiments with several different backbone models. As shown in Table 10, Retro* significantly improves the average nDCG@10 across all backbone models: Qwen2.5-Instruct (7B) from 22.9 to 36.6, Llama2-chat (7B) from 8.2 to 30.9, Mistral-Instruct-v0.1 (7B) from 8.6 to 30.1, Llama3.1-Instruct (8B) from 17.3 to 34.4, and Qwen3 (8B) from 29.4 to 36.1. Furthermore, applying test-time scaling further improves performance consistently for all backbones as shown in Figure 6. These results demonstrate that our approach consistently and substantially enhances ranking performance across diverse backbones, while test-time scaling remains effective with each backbone, further highlighting its robustness and broad applicability as a general retrieval model.", "source": "marker_v2", "marker_block_id": "/page/16/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0094", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 17, "page_end": 17, "type": "Text", "text": "In this section, we analyze the impact of the length control instruction used during the distillation from the teacher model. We augment the prompt template (shown in Figure 8) with an explicit instruction at the beginning of the task description. The modified prompt template is shown below:", "source": "marker_v2", "marker_block_id": "/page/16/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0095", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 17, "page_end": 17, "type": "Code", "text": "Here is the **relevance definition** in a retrieval task: {relevance_definition}", "source": "marker_v2", "marker_block_id": "/page/16/Code/12"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0096", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 18, "page_end": 18, "type": "TableGroup", "text": "Table 10: nDCG@10 results on the BRIGHT benchmark across different backbone models. All backbone models re-rank the top-100 documents retrieved by BGE-Reasoner-Embed. The retrieval stage and the re-ranking stage both utilize the original query. Models Avg. Stack Excha ange Coc ling Tì neorem-ba ased 11104015 12.8 Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Qwen2.5-Instruct (7B) 22.9 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 Retro* (7B) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 Tesi t-Time S caling (Mean- Score@. 16) Retro* (7B) 38.7 58.4 59.2 35.0 49.3 33.9 37.7 41.1 18.8 33.5 10.7 40.2 46.7 Llama2-chat (7B) 8.2 13.4 14.6 8.2 11.2 7.0 7.6 10.6 7.6 4.4 2.4 3.2 8.7 Retro* (7B) 25.4 43.7 40.1 22.0 35.8 20.7 26.8 29.7 18.1 19.4 6.6 22.0 19.5 Tesi -Time S caling (Mean- Score@. 16) Retro* (7B) 30.9 53.3 49.6 28.8 42.8 25.7 29.9 34.3 22.1 25.1 7.5 29.2 23.1 Mistral-Instruct-v0.1 (7B) 8.6 17.2 15.4 6.9 11.6 7.7 8.3 10.6 6.0 7.7 2.5 3.8 5.5 Retro* (7B) 27.8 49.1 42.4 24.4 38.0 23.7 29.7 31.9 15.5 20.7 9.3 24.5 24.5 Tesi -Time S caling (Mean- Score@. 16) Retro* (7B) 30.1 53.9 46.0 27.3 43.0 25.7 30.9 31.6 15.0 24.0 10.1 27.8 26.1 Llama3.1-Instruct (8B) 17.3 35.0 27.8 17.3 30.0 11.8 19.5 21.3 8.8 4.8 4.2 11.4 15.1 Retro* (8B) 34.4 56.7 53.5 31.3 47.3 31.3 32.7 40.2 19.9 21.2 9.4 33.0 36.4 Test -Time S caling (Mean- Score@. 16) Retro* (8B) 36.7 60.2 55.9 33.5 49.7 33.6 36.2 42.0 19.0 24.7 10.3 38.4 36.4 Qwen3 (8B) 29.4 53.5 53.8 28.3 34.1 26.3 29.2 33.1 14.1 8.4 6.7 20.6 44.4 Retro* (8B) 36.1 55.0 56.2 34.9 42.0 35.9 35.6 42.5 16.7 21.9 8.4 35.4 48.7 Test -Time S caling (Mean- Score@. 16) Retro* (8B) 38.8 57.6 58.5 37.1 45.8 38.3 39.3 45.4 17.3 26.6 10.6 40.4 48.8", "source": "marker_v2", "marker_block_id": "/page/17/TableGroup/65"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0097", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 18, "page_end": 18, "type": "FigureGroup", "text": "Figure 6: Effectiveness of Test-Time Scaling for Retro*. ( Left ): Test-time scaling brings significant performance improvements even on the traditional BEIR benchmark. ( Right ): Test-time scaling is consistently effective across different backbone models.", "source": "marker_v2", "marker_block_id": "/page/17/FigureGroup/66"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0098", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 18, "page_end": 18, "type": "Code", "text": "Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps (**Please ensure your entire analysis and annotation across all steps does not exceed 512 tokens**). ... (The rest of the prompt template remains the same)", "source": "marker_v2", "marker_block_id": "/page/17/Code/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0099", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 18, "page_end": 18, "type": "Text", "text": "To evaluate the effect of this instruction on both the reasoning length and the model's performance, we construct two distillation datasets from the teacher model under two conditions: one with the instruction and one without it. We then train student models on these datasets, respectively. The impact on reasoning length is illustrated in Figure 7, while the model performance is reported in Table 11.", "source": "marker_v2", "marker_block_id": "/page/17/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0100", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 18, "page_end": 18, "type": "Text", "text": "As shown in Figure 7, the length control instruction substantially shortens the reasoning trajectories, yielding an average trajectory length comparable to that of the backbone model. Meanwhile, Table 11 shows that the model trained with this instruction achieves an average nDCG@10 of 36.6, essentially matching the 36.4 achieved without it. These results demonstrate that the instruction effectively constrains the reasoning length for efficiency without compromising re-ranking accuracy. Furthermore, although the reasoning length of our trained model is close to that of the backbone,", "source": "marker_v2", "marker_block_id": "/page/17/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0101", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 19, "page_end": 19, "type": "FigureGroup", "text": "Figure 7: Comparison of average completion tokens on BRIGHT benchmark for different models. The model trained with the length control instruction (w/ Length Control) effectively reduces the response length compared to training without it (w/o Length Control).", "source": "marker_v2", "marker_block_id": "/page/18/FigureGroup/195"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0102", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 19, "page_end": 19, "type": "TableGroup", "text": "Table 11: nDCG@10 results on the BRIGHT benchmark for ablation study on the impact of the length control instruction. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Qwen2.5-Instruct (7B) 22.9 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 w/ Length Control + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 35.0 20.6 7.9 27.9 36.6 + SFT + RL (Composite Reward) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 w/o Length Control + only-SFT 30.7 46.8 50.2 30.5 39.4 25.7 30.1 35.8 14.4 18.0 7.6 27.9 41.6 + SFT + RL (Composite Reward) 36.4 53.3 55.6 33.7 48.7 33.3 35.6 39.5 16.5 31.1 8.3 36.4 45.1", "source": "marker_v2", "marker_block_id": "/page/18/TableGroup/196"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0103", "section": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION", "page_start": 19, "page_end": 19, "type": "Text", "text": "it exhibits stronger ranking performance, suggesting that the improvement does not arise from generating longer reasoning trajectories. Instead, it stems from our effective training strategy, which equips the model with powerful reasoning and ranking capabilities.", "source": "marker_v2", "marker_block_id": "/page/18/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0104", "section": "I OUT-OF-DOMAIN GENERALIZATION ON R2MED", "page_start": 19, "page_end": 19, "type": "Text", "text": "To evaluate the out-of-domain generalizability of our rubric, we evaluate Retro* on R2MED (Li et al., 2025) , a biomedical reasoning retrieval benchmark that is outside the scientific, programming, and mathematical domains used during training. By replacing only the task-specific relevance definitions while keeping the task-agnostic scoring criteria, Retro* is able to generalize effectively to this unseen domain. Following the setup of ReasonRank, we use E5-mistral-7b-instruct (Wang et al., 2024) as the first-stage retriever, re-rank the top-100 retrieved candidates, and report nDCG@10. As summarized in Table 12, Retro* outperforms all other re-ranking baselines, demonstrating both the robustness of its rubric-based scoring and its strong cross-domain generalization capability.", "source": "marker_v2", "marker_block_id": "/page/18/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0105", "section": "J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING", "page_start": 19, "page_end": 19, "type": "Text", "text": "We provide the full relevance rubrics for our rubric-based relevance scoring mechanism in Figure 8. The rubrics are designed to guide the LLMs to reason about the relevance between a query and a candidate document through a three-step reasoning process (query analysis, document analysis, and relevance annotation) to produce a fine-grained relevance score.", "source": "marker_v2", "marker_block_id": "/page/18/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0106", "section": "J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING", "page_start": 20, "page_end": 20, "type": "Code", "text": "Here is the **relevance definition** in a retrieval task: {relevance_definition} Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps. 1. Query Analysis: Think to reason and describe what information would be most helpful in answering the query. 2. Document Analysis: Discuss how the information provided by the document fulfills or fails to fulfill the requirements implied by the query. 3. Relevance Annotation: Based on the relevance definition and the insights from the previous two steps, clearly justify your final relevance annotation result and annotate an integer score from a scale of 0 to 100. Please use the following guide: - **80-100 (Highly Relevant):** The document directly and comprehensively addresses the query's intent. It is a core and authoritative answer. - **60-80 (Relevant):** The document substantially addresses the query's intent, providing most of the key information, but might miss some minor details. - **40-60 (Moderately Relevant):** The document is on-topic and addresses a part of the query's intent, but it is not a comprehensive answer. - **20-40 (Slightly Relevant):** The document mentions keywords from the query, but its main topic is different. It offers very limited value. - **0-20 (Irrelevant):** The document does not address the query's intent at all and is off-topic. After providing your detailed analysis and justification for all the steps above, conclude your entire response with the final relevance score. The score must be placed strictly between the <score> tags. There should be no other text or explanation inside the tags: <score> [From a scale of 0 to 100, annotate the degree of relevance between the query and the document .] </score> Query ({query_type}): [Begin of Query] {query} [End of Query] Document ({doc_type}): [Begin of Document] {doc} [End of Document]", "source": "marker_v2", "marker_block_id": "/page/19/Code/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0107", "section": "J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING", "page_start": 20, "page_end": 20, "type": "Caption", "text": "Figure 8: The full relevance rubrics for rubric-based relevance scoring.", "source": "marker_v2", "marker_block_id": "/page/19/Caption/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0108", "section": "J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING", "page_start": 20, "page_end": 20, "type": "TableGroup", "text": "Table 12: nDCG@10 results on the R2MED benchmark, where all methods re-rank the top-100 documents retrieved by E5-mistral-7b-instruct. The retrieval stage and the re-ranking stage both utilize the original query. Results marked with † are reported by ReasonRank. Models Methods Avg. Biolo. Bioin. Med-Sci. Med-Exam. Med-Diag. PMC-Treat. PMC-Cli. IIYi-Cli. E5-mistral-7b-instruct Retriever 24.0 22.9 42.3 41.5 7.4 12.4 18.5 24.9 21.8 Reasoning-Enhanced Re-Ranking Baselines Rank1† (7B) Pointwise 32.3 32.6 55.6 54.7 12.8 20.0 34.4 30.2 18.2 Rank1† (32B) Pointwise 39.1 31.8 61.7 59.7 16.6 26.9 41.3 45.6 29.5 ReasonRank† (7B) Listwise 39.5 46.8 59.7 60.1 16.5 24.9 39.2 39.1 29.9 ReasonRank† (32B) Listwise 42.9 45.6 67.7 63.5 18.9 30.6 41.1 46.1 29.4 Retro* (7B) Pointwise 38.7 47.6 59.7 60.8 12.7 25.2 40.7 39.0 24.2 Retro* (32B) Pointwise 44.5 48.8 68.0 67.3 16.6 34.2 43.3 45.4 32.6 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 42.6 49.9 62.4 62.4 15.7 29.0 41.9 46.2 32.9 Retro* (32B) Pointwise 46.2 51.9 67.8 67.2 19.2 35.7 43.8 48.7 35.6", "source": "marker_v2", "marker_block_id": "/page/19/TableGroup/245"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0109", "section": "K ANALYSIS OF THE NECESSITY OF REASONING", "page_start": 20, "page_end": 20, "type": "Text", "text": "To investigate the necessity of reasoning for re-ranking performance, we conduct an ablation study by removing the structured reasoning steps from our relevance rubrics. In the original rubrics, the model is prompted to analyze both the query and the candidate document before producing a detailed relevance score. In the ablated variant, the model instead outputs a single score directly, without any reasoning trajectory or rubric-guided analysis, as illustrated in Figure 9.", "source": "marker_v2", "marker_block_id": "/page/19/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0110", "section": "K ANALYSIS OF THE NECESSITY OF REASONING", "page_start": 21, "page_end": 21, "type": "TableGroup", "text": "Table 13: Relevance definitions for each dataset in the BRIGHT benchmark. Dataset Relevance Definition biology Given a query (biology post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. earth_science Given a query (earth science post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. economics Given a query (economics post) and a document (passage), the document is rele vant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. psychology Given a query (psychology post) and a document (passage), the document is rele vant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. robotics Given a query (robotics post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. stackoverflow Given a query (Stack Overflow post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. sustainable_living Given a query (sustainable living post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. leetcode Given a query (LeetCode problem) and a document (coding problem solution), the document is relevant to the query if the underlying algorithms or data struc tures used in the document can provide helpful insights for solving the problem in the query. pony Given a query (Pony coding instruction) and a document (Pony documentation passage), the document is relevant to the query if the Pony syntax described in the document is necessary for beginners with no prior knowledge of Pony to complete the coding instruction in the query. aops Given a query (math problem) and a document (math problem solution), the doc ument is relevant to the query if the theorems used in the document can provide helpful insights for solving the problem in the query. theoremqa_questions Given a query (math problem) and a document (math problem solution), the doc ument is relevant to the query if the theorems used in the document can provide helpful insights for solving the problem in the query. theoremqa_theorems Given a query (math problem) and a document (math-related passage), the doc ument is relevant to the query if the theorem described in the document can help solve the problem in the query.", "source": "marker_v2", "marker_block_id": "/page/20/TableGroup/180"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0111", "section": "K ANALYSIS OF THE NECESSITY OF REASONING", "page_start": 21, "page_end": 21, "type": "Text", "text": "This variant of Retro* is trained on the same dataset and with the same RL algorithm as the original model. We focus the comparison specifically on the RL stage to avoid introducing confounding factors, such as potential biases originating from the SFT teacher model. By keeping the learning signal consistent, this setup effectively isolates the impact of reasoning on re-ranking performance. As shown in Table 16, removing the reasoning trajectory results in a substantial performance drop across all datasets. These results confirm that rubric-guided reasoning enhances the fidelity of relevance estimation under RL training. By structuring the task into intermediate steps, the model can better capture how different aspects of relevance contribute to the final judgment. Without this reasoning guidance, the model struggles to learn the underlying compositional logic of the relevance rubric, leading to the observed performance drop.", "source": "marker_v2", "marker_block_id": "/page/20/Text/3"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0112", "section": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS", "page_start": 21, "page_end": 21, "type": "Text", "text": "In this section, we provide the detailed relevance definitions used in our evaluations on the BRIGHT, BEIR and R2MED benchmarks. In reasoning-intensive retrieval scenarios, the relevance definitions are more complex, while in traditional scenarios, they are more straightforward. The specific defi-", "source": "marker_v2", "marker_block_id": "/page/20/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0113", "section": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS", "page_start": 22, "page_end": 22, "type": "TableGroup", "text": "Table 14: Relevance definitions for each dataset in the BEIR benchmark. Dataset Relevance Definition TREC-COVID Given a query (COVID-19 related query) and a document (document), the document is relevant to the query if the document answers the query. DBPedia Given a query (query) and a document (entity description from DBpedia), the document is relevant to the query if the entity described in the document matches the query. SciFact Given a query (scientific claim) and a document (document), the document is relevant to the query if the document provides evidence supporting or refuting the scientific claim. NFCorpus Given a query (question) and a document (document), the document is relevant to the query if the document can best answer the question. Signal-1M Given a query (news event or topic) and a document (news headline or summary), the document is relevant to the query if it reports on, summarizes, or directly relates to the same news event or topic described in the query. Robust04 Given a query (information need) and a document (news or government document), the document is relevant to the query if it contains information that satisfies the intent or topic described in the query, even if phrased differently. TREC-NEWS Given a query (contemporary news topic or event) and a document (news article from The Washington Post), the document is relevant to the query if it discusses, explains, or provides factual coverage of the specific event or topic mentioned in the query. Table 15: Relevance definitions for each dataset in the R2MED benchmark.", "source": "marker_v2", "marker_block_id": "/page/21/TableGroup/181"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0114", "section": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS", "page_start": 22, "page_end": 22, "type": "TableGroup", "text": "Dataset Relevance Definition Biology Given a query (biology post) and a document (passage), the document is relevant to the query if the document helps answer the query. Medical-Sciences Given a query (medical science post) and a document (passage), the document is relevant to the query if the document helps answer the query. Bioinformatics Given a query (bioinformatics post) and a document (passage), the document is relevant to the query if the document helps answer the query. MedXpertQA-Exam Given a query (medical exam) and a document (passage), the document is relevant to the query if the document helps answer the query. MedQA-Diag Given a query (medical exam) and a document (passage), the document is relevant to the query if the document helps answer the query. PMC-Treatment Given a query (clinical case) and a document (passage), the document is relevant to the query if the document helps answer the query. PMC-Clinical Given a query (clinical case) and a document (case), the document is relevant to the query if it helps diagnose the query case. IIYi-Clinical Given a query (clinical case) and a document (case), the document is relevant to the query if it helps diagnose the query case. Table 16: Performance comparison on the BRIGHT benchmark, showing that reasoning-enhanced re-ranking significantly outperforms models trained without reasoning.", "source": "marker_v2", "marker_block_id": "/page/21/TableGroup/182"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0115", "section": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS", "page_start": 22, "page_end": 22, "type": "Table", "text": "Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 No Reason (only-RL) Reason (only-RL) 24.8 35.1 38.4 56.7 40.2 52.9 22.3 33.2 32.4 45.1 20.5 28.1 25.6 32.5 26.0 35.8 19.6 21.2 16.9 36.3 4.7 8.6 17.7 29.8 33.8 41.0", "source": "marker_v2", "marker_block_id": "/page/21/Table/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0116", "section": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS", "page_start": 22, "page_end": 22, "type": "Text", "text": "nitions for the BRIGHT benchmark are listed in Table 13, BEIR are listed in Table 14, and those for R2MED are listed in Table 15. We use these relevance definitions for both training and evaluation.", "source": "marker_v2", "marker_block_id": "/page/21/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0117", "section": "M REASONING EXAMPLES", "page_start": 22, "page_end": 22, "type": "Text", "text": "We provide some examples to present the reasoning process of Retro* in Table 17 (Suatainable Living), Table 18 (Pony), and Table 19 (TheoremQA Theorems).", "source": "marker_v2", "marker_block_id": "/page/21/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0118", "section": "M REASONING EXAMPLES", "page_start": 23, "page_end": 23, "type": "Code", "text": "Here is the **relevance definition** in a retrieval task: {relevance_definition} Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps. Based on the relevance definition, annotate an integer score from a scale of 0 to 100. Please use the following guide: 80-100 (Highly Relevant), 60-80 (Relevant), 40-60 (Moderately Relevant), 20-40 (Slightly Relevant), 0-20 (Irrelevant). Without any explanation, directly providing your final relevance score. The score must be placed strictly between the <score> tags. There should be no other text or explanation inside the tags: <score> [From a scale of 0 to 100, annotate the degree of relevance between the query and the document .] </score> Query ({query_type}): [Begin of Query] {query} [End of Query] Document ({doc_type}): [Begin of Document] {doc} [End of Document]", "source": "marker_v2", "marker_block_id": "/page/22/Code/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0119", "section": "M REASONING EXAMPLES", "page_start": 23, "page_end": 23, "type": "Caption", "text": "Figure 9: The modified relevance rubrics for reasoning-free relevance scoring.", "source": "marker_v2", "marker_block_id": "/page/22/Caption/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0120", "section": "Table 17: Reasoning examples of Retro* (7B) on the Sustainable Living dataset of BRIGHT.", "page_start": 24, "page_end": 24, "type": "Text", "text": "Relevance Definition: Given a query (sustainable living post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query.", "source": "marker_v2", "marker_block_id": "/page/23/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0121", "section": "Query", "page_start": 24, "page_end": 24, "type": "Text", "text": "Are solar powered cars sustainable and are they a good idea for future transportation?\\n \\nAs population rises, fossil fuels will start depleting so are solar powered cars a good idea? How much power can they produce when it is cloudy?", "source": "marker_v2", "marker_block_id": "/page/23/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0122", "section": "Positive Document", "page_start": 24, "page_end": 24, "type": "Text", "text": "The efficiency of the solar cells used in a [ photovoltaic system\\n ](/wiki/Photovoltaic_system \"Photovoltaic system\") , in combination with\\nlatitude and climate, determines the annual energy output of the system. For\\nexample , a solar panel with 20% efficiency and an area of 1 m 2 will produce\\n 200 kWh/yr at Standard Test Conditions if exposed to the Standard Test\\nCondition solar irradiance value of 1000 W/m 2 for 2.74 hours a day. Usually\\nsolar panels are exposed to sunlight for longer than this in a given day, but\\nthe solar irradiance is less than 1000 W/m 2 for most of the day. A solar\\npanel can produce more when the Sun is high in Earth's sky and will produce\\nless in cloudy conditions or when the Sun is low in the sky, usually the Sun\\nis lower in the sky in the winter.", "source": "marker_v2", "marker_block_id": "/page/23/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0123", "section": "Reasoning Process", "page_start": 24, "page_end": 24, "type": "ListGroup", "text": "1. Query Analysis: The query seeks an evaluation of solar-powered cars in terms of sustainability and their viability as future transportation. It specifically asks whether solar cars are sustainable and produce usable power under cloudy conditions. A helpful response would discuss solar car efficiency, energy capture, potential as a sustainable transport solution, and the impact of weather conditions on system output. 2. Document Analysis: The passage explains how solar panel efficiency, climate, and solar patterns affect energy output, particularly noting reduced power under cloudy skies and low-sunlight conditions. While it validates solar panel performance under varying light conditions—directly relevant to solar car feasibility—it does not mention solar-powered cars, automotive application, transportation systems, or sustainability over time. However, it provides foundational data on power generation under cloudiness, addressing part of the query. 3. Relevance Annotation: The document supplies critical information about solar panel energy output affected by cloudiness, which is pertinent to evaluating solar-powered cars. However, it does not link this to transportation solutions, sustainability assessment of solar cars, or holistic future outlook. It offers technical underpinnings but lacks domain-specific context regarding vehicles or long-term strategies. Thus, while informative for part of the query (especially on power availability in cloudy conditions), it omits major integrative insights needed for a comprehensive answer.", "source": "marker_v2", "marker_block_id": "/page/23/ListGroup/194"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0124", "section": "Reasoning Process", "page_start": 24, "page_end": 24, "type": "Text", "text": "<score> 65 </score>", "source": "marker_v2", "marker_block_id": "/page/23/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0125", "section": "Negative Document", "page_start": 24, "page_end": 24, "type": "Text", "text": "The first solar family car was built in 2013. [16] Researchers at [ Case\\nWestern Reserve University ](/wiki/Case_Western_Reserve_University \"Case\\nWestern Reserve University\") , have also developed a solar car which can\\nrecharge more quickly, due to materials used in the solar panels. [17]", "source": "marker_v2", "marker_block_id": "/page/23/Text/13"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0126", "section": "Reasoning Process", "page_start": 24, "page_end": 24, "type": "ListGroup", "text": "1. Query Analysis: The query seeks to evaluate the sustainability and practicality of solar-powered cars, particularly in the context of future transportation. It emphasizes two key aspects: (1) whether they are sustainable (e.g., environmental impact, energy efficiency), and (2) whether they are a good idea for addressing fossil fuel depletion and scalability, especially when sunlight availability fluctuates under clouds. Domain experts would need information on energy output, charging capacity, environmental benefits, and real-world feasibility. 2. Document Analysis: The document mentions a solar car from 2013 and references research improving charging speed with advanced materials. However, it lacks any discussion of sustainability, energy production, energy cloud dependency, or broader transportation implications. It provides only a limited technical note on material advancements without addressing the core sustainability or societal questions raised. 3. Relevance Annotation: While the document is tangentially related—mentioning solar-powered cars—it fails to address the critical concepts in the query, such as sustainability metrics, energy output under cloudy conditions, or long-term viability. It does not offer references that would help draft a comprehensive answer. The information is too minimal and outdated to support expert judgment on the broader query.", "source": "marker_v2", "marker_block_id": "/page/23/ListGroup/195"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0127", "section": "Reasoning Process", "page_start": 24, "page_end": 24, "type": "Text", "text": "<score> 35 </score>", "source": "marker_v2", "marker_block_id": "/page/23/Text/18"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0128", "section": "Table 18: Reasoning examples of Retro* (7B) on the Pony dataset of BRIGHT.", "page_start": 25, "page_end": 25, "type": "Text", "text": "Relevance Definition: Given a query (Pony coding instruction) and a document (Pony documentation passage), the document is relevant to the query if the Pony syntax described in the document is necessary for beginners with no prior knowledge of Pony to complete the coding instruction in the query.", "source": "marker_v2", "marker_block_id": "/page/24/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0129", "section": "Query", "page_start": 25, "page_end": 25, "type": "Text", "text": "I will use the programming language pony.\\nProblem :\\nWrite a function to determine if a string consisting of alphabets is a palindrome.\\n \\nHere is the code template:\\nfun is_palindrome(str: String): Bool ? =>\\n ...", "source": "marker_v2", "marker_block_id": "/page/24/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0130", "section": "Positive Document", "page_start": 25, "page_end": 25, "type": "Text", "text": "## Functions\\n \\nPony functions are quite like functions (or methods) in other languages. They can have 0 or more parameters and 0 or 1 return values. If the return type is omitted then the function will have a return value of 'None'.\\n \\n \"'pony\\nclass C\\nfun add(x: U32, y: U32): U32 =>\\nx + y\\n \\nfun nop() =>\\nadd (1, 2) // Pointless, we ignore the result\\n \"'\\n \\nThe function parameters (if any) are specified in parentheses after the function name. Functions that don't take any parameters still need to have the parentheses.\\n \\nEach parameter is given a name and a type. In our example function 'add' has 2 parameters, 'x' and 'y', both of which are type 'U32'. The values passed to a function call (the '1' and '2' in our example) are called arguments and when the call is made they are evaluated and assigned to the parameters. Parameters may not be assigned to within the function - they are effectively declared 'let'.\\n \\nAfter the parameters comes the return type. If nothing will be returned this is simply omitted.\\n \\nAfter the return value, there's a '=>' and then finally the function body. The value returned is simply the value of the function body (remember that everything is an expression), which is simply the value of the last command in the function. Reasoning Process:", "source": "marker_v2", "marker_block_id": "/page/24/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0131", "section": "1. Query Analysis", "page_start": 25, "page_end": 25, "type": "Text", "text": "The query asks to write a function in Pony that determines whether a string is a palindrome. The key elements needed are: (1) a function taking a parameter of type 'String' and returning a 'Bool', (2) string handling in Pony, (3) string reversal/iteration, and (4) comparison logic. However, for a beginner with no prior knowledge, the most critical information is understanding how to define a function in Pony-especially the syntax for defining a function with a parameter, return type, and body. This is foundational for structuring any function, including one for palindrome detection.", "source": "marker_v2", "marker_block_id": "/page/24/Text/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0132", "section": "2. Document Analysis", "page_start": 25, "page_end": 25, "type": "Text", "text": "The document explains Pony function syntax in depth, covering parameter specification, return types (including optional ones), function bodies, and return values using a basic example ('add'). It clarifies that functions use 'fun', can have parameter lists with types, return statements via evaluation of the final expression, and can omit return types for 'None'. While it does not mention string operations, it provides essential syntax needed to write any function, including 'is_palindrome'.", "source": "marker_v2", "marker_block_id": "/page/24/Text/10"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0133", "section": "3. Relevance Annotation", "page_start": 25, "page_end": 25, "type": "Text", "text": "The document does not address handling strings or palindrome logic directly, but it fully covers the necessary syntactic structure for defining the function in the query-parameterized functions with return types, the 'fun' statement, and function bodies. This is foundational knowledge a beginner must have to implement the requested function. While not comprehensive for the full task, it supplies the core syntactic framework. Thus, it is highly relevant to the coding instruction in terms of necessary beginner syntax.", "source": "marker_v2", "marker_block_id": "/page/24/Text/12"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0134", "section": "3. Relevance Annotation", "page_start": 25, "page_end": 25, "type": "Text", "text": "<score> 75 </score>", "source": "marker_v2", "marker_block_id": "/page/24/Text/13"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0135", "section": "Negative Document", "page_start": 25, "page_end": 25, "type": "Text", "text": "## Control Structures\\n \\nTo do real work in a program you have to be able to make decisions, iterate through collections of items and perform actions repeatedly. For this, you need control structures. Pony has control structures that will be familiar to programmers who have used most languages, such as 'if', 'while' and 'for', but in Pony, they work slightly differently.\\n Reasoning Process:", "source": "marker_v2", "marker_block_id": "/page/24/Text/15"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0136", "section": "Negative Document", "page_start": 25, "page_end": 25, "type": "ListGroup", "text": "1. Query Analysis: The query asks for a function in Pony to check if a string is a palindrome. This requires understanding of string manipulation, comparison, and possibly loops or recursion. Key concepts for beginners include: defining a function with the correct signature (e.g., 'String → Bool'), accessing characters in a string, reverse comparison, and possibly handling case sensitivity or ignoring non-alphabetic characters. The critical syntax needed includes function definition, type parameters, string indexing, and comparison logic. 2. Document Analysis: The document discusses general programming control structures ('if', 'while', 'for') and notes that these work similarly in Pony. However, it provides no specific examples, syntax, or details on string handling, function syntax, or palindrome logic. It fails to mention how to manipulate strings, access characters, or implement palindrome detection-core needs for the query. The content is introductory and abstract, focusing on high-level structure rather than concrete, applicable code. 3. Relevance Annotation: The document touches on conditional and iterative constructs, which are tangential to palindrome logic, but it does not provide the necessary syntax or examples for completing the task. It lacks any mention of string properties, indexing, or function definition relevant to the query. For a beginner, this passage would offer minimal direct assistance. Therefore, it only shares conceptual keywords (e.g., \"if\", \"while\") but misses all domain-specific syntax.", "source": "marker_v2", "marker_block_id": "/page/24/ListGroup/219"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0137", "section": "Negative Document", "page_start": 25, "page_end": 25, "type": "Text", "text": "<score> 5 </score>", "source": "marker_v2", "marker_block_id": "/page/24/Text/19"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0138", "section": "Table 19: Reasoning examples of Retro* (7B) on the TheoremQA Theorems dataset of BRIGHT.", "page_start": 26, "page_end": 26, "type": "Text", "text": "Relevance Definition: Given a query (math problem) and a document (math-related passage), the document is relevant to the query if the theorem described in the document can help solve the problem in the query.", "source": "marker_v2", "marker_block_id": "/page/25/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0139", "section": "Query", "page_start": 26, "page_end": 26, "type": "Text", "text": "In a party, how many guests do you need to have to ensure that either four people all know each other or four people are all complete strangers to one another?", "source": "marker_v2", "marker_block_id": "/page/25/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0140", "section": "Positive Document", "page_start": 26, "page_end": 26, "type": "Text", "text": "\\\\section{Ramsey's Theorem}\\nTags : Ramsey Theory, Named Theorems, Combinatorics\\n \\n \\\\begin{theorem}\\nIn any coloring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs.\\nFor 2 colors, Ramsey's theorem states that for any pair of positive integers $\\\\tuple {r, s}$, there exists a least positive integer $\\\\map R {r, s}$ such that for any complete graph on $\\\\map R {r, s}$ vertices, whose edges are colored red or blue, there exists either a complete subgraph on $r$ vertices which is entirely red, or a complete subgraph on $s$ vertices which is entirely blue.\\nMore generally, for any given number of colors $c$, and any given integers $n_1, \\\\ldots, n_c$, there is a number $\\\\map R {n_1, \\\\ldots, n_c}$ such that:\\n :if the edges of a complete graph of order $\\\\map R {n_1, \\\\ldots, n_c}$ are colored with $c$ different colours, then for some $i$ between $1$ and $c$, it must contain a complete subgraph of order $n_i$ whose edges are all color $i$.\\nThis number $\\\\map R {n_1, \\\\ldots, n_c}$ is called the Ramsey number for $n_1, \\\\ldots, n_c$.\\nThe special case above has $c = 2$ (and $n_1 = r$ and $n_2 = s$).\\nHere $\\\\map R {r, s}$ signifies an integer that depends on both $r$ and $s$. It is understood to represent the smallest integer for which the theorem holds.\\n \\\\end{theorem}\\n \\n \\\\begin{proof}\\nFirst we prove the theorem for the 2-color case, by induction on $r + s$.\\nIt is clear from the definition that\\n :$\\\\forall n \\\\in \\\\N: \\\\map R {n, 1} = \\\\map R {1, n} = 1$\\nbecause the complete graph on one node has no edges.\\nThis is the base case.\\nWe prove that $R \\\\left({r, s}\\\\right)$ exists by finding an explicit bound for it.\\nBy the inductive hypothesis, $\\\\map R {r - 1, s}$ and $\\\\map R {r, s - 1}$ exist.\\n \\\\end{proof}\\n \\n", "source": "marker_v2", "marker_block_id": "/page/25/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0141", "section": "Reasoning Process", "page_start": 26, "page_end": 26, "type": "ListGroup", "text": "1. Query Analysis: The query asks for the minimum number of guests (people) in a party such that either 4 people all know each other (a complete subgraph $K_4$ in a \"knows\"-graph) or 4 people are all strangers to each other (a complete subgraph $K_4'$ in a \"strangers\"-graph). This is a classic Ramsey number problem, specifically asking for $R(4,4)$, the smallest number of guests such that in any 2-coloring of the edges (representing know-or-stranger), there must be a monochromatic $K_4$. The key concept needed is Ramsey theory, particularly the Ramsey number $R(4,4)$. 2. Document Analysis: The document presents Ramsey's Theorem, defining the Ramsey number $\\map R {r,s}$ as the smallest number such that any 2-coloring of the edges of a complete graph on $\\map R {r,s}$ vertices guarantees either an all-red $K_r$ or all-blue $K_s$. It confirms the theorem for $c=2$, which directly applies to the query's 2-coloring framework. While it does not explicitly state $R(4,4)$ or compute its value (which is 18), the theorem provides the theoretical foundation to solve the query. From this, one could deduce that any graph on 18 or more vertices necessarily contains either a $K_4$ or $\\overline {K}_4$, depending on the coloring. 3. Relevance Annotation: The document is highly relevant because it introduces and explains Ramsey's Theorem, the core mathematical principle required to solve the query. Although it does not provide the specific value of $R(4,4)$, it enables one to derive it via the theorem. It directly supports solving the problem by offering the theoretical framework.", "source": "marker_v2", "marker_block_id": "/page/25/ListGroup/232"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0142", "section": "Reasoning Process", "page_start": 26, "page_end": 26, "type": "Text", "text": "<score> 95 </score>", "source": "marker_v2", "marker_block_id": "/page/25/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0143", "section": "Negative Document", "page_start": 26, "page_end": 26, "type": "Text", "text": "\\\\section{Infinite Ramsey's Theorem}\\nTags : Ramsey Theory, Named Theorems\\n \\n \\\\begin{theorem}\\nLet $k, n \\\\in \\\\N$.\\nFor any set $S$, let $S^{\\\\paren n}$ denote the set $\\\\set {\\\\set {s_1, \\\\ldots, s_n}: \\\\text{each } s_i \\\\in S}$ of cardinality $n$ subsets of $S$.\\nLet $X$ be an infinite set.\\nThen :\\n :for every partition $P$ of $X^{\\\\paren n}$ into $k$ many components\\n :there is an infinite subset $Y \\\\subseteq X$\\nsuch that:\\n :each member of $Y^{\\\\paren n}$ is in the same component of $P$.\\n \\\\end{theorem}\\n \\n \\\\begin{proof}\\nWe will prove the theorem for fixed $k$ by induction on $n$.\\n \\\\end{proof}\\n \\n", "source": "marker_v2", "marker_block_id": "/page/25/Text/13"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0144", "section": "Reasoning Process", "page_start": 26, "page_end": 26, "type": "ListGroup", "text": "1. Query Analysis: The query asks for the minimum number of guests (n) at a party such that either four people all know each other (a clique of size 4 in a social graph) or four mutually unknown people exist (an independent set of size 4). This is a Ramsey theory problem specifically involving the Ramsey number R(4,4), which is the smallest number n such that any 2-coloring of the edges of a complete graph on n vertices guarantees a monochromatic clique of size 4 or an independent set of size 4. The key information needed is a known result about R(4,4), preferably its value or a discussion of its combinatorial implications. 2. Document Analysis: The document presents the Infinite Ramsey Theorem, which states that for any partition of the n-element subsets of an infinite set into finitely many components, there exists an infinite subset that monochromatic. This is a much more general and abstract result. While it is situated in Ramsey theory, it deals with infinite sets and n-element subsets, and does not address the finite Ramsey number R(4,4) or any finite Ramsey-type problem. It does not mention graph theory, social networks, cliques, or independent sets in the context of a finite party problem. Thus, it fails to provide any specific insight into the numerical or combinatorial condition required to solve the query. 3. Relevance Annotation: The document is thematically related (Ramsey Theory) but addresses a fundamentally different domain (infinite sets, infinite Ramsey Theorem) and offers no useful method or result for determining R(4,4) or solving the finite problem. It cannot help directly in solving the given social puzzle. While both involve Ramsey theory, the connection is too abstract and generic without addressing the specific problem or its mathematical tools.", "source": "marker_v2", "marker_block_id": "/page/25/ListGroup/233"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0145", "section": "Reasoning Process", "page_start": 26, "page_end": 26, "type": "Text", "text": "<score> 10 </score>", "source": "marker_v2", "marker_block_id": "/page/25/Text/18"}

iclr26/0WGl8PNMSA/appendix_text_v3.txt

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+[p. 14 | section: OVERVIEW OF APPENDIX | type: ListGroup]
+Appendix A: The Use of LLMs Appendix B: Baselines Appendix C: Training Details Appendix D: Detailed BM25 and ReasonIR Results on BRIGHT Appendix E: Evaluation on BEIR Appendix F: Analysis of the Hyperparameter \alpha Appendix G: Different Backbone Models Appendix H: Analysis of the Length Control Instruction for Distillation Appendix I: Out-of-Domain Generalization on R2MED Appendix J: Rubrics of Rubric-based Relevance Scoring Appendix K: Analysis of the Necessity of Reasoning Appendix L: Task Relevance Definitions for Different Benchmarks Appendix M: Reasoning Examples
+
+[p. 14 | section: A THE USE OF LLMS | type: Text]
+We used the LLMs to assist with writing. Specifically, their use included grammar checking, rephrasing for clarity, and textual polishing. Additionally, we utilized the LLMs to help draft Python codes for plotting figures. The LLMs used for these purposes include Gemini 2.5 Pro<sup>2</sup>, ChatGPT<sup>3</sup>, DeepSeek-V3.1<sup>4</sup>.
+
+[p. 14 | section: B BASELINES | type: Text]
+This section provides additional details for each of the baseline models used in our comparative analysis. As outlined in the experimental setup 4.1, we categorize these models into two groups: non-reasoning and reasoning-enhanced approaches. For each baseline listed below, we describe its core methodology and implementation details:
+
+[p. 14 | section: B BASELINES | type: ListGroup]
+RankLLaMA: A pointwise re-ranking model that jointly encodes the query and document, generating a scalar relevance score by projecting the representation of the end-of-sequence token through a linear layer. The model is trained with a contrastive loss. RankZephyr: A listwise re-ranking model that takes a query and a set of candidate documents as input and outputs their relative ranking order. It employs a sliding window strategy to to handle large lists of candidates. The model is trained on MS MARCO (Bajaj et al., 2016) dataset via knowledge distillation from GPT-3.5 (Ouyang et al., 2022) and GPT-4 (Achiam et al., 2023). JudgeRank : A zero-shot, reasoning-enhanced pointwise re-ranking method. It utilizes carefully designed prompts to guide LLMs through explicit reasoning steps before producing the final relevance judgment ("yes" or "no"). Rank1: A reasoning-enhanced pointwise re-ranking model. For each query-document pair, the model generates a reasoning process and outputs a binary relevance judgment ("yes" or "no"). Rank1 is trained on reasoning trajectories generated by DeepSeek-R1 (Guo et al., 2025) on the MS MARCO dataset. Rank-R1: A reasoning-enhanced setwise (Zhuang et al., 2024) re-ranking model. Given a query and a candidate set, the model selects the most relevant document and applies a heap-sort procedure to obtain top-k results. The model is trained on the MS MARCO dataset with the GRPO algorithm.
+
+[p. 14 | section: B BASELINES | type: Footnote]
+2
+
+[p. 14 | section: B BASELINES | type: Footnote]
+3
+
+[p. 14 | section: B BASELINES | type: Footnote]
+4
+
+[p. 15 | section: B BASELINES | type: TableGroup]
+Table 4: Hyperparameters for the SFT stage. Learning Epochs WarmUp LR Batch Size Gradient Rate Ratio Scheduler Per-Device Accumulation 10^{-5} 1 0.1 cosine 1 8 Table 5: Hyperparameters for the RL stage with GRPO.
+
+[p. 15 | section: B BASELINES | type: TableGroup]
+\alpha \mid \tau \mid N Learning Rate Epochs Batch Size Mini Batch Size Micro Batch Size Per-Device KL Coefficient Temperature 0.75 20 8 10^{-6} 1 256 256 8 0.005 1.0 Table 6: Detailed nDCG@10 results for Retro* on the BRIGHT benchmark. Retro* re-ranks the top-100 documents retrieved by either BM25 or ReasonIR. The retrieval stage utilized a GPT-4 reasoning query, while the re-ranking stage utilized the original query.
+
+[p. 15 | section: B BASELINES | type: Table]
+Models Avg. Stack Exch ange Coc ling Th ieorem-ba ased Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BM25 27.0 53.6 54.1 24.3 38.7 18.9 27.7 26.3 19.3 17.6 3.9 19.2 20.8 Retro* (7B) 35.3 56.4 56.1 30.8 46.4 31.6 36.7 39.8 22.7 28.2 7.3 27.6 40.4 Retro* (32B) 36.6 61.6 59.4 35.9 47.8 33.6 35.6 43.2 18.8 29.2 6.6 28.1 39.3 , , Test- Time S caling ( Mean-So ore@ 16) Retro* (7B) 37.0 60.7 59.0 31.9 48.2 32.1 34.9 40.8 25.2 33.2 8.5 29.8 40.1 Retro* (32B) 38.5 64.0 61.6 36.9 50.1 33.9 37.7 45.2 19.9 32.3 8.5 30.6 41.5 ReasonIR 30.6 43.4 43.0 33.1 39.6 20.9 31.0 27.0 31.6 19.5 7.4 33.9 36.9 Retro* (7B) 36.8 54.7 54.5 33.5 47.7 32.5 40.1 41.2 22.7 28.9 8.3 34.1 43.7 Retro* (32B) 37.4 60.7 56.1 37.6 47.7 31.3 38.6 45.7 19.0 27.3 9.0 33.0 43.2 Test- Time S caling ( Mean-So ore@ 16) Retro* (7B) 38.4 60.4 57.4 34.8 48.2 31.6 37.9 41.9 24.9 32.1 9.0 38.1 44.0 Retro* (32B) 39.5 64.7 57.5 38.5 49.7 31.7 42.6 47.3 19.4 30.2 10.0 37.8 44.8
+
+[p. 15 | section: B BASELINES | type: Text]
+• ReasonRank : A reasoning-enhanced listwise re-ranking model. It introduces an automated data synthesis framework to generate high-quality reasoning-intensive training data. The model is trained on this synthesized dataset in two stages: SFT with reasoning trajectories distilled from DeepSeek-R1, followed by GRPO with a multi-view re-ranking reward.
+
+[p. 15 | section: C Training Detials | type: Text]
+For the SFT stage, we use the LLaMA-Factory framework (Zheng et al., 2024b), fine-tuning both the 7B and 32B models on a single node equipped with 8 NVIDIA H100 GPUs. For the RL stage, we employ the GRPO algorithm through the VeRL framework (Sheng et al., 2025). In our main experiments, we set the hyperparameter \alpha to 0.75 and \tau to 20, as 20 represents a meaningful interval between relevance levels in our rubrics 3.1.1. An ablation study on the impact of different \alpha values is presented in Appendix F. The 7B model is trained on a single node, while the 32B model is trained across two nodes. Detailed hyperparameters for the SFT and RL stages are provided in Table 4 and Table 5, respectively.
+
+[p. 15 | section: D Detailed BM25 and ReasonIR Results on BRIGHT | type: Text]
+This section provides the complete, per-dataset results on the BRIGHT benchmark, corresponding to the summarized analysis in the main body. Table 6 details the nDCG@10 scores of Retro* when re-ranking the top-100 documents retrieved by two different first-stage retrievers: BM25 and ReasonIR. The results highlight the model's robust and consistent performance across various domains, regardless of the initial retrieval method.
+
+[p. 15 | section: D Detailed BM25 and ReasonIR Results on BRIGHT | type: Text]
+ReasonIR further introduces a zero-shot re-ranking method (QwenRerank) based on Qwen2.5-Instruct-32B, and we conduct a detailed comparison between this method and Retro*. However, QwenRerank computes its final ranking scores by fusing normalized retriever and re-ranker outputs with 0.5 \times s_{\rm reranker} + 0.5 \times s_{\rm retriever} , meaning that its reported performance reflects the joint effect of
+
+[p. 16 | section: D Detailed BM25 and ReasonIR Results on BRIGHT | type: TableGroup]
+Table 7: Comparison of Retro* with QwenRerank from ReasonIR under two evaluation settings, where all methods re-rank the top-100 documents retrieved by ReasonIR. Retro* consistently achieves higher performance in both settings. Results marked with † are reported by ReasonIR. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. ReasonIR 30.6 43.4 43.0 33.1 39.6 20.9 31.0 27.0 31.6 19.5 7.4 33.9 36.9 Re-ranking w/o Score Fusion QwenRerank† (32B) 30.3 50.2 47.5 23.6 35.8 24.7 28.1 29.9 30.3 26.5 5.5 20.7 40.8 Retro* (7B) 36.8 54.7 54.5 33.5 47.7 32.5 40.1 41.2 22.7 28.9 8.3 34.1 43.7 Retro* (32B) 37.4 60.7 56.1 37.6 47.7 31.3 38.6 45.7 19.0 27.3 9.0 33.0 43.2 Retro* (7B, Mean-Score@16) 38.4 60.4 57.4 34.8 48.2 31.6 37.9 41.9 24.9 32.1 9.0 38.1 44.0 Retro* (32B, Mean-Score@16) 39.5 64.7 57.5 38.5 49.7 31.7 42.6 47.3 19.4 30.2 10.0 37.8 44.8 Re-ranking w/ Score Fusion QwenRerank† (32B) 36.9 58.2 53.2 32.0 43.6 28.8 37.6 36.0 33.2 34.8 7.9 32.6 45.0 Retro* (7B) 38.4 54.2 55.9 35.0 49.7 32.4 40.2 41.7 26.1 32.7 10.9 36.9 45.0 Retro* (32B) 39.6 60.0 58.2 38.4 51.1 31.4 39.2 45.3 25.0 33.4 10.5 37.0 45.4 Retro* (7B, Mean-Score@16) 39.0 56.8 57.1 36.0 49.8 31.7 38.2 42.3 27.1 34.1 10.4 39.2 44.9 Retro* (32B, Mean-Score@16) 40.2 60.1 58.4 38.5 51.4 32.1 41.5 46.3 25.2 33.3 11.1 38.4 46.2 Table 8: nDCG@10 results on the BEIR benchmark, where all methods re-rank the top-100 documents retrieved by BM25 provided by Lin et al. (2021) . The retrieval stage and the re-ranking stage both utilize the original query. Results marked with † are reported by ReasonRank.
+
+[p. 16 | section: D Detailed BM25 and ReasonIR Results on BRIGHT | type: Table]
+Models Methods Avg. TREC-COVID DBPedia SciFact NFCorpus Signal-1M Robust04 TREC-NEWS BM25 Retriever 43.7 59.5 31.8 67.9 33.8 33.0 40.7 39.5 Non-Reasoning Re-Ranking Baselines RankZephyr† (7B) Listwise 54.1 82.9 44.4 75.4 38.3 31.4 53.7 52.8 Reasoning-Enhanced Re-Ranking Baselines Rank1† (7B) Pointwise 50.7 79.0 35.8 73.3 37.5 25.4 57.1 47.7 Rank1† (32B) Pointwise 51.0 80.6 34.8 74.8 37.3 25.6 58.3 45.6 Rank-R1† (7B) Setwise 53.6 83.7 42.3 72.2 38.9 33.1 54.5 50.6 Rank-R1† (14B) Setwise 54.6 84.6 44.1 76.0 38.6 33.0 56.9 49.2 ReasonRank† (7B) Listwise 54.4 82.0 46.0 75.6 39.6 31.4 55.4 50.5 ReasonRank† (32B) Listwise 55.4 83.2 45.7 77.2 40.0 31.1 58.7 52.2 Retro* (7B) Pointwise 55.8 84.7 45.9 77.1 37.1 31.2 64.7 49.7 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 56.8 85.4 46.7 78.5 38.1 32.1 65.8 51.0
+
+[p. 16 | section: D Detailed BM25 and ReasonIR Results on BRIGHT | type: Text]
+both retriever and re-ranker rather than its standalone re-ranking capability. To ensure a fair comparison, we compare both models under the same evaluation settings. As shown in Table 7, Retro* consistently outperforms QwenRerank across all evaluation settings, indicating substantially stronger re-ranking ability. These results suggest that most of the gains attributed to QwenRerank largely come from the strong retriever ReasonIR, whereas Retro* achieves higher performance purely from its re-ranking capability.
+
+[p. 16 | section: E EVALUATION ON BEIR | type: Text]
+To assess the generalizability of our model, we further evaluate its performance in traditional retrieval scenarios. Following ReasonRank (Liu et al., 2025) , we select seven datasets from the BEIR benchmark (Thakur et al., 2021) , for their relatively small number of queries. In the retrieval stage, BM25 is applied with the original query to obtain candidate documents, after which all re-ranking methods re-rank the top-100 BM25 results. We report nDCG@10 as the performance metric.
+
+[p. 16 | section: E EVALUATION ON BEIR | type: Text]
+In this scenario, we utilize the MS MARCO dataset as our training data. Specifically, we construct 24,000 query-document pairs for both SFT and RL training. The RL stage is trained for 3 epochs, while the other training settings are consistent with Section 4.1.
+
+[p. 16 | section: E EVALUATION ON BEIR | type: Text]
+The evaluation results on BEIR, as shown in Table 8, demonstrate the strong generalizability of Retro* to traditional re-ranking tasks. The Retro* (7B) model achieves an average nDCG@10 of 55.8, outperforming all non-reasoning and reasoning-enhanced baselines. These results confirm
+
+[p. 17 | section: E EVALUATION ON BEIR | type: TableGroup]
+Table 9: nDCG@10 results on the BRIGHT benchmark with models trained using varying α values. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 15.7 20.6 7.9 27.9 36.6 + SFT + RL (α = 0.00) 30.8 43.6 48.7 30.8 36.7 25.6 28.5 37.7 13.1 28.6 5.6 30.6 40.6 + SFT + RL (α = 1.00) 33.2 49.4 51.8 29.9 44.2 27.6 33.4 36.4 20.1 23.3 8.6 32.0 41.3 + SFT + RL (α = 0.25) 36.1 53.0 55.1 33.3 46.3 34.3 36.2 40.3 17.3 29.3 7.0 35.2 45.8 + SFT + RL (α = 0.50) 35.8 51.3 54.3 32.7 47.4 31.7 35.0 39.3 20.7 29.2 8.2 34.6 44.6 + SFT + RL (α = 0.75) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0
+
+[p. 17 | section: E EVALUATION ON BEIR | type: Text]
+that our reasoning-enhanced pointwise approach is general-purpose and suitable for both reasoningintensive and traditional retrieval scenarios. Moreover, by integrating over 16 sampling scores, the model achieves a final nDCG@10 of 56.8, indicating the effectiveness of test-time scaling even on traditional benchmarks, as illustrated in Figure 6.
+
+[p. 17 | section: F ANALYSIS OF THE HYPERPARAMETER α | type: Text]
+Table 9 reports the performance of training with different weights α for the composite rewards. When α = 0 or α = 1, the model degenerates into using only one of the composite rewards, resulting in suboptimal performance. In particular, training with only the intra-document reward (α = 1) clearly outperforms training with only the inter-document reward (α = 0), suggesting that the intra-reward provides a stronger optimization signal for model learning. This observation aligns with its role in stabilizing training by encouraging more consistent reasoning trajectories within a document.
+
+[p. 17 | section: F ANALYSIS OF THE HYPERPARAMETER α | type: Text]
+However, despite its dominance, the intra-reward alone still underperforms any weighted combination of the two rewards. Across all α ∈ (0, 1), we observe consistent performance gains over using either reward alone, demonstrating that the intra- and inter-document rewards serve complementary purposes. While the intra-reward promotes stable and learnable ranking behavior, the inter-reward introduces document-level discrimination that further enhances final ranking performance.
+
+[p. 17 | section: F ANALYSIS OF THE HYPERPARAMETER α | type: Text]
+These results indicate that effective reward balancing enables the model to simultaneously exploit stable intra-document ranking signals and informative inter-document comparisons. Notably, performance peaks when α is biased toward the intra-reward (e.g., α = 0.75), highlighting that the intra-reward should dominate training dynamics, while the inter-reward acts as an essential complementary signal that enhances ranking performance.
+
+[p. 17 | section: G DIFFERENT BACKBONE MODELS | type: Text]
+To demonstrate the generalizability and effectiveness of our Retro*, we conducted experiments with several different backbone models. As shown in Table 10, Retro* significantly improves the average nDCG@10 across all backbone models: Qwen2.5-Instruct (7B) from 22.9 to 36.6, Llama2-chat (7B) from 8.2 to 30.9, Mistral-Instruct-v0.1 (7B) from 8.6 to 30.1, Llama3.1-Instruct (8B) from 17.3 to 34.4, and Qwen3 (8B) from 29.4 to 36.1. Furthermore, applying test-time scaling further improves performance consistently for all backbones as shown in Figure 6. These results demonstrate that our approach consistently and substantially enhances ranking performance across diverse backbones, while test-time scaling remains effective with each backbone, further highlighting its robustness and broad applicability as a general retrieval model.
+
+[p. 17 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Text]
+In this section, we analyze the impact of the length control instruction used during the distillation from the teacher model. We augment the prompt template (shown in Figure 8) with an explicit instruction at the beginning of the task description. The modified prompt template is shown below:
+
+[p. 17 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Code]
+Here is the **relevance definition** in a retrieval task: {relevance_definition}
+
+[p. 18 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: TableGroup]
+Table 10: nDCG@10 results on the BRIGHT benchmark across different backbone models. All backbone models re-rank the top-100 documents retrieved by BGE-Reasoner-Embed. The retrieval stage and the re-ranking stage both utilize the original query. Models Avg. Stack Excha ange Coc ling Tì neorem-ba ased 11104015 12.8 Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Qwen2.5-Instruct (7B) 22.9 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 Retro* (7B) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 Tesi t-Time S caling (Mean- Score@. 16) Retro* (7B) 38.7 58.4 59.2 35.0 49.3 33.9 37.7 41.1 18.8 33.5 10.7 40.2 46.7 Llama2-chat (7B) 8.2 13.4 14.6 8.2 11.2 7.0 7.6 10.6 7.6 4.4 2.4 3.2 8.7 Retro* (7B) 25.4 43.7 40.1 22.0 35.8 20.7 26.8 29.7 18.1 19.4 6.6 22.0 19.5 Tesi -Time S caling (Mean- Score@. 16) Retro* (7B) 30.9 53.3 49.6 28.8 42.8 25.7 29.9 34.3 22.1 25.1 7.5 29.2 23.1 Mistral-Instruct-v0.1 (7B) 8.6 17.2 15.4 6.9 11.6 7.7 8.3 10.6 6.0 7.7 2.5 3.8 5.5 Retro* (7B) 27.8 49.1 42.4 24.4 38.0 23.7 29.7 31.9 15.5 20.7 9.3 24.5 24.5 Tesi -Time S caling (Mean- Score@. 16) Retro* (7B) 30.1 53.9 46.0 27.3 43.0 25.7 30.9 31.6 15.0 24.0 10.1 27.8 26.1 Llama3.1-Instruct (8B) 17.3 35.0 27.8 17.3 30.0 11.8 19.5 21.3 8.8 4.8 4.2 11.4 15.1 Retro* (8B) 34.4 56.7 53.5 31.3 47.3 31.3 32.7 40.2 19.9 21.2 9.4 33.0 36.4 Test -Time S caling (Mean- Score@. 16) Retro* (8B) 36.7 60.2 55.9 33.5 49.7 33.6 36.2 42.0 19.0 24.7 10.3 38.4 36.4 Qwen3 (8B) 29.4 53.5 53.8 28.3 34.1 26.3 29.2 33.1 14.1 8.4 6.7 20.6 44.4 Retro* (8B) 36.1 55.0 56.2 34.9 42.0 35.9 35.6 42.5 16.7 21.9 8.4 35.4 48.7 Test -Time S caling (Mean- Score@. 16) Retro* (8B) 38.8 57.6 58.5 37.1 45.8 38.3 39.3 45.4 17.3 26.6 10.6 40.4 48.8
+
+[p. 18 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: FigureGroup]
+Figure 6: Effectiveness of Test-Time Scaling for Retro*. ( Left ): Test-time scaling brings significant performance improvements even on the traditional BEIR benchmark. ( Right ): Test-time scaling is consistently effective across different backbone models.
+
+[p. 18 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Code]
+Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps (**Please ensure your entire analysis and annotation across all steps does not exceed 512 tokens**). ... (The rest of the prompt template remains the same)
+
+[p. 18 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Text]
+To evaluate the effect of this instruction on both the reasoning length and the model's performance, we construct two distillation datasets from the teacher model under two conditions: one with the instruction and one without it. We then train student models on these datasets, respectively. The impact on reasoning length is illustrated in Figure 7, while the model performance is reported in Table 11.
+
+[p. 18 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Text]
+As shown in Figure 7, the length control instruction substantially shortens the reasoning trajectories, yielding an average trajectory length comparable to that of the backbone model. Meanwhile, Table 11 shows that the model trained with this instruction achieves an average nDCG@10 of 36.6, essentially matching the 36.4 achieved without it. These results demonstrate that the instruction effectively constrains the reasoning length for efficiency without compromising re-ranking accuracy. Furthermore, although the reasoning length of our trained model is close to that of the backbone,
+
+[p. 19 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: FigureGroup]
+Figure 7: Comparison of average completion tokens on BRIGHT benchmark for different models. The model trained with the length control instruction (w/ Length Control) effectively reduces the response length compared to training without it (w/o Length Control).
+
+[p. 19 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: TableGroup]
+Table 11: nDCG@10 results on the BRIGHT benchmark for ablation study on the impact of the length control instruction. Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Qwen2.5-Instruct (7B) 22.9 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 w/ Length Control + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 35.0 20.6 7.9 27.9 36.6 + SFT + RL (Composite Reward) 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 w/o Length Control + only-SFT 30.7 46.8 50.2 30.5 39.4 25.7 30.1 35.8 14.4 18.0 7.6 27.9 41.6 + SFT + RL (Composite Reward) 36.4 53.3 55.6 33.7 48.7 33.3 35.6 39.5 16.5 31.1 8.3 36.4 45.1
+
+[p. 19 | section: H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION | type: Text]
+it exhibits stronger ranking performance, suggesting that the improvement does not arise from generating longer reasoning trajectories. Instead, it stems from our effective training strategy, which equips the model with powerful reasoning and ranking capabilities.
+
+[p. 19 | section: I OUT-OF-DOMAIN GENERALIZATION ON R2MED | type: Text]
+To evaluate the out-of-domain generalizability of our rubric, we evaluate Retro* on R2MED (Li et al., 2025) , a biomedical reasoning retrieval benchmark that is outside the scientific, programming, and mathematical domains used during training. By replacing only the task-specific relevance definitions while keeping the task-agnostic scoring criteria, Retro* is able to generalize effectively to this unseen domain. Following the setup of ReasonRank, we use E5-mistral-7b-instruct (Wang et al., 2024) as the first-stage retriever, re-rank the top-100 retrieved candidates, and report nDCG@10. As summarized in Table 12, Retro* outperforms all other re-ranking baselines, demonstrating both the robustness of its rubric-based scoring and its strong cross-domain generalization capability.
+
+[p. 19 | section: J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING | type: Text]
+We provide the full relevance rubrics for our rubric-based relevance scoring mechanism in Figure 8. The rubrics are designed to guide the LLMs to reason about the relevance between a query and a candidate document through a three-step reasoning process (query analysis, document analysis, and relevance annotation) to produce a fine-grained relevance score.
+
+[p. 20 | section: J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING | type: Code]
+Here is the **relevance definition** in a retrieval task: {relevance_definition} Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps. 1. Query Analysis: Think to reason and describe what information would be most helpful in answering the query. 2. Document Analysis: Discuss how the information provided by the document fulfills or fails to fulfill the requirements implied by the query. 3. Relevance Annotation: Based on the relevance definition and the insights from the previous two steps, clearly justify your final relevance annotation result and annotate an integer score from a scale of 0 to 100. Please use the following guide: - **80-100 (Highly Relevant):** The document directly and comprehensively addresses the query's intent. It is a core and authoritative answer. - **60-80 (Relevant):** The document substantially addresses the query's intent, providing most of the key information, but might miss some minor details. - **40-60 (Moderately Relevant):** The document is on-topic and addresses a part of the query's intent, but it is not a comprehensive answer. - **20-40 (Slightly Relevant):** The document mentions keywords from the query, but its main topic is different. It offers very limited value. - **0-20 (Irrelevant):** The document does not address the query's intent at all and is off-topic. After providing your detailed analysis and justification for all the steps above, conclude your entire response with the final relevance score. The score must be placed strictly between the <score> tags. There should be no other text or explanation inside the tags: <score> [From a scale of 0 to 100, annotate the degree of relevance between the query and the document .] </score> Query ({query_type}): [Begin of Query] {query} [End of Query] Document ({doc_type}): [Begin of Document] {doc} [End of Document]
+
+[p. 20 | section: J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING | type: Caption]
+Figure 8: The full relevance rubrics for rubric-based relevance scoring.
+
+[p. 20 | section: J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING | type: TableGroup]
+Table 12: nDCG@10 results on the R2MED benchmark, where all methods re-rank the top-100 documents retrieved by E5-mistral-7b-instruct. The retrieval stage and the re-ranking stage both utilize the original query. Results marked with † are reported by ReasonRank. Models Methods Avg. Biolo. Bioin. Med-Sci. Med-Exam. Med-Diag. PMC-Treat. PMC-Cli. IIYi-Cli. E5-mistral-7b-instruct Retriever 24.0 22.9 42.3 41.5 7.4 12.4 18.5 24.9 21.8 Reasoning-Enhanced Re-Ranking Baselines Rank1† (7B) Pointwise 32.3 32.6 55.6 54.7 12.8 20.0 34.4 30.2 18.2 Rank1† (32B) Pointwise 39.1 31.8 61.7 59.7 16.6 26.9 41.3 45.6 29.5 ReasonRank† (7B) Listwise 39.5 46.8 59.7 60.1 16.5 24.9 39.2 39.1 29.9 ReasonRank† (32B) Listwise 42.9 45.6 67.7 63.5 18.9 30.6 41.1 46.1 29.4 Retro* (7B) Pointwise 38.7 47.6 59.7 60.8 12.7 25.2 40.7 39.0 24.2 Retro* (32B) Pointwise 44.5 48.8 68.0 67.3 16.6 34.2 43.3 45.4 32.6 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 42.6 49.9 62.4 62.4 15.7 29.0 41.9 46.2 32.9 Retro* (32B) Pointwise 46.2 51.9 67.8 67.2 19.2 35.7 43.8 48.7 35.6
+
+[p. 20 | section: K ANALYSIS OF THE NECESSITY OF REASONING | type: Text]
+To investigate the necessity of reasoning for re-ranking performance, we conduct an ablation study by removing the structured reasoning steps from our relevance rubrics. In the original rubrics, the model is prompted to analyze both the query and the candidate document before producing a detailed relevance score. In the ablated variant, the model instead outputs a single score directly, without any reasoning trajectory or rubric-guided analysis, as illustrated in Figure 9.
+
+[p. 21 | section: K ANALYSIS OF THE NECESSITY OF REASONING | type: TableGroup]
+Table 13: Relevance definitions for each dataset in the BRIGHT benchmark. Dataset Relevance Definition biology Given a query (biology post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. earth_science Given a query (earth science post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. economics Given a query (economics post) and a document (passage), the document is rele vant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. psychology Given a query (psychology post) and a document (passage), the document is rele vant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. robotics Given a query (robotics post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. stackoverflow Given a query (Stack Overflow post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. sustainable_living Given a query (sustainable living post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query. leetcode Given a query (LeetCode problem) and a document (coding problem solution), the document is relevant to the query if the underlying algorithms or data struc tures used in the document can provide helpful insights for solving the problem in the query. pony Given a query (Pony coding instruction) and a document (Pony documentation passage), the document is relevant to the query if the Pony syntax described in the document is necessary for beginners with no prior knowledge of Pony to complete the coding instruction in the query. aops Given a query (math problem) and a document (math problem solution), the doc ument is relevant to the query if the theorems used in the document can provide helpful insights for solving the problem in the query. theoremqa_questions Given a query (math problem) and a document (math problem solution), the doc ument is relevant to the query if the theorems used in the document can provide helpful insights for solving the problem in the query. theoremqa_theorems Given a query (math problem) and a document (math-related passage), the doc ument is relevant to the query if the theorem described in the document can help solve the problem in the query.
+
+[p. 21 | section: K ANALYSIS OF THE NECESSITY OF REASONING | type: Text]
+This variant of Retro* is trained on the same dataset and with the same RL algorithm as the original model. We focus the comparison specifically on the RL stage to avoid introducing confounding factors, such as potential biases originating from the SFT teacher model. By keeping the learning signal consistent, this setup effectively isolates the impact of reasoning on re-ranking performance. As shown in Table 16, removing the reasoning trajectory results in a substantial performance drop across all datasets. These results confirm that rubric-guided reasoning enhances the fidelity of relevance estimation under RL training. By structuring the task into intermediate steps, the model can better capture how different aspects of relevance contribute to the final judgment. Without this reasoning guidance, the model struggles to learn the underlying compositional logic of the relevance rubric, leading to the observed performance drop.
+
+[p. 21 | section: L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS | type: Text]
+In this section, we provide the detailed relevance definitions used in our evaluations on the BRIGHT, BEIR and R2MED benchmarks. In reasoning-intensive retrieval scenarios, the relevance definitions are more complex, while in traditional scenarios, they are more straightforward. The specific defi-
+
+[p. 22 | section: L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS | type: TableGroup]
+Table 14: Relevance definitions for each dataset in the BEIR benchmark. Dataset Relevance Definition TREC-COVID Given a query (COVID-19 related query) and a document (document), the document is relevant to the query if the document answers the query. DBPedia Given a query (query) and a document (entity description from DBpedia), the document is relevant to the query if the entity described in the document matches the query. SciFact Given a query (scientific claim) and a document (document), the document is relevant to the query if the document provides evidence supporting or refuting the scientific claim. NFCorpus Given a query (question) and a document (document), the document is relevant to the query if the document can best answer the question. Signal-1M Given a query (news event or topic) and a document (news headline or summary), the document is relevant to the query if it reports on, summarizes, or directly relates to the same news event or topic described in the query. Robust04 Given a query (information need) and a document (news or government document), the document is relevant to the query if it contains information that satisfies the intent or topic described in the query, even if phrased differently. TREC-NEWS Given a query (contemporary news topic or event) and a document (news article from The Washington Post), the document is relevant to the query if it discusses, explains, or provides factual coverage of the specific event or topic mentioned in the query. Table 15: Relevance definitions for each dataset in the R2MED benchmark.
+
+[p. 22 | section: L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS | type: TableGroup]
+Dataset Relevance Definition Biology Given a query (biology post) and a document (passage), the document is relevant to the query if the document helps answer the query. Medical-Sciences Given a query (medical science post) and a document (passage), the document is relevant to the query if the document helps answer the query. Bioinformatics Given a query (bioinformatics post) and a document (passage), the document is relevant to the query if the document helps answer the query. MedXpertQA-Exam Given a query (medical exam) and a document (passage), the document is relevant to the query if the document helps answer the query. MedQA-Diag Given a query (medical exam) and a document (passage), the document is relevant to the query if the document helps answer the query. PMC-Treatment Given a query (clinical case) and a document (passage), the document is relevant to the query if the document helps answer the query. PMC-Clinical Given a query (clinical case) and a document (case), the document is relevant to the query if it helps diagnose the query case. IIYi-Clinical Given a query (clinical case) and a document (case), the document is relevant to the query if it helps diagnose the query case. Table 16: Performance comparison on the BRIGHT benchmark, showing that reasoning-enhanced re-ranking significantly outperforms models trained without reasoning.
+
+[p. 22 | section: L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS | type: Table]
+Models Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 No Reason (only-RL) Reason (only-RL) 24.8 35.1 38.4 56.7 40.2 52.9 22.3 33.2 32.4 45.1 20.5 28.1 25.6 32.5 26.0 35.8 19.6 21.2 16.9 36.3 4.7 8.6 17.7 29.8 33.8 41.0
+
+[p. 22 | section: L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS | type: Text]
+nitions for the BRIGHT benchmark are listed in Table 13, BEIR are listed in Table 14, and those for R2MED are listed in Table 15. We use these relevance definitions for both training and evaluation.
+
+[p. 22 | section: M REASONING EXAMPLES | type: Text]
+We provide some examples to present the reasoning process of Retro* in Table 17 (Suatainable Living), Table 18 (Pony), and Table 19 (TheoremQA Theorems).
+
+[p. 23 | section: M REASONING EXAMPLES | type: Code]
+Here is the **relevance definition** in a retrieval task: {relevance_definition} Now given a **query** ({query_type}) and a **document** ({doc_type}) in this retrieval task, your mission is to perform the following steps. Based on the relevance definition, annotate an integer score from a scale of 0 to 100. Please use the following guide: 80-100 (Highly Relevant), 60-80 (Relevant), 40-60 (Moderately Relevant), 20-40 (Slightly Relevant), 0-20 (Irrelevant). Without any explanation, directly providing your final relevance score. The score must be placed strictly between the <score> tags. There should be no other text or explanation inside the tags: <score> [From a scale of 0 to 100, annotate the degree of relevance between the query and the document .] </score> Query ({query_type}): [Begin of Query] {query} [End of Query] Document ({doc_type}): [Begin of Document] {doc} [End of Document]
+
+[p. 23 | section: M REASONING EXAMPLES | type: Caption]
+Figure 9: The modified relevance rubrics for reasoning-free relevance scoring.
+
+[p. 24 | section: Table 17: Reasoning examples of Retro* (7B) on the Sustainable Living dataset of BRIGHT. | type: Text]
+Relevance Definition: Given a query (sustainable living post) and a document (passage), the document is relevant to the query if the critical concepts or theories discussed in the document can provide references for domain experts to draft an answer to the query.
+
+[p. 24 | section: Query | type: Text]
+Are solar powered cars sustainable and are they a good idea for future transportation?\n \nAs population rises, fossil fuels will start depleting so are solar powered cars a good idea? How much power can they produce when it is cloudy?
+
+[p. 24 | section: Positive Document | type: Text]
+The efficiency of the solar cells used in a [ photovoltaic system\n ](/wiki/Photovoltaic_system "Photovoltaic system") , in combination with\nlatitude and climate, determines the annual energy output of the system. For\nexample , a solar panel with 20% efficiency and an area of 1 m 2 will produce\n 200 kWh/yr at Standard Test Conditions if exposed to the Standard Test\nCondition solar irradiance value of 1000 W/m 2 for 2.74 hours a day. Usually\nsolar panels are exposed to sunlight for longer than this in a given day, but\nthe solar irradiance is less than 1000 W/m 2 for most of the day. A solar\npanel can produce more when the Sun is high in Earth's sky and will produce\nless in cloudy conditions or when the Sun is low in the sky, usually the Sun\nis lower in the sky in the winter.
+
+[p. 24 | section: Reasoning Process | type: ListGroup]
+1. Query Analysis: The query seeks an evaluation of solar-powered cars in terms of sustainability and their viability as future transportation. It specifically asks whether solar cars are sustainable and produce usable power under cloudy conditions. A helpful response would discuss solar car efficiency, energy capture, potential as a sustainable transport solution, and the impact of weather conditions on system output. 2. Document Analysis: The passage explains how solar panel efficiency, climate, and solar patterns affect energy output, particularly noting reduced power under cloudy skies and low-sunlight conditions. While it validates solar panel performance under varying light conditions—directly relevant to solar car feasibility—it does not mention solar-powered cars, automotive application, transportation systems, or sustainability over time. However, it provides foundational data on power generation under cloudiness, addressing part of the query. 3. Relevance Annotation: The document supplies critical information about solar panel energy output affected by cloudiness, which is pertinent to evaluating solar-powered cars. However, it does not link this to transportation solutions, sustainability assessment of solar cars, or holistic future outlook. It offers technical underpinnings but lacks domain-specific context regarding vehicles or long-term strategies. Thus, while informative for part of the query (especially on power availability in cloudy conditions), it omits major integrative insights needed for a comprehensive answer.
+
+[p. 24 | section: Reasoning Process | type: Text]
+<score> 65 </score>
+
+[p. 24 | section: Negative Document | type: Text]
+The first solar family car was built in 2013. [16] Researchers at [ Case\nWestern Reserve University ](/wiki/Case_Western_Reserve_University "Case\nWestern Reserve University") , have also developed a solar car which can\nrecharge more quickly, due to materials used in the solar panels. [17]
+
+[p. 24 | section: Reasoning Process | type: ListGroup]
+1. Query Analysis: The query seeks to evaluate the sustainability and practicality of solar-powered cars, particularly in the context of future transportation. It emphasizes two key aspects: (1) whether they are sustainable (e.g., environmental impact, energy efficiency), and (2) whether they are a good idea for addressing fossil fuel depletion and scalability, especially when sunlight availability fluctuates under clouds. Domain experts would need information on energy output, charging capacity, environmental benefits, and real-world feasibility. 2. Document Analysis: The document mentions a solar car from 2013 and references research improving charging speed with advanced materials. However, it lacks any discussion of sustainability, energy production, energy cloud dependency, or broader transportation implications. It provides only a limited technical note on material advancements without addressing the core sustainability or societal questions raised. 3. Relevance Annotation: While the document is tangentially related—mentioning solar-powered cars—it fails to address the critical concepts in the query, such as sustainability metrics, energy output under cloudy conditions, or long-term viability. It does not offer references that would help draft a comprehensive answer. The information is too minimal and outdated to support expert judgment on the broader query.
+
+[p. 24 | section: Reasoning Process | type: Text]
+<score> 35 </score>
+
+[p. 25 | section: Table 18: Reasoning examples of Retro* (7B) on the Pony dataset of BRIGHT. | type: Text]
+Relevance Definition: Given a query (Pony coding instruction) and a document (Pony documentation passage), the document is relevant to the query if the Pony syntax described in the document is necessary for beginners with no prior knowledge of Pony to complete the coding instruction in the query.
+
+[p. 25 | section: Query | type: Text]
+I will use the programming language pony.\nProblem :\nWrite a function to determine if a string consisting of alphabets is a palindrome.\n \nHere is the code template:\nfun is_palindrome(str: String): Bool ? =>\n ...
+
+[p. 25 | section: Positive Document | type: Text]
+## Functions\n \nPony functions are quite like functions (or methods) in other languages. They can have 0 or more parameters and 0 or 1 return values. If the return type is omitted then the function will have a return value of 'None'.\n \n "'pony\nclass C\nfun add(x: U32, y: U32): U32 =>\nx + y\n \nfun nop() =>\nadd (1, 2) // Pointless, we ignore the result\n "'\n \nThe function parameters (if any) are specified in parentheses after the function name. Functions that don't take any parameters still need to have the parentheses.\n \nEach parameter is given a name and a type. In our example function 'add' has 2 parameters, 'x' and 'y', both of which are type 'U32'. The values passed to a function call (the '1' and '2' in our example) are called arguments and when the call is made they are evaluated and assigned to the parameters. Parameters may not be assigned to within the function - they are effectively declared 'let'.\n \nAfter the parameters comes the return type. If nothing will be returned this is simply omitted.\n \nAfter the return value, there's a '=>' and then finally the function body. The value returned is simply the value of the function body (remember that everything is an expression), which is simply the value of the last command in the function. Reasoning Process:
+
+[p. 25 | section: 1. Query Analysis | type: Text]
+The query asks to write a function in Pony that determines whether a string is a palindrome. The key elements needed are: (1) a function taking a parameter of type 'String' and returning a 'Bool', (2) string handling in Pony, (3) string reversal/iteration, and (4) comparison logic. However, for a beginner with no prior knowledge, the most critical information is understanding how to define a function in Pony-especially the syntax for defining a function with a parameter, return type, and body. This is foundational for structuring any function, including one for palindrome detection.
+
+[p. 25 | section: 2. Document Analysis | type: Text]
+The document explains Pony function syntax in depth, covering parameter specification, return types (including optional ones), function bodies, and return values using a basic example ('add'). It clarifies that functions use 'fun', can have parameter lists with types, return statements via evaluation of the final expression, and can omit return types for 'None'. While it does not mention string operations, it provides essential syntax needed to write any function, including 'is_palindrome'.
+
+[p. 25 | section: 3. Relevance Annotation | type: Text]
+The document does not address handling strings or palindrome logic directly, but it fully covers the necessary syntactic structure for defining the function in the query-parameterized functions with return types, the 'fun' statement, and function bodies. This is foundational knowledge a beginner must have to implement the requested function. While not comprehensive for the full task, it supplies the core syntactic framework. Thus, it is highly relevant to the coding instruction in terms of necessary beginner syntax.
+
+[p. 25 | section: 3. Relevance Annotation | type: Text]
+<score> 75 </score>
+
+[p. 25 | section: Negative Document | type: Text]
+## Control Structures\n \nTo do real work in a program you have to be able to make decisions, iterate through collections of items and perform actions repeatedly. For this, you need control structures. Pony has control structures that will be familiar to programmers who have used most languages, such as 'if', 'while' and 'for', but in Pony, they work slightly differently.\n Reasoning Process:
+
+[p. 25 | section: Negative Document | type: ListGroup]
+1. Query Analysis: The query asks for a function in Pony to check if a string is a palindrome. This requires understanding of string manipulation, comparison, and possibly loops or recursion. Key concepts for beginners include: defining a function with the correct signature (e.g., 'String → Bool'), accessing characters in a string, reverse comparison, and possibly handling case sensitivity or ignoring non-alphabetic characters. The critical syntax needed includes function definition, type parameters, string indexing, and comparison logic. 2. Document Analysis: The document discusses general programming control structures ('if', 'while', 'for') and notes that these work similarly in Pony. However, it provides no specific examples, syntax, or details on string handling, function syntax, or palindrome logic. It fails to mention how to manipulate strings, access characters, or implement palindrome detection-core needs for the query. The content is introductory and abstract, focusing on high-level structure rather than concrete, applicable code. 3. Relevance Annotation: The document touches on conditional and iterative constructs, which are tangential to palindrome logic, but it does not provide the necessary syntax or examples for completing the task. It lacks any mention of string properties, indexing, or function definition relevant to the query. For a beginner, this passage would offer minimal direct assistance. Therefore, it only shares conceptual keywords (e.g., "if", "while") but misses all domain-specific syntax.
+
+[p. 25 | section: Negative Document | type: Text]
+<score> 5 </score>
+
+[p. 26 | section: Table 19: Reasoning examples of Retro* (7B) on the TheoremQA Theorems dataset of BRIGHT. | type: Text]
+Relevance Definition: Given a query (math problem) and a document (math-related passage), the document is relevant to the query if the theorem described in the document can help solve the problem in the query.
+
+[p. 26 | section: Query | type: Text]
+In a party, how many guests do you need to have to ensure that either four people all know each other or four people are all complete strangers to one another?
+
+[p. 26 | section: Positive Document | type: Text]
+\\section{Ramsey's Theorem}\nTags : Ramsey Theory, Named Theorems, Combinatorics\n \n \\begin{theorem}\nIn any coloring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs.\nFor 2 colors, Ramsey's theorem states that for any pair of positive integers $\\tuple {r, s}$, there exists a least positive integer $\\map R {r, s}$ such that for any complete graph on $\\map R {r, s}$ vertices, whose edges are colored red or blue, there exists either a complete subgraph on $r$ vertices which is entirely red, or a complete subgraph on $s$ vertices which is entirely blue.\nMore generally, for any given number of colors $c$, and any given integers $n_1, \\ldots, n_c$, there is a number $\\map R {n_1, \\ldots, n_c}$ such that:\n :if the edges of a complete graph of order $\\map R {n_1, \\ldots, n_c}$ are colored with $c$ different colours, then for some $i$ between $1$ and $c$, it must contain a complete subgraph of order $n_i$ whose edges are all color $i$.\nThis number $\\map R {n_1, \\ldots, n_c}$ is called the Ramsey number for $n_1, \\ldots, n_c$.\nThe special case above has $c = 2$ (and $n_1 = r$ and $n_2 = s$).\nHere $\\map R {r, s}$ signifies an integer that depends on both $r$ and $s$. It is understood to represent the smallest integer for which the theorem holds.\n \\end{theorem}\n \n \\begin{proof}\nFirst we prove the theorem for the 2-color case, by induction on $r + s$.\nIt is clear from the definition that\n :$\\forall n \\in \\N: \\map R {n, 1} = \\map R {1, n} = 1$\nbecause the complete graph on one node has no edges.\nThis is the base case.\nWe prove that $R \\left({r, s}\\right)$ exists by finding an explicit bound for it.\nBy the inductive hypothesis, $\\map R {r - 1, s}$ and $\\map R {r, s - 1}$ exist.\n \\end{proof}\n \n
+
+[p. 26 | section: Reasoning Process | type: ListGroup]
+1. Query Analysis: The query asks for the minimum number of guests (people) in a party such that either 4 people all know each other (a complete subgraph $K_4$ in a "knows"-graph) or 4 people are all strangers to each other (a complete subgraph $K_4'$ in a "strangers"-graph). This is a classic Ramsey number problem, specifically asking for $R(4,4)$, the smallest number of guests such that in any 2-coloring of the edges (representing know-or-stranger), there must be a monochromatic $K_4$. The key concept needed is Ramsey theory, particularly the Ramsey number $R(4,4)$. 2. Document Analysis: The document presents Ramsey's Theorem, defining the Ramsey number $\map R {r,s}$ as the smallest number such that any 2-coloring of the edges of a complete graph on $\map R {r,s}$ vertices guarantees either an all-red $K_r$ or all-blue $K_s$. It confirms the theorem for $c=2$, which directly applies to the query's 2-coloring framework. While it does not explicitly state $R(4,4)$ or compute its value (which is 18), the theorem provides the theoretical foundation to solve the query. From this, one could deduce that any graph on 18 or more vertices necessarily contains either a $K_4$ or $\overline {K}_4$, depending on the coloring. 3. Relevance Annotation: The document is highly relevant because it introduces and explains Ramsey's Theorem, the core mathematical principle required to solve the query. Although it does not provide the specific value of $R(4,4)$, it enables one to derive it via the theorem. It directly supports solving the problem by offering the theoretical framework.
+
+[p. 26 | section: Reasoning Process | type: Text]
+<score> 95 </score>
+
+[p. 26 | section: Negative Document | type: Text]
+\\section{Infinite Ramsey's Theorem}\nTags : Ramsey Theory, Named Theorems\n \n \\begin{theorem}\nLet $k, n \\in \\N$.\nFor any set $S$, let $S^{\\paren n}$ denote the set $\\set {\\set {s_1, \\ldots, s_n}: \\text{each } s_i \\in S}$ of cardinality $n$ subsets of $S$.\nLet $X$ be an infinite set.\nThen :\n :for every partition $P$ of $X^{\\paren n}$ into $k$ many components\n :there is an infinite subset $Y \\subseteq X$\nsuch that:\n :each member of $Y^{\\paren n}$ is in the same component of $P$.\n \\end{theorem}\n \n \\begin{proof}\nWe will prove the theorem for fixed $k$ by induction on $n$.\n \\end{proof}\n \n
+
+[p. 26 | section: Reasoning Process | type: ListGroup]
+1. Query Analysis: The query asks for the minimum number of guests (n) at a party such that either four people all know each other (a clique of size 4 in a social graph) or four mutually unknown people exist (an independent set of size 4). This is a Ramsey theory problem specifically involving the Ramsey number R(4,4), which is the smallest number n such that any 2-coloring of the edges of a complete graph on n vertices guarantees a monochromatic clique of size 4 or an independent set of size 4. The key information needed is a known result about R(4,4), preferably its value or a discussion of its combinatorial implications. 2. Document Analysis: The document presents the Infinite Ramsey Theorem, which states that for any partition of the n-element subsets of an infinite set into finitely many components, there exists an infinite subset that monochromatic. This is a much more general and abstract result. While it is situated in Ramsey theory, it deals with infinite sets and n-element subsets, and does not address the finite Ramsey number R(4,4) or any finite Ramsey-type problem. It does not mention graph theory, social networks, cliques, or independent sets in the context of a finite party problem. Thus, it fails to provide any specific insight into the numerical or combinatorial condition required to solve the query. 3. Relevance Annotation: The document is thematically related (Ramsey Theory) but addresses a fundamentally different domain (infinite sets, infinite Ramsey Theorem) and offers no useful method or result for determining R(4,4) or solving the finite problem. It cannot help directly in solving the given social puzzle. While both involve Ramsey theory, the connection is too abstract and generic without addressing the specific problem or its mathematical tools.
+
+[p. 26 | section: Reasoning Process | type: Text]
+<score> 10 </score>

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+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0002", "section": "1 Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Enhancing the reasoning capabilities of LLMs for reasoning-intensive tasks is a central focus of current research. One promising strategy is test-time scaling, which guides or reinforces LLMs to", "source": "marker_v2", "marker_block_id": "/page/0/Text/12"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0003", "section": "1 Introduction", "page_start": 1, "page_end": 1, "type": "Footnote", "text": "* Core Contributors.", "source": "marker_v2", "marker_block_id": "/page/0/Footnote/13"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0004", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "generate long-form thoughts before arriving at a final answer at inference time (Wei et al., 2022; Jaech et al., 2024; Guo et al., 2025) . This approach also enables the LLMs to explore multiple reasoning paths, evaluate alternatives, and ultimately arrive at more accurate solutions for complex problems (Wang et al., 2022) . Inspired by these advances, recent information retrieval (IR) research has begun to leverage the reasoning capabilities of LLMs for reasoning-intensive document retrieval tasks (Su et al., 2024; Niu et al., 2024; Zhuang et al., 2025; Weller et al., 2025) . Current methods typically follow one of two paths: some directly prompt general-purpose LLMs to perform fine-grained relevance analysis, while others optimize these models with fine-tuning algorithms to elicit more structured and systematic reasoning behaviors. Despite recent progress, current approaches exhibit three key limitations in relevance-measuring functionality, test-time scalability, and parallelism:", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0005", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "Lack of relevance-measuring functionality. Many RAG applications require a specific functionality: the direct and interpretable measurement of document relevance. However, existing methods primarily provide relative ranking orders, which cannot capture the absolute level of relevance needed by downstream tasks. Inflexible test-time scalability. Existing methods mainly focus on generating a single, longform thought to reach an answer. However, they neglect the significant potential of exploring and integrating multiple reasoning paths to achieve more reliable performance. Limited parallelism capability. Existing methods, which are primarily listwise (Sun et al., 2023) or setwise (Zhuang et al., 2024) , must sequentially process the entire candidate set to produce the final retrieval result. This inherently sequential design is prone to substantial latency, especially when handling a large group of candidate documents.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/205"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0006", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "In this work, we propose Retro* (Retro-star), a novel LLM-based retrieval model designed for reasoning-intensive IR tasks. Distinct from existing approaches, Retro* is built on two key designs:", "source": "marker_v2", "marker_block_id": "/page/1/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0007", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "Rubric-based relevance scoring. Retro* introduces a fine-grained set of relevance rubrics, which explicitly define the relevance scores and their interpretations. Based on these rubrics, Retro* performs pointwise reasoning on the relationship between a query and its candidate documents, producing concrete relevance scores with clear, interpretable meanings. This design enables direct measurement of relevance, rather than merely providing a relative ordering of documents. Test-time scaling by score integration. Building on its rubric-based scoring, Retro* supports test-time scaling by generating multiple trajectories for each query-document pair and integrating their individual scores based on score similarity, resulting in a more reliable and stable estimate of document relevance.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/206"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0008", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "With these designs, Retro* can serve both relevance measuring and re-ranking applications. Furthermore, its architecture naturally supports both flexible test-time scaling and high parallelism, making it proficient at performing effective and efficient reasoning for complex retrieval problems.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0009", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "To bring these designs to their full potential, we introduce a novel reinforcement learning (RL) algorithm with two composite rewards to further optimize Retro*'s capabilities. The composite rewards are designed to fully exploit the trajectories of every training sample during RL training. The Intra-Document Reward guides the policy model to assign accurate relevance scores for each individual document, whereas the Inter-Document Reward incentivizes the policy model to effectively discriminate the relevant document from an irrelevant one. To stabilize the training process and provide Retro* with an initial reasoning ability, we incorporate a warm-up supervised fine-tuning (SFT) stage. This stage not only equips the model with basic reasoning skills, but also shapes the model to generate concise and well-structured thoughts before the RL stage.", "source": "marker_v2", "marker_block_id": "/page/1/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0010", "section": "1 Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "To evaluate the effectiveness of our training strategy and the overall performance of Retro* on reasoning-intensive IR tasks, we conduct experiments on BRIGHT (Su et al., 2024) , a comprehensive benchmark encompassing 12 datasets across science, mathematics, and programming. Experimental results demonstrate that Retro* achieves significant improvements over strong baseline methods, with substantial performance gains from the proposed test-time scaling mechanism and reinforcement learning method. To facilitate future research in this area, all resources are released at Retro-star .", "source": "marker_v2", "marker_block_id": "/page/1/Text/10"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0011", "section": "1 Introduction", "page_start": 3, "page_end": 3, "type": "Code", "text": "Here is the relevance definition... RELEVANCE_PLACEHOLDER Now given a query and a document... your mission is to perform the following steps. 1. Query Analysis: Think to reason and describe what information would... 2. Document Analysis: Discuss how the information provided by the document... 3. Relevance Annotation: ... annotate an integer score from 0 to 100. ...following guide: - 80-100 (Highly Relevant): ... - 60-80 (Relevant): ... - 40-60 (Moderately Relevant): ... - 20-40 (Slightly Relevant): ... - 0-20 (Irrelevant): ... ...conclude your entire response with the final relevance score... <score>[...]</score> Query:[Begin of Query]QUERY_INPUT[End of Query] Document:[Begin of Document]DOCUMENT_INPUT[End of Document]", "source": "marker_v2", "marker_block_id": "/page/2/Code/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0012", "section": "1 Introduction", "page_start": 3, "page_end": 3, "type": "Caption", "text": "Figure 1: Relevance rubric for Retro*. The Relevance Placeholder allows users to specify the definition of relevance, while a 5-level criteria ensures consistent and interpretable scoring result.", "source": "marker_v2", "marker_block_id": "/page/2/Caption/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0013", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Reasoning Large Language Models. Enhancing the reasoning capabilities of LLMs is crucial for tackling complex tasks. Techniques such as chain-of-thought prompting (Wei et al., 2022) , which guide LLMs to reason step by step before producing the final answer, have shown significant performance gains. More advanced sampling strategies, including self-consistency (Wang et al., 2022) , tree-of-thought (Yao et al., 2023) , and Monte Carlo tree search (Xie et al., 2024) , further enhance their reasoning quality and reliability. To unlock the full potential of LLM reasoning, recent research has increasingly explored reinforcement learning, which directly optimizes the model to generate high-quality reasoning trajectories (Jaech et al., 2024; Guo et al., 2025; Yang et al., 2025a) .", "source": "marker_v2", "marker_block_id": "/page/2/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0014", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Reasoning-enhanced IR Methods. Inspired by the recent advances in reasoning-capable LLMs, a growing body of research has begun adapting these paradigms to IR, with re-ranking tasks emerging as a primary focus. Preliminary studies have explored a variety of strategies, ranging from zeroshot prompting (Niu et al., 2024) , to distilling reasoning trajectories from powerful reasoning LLMs through supervised fine-tuning (Weller et al., 2025; Yang et al., 2025b) , and even reinforcement learning with carefully designed re-ranking rewards (Zhuang et al., 2025; Liu et al., 2025) . Despite the promising progress of these approaches, there remains a lack of effective methods for directly estimating the strength of relevance between query and document. Moreover, existing methods face limitations in terms of test-time scalability and parallelism, which significantly hinder their overall accuracy and inference efficiency.", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0015", "section": "3 METHODOLOGY", "page_start": 3, "page_end": 3, "type": "Text", "text": "In this section, we first introduce the basic framework of Retro*, including the rubric-based mechanism for relevance scoring and the score integration strategy for test-time scaling. We then describe how we optimize Retro*'s performance by reinforcement learning with tailored rewards.", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0016", "section": "3.1 RUBRIC-BASED RELEVANCE SCORING", "page_start": 3, "page_end": 3, "type": "Text", "text": "Retro* is designed to both measure the absolute relevance of each document and re-rank a set of candidate documents. To this end, we introduce a rubric-based scoring mechanism that guides the model to perform reasoning on the relationship between a query and its candidate documents based on a well-defined relevance rubric, yielding relevance scores with interpretable meanings.", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0017", "section": "3.1.1 RELEVANCE RUBRIC", "page_start": 3, "page_end": 3, "type": "Text", "text": "The relevance rubric (Γ) consists of two parts. One is the Relevance Definition, where the specific intent of the retrieval task is declared in the [Relevance Placeholder]. For example, we may specify an intent to retrieve proofs that are grounded in the same underlying theorem as the input. The other one is the Scoring Criteria, which defines the scope and rules for assigning relevance scores. In", "source": "marker_v2", "marker_block_id": "/page/2/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0018", "section": "3.1.1 RELEVANCE RUBRIC", "page_start": 4, "page_end": 4, "type": "FigureGroup", "text": "Figure 2: An overview of the two-stage training. SFT : the model is warmed up with a filtered data from a powerful teacher model. RL : the model is reinforced with the tailored composite reward.", "source": "marker_v2", "marker_block_id": "/page/3/FigureGroup/142"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0019", "section": "3.1.1 RELEVANCE RUBRIC", "page_start": 4, "page_end": 4, "type": "Text", "text": "our work, the relevance score is represented as an integer between 0 and 100, where higher scores indicate stronger relevance. The scope is partitioned into multiple intervals, each with explicit, interpretable meaning. For instance, a score within the range of 80-100 indicates that the candidate document is highly relevant and comprehensively addresses the information need of the query. An overview of the rubrics is shown in Figure 1, with the full rubrics provided in Appendix J.", "source": "marker_v2", "marker_block_id": "/page/3/Text/3"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0020", "section": "3.1.1 RELEVANCE RUBRIC", "page_start": 4, "page_end": 4, "type": "Text", "text": "Based on this well-defined rubric, Retro* is prompted to reason about the relevance between a given query (q) and a candidate document (d), generating a reasoning trajectory (y) along with a corresponding relevance score (s): Retro (\\Gamma, q, d) \\rightarrow (y, s) . See Appendix M for examples.", "source": "marker_v2", "marker_block_id": "/page/3/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0021", "section": "3.1.2 TEST-TIME SCALING VIA SCORE INTEGRATION", "page_start": 4, "page_end": 4, "type": "Text", "text": "To enhance retrieval accuracy, Retro* leverages test-time scaling by sampling K times for each query-document pair, resulting in a set of reasoning trajectories: \\{(y_1, s_1), \\ldots, (y_K, s_K)\\} . A common approach to integrate these results is majority voting, where the most frequent score is chosen as the final score. While this approach works well for highly discrete outputs, it is not appropriate in Retro*, as drawing a reliable result would require a vast number of samples, making the process computationally expensive and impractical.", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0022", "section": "3.1.2 TEST-TIME SCALING VIA SCORE INTEGRATION", "page_start": 4, "page_end": 4, "type": "Text", "text": "To this end, we propose a Score Integration strategy in a simple yet effective way: \\bar{s} \\leftarrow \\sum_K w_i * s_i / \\sum_K w_i , where s_i is the relevance score from the i-th trajectory and w_i is its associated weight. The weights can be set based on the generation likelihood of each trajectory. When likelihoods are unavailable or just for simplicity, a uniform weighting scheme, w_i = 1/K , can be used.", "source": "marker_v2", "marker_block_id": "/page/3/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0023", "section": "3.2 Training Strategy", "page_start": 4, "page_end": 4, "type": "Text", "text": "To optimize Retro*'s reasoning capabilities for reasoning-intensive document retrieval tasks, we propose a two-stage training strategy. The process starts with a supervised fine-tuning (SFT) stage to warm up the model, followed by a reinforcement learning (RL) stage for further performance enhancement. The overview of the training strategy is illustrated in Figure 2.", "source": "marker_v2", "marker_block_id": "/page/3/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0024", "section": "3.2.1 Supervised Fine-Tuning", "page_start": 4, "page_end": 4, "type": "Text", "text": "In the first stage, we perform SFT to equip the model with an initial reasoning ability and shape the model to generate concise and well-structured thoughts. The key of this stage lies in our approach to Training Data Curation , which involves two crucial steps:", "source": "marker_v2", "marker_block_id": "/page/3/Text/11"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0025", "section": "3.2.1 Supervised Fine-Tuning", "page_start": 5, "page_end": 5, "type": "Text", "text": "Data Sourcing. We begin with a collection of query-document pairs \\{(q,d)_1,\\ldots,(q,d)_M\\} . For each pair, we leverage a powerful teacher model \\mathbb T to reason about the relationship between q and d based on our relevance rubric: \\mathbb T(\\Gamma,q,d)\\to (y,s) . Besides, the teacher model is also guided to keep its thoughts concise, with an explicit length control instruction.", "source": "marker_v2", "marker_block_id": "/page/4/Text/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0026", "section": "3.2.1 Supervised Fine-Tuning", "page_start": 5, "page_end": 5, "type": "Text", "text": "Data Filtering . To obtain high-quality training data, we filter the raw trajectories with score integration. Specifically, we sample the teacher model K times for each query-document pair, resulting in a group of raw trajectories \\{(y_1, s_1), \\ldots, (y_K, s_K)\\} . We then integrate these scores to a score \\bar{s} , as it serves as a reliable reference. Finally, the trajectory whose score is closest to \\bar{s} is selected, so that only one trajectory is used for each query-document pair, resulting in a curated dataset for SFT training: \\{(q, d, \\hat{y}, \\hat{s})_1, \\ldots (q, d, \\hat{y}, \\hat{s})_M\\} , where (\\hat{y}, \\hat{s}) is the selected trajectory.", "source": "marker_v2", "marker_block_id": "/page/4/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0027", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Text", "text": "In the second stage, we take the SFT model as the initial policy model and perform RL to further optimize its reasoning capability. As discussed earlier, Retro* is designed to achieve two key functionalities: accurately scoring the absolute relevance of individual documents and correctly ranking them by assigning higher scores to more relevant ones. To jointly optimize these functionalities, we introduce a composite reward that fully exploits the trajectories of each training sample during RL.", "source": "marker_v2", "marker_block_id": "/page/4/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0028", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Text", "text": "Intra-Document Reward. Intra-document reward is designed to improve the scoring accuracy for each individual document. It incentivizes the model to generate high-quality reasoning trajectories that produce stable and accurate relevance scores for the same query-document pair across multiple attempts. To this end, the reward is computed in two steps. 1) Rolling Out: For each query-document pair (q,d), the model rolls out N trajectories: \\{(y_1,s_1),\\ldots,(y_N,s_N)\\} . 2) Reward Assignment: The integrated score \\bar{s} over all trajectories presents a more reliable result than each individual score in expectation. As such, the trajectories with scores closer to \\bar{s} are preferred, while those deviating further from \\bar{s} are disfavored. For simplicity and robustness, we adopt a ternary function, where the trajectory with the closest score is assigned a reward +1, the furthest one is assigned -1, while the others are assigned 0. To prune the trivial cases where all trajectories already reach an agreement, we also introduce a threshold \\tau requiring a minimum gap between \\bar{s} and the furthest deviate score. The above reward is formulated as the following function:", "source": "marker_v2", "marker_block_id": "/page/4/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0029", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Equation", "text": "R_{\\mathrm{intra}}(y,s) = \\begin{cases} +1 & \\text{if } s \\text{ is closest to } \\bar{s}, \\text{ and the threshold } \\tau \\text{ constraints holds} \\\\ -1 & \\text{if } s \\text{ is furthest from } \\bar{s}, \\text{ and the threshold } \\tau \\text{ constraints holds} \\end{cases}. \\tag{1}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0030", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Text", "text": "Inter-Document Reward. Inter-document reward focuses on improving the reranking performance for a group of candidate documents. It incentivizes the model to assign higher relevance scores to more relevant documents, thereby resulting in a correct ranking for a given task. In our work, we sample one positive (d^+) and one negative (d^-) document from the candidate set for each query, and the reward is computed via the following steps: 1) Rolling Out: For each document d \\in \\{d^+, d^-\\} , the model rolls out N trajectories: \\{(y_1^d, s_1^d), \\dots, (y_N^d, s_N^d) \\mid d \\in \\{d^+, d^-\\}\\} . 2) Reward Assignment: The trajectories of both positive and negative samples are evaluated based on whether their scores correctly reflect the ranking. For a positive sample's trajectory (y_i^+, s_i^+) , the reward is the proportion of negative ones whose scores are dominated by s_i^+ . Conversely, for a negative sample's trajectory (y_j^-, s_j^-) , the reward is the proportion of positive ones whose scores dominate s_j^- . These relationships are formally defined by the following equations:", "source": "marker_v2", "marker_block_id": "/page/4/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0031", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Equation", "text": "R_{\\text{inter}}(y_i^+, s_i^+) = \\frac{1}{N} \\sum_{j=1}^N \\mathbb{I}(s_i^+ > s_j^-), \\quad R_{\\text{inter}}(y_j^-, s_j^-) = \\frac{1}{N} \\sum_{i=1}^N \\mathbb{I}(s_j^- < s_i^+), \\tag{2}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0032", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\mathbb{I}(\\cdot) is the indicator function, and N is the number of trajectories for each q-d sample.", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0033", "section": "3.2.2 REINFORCEMENT LEARNING", "page_start": 5, "page_end": 5, "type": "Text", "text": "The intra-document reward and inter-document reward are combined with a parameter \\alpha \\in (0,1) to obtain the composite reward: R(y,s) = \\alpha \\cdot R_{\\mathrm{intra}}(y,s) + (1-\\alpha) \\cdot R_{\\mathrm{inter}}(y,s) , where R_{\\mathrm{intra}} guides the model to assign reliable relevance scores for each individual document, and R_{\\mathrm{inter}} incentivizes it to capture the relative rankings within a group of candidate documents. The composite reward is then optimized using the Group Relative Policy Optimization (GRPO) algorithm (Shao et al., 2024), with further analysis of the hyperparameter \\alpha provided in Appendix F.", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0034", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "In this section, we evaluate the overall performance of Retro* and the effectiveness of our detailed strategies. We focus on the following questions: 1) RQ1: How does Retro* perform in reasoningintensive IR scenarios? 2) RQ2: How does Retro*'s performance compare to other non-reasoning and reasoning-enhanced re-ranking methods? 3) RQ3: How scalable is Retro* with the size of the backbone model and the number of test-time samples? 4) RQ4: How does Retro*'s parallelism capacity impact its efficiency compared to listwise and setwise methods, particularly as the number of candidate documents grows? 5) RQ5: Does Retro*'s rubric-based scoring mechanism provide a more reliable measurement of absolute relevance strength compared to those uncalibrated baselines? 6) RQ6: How do the key components of our proposed training strategy individually and collectively contribute to the effectiveness of Retro*?", "source": "marker_v2", "marker_block_id": "/page/5/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0035", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 6, "page_end": 6, "type": "Text", "text": "Baselines and Backbone Models. Our comparison includes several leading re-ranking models, categorized as non-reasoning and reasoning-enhanced approaches. For the non-reasoning baselines, we choose the pointwise model RankLLaMA (Ma et al., 2024) and the listwise model RankZephyr (Pradeep et al., 2023) . In particular, RankLLaMA is built upon the Llama-2 (Touvron et al., 2023) , and RankZephyr is built upon the Mistral-v0.1 (Jiang et al., 2023) . For the reasoning-enhanced baselines, we compare against several powerful approaches built upon the Qwen2.5-Instruct family (Qwen et al., 2025) . These include the fine-tuned models Rank1 (Weller et al., 2025) , Rank-R1 (Zhuang et al., 2025) , and ReasonRank (Liu et al., 2025) , as well as the zero-shot method JudgeRank (Niu et al., 2024) . The details for each model are provided in Appendix B. To ensure a fair comparison, we align with the baselines by employing Qwen2.5-7B-Instruct and Qwen2.5-32B-Instruct as our backbone models. In addition, we also provide results trained on other backbone models in Appendix G.", "source": "marker_v2", "marker_block_id": "/page/5/Text/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0036", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 6, "page_end": 6, "type": "Text", "text": "Evaluation Settings. We evaluate all baselines and Retro* on the BRIGHT (Su et al., 2024) benchmark, which is designed for reasoning-intensive IR. We define the relevance following the BRIGHT benchmark and provide the detailed definitions in Appendix L. Our Retro* evaluation is conducted using the FlagEmbedding (Xiao et al., 2024) framework, and inference is accelerated with SGLang (Zheng et al., 2024a) . For simplicity, we employ a uniform weighting scheme for our score integration strategy, which we denote as mean-score@k. To provide a more challenging and comprehensive evaluation, we use the powerful BGE-Reasoner-Embed-0821 1 (BGE-Reasoner-Embed) as the firststage retriever, which is the current state-of-the-art embedding model on the BRIGHT benchmark. We utilize its publicly available search results, as they provide more positive document candidates. In our evaluation, all methods re-rank the top-100 documents retrieved by this embedder with the original query, and we report nDCG@10 as the performance metric.", "source": "marker_v2", "marker_block_id": "/page/5/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0037", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 6, "page_end": 6, "type": "Text", "text": "Training Data. We construct our training data based on the BGE-Reasoner-Data, originally released with the BGE-Reasoner-Embed model. BGE-Reasoner-Data is a synthetic, reasoning-centric retrieval dataset that covers all domains in the BRIGHT benchmark. Specifically, its queries are constructed using a document-to-query generation pipeline, where documents from each BRIGHT domain are used as source material to generate synthetic reasoning-intensive queries. These queries are then used to retrieve the candidate documents, which are finally annotated as positives or negatives using powerful LLMs. As a result, the dataset provides high-quality synthetic queries and relevance annotations, suitable for training reasoning-intensive retrieval models. From this dataset, we sample 500 queries per dataset for SFT and 1,000 queries per dataset for RL. Each query is associated with one positive and one negative document, yielding a total of 12,000 training samples for SFT and 24,000 for RL. For SFT, we obtain the reasoning trajectories from a strong teacher model, Qwen3-235B-A22B (Yang et al., 2025a) . For each training sample, we sample eight trajectories from the teacher model and train the model with only one selected trajectory. Also, we augment the original prompt template (shown in Figure 8) with an explicit instruction asking the teacher model to keep its reasoning concise within 512 tokens as described in Section 3.2.1. Generating all trajectories for SFT under this setting on 8 NVIDIA H100 GPUs takes less than 6 hours. We discuss", "source": "marker_v2", "marker_block_id": "/page/5/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0038", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 6, "page_end": 6, "type": "Footnote", "text": "1 BGE-Reasoner-Embed-0821: master/research/BGE_Reasoner", "source": "marker_v2", "marker_block_id": "/page/5/Footnote/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0039", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Table 1: Performance on BRIGHT benchmark (nDCG@10), where all methods re-rank the top-100 documents retrieved by BGE-Reasoner-Embed. Retro* achieves the leading performance, with testtime scaling further pushing its edge. Models Methods Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed Retriever 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Non-Reasoning Re-Ranking Baselines RankLLaMA (7B) Pointwise 19.7 20.8 31.7 11.1 19.1 18.2 10.9 20.0 16.7 57.9 6.3 10.3 13.4 RankLLaMA (14B) Pointwise 21.3 26.4 34.1 19.1 24.4 19.9 15.6 22.0 17.2 41.8 6.9 11.8 16.6 RankZephyr (7B) Listwise 20.8 27.1 22.7 19.9 21.9 13.2 8.6 22.3 22.1 50.6 7.8 21.3 12.4 Reasoning-Enhanced Re-Ranking Baselines JudgeRank (7B) Pointwise 12.7 14.7 16.9 10.8 9.5 7.7 7.1 10.8 11.4 16.7 5.8 9.2 31.9 JudgeRank (32B) Pointwise 17.4 21.4 26.0 13.1 12.9 10.5 15.8 16.2 19.7 19.9 5.2 16.4 31.5 Rank1 (7B) Pointwise 25.9 43.2 33.1 21.6 33.2 19.8 20.7 28.8 7.5 28.2 8.3 30.9 35.7 Rank1 (32B) Pointwise 29.7 46.0 31.5 27.2 33.9 19.5 22.8 33.1 17.2 36.2 15.8 28.2 44.6 Rank-R1 (7B) Setwise 25.8 34.9 29.7 26.8 35.5 21.6 17.5 29.4 24.2 15.6 5.8 25.1 43.1 Rank-R1 (14B) Setwise 31.8 46.6 43.3 28.9 42.2 30.3 26.5 38.0 18.5 18.5 10.9 33.9 44.0 ReasonRank (7B) Listwise 33.5 48.9 44.4 33.1 44.5 31.1 30.8 39.1 22.8 21.8 7.7 37.1 40.1 ReasonRank (32B) Listwise 36.6 54.9 50.1 38.0 49.1 35.1 35.3 44.6 23.2 15.8 10.1 39.2 44.4 Our Models Retro* (7B) Pointwise 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 Retro* (32B) Pointwise 38.5 59.4 58.3 41.8 48.3 37.0 38.4 44.1 13.9 27.8 10.3 36.6 45.7 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 38.7 58.4 59.2 35.0 49.3 33.9 37.7 41.1 18.8 33.5 10.7 40.2 46.7 Retro* (32B) Pointwise 40.6 61.4 61.3 41.7 50.8 37.8 41.9 46.8 13.5 32.0 12.2 39.7 47.8 Table 2: Performance (nDCG@10) on the BRIGHT benchmark using different first-stage retrievers: BM25, ReasonIR, where the top-100 documents are re-ranked by Retro*", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/215"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0040", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 7, "page_end": 7, "type": "Table", "text": "Models BM25 Retro* (7B) Retro* (32B) ReasonIR Retro* (7B) Retro* (32B) @1 @16 @1 @16 @1 @16 @1 @16 Avg. 27.0 35.3 37.0 36.6 38.5 30.6 36.8 38.4 37.4 39.5", "source": "marker_v2", "marker_block_id": "/page/6/Table/4"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0041", "section": "4.1 EXPERIMENTAL SETUP", "page_start": 7, "page_end": 7, "type": "Text", "text": "the impact of this length control instruction in Appendix H. The training details of SFT and RL are available in Appendix C.", "source": "marker_v2", "marker_block_id": "/page/6/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0042", "section": "4.2 MAIN RESULTS (FOR RQ1 AND RQ2)", "page_start": 7, "page_end": 7, "type": "Text", "text": "Results in Table 1 clearly demonstrate that our Retro* models achieve state-of-the-art performance on the BRIGHT benchmark. Specifically, our Retro* (7B) achieves an average nDCG@10 of 36.6, substantially outperforming all other 7B-scale non-reasoning and reasoning-enhanced baselines, and surpassing ReasonRank (7B) by 3.1 points. Scaling up to the 32B extends this lead, achieving a remarkable score of 38.5, and surpassing ReasonRank (32B) by 1.9 points.", "source": "marker_v2", "marker_block_id": "/page/6/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0043", "section": "4.2 MAIN RESULTS (FOR RQ1 AND RQ2)", "page_start": 7, "page_end": 7, "type": "Text", "text": "Furthermore, with test-time scaling, the performance of our models is further improved. Specifically, averaging over 16 sampling scores (mean-score@16) boosts the 7B model to 38.7, while enhancing the 32B model to 40.6. Notably, the scaled 7B model (38.7) not only surpasses all baselines but also exceeds the performance of our own standard 32B model (38.5), powerfully demonstrating both the effectiveness and potential of test-time scaling.", "source": "marker_v2", "marker_block_id": "/page/6/Text/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0044", "section": "4.2 MAIN RESULTS (FOR RQ1 AND RQ2)", "page_start": 7, "page_end": 7, "type": "Text", "text": "Additionally, we evaluate its performance on candidates from different first-stage retrievers, namely BM25 and ReasonIR (Shao et al., 2025) . As shown in Table 2, our model's performance remains consistent across different first-stage retrievers, which demonstrates the effectiveness and robustness of its ranking capabilities. More detailed results for BM25 and ReasonIR are provided in Appendix D. To further assess the out-of-domain generalizability of our rubric, we evaluate Retro* on R2MED (Li et al., 2025) , a biomedical reasoning retrieval benchmark that lies outside the scientific, programming, and mathematical domains used during training. We provide detailed analysis of these results in Appendix I. In addition to Retro*'s effectiveness in reasoning-intensive scenarios, we also empirically validate its generalizability on traditional IR scenarios using the BEIR (Thakur et al., 2021) , with detailed results provided in Appendix E.", "source": "marker_v2", "marker_block_id": "/page/6/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0045", "section": "4.2 MAIN RESULTS (FOR RQ1 AND RQ2)", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 3: (Left): average performance (nDCG@10) on BRIGHT benchmark. Retro*'s re-ranking performance consistently improves with increased model scale and test-time samples. (Right): inference time on the TheoT. dataset from the BRIGHT benchmark. Retro* exhibits a significantly lower time latency than other methods as the number of candidate documents increases.", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/103"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0046", "section": "4.3 Performance of Scaling (For RQ3)", "page_start": 8, "page_end": 8, "type": "Text", "text": "To investigate the scalability of Retro*, we conduct experiments under two scaling settings: scaling the model size and scaling the number of sampling trajectories at test-time.", "source": "marker_v2", "marker_block_id": "/page/7/Text/5"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0047", "section": "4.3 Performance of Scaling (For RQ3)", "page_start": 8, "page_end": 8, "type": "Text", "text": "Model Size Scaling . As shown in Figure 3, the performance of Retro* improves consistently as the model size increases. Specifically, under single-sample inference (N = 1), the nDCG@10 rises substantially from 32.4 for the 3B model to 36.6 for the 7B, and further to 38.5 for the 32B. This scaling trend remains consistent across different numbers of sampling generations. These findings highlight the scaling benefits of larger LLMs, indicating that larger and more capable LLMs exhibit stronger reasoning capabilities, enabling better comprehension of queries, more nuanced document analysis, and more accurate relevance estimates within our framework.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0048", "section": "4.3 Performance of Scaling (For RQ3)", "page_start": 8, "page_end": 8, "type": "Text", "text": "Test-Time Scaling . As shown in Figure 3, the performance of Retro* improves consistently as the number of sampling trajectories increases. Specifically, for the 7B model, nDCG@10 improves from 36.6 \\, (N=1) to 38.7 \\, (N=16) , with consistent gains at intermediate sampling steps. This scaling trend remains consistent across all model sizes. These results underscore the effectiveness of test-time scaling, demonstrating that integrating multiple reasoning trajectories leads to more accurate and reliable relevance scoring.", "source": "marker_v2", "marker_block_id": "/page/7/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0049", "section": "4.4 EFFICIENCY OF PARALLELISM (FOR RQ4)", "page_start": 8, "page_end": 8, "type": "Text", "text": "Listwise and setwise re-ranking methods have limited parallelism capabilities, leading to significant latency when processing a large group of candidate documents. This inefficiency stems directly from their inherently sequential processing nature, which lacks the capability for effective document-level batching. In contrast, the pointwise approach evaluates each query-document pair independently. This property enables massive parallelism and is inherently more efficient in terms of both inference time and throughput. To assess the practical efficiency gains from parallel processing, we compare the inference times of models with different re-ranking manners across varying numbers of candidate documents. This experiment is conducted on the TheoT. dataset using 4 NVIDIA H100 GPUs.", "source": "marker_v2", "marker_block_id": "/page/7/Text/9"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0050", "section": "4.4 EFFICIENCY OF PARALLELISM (FOR RQ4)", "page_start": 8, "page_end": 8, "type": "Text", "text": "The results presented in Figure 3 empirically confirm the benefits of this massive parallelism. Retro* demonstrates a significantly slower increase in inference time as the number of candidate documents grows. In contrast, the setwise model Rank-R1 exhibits extremely poor scalability, with inference time becoming prohibitively expensive even for a modest number of documents. Although the listwise model ReasonRank supports query-level batching, it still experiences a much steeper increase in latency. These findings demonstrate that the parallelism capability of Retro* delivers significant efficiency, making it a far more practical and scalable solution for real-world IR applications.", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0051", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 8, "page_end": 8, "type": "Text", "text": "A primary limitation of existing models is their inability to provide a direct and interpretable measurement of relevance. Although pointwise models like RankLLaMA and Rank1 can produce absolute scores, their logit-based or probability-based scores lack clear and interpretable functionality", "source": "marker_v2", "marker_block_id": "/page/7/Text/12"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0052", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 9, "page_end": 9, "type": "FigureGroup", "text": "Figure 4: Score distributions from pointwise models on a sample of positive and negative documents on the BRIGHT benchmark. The intensity of the color represents the density of scores, with darker hues indicating a larger proportion of documents are assigned scores in that range.", "source": "marker_v2", "marker_block_id": "/page/8/FigureGroup/69"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0053", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 9, "page_end": 9, "type": "TableGroup", "text": "Table 3: Ablation study on the key components of our training strategy. Models Avg. Stack Excha nge Coc ling Tl neorem-ba ased Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. Qwen2.5-7B-Instruct 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 + SFT + RL (Composite Reward) 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 15.7 20.6 7.9 27.9 36.6 + only-RL (Composite Reward) 35.1 56.7 52.9 33.2 45.1 28.1 32.5 35.8 21.2 36.3 8.6 29.8 41.0 + SFT + RL (Intra-Reward) 33.2 49.4 51.8 29.9 44.2 27.6 33.4 36.4 20.1 23.3 8.6 32.0 41.3 + SFT + RL (Inter-Reward) 30.8 43.6 48.7 30.8 36.7 25.6 28.5 37.7 13.1 28.6 5.6 30.6 40.6", "source": "marker_v2", "marker_block_id": "/page/8/TableGroup/70"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0054", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 9, "page_end": 9, "type": "FigureGroup", "text": "Figure 5: Training dynamics of Retro* (7B) during the RL stage. ( Left ): The training reward steadily increases over training steps. ( Right ): along with the improved reward, the retrieval accuracy (nDCG@10) improves consistently with the training steps.", "source": "marker_v2", "marker_block_id": "/page/8/FigureGroup/71"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0055", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 9, "page_end": 9, "type": "Text", "text": "for measuring relevance. As shown in Figure 4, this deficiency is evident. The score distributions of RankLLaMA for positive and negative documents are heavily mixed, making it impossible to establish a meaningful threshold to filter out the negative documents. Similarly, while Rank1's scores exhibit a binary tendency, a significant number of negative documents still receive high probability scores, undermining the reliability of its relevance scoring.", "source": "marker_v2", "marker_block_id": "/page/8/Text/7"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0056", "section": "4.5 SCORING OF RELEVANCE (FOR RQ5)", "page_start": 9, "page_end": 9, "type": "Text", "text": "In contrast, Retro* demonstrates a clean and consistent separation between positive and negative documents. Aligned with its explicit relevance rubric, positive documents consistently receive high scores (typically above 60), while negative documents are assigned low scores. This clear separation demonstrates that Retro* not only excels at relative ranking but also successfully provides the crucial functionality of relevance measurement, a key advantage for downstream applications.", "source": "marker_v2", "marker_block_id": "/page/8/Text/8"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0057", "section": "4.6 ABLATION STUDY (FOR RQ6)", "page_start": 9, "page_end": 9, "type": "Text", "text": "We conduct ablation studies on the 7B model to validate the contribution of each component in our training strategy. All variants follow the same training data and process as the main experiments, differing only in the component being ablated. Results are shown in the Table 3. As a baseline, the backbone Qwen2.5-7B-Instruct achieves an average nDCG@10 of 22.9 without any training. After our two-stage training with the composite reward, the performance significantly improves to 36.6.", "source": "marker_v2", "marker_block_id": "/page/8/Text/10"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0058", "section": "4.6 ABLATION STUDY (FOR RQ6)", "page_start": 10, "page_end": 10, "type": "Text", "text": "The following experiments analyze the contribution of each component to this overall improvement of 13.7 points.", "source": "marker_v2", "marker_block_id": "/page/9/Text/1"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0059", "section": "4.6 ABLATION STUDY (FOR RQ6)", "page_start": 10, "page_end": 10, "type": "Text", "text": "Effect of the Two-Stage Training. Training with SFT alone improves performance to 30.1 (+7.2), indicating that learning from the teacher model's reasoning trajectories provides the model with an initial ranking ability. In comparison, training with RL alone achieves a higher score of 35.1 (+12.2), also outperforming other baselines of similar model size, demonstrating the importance of rankingoriented rewards in enhancing the model's performance. Furthermore, training with both SFT and RL produces a better result of 36.6 (+13.7). This result indicates that combining the two stages helps the model perform more effective exploration and exploitation during the RL stage, while also demonstrating that the teacher-generated SFT trajectories are not strictly required, as smaller models trained with RL alone can already achieve competitive performance.", "source": "marker_v2", "marker_block_id": "/page/9/Text/2"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0060", "section": "4.6 ABLATION STUDY (FOR RQ6)", "page_start": 10, "page_end": 10, "type": "Text", "text": "Effect of the Composite Rewards. We analyze the contribution of both intra-reward and interreward under the full two-stage training setup. Training with intra-reward improves performance from 30.1 to 33.2, while using only the inter-reward has a limited improvement to 30.8. In contrast, combining both rewards results in a final score of 36.6. These results demonstrate that without intra-reward, the model cannot generate a reliable trajectory for a given query-document, which introduces noisy learning signals and hinders effective learning. Without inter-reward, the model struggles to distinguish between the positive and negative documents. With composite reward, the model learns more steadily, as illustrated in Figure 5, which shows that both the training reward and nDCG@10 on the BRIGHT benchmark steadily increase throughout the training process.", "source": "marker_v2", "marker_block_id": "/page/9/Text/3"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0061", "section": "5 CONCLUSION", "page_start": 10, "page_end": 10, "type": "Text", "text": "This paper proposes Retro*, a novel approach for reasoning-intensive document retrieval. Retro* introduces a rubric-based relevance scoring mechanism, which enables the LLMs to reason about the relationship between a task and a document based on well-defined criteria. Additionally, Retro* also supports test- time scaling by combining multiple reasoning trajectories via score integration, which produces more reliable relevance estimates. To optimize Retro*'s reasoning capabilities for document retrieval tasks, we propose a two-stage training strategy which includes SFT for warm up and RL with composite rewards for scoring and ranking functionalities. Empirical experiments on the BRIGHT benchmark demonstrate that Retro* outperforms existing methods and achieves state-of-the-art performance, with flexible test-time scalability and massive parallelism capability.", "source": "marker_v2", "marker_block_id": "/page/9/Text/5"}

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+      "title": "AUTHOR CONTRIBUTIONS",
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+      "title": "REFERENCES",
+      "heading_level": null,
+      "page_id": 9,
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+      "title": "OVERVIEW OF APPENDIX",
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+    {
+      "title": "A THE USE OF LLMS",
+      "heading_level": null,
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+      "polygon": [
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+      ]
+    },
+    {
+      "title": "B BASELINES",
+      "heading_level": null,
+      "page_id": 13,
+      "polygon": [
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+    {
+      "title": "C Training Detials",
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+    {
+      "title": "D Detailed BM25 and ReasonIR Results on BRIGHT",
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+    {
+      "title": "E EVALUATION ON BEIR",
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+    {
+      "title": "F ANALYSIS OF THE HYPERPARAMETER \u03b1",
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+      "page_id": 16,
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+    {
+      "title": "G DIFFERENT BACKBONE MODELS",
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+      "polygon": [
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+    },
+    {
+      "title": "H ANALYSIS OF THE LENGTH CONTROL INSTRUCTION FOR DISTILLATION",
+      "heading_level": null,
+      "page_id": 16,
+      "polygon": [
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+    {
+      "title": "I OUT-OF-DOMAIN GENERALIZATION ON R2MED",
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+    {
+      "title": "J RUBRICS OF RUBRIC-BASED RELEVANCE SCORING",
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+      "title": "K ANALYSIS OF THE NECESSITY OF REASONING",
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+      "title": "L TASK RELEVANCE DEFINITIONS FOR DIFFERENT BENCHMARKS",
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+      "title": "M REASONING EXAMPLES",
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+      "title": "Table 17: Reasoning examples of Retro* (7B) on the Sustainable Living dataset of BRIGHT.",
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iclr26/0WGl8PNMSA/model_text_v3.txt

@@ -0,0 +1,185 @@
+[p. 1 | section: ABSTRACT | type: Text]
+With the growing popularity of LLM agents and RAG, it has become increasingly important to retrieve documents that are essential for solving a task, even when their connection to the task is indirect or implicit. Addressing this problem requires fine-grained reasoning to accurately assess the relevance between the task and each candidate document. This capability, however, poses a significant challenge for existing IR techniques. Despite recent progress in reasoningenhanced IR, existing approaches still face significant challenges in applicability, scalability, and efficiency. In this work, we propose Retro*, a novel approach for reasoning-intensive document retrieval. Our method introduces a rubric-based relevance scoring mechanism, enabling the model to reason about the relationship between a task and a document based on explicitly defined criteria, whereby producing a fine-grained, interpretable relevance score. Retro* also supports testtime scaling by combining multiple reasoning trajectories via score integration, which produces more reliable relevance estimates. To optimize Retro*'s reasoning capabilities, we introduce a novel reinforcement learning algorithm tailored for its relevance scoring mechanism, which employs two composite rewards to fully exploit the trajectories of each training sample. Our experiments show that Retro* outperforms existing document retrieval methods with notable advantages, leading to state-of-the-art performance on the BRIGHT benchmark.
+
+[p. 1 | section: 1 Introduction | type: Text]
+Large language model (LLM) agents have become increasingly important for tackling complex tasks such as software engineering, mathematics, and scientific research (Chan et al., 2024; Jin et al., 2025; Wei et al., 2025; Phan et al., 2025). In these applications, retrieval-augmented generation (RAG) (Lewis et al., 2020; Gao et al., 2023) plays a crucial role, as access to external knowledge is often necessary to produce high-quality solutions. However, in many scenarios, retrieval models must identify useful documents, even when their connection to the task is indirect or implicit, which makes the retrieval process particularly challenging. For example, in software engineering, a retrieval model may need to locate programs that share similar design patterns with the target problem rather than matching exact code snippets (Jimenez et al., 2023). In mathematics, it might involve retrieving proofs derived from the same underlying theorem, even if they are expressed differently (Chen et al., 2023). Solving such tasks requires fine-grained reasoning to bridge subtle connections between the task and candidate documents. However, existing retrieval models are primarily designed to capture straightforward semantic relationships, such as matching question-answer pairs or identifying paraphrases (Lee et al., 2019; Karpukhin et al., 2020). Consequently, they often struggle with the complex reasoning required to uncover these deeper, more abstract connections.
+
+[p. 1 | section: 1 Introduction | type: Text]
+Enhancing the reasoning capabilities of LLMs for reasoning-intensive tasks is a central focus of current research. One promising strategy is test-time scaling, which guides or reinforces LLMs to
+
+[p. 1 | section: 1 Introduction | type: Footnote]
+* Core Contributors.
+
+[p. 2 | section: 1 Introduction | type: Text]
+generate long-form thoughts before arriving at a final answer at inference time (Wei et al., 2022; Jaech et al., 2024; Guo et al., 2025) . This approach also enables the LLMs to explore multiple reasoning paths, evaluate alternatives, and ultimately arrive at more accurate solutions for complex problems (Wang et al., 2022) . Inspired by these advances, recent information retrieval (IR) research has begun to leverage the reasoning capabilities of LLMs for reasoning-intensive document retrieval tasks (Su et al., 2024; Niu et al., 2024; Zhuang et al., 2025; Weller et al., 2025) . Current methods typically follow one of two paths: some directly prompt general-purpose LLMs to perform fine-grained relevance analysis, while others optimize these models with fine-tuning algorithms to elicit more structured and systematic reasoning behaviors. Despite recent progress, current approaches exhibit three key limitations in relevance-measuring functionality, test-time scalability, and parallelism:
+
+[p. 2 | section: 1 Introduction | type: ListGroup]
+Lack of relevance-measuring functionality. Many RAG applications require a specific functionality: the direct and interpretable measurement of document relevance. However, existing methods primarily provide relative ranking orders, which cannot capture the absolute level of relevance needed by downstream tasks. Inflexible test-time scalability. Existing methods mainly focus on generating a single, longform thought to reach an answer. However, they neglect the significant potential of exploring and integrating multiple reasoning paths to achieve more reliable performance. Limited parallelism capability. Existing methods, which are primarily listwise (Sun et al., 2023) or setwise (Zhuang et al., 2024) , must sequentially process the entire candidate set to produce the final retrieval result. This inherently sequential design is prone to substantial latency, especially when handling a large group of candidate documents.
+
+[p. 2 | section: 1 Introduction | type: Text]
+In this work, we propose Retro* (Retro-star), a novel LLM-based retrieval model designed for reasoning-intensive IR tasks. Distinct from existing approaches, Retro* is built on two key designs:
+
+[p. 2 | section: 1 Introduction | type: ListGroup]
+Rubric-based relevance scoring. Retro* introduces a fine-grained set of relevance rubrics, which explicitly define the relevance scores and their interpretations. Based on these rubrics, Retro* performs pointwise reasoning on the relationship between a query and its candidate documents, producing concrete relevance scores with clear, interpretable meanings. This design enables direct measurement of relevance, rather than merely providing a relative ordering of documents. Test-time scaling by score integration. Building on its rubric-based scoring, Retro* supports test-time scaling by generating multiple trajectories for each query-document pair and integrating their individual scores based on score similarity, resulting in a more reliable and stable estimate of document relevance.
+
+[p. 2 | section: 1 Introduction | type: Text]
+With these designs, Retro* can serve both relevance measuring and re-ranking applications. Furthermore, its architecture naturally supports both flexible test-time scaling and high parallelism, making it proficient at performing effective and efficient reasoning for complex retrieval problems.
+
+[p. 2 | section: 1 Introduction | type: Text]
+To bring these designs to their full potential, we introduce a novel reinforcement learning (RL) algorithm with two composite rewards to further optimize Retro*'s capabilities. The composite rewards are designed to fully exploit the trajectories of every training sample during RL training. The Intra-Document Reward guides the policy model to assign accurate relevance scores for each individual document, whereas the Inter-Document Reward incentivizes the policy model to effectively discriminate the relevant document from an irrelevant one. To stabilize the training process and provide Retro* with an initial reasoning ability, we incorporate a warm-up supervised fine-tuning (SFT) stage. This stage not only equips the model with basic reasoning skills, but also shapes the model to generate concise and well-structured thoughts before the RL stage.
+
+[p. 2 | section: 1 Introduction | type: Text]
+To evaluate the effectiveness of our training strategy and the overall performance of Retro* on reasoning-intensive IR tasks, we conduct experiments on BRIGHT (Su et al., 2024) , a comprehensive benchmark encompassing 12 datasets across science, mathematics, and programming. Experimental results demonstrate that Retro* achieves significant improvements over strong baseline methods, with substantial performance gains from the proposed test-time scaling mechanism and reinforcement learning method. To facilitate future research in this area, all resources are released at Retro-star .
+
+[p. 3 | section: 1 Introduction | type: Code]
+Here is the relevance definition... RELEVANCE_PLACEHOLDER Now given a query and a document... your mission is to perform the following steps. 1. Query Analysis: Think to reason and describe what information would... 2. Document Analysis: Discuss how the information provided by the document... 3. Relevance Annotation: ... annotate an integer score from 0 to 100. ...following guide: - 80-100 (Highly Relevant): ... - 60-80 (Relevant): ... - 40-60 (Moderately Relevant): ... - 20-40 (Slightly Relevant): ... - 0-20 (Irrelevant): ... ...conclude your entire response with the final relevance score... <score>[...]</score> Query:[Begin of Query]QUERY_INPUT[End of Query] Document:[Begin of Document]DOCUMENT_INPUT[End of Document]
+
+[p. 3 | section: 1 Introduction | type: Caption]
+Figure 1: Relevance rubric for Retro*. The Relevance Placeholder allows users to specify the definition of relevance, while a 5-level criteria ensures consistent and interpretable scoring result.
+
+[p. 3 | section: 2 RELATED WORK | type: Text]
+Reasoning Large Language Models. Enhancing the reasoning capabilities of LLMs is crucial for tackling complex tasks. Techniques such as chain-of-thought prompting (Wei et al., 2022) , which guide LLMs to reason step by step before producing the final answer, have shown significant performance gains. More advanced sampling strategies, including self-consistency (Wang et al., 2022) , tree-of-thought (Yao et al., 2023) , and Monte Carlo tree search (Xie et al., 2024) , further enhance their reasoning quality and reliability. To unlock the full potential of LLM reasoning, recent research has increasingly explored reinforcement learning, which directly optimizes the model to generate high-quality reasoning trajectories (Jaech et al., 2024; Guo et al., 2025; Yang et al., 2025a) .
+
+[p. 3 | section: 2 RELATED WORK | type: Text]
+Reasoning-enhanced IR Methods. Inspired by the recent advances in reasoning-capable LLMs, a growing body of research has begun adapting these paradigms to IR, with re-ranking tasks emerging as a primary focus. Preliminary studies have explored a variety of strategies, ranging from zeroshot prompting (Niu et al., 2024) , to distilling reasoning trajectories from powerful reasoning LLMs through supervised fine-tuning (Weller et al., 2025; Yang et al., 2025b) , and even reinforcement learning with carefully designed re-ranking rewards (Zhuang et al., 2025; Liu et al., 2025) . Despite the promising progress of these approaches, there remains a lack of effective methods for directly estimating the strength of relevance between query and document. Moreover, existing methods face limitations in terms of test-time scalability and parallelism, which significantly hinder their overall accuracy and inference efficiency.
+
+[p. 3 | section: 3 METHODOLOGY | type: Text]
+In this section, we first introduce the basic framework of Retro*, including the rubric-based mechanism for relevance scoring and the score integration strategy for test-time scaling. We then describe how we optimize Retro*'s performance by reinforcement learning with tailored rewards.
+
+[p. 3 | section: 3.1 RUBRIC-BASED RELEVANCE SCORING | type: Text]
+Retro* is designed to both measure the absolute relevance of each document and re-rank a set of candidate documents. To this end, we introduce a rubric-based scoring mechanism that guides the model to perform reasoning on the relationship between a query and its candidate documents based on a well-defined relevance rubric, yielding relevance scores with interpretable meanings.
+
+[p. 3 | section: 3.1.1 RELEVANCE RUBRIC | type: Text]
+The relevance rubric (Γ) consists of two parts. One is the Relevance Definition, where the specific intent of the retrieval task is declared in the [Relevance Placeholder]. For example, we may specify an intent to retrieve proofs that are grounded in the same underlying theorem as the input. The other one is the Scoring Criteria, which defines the scope and rules for assigning relevance scores. In
+
+[p. 4 | section: 3.1.1 RELEVANCE RUBRIC | type: FigureGroup]
+Figure 2: An overview of the two-stage training. SFT : the model is warmed up with a filtered data from a powerful teacher model. RL : the model is reinforced with the tailored composite reward.
+
+[p. 4 | section: 3.1.1 RELEVANCE RUBRIC | type: Text]
+our work, the relevance score is represented as an integer between 0 and 100, where higher scores indicate stronger relevance. The scope is partitioned into multiple intervals, each with explicit, interpretable meaning. For instance, a score within the range of 80-100 indicates that the candidate document is highly relevant and comprehensively addresses the information need of the query. An overview of the rubrics is shown in Figure 1, with the full rubrics provided in Appendix J.
+
+[p. 4 | section: 3.1.1 RELEVANCE RUBRIC | type: Text]
+Based on this well-defined rubric, Retro* is prompted to reason about the relevance between a given query (q) and a candidate document (d), generating a reasoning trajectory (y) along with a corresponding relevance score (s): Retro (\Gamma, q, d) \rightarrow (y, s) . See Appendix M for examples.
+
+[p. 4 | section: 3.1.2 TEST-TIME SCALING VIA SCORE INTEGRATION | type: Text]
+To enhance retrieval accuracy, Retro* leverages test-time scaling by sampling K times for each query-document pair, resulting in a set of reasoning trajectories: \{(y_1, s_1), \ldots, (y_K, s_K)\} . A common approach to integrate these results is majority voting, where the most frequent score is chosen as the final score. While this approach works well for highly discrete outputs, it is not appropriate in Retro*, as drawing a reliable result would require a vast number of samples, making the process computationally expensive and impractical.
+
+[p. 4 | section: 3.1.2 TEST-TIME SCALING VIA SCORE INTEGRATION | type: Text]
+To this end, we propose a Score Integration strategy in a simple yet effective way: \bar{s} \leftarrow \sum_K w_i * s_i / \sum_K w_i , where s_i is the relevance score from the i-th trajectory and w_i is its associated weight. The weights can be set based on the generation likelihood of each trajectory. When likelihoods are unavailable or just for simplicity, a uniform weighting scheme, w_i = 1/K , can be used.
+
+[p. 4 | section: 3.2 Training Strategy | type: Text]
+To optimize Retro*'s reasoning capabilities for reasoning-intensive document retrieval tasks, we propose a two-stage training strategy. The process starts with a supervised fine-tuning (SFT) stage to warm up the model, followed by a reinforcement learning (RL) stage for further performance enhancement. The overview of the training strategy is illustrated in Figure 2.
+
+[p. 4 | section: 3.2.1 Supervised Fine-Tuning | type: Text]
+In the first stage, we perform SFT to equip the model with an initial reasoning ability and shape the model to generate concise and well-structured thoughts. The key of this stage lies in our approach to Training Data Curation , which involves two crucial steps:
+
+[p. 5 | section: 3.2.1 Supervised Fine-Tuning | type: Text]
+Data Sourcing. We begin with a collection of query-document pairs \{(q,d)_1,\ldots,(q,d)_M\} . For each pair, we leverage a powerful teacher model \mathbb T to reason about the relationship between q and d based on our relevance rubric: \mathbb T(\Gamma,q,d)\to (y,s) . Besides, the teacher model is also guided to keep its thoughts concise, with an explicit length control instruction.
+
+[p. 5 | section: 3.2.1 Supervised Fine-Tuning | type: Text]
+Data Filtering . To obtain high-quality training data, we filter the raw trajectories with score integration. Specifically, we sample the teacher model K times for each query-document pair, resulting in a group of raw trajectories \{(y_1, s_1), \ldots, (y_K, s_K)\} . We then integrate these scores to a score \bar{s} , as it serves as a reliable reference. Finally, the trajectory whose score is closest to \bar{s} is selected, so that only one trajectory is used for each query-document pair, resulting in a curated dataset for SFT training: \{(q, d, \hat{y}, \hat{s})_1, \ldots (q, d, \hat{y}, \hat{s})_M\} , where (\hat{y}, \hat{s}) is the selected trajectory.
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Text]
+In the second stage, we take the SFT model as the initial policy model and perform RL to further optimize its reasoning capability. As discussed earlier, Retro* is designed to achieve two key functionalities: accurately scoring the absolute relevance of individual documents and correctly ranking them by assigning higher scores to more relevant ones. To jointly optimize these functionalities, we introduce a composite reward that fully exploits the trajectories of each training sample during RL.
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Text]
+Intra-Document Reward. Intra-document reward is designed to improve the scoring accuracy for each individual document. It incentivizes the model to generate high-quality reasoning trajectories that produce stable and accurate relevance scores for the same query-document pair across multiple attempts. To this end, the reward is computed in two steps. 1) Rolling Out: For each query-document pair (q,d), the model rolls out N trajectories: \{(y_1,s_1),\ldots,(y_N,s_N)\} . 2) Reward Assignment: The integrated score \bar{s} over all trajectories presents a more reliable result than each individual score in expectation. As such, the trajectories with scores closer to \bar{s} are preferred, while those deviating further from \bar{s} are disfavored. For simplicity and robustness, we adopt a ternary function, where the trajectory with the closest score is assigned a reward +1, the furthest one is assigned -1, while the others are assigned 0. To prune the trivial cases where all trajectories already reach an agreement, we also introduce a threshold \tau requiring a minimum gap between \bar{s} and the furthest deviate score. The above reward is formulated as the following function:
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Equation]
+R_{\mathrm{intra}}(y,s) = \begin{cases} +1 & \text{if } s \text{ is closest to } \bar{s}, \text{ and the threshold } \tau \text{ constraints holds} \\ -1 & \text{if } s \text{ is furthest from } \bar{s}, \text{ and the threshold } \tau \text{ constraints holds} \end{cases}. \tag{1}
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Text]
+Inter-Document Reward. Inter-document reward focuses on improving the reranking performance for a group of candidate documents. It incentivizes the model to assign higher relevance scores to more relevant documents, thereby resulting in a correct ranking for a given task. In our work, we sample one positive (d^+) and one negative (d^-) document from the candidate set for each query, and the reward is computed via the following steps: 1) Rolling Out: For each document d \in \{d^+, d^-\} , the model rolls out N trajectories: \{(y_1^d, s_1^d), \dots, (y_N^d, s_N^d) \mid d \in \{d^+, d^-\}\} . 2) Reward Assignment: The trajectories of both positive and negative samples are evaluated based on whether their scores correctly reflect the ranking. For a positive sample's trajectory (y_i^+, s_i^+) , the reward is the proportion of negative ones whose scores are dominated by s_i^+ . Conversely, for a negative sample's trajectory (y_j^-, s_j^-) , the reward is the proportion of positive ones whose scores dominate s_j^- . These relationships are formally defined by the following equations:
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Equation]
+R_{\text{inter}}(y_i^+, s_i^+) = \frac{1}{N} \sum_{j=1}^N \mathbb{I}(s_i^+ > s_j^-), \quad R_{\text{inter}}(y_j^-, s_j^-) = \frac{1}{N} \sum_{i=1}^N \mathbb{I}(s_j^- < s_i^+), \tag{2}
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Text]
+where \mathbb{I}(\cdot) is the indicator function, and N is the number of trajectories for each q-d sample.
+
+[p. 5 | section: 3.2.2 REINFORCEMENT LEARNING | type: Text]
+The intra-document reward and inter-document reward are combined with a parameter \alpha \in (0,1) to obtain the composite reward: R(y,s) = \alpha \cdot R_{\mathrm{intra}}(y,s) + (1-\alpha) \cdot R_{\mathrm{inter}}(y,s) , where R_{\mathrm{intra}} guides the model to assign reliable relevance scores for each individual document, and R_{\mathrm{inter}} incentivizes it to capture the relative rankings within a group of candidate documents. The composite reward is then optimized using the Group Relative Policy Optimization (GRPO) algorithm (Shao et al., 2024), with further analysis of the hyperparameter \alpha provided in Appendix F.
+
+[p. 6 | section: 4 EXPERIMENTS | type: Text]
+In this section, we evaluate the overall performance of Retro* and the effectiveness of our detailed strategies. We focus on the following questions: 1) RQ1: How does Retro* perform in reasoningintensive IR scenarios? 2) RQ2: How does Retro*'s performance compare to other non-reasoning and reasoning-enhanced re-ranking methods? 3) RQ3: How scalable is Retro* with the size of the backbone model and the number of test-time samples? 4) RQ4: How does Retro*'s parallelism capacity impact its efficiency compared to listwise and setwise methods, particularly as the number of candidate documents grows? 5) RQ5: Does Retro*'s rubric-based scoring mechanism provide a more reliable measurement of absolute relevance strength compared to those uncalibrated baselines? 6) RQ6: How do the key components of our proposed training strategy individually and collectively contribute to the effectiveness of Retro*?
+
+[p. 6 | section: 4.1 EXPERIMENTAL SETUP | type: Text]
+Baselines and Backbone Models. Our comparison includes several leading re-ranking models, categorized as non-reasoning and reasoning-enhanced approaches. For the non-reasoning baselines, we choose the pointwise model RankLLaMA (Ma et al., 2024) and the listwise model RankZephyr (Pradeep et al., 2023) . In particular, RankLLaMA is built upon the Llama-2 (Touvron et al., 2023) , and RankZephyr is built upon the Mistral-v0.1 (Jiang et al., 2023) . For the reasoning-enhanced baselines, we compare against several powerful approaches built upon the Qwen2.5-Instruct family (Qwen et al., 2025) . These include the fine-tuned models Rank1 (Weller et al., 2025) , Rank-R1 (Zhuang et al., 2025) , and ReasonRank (Liu et al., 2025) , as well as the zero-shot method JudgeRank (Niu et al., 2024) . The details for each model are provided in Appendix B. To ensure a fair comparison, we align with the baselines by employing Qwen2.5-7B-Instruct and Qwen2.5-32B-Instruct as our backbone models. In addition, we also provide results trained on other backbone models in Appendix G.
+
+[p. 6 | section: 4.1 EXPERIMENTAL SETUP | type: Text]
+Evaluation Settings. We evaluate all baselines and Retro* on the BRIGHT (Su et al., 2024) benchmark, which is designed for reasoning-intensive IR. We define the relevance following the BRIGHT benchmark and provide the detailed definitions in Appendix L. Our Retro* evaluation is conducted using the FlagEmbedding (Xiao et al., 2024) framework, and inference is accelerated with SGLang (Zheng et al., 2024a) . For simplicity, we employ a uniform weighting scheme for our score integration strategy, which we denote as mean-score@k. To provide a more challenging and comprehensive evaluation, we use the powerful BGE-Reasoner-Embed-0821 1 (BGE-Reasoner-Embed) as the firststage retriever, which is the current state-of-the-art embedding model on the BRIGHT benchmark. We utilize its publicly available search results, as they provide more positive document candidates. In our evaluation, all methods re-rank the top-100 documents retrieved by this embedder with the original query, and we report nDCG@10 as the performance metric.
+
+[p. 6 | section: 4.1 EXPERIMENTAL SETUP | type: Text]
+Training Data. We construct our training data based on the BGE-Reasoner-Data, originally released with the BGE-Reasoner-Embed model. BGE-Reasoner-Data is a synthetic, reasoning-centric retrieval dataset that covers all domains in the BRIGHT benchmark. Specifically, its queries are constructed using a document-to-query generation pipeline, where documents from each BRIGHT domain are used as source material to generate synthetic reasoning-intensive queries. These queries are then used to retrieve the candidate documents, which are finally annotated as positives or negatives using powerful LLMs. As a result, the dataset provides high-quality synthetic queries and relevance annotations, suitable for training reasoning-intensive retrieval models. From this dataset, we sample 500 queries per dataset for SFT and 1,000 queries per dataset for RL. Each query is associated with one positive and one negative document, yielding a total of 12,000 training samples for SFT and 24,000 for RL. For SFT, we obtain the reasoning trajectories from a strong teacher model, Qwen3-235B-A22B (Yang et al., 2025a) . For each training sample, we sample eight trajectories from the teacher model and train the model with only one selected trajectory. Also, we augment the original prompt template (shown in Figure 8) with an explicit instruction asking the teacher model to keep its reasoning concise within 512 tokens as described in Section 3.2.1. Generating all trajectories for SFT under this setting on 8 NVIDIA H100 GPUs takes less than 6 hours. We discuss
+
+[p. 6 | section: 4.1 EXPERIMENTAL SETUP | type: Footnote]
+1 BGE-Reasoner-Embed-0821: master/research/BGE_Reasoner
+
+[p. 7 | section: 4.1 EXPERIMENTAL SETUP | type: TableGroup]
+Table 1: Performance on BRIGHT benchmark (nDCG@10), where all methods re-rank the top-100 documents retrieved by BGE-Reasoner-Embed. Retro* achieves the leading performance, with testtime scaling further pushing its edge. Models Methods Avg. StackExchange Coding Theorem-based Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. BGE-Reasoner-Embed Retriever 32.5 42.6 42.6 27.8 37.3 26.4 29.6 30.6 36.9 25.7 9.8 34.9 46.1 Non-Reasoning Re-Ranking Baselines RankLLaMA (7B) Pointwise 19.7 20.8 31.7 11.1 19.1 18.2 10.9 20.0 16.7 57.9 6.3 10.3 13.4 RankLLaMA (14B) Pointwise 21.3 26.4 34.1 19.1 24.4 19.9 15.6 22.0 17.2 41.8 6.9 11.8 16.6 RankZephyr (7B) Listwise 20.8 27.1 22.7 19.9 21.9 13.2 8.6 22.3 22.1 50.6 7.8 21.3 12.4 Reasoning-Enhanced Re-Ranking Baselines JudgeRank (7B) Pointwise 12.7 14.7 16.9 10.8 9.5 7.7 7.1 10.8 11.4 16.7 5.8 9.2 31.9 JudgeRank (32B) Pointwise 17.4 21.4 26.0 13.1 12.9 10.5 15.8 16.2 19.7 19.9 5.2 16.4 31.5 Rank1 (7B) Pointwise 25.9 43.2 33.1 21.6 33.2 19.8 20.7 28.8 7.5 28.2 8.3 30.9 35.7 Rank1 (32B) Pointwise 29.7 46.0 31.5 27.2 33.9 19.5 22.8 33.1 17.2 36.2 15.8 28.2 44.6 Rank-R1 (7B) Setwise 25.8 34.9 29.7 26.8 35.5 21.6 17.5 29.4 24.2 15.6 5.8 25.1 43.1 Rank-R1 (14B) Setwise 31.8 46.6 43.3 28.9 42.2 30.3 26.5 38.0 18.5 18.5 10.9 33.9 44.0 ReasonRank (7B) Listwise 33.5 48.9 44.4 33.1 44.5 31.1 30.8 39.1 22.8 21.8 7.7 37.1 40.1 ReasonRank (32B) Listwise 36.6 54.9 50.1 38.0 49.1 35.1 35.3 44.6 23.2 15.8 10.1 39.2 44.4 Our Models Retro* (7B) Pointwise 36.6 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 Retro* (32B) Pointwise 38.5 59.4 58.3 41.8 48.3 37.0 38.4 44.1 13.9 27.8 10.3 36.6 45.7 Test-Time Scaling (Mean-Score@16) Retro* (7B) Pointwise 38.7 58.4 59.2 35.0 49.3 33.9 37.7 41.1 18.8 33.5 10.7 40.2 46.7 Retro* (32B) Pointwise 40.6 61.4 61.3 41.7 50.8 37.8 41.9 46.8 13.5 32.0 12.2 39.7 47.8 Table 2: Performance (nDCG@10) on the BRIGHT benchmark using different first-stage retrievers: BM25, ReasonIR, where the top-100 documents are re-ranked by Retro*
+
+[p. 7 | section: 4.1 EXPERIMENTAL SETUP | type: Table]
+Models BM25 Retro* (7B) Retro* (32B) ReasonIR Retro* (7B) Retro* (32B) @1 @16 @1 @16 @1 @16 @1 @16 Avg. 27.0 35.3 37.0 36.6 38.5 30.6 36.8 38.4 37.4 39.5
+
+[p. 7 | section: 4.1 EXPERIMENTAL SETUP | type: Text]
+the impact of this length control instruction in Appendix H. The training details of SFT and RL are available in Appendix C.
+
+[p. 7 | section: 4.2 MAIN RESULTS (FOR RQ1 AND RQ2) | type: Text]
+Results in Table 1 clearly demonstrate that our Retro* models achieve state-of-the-art performance on the BRIGHT benchmark. Specifically, our Retro* (7B) achieves an average nDCG@10 of 36.6, substantially outperforming all other 7B-scale non-reasoning and reasoning-enhanced baselines, and surpassing ReasonRank (7B) by 3.1 points. Scaling up to the 32B extends this lead, achieving a remarkable score of 38.5, and surpassing ReasonRank (32B) by 1.9 points.
+
+[p. 7 | section: 4.2 MAIN RESULTS (FOR RQ1 AND RQ2) | type: Text]
+Furthermore, with test-time scaling, the performance of our models is further improved. Specifically, averaging over 16 sampling scores (mean-score@16) boosts the 7B model to 38.7, while enhancing the 32B model to 40.6. Notably, the scaled 7B model (38.7) not only surpasses all baselines but also exceeds the performance of our own standard 32B model (38.5), powerfully demonstrating both the effectiveness and potential of test-time scaling.
+
+[p. 7 | section: 4.2 MAIN RESULTS (FOR RQ1 AND RQ2) | type: Text]
+Additionally, we evaluate its performance on candidates from different first-stage retrievers, namely BM25 and ReasonIR (Shao et al., 2025) . As shown in Table 2, our model's performance remains consistent across different first-stage retrievers, which demonstrates the effectiveness and robustness of its ranking capabilities. More detailed results for BM25 and ReasonIR are provided in Appendix D. To further assess the out-of-domain generalizability of our rubric, we evaluate Retro* on R2MED (Li et al., 2025) , a biomedical reasoning retrieval benchmark that lies outside the scientific, programming, and mathematical domains used during training. We provide detailed analysis of these results in Appendix I. In addition to Retro*'s effectiveness in reasoning-intensive scenarios, we also empirically validate its generalizability on traditional IR scenarios using the BEIR (Thakur et al., 2021) , with detailed results provided in Appendix E.
+
+[p. 8 | section: 4.2 MAIN RESULTS (FOR RQ1 AND RQ2) | type: FigureGroup]
+Figure 3: (Left): average performance (nDCG@10) on BRIGHT benchmark. Retro*'s re-ranking performance consistently improves with increased model scale and test-time samples. (Right): inference time on the TheoT. dataset from the BRIGHT benchmark. Retro* exhibits a significantly lower time latency than other methods as the number of candidate documents increases.
+
+[p. 8 | section: 4.3 Performance of Scaling (For RQ3) | type: Text]
+To investigate the scalability of Retro*, we conduct experiments under two scaling settings: scaling the model size and scaling the number of sampling trajectories at test-time.
+
+[p. 8 | section: 4.3 Performance of Scaling (For RQ3) | type: Text]
+Model Size Scaling . As shown in Figure 3, the performance of Retro* improves consistently as the model size increases. Specifically, under single-sample inference (N = 1), the nDCG@10 rises substantially from 32.4 for the 3B model to 36.6 for the 7B, and further to 38.5 for the 32B. This scaling trend remains consistent across different numbers of sampling generations. These findings highlight the scaling benefits of larger LLMs, indicating that larger and more capable LLMs exhibit stronger reasoning capabilities, enabling better comprehension of queries, more nuanced document analysis, and more accurate relevance estimates within our framework.
+
+[p. 8 | section: 4.3 Performance of Scaling (For RQ3) | type: Text]
+Test-Time Scaling . As shown in Figure 3, the performance of Retro* improves consistently as the number of sampling trajectories increases. Specifically, for the 7B model, nDCG@10 improves from 36.6 \, (N=1) to 38.7 \, (N=16) , with consistent gains at intermediate sampling steps. This scaling trend remains consistent across all model sizes. These results underscore the effectiveness of test-time scaling, demonstrating that integrating multiple reasoning trajectories leads to more accurate and reliable relevance scoring.
+
+[p. 8 | section: 4.4 EFFICIENCY OF PARALLELISM (FOR RQ4) | type: Text]
+Listwise and setwise re-ranking methods have limited parallelism capabilities, leading to significant latency when processing a large group of candidate documents. This inefficiency stems directly from their inherently sequential processing nature, which lacks the capability for effective document-level batching. In contrast, the pointwise approach evaluates each query-document pair independently. This property enables massive parallelism and is inherently more efficient in terms of both inference time and throughput. To assess the practical efficiency gains from parallel processing, we compare the inference times of models with different re-ranking manners across varying numbers of candidate documents. This experiment is conducted on the TheoT. dataset using 4 NVIDIA H100 GPUs.
+
+[p. 8 | section: 4.4 EFFICIENCY OF PARALLELISM (FOR RQ4) | type: Text]
+The results presented in Figure 3 empirically confirm the benefits of this massive parallelism. Retro* demonstrates a significantly slower increase in inference time as the number of candidate documents grows. In contrast, the setwise model Rank-R1 exhibits extremely poor scalability, with inference time becoming prohibitively expensive even for a modest number of documents. Although the listwise model ReasonRank supports query-level batching, it still experiences a much steeper increase in latency. These findings demonstrate that the parallelism capability of Retro* delivers significant efficiency, making it a far more practical and scalable solution for real-world IR applications.
+
+[p. 8 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: Text]
+A primary limitation of existing models is their inability to provide a direct and interpretable measurement of relevance. Although pointwise models like RankLLaMA and Rank1 can produce absolute scores, their logit-based or probability-based scores lack clear and interpretable functionality
+
+[p. 9 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: FigureGroup]
+Figure 4: Score distributions from pointwise models on a sample of positive and negative documents on the BRIGHT benchmark. The intensity of the color represents the density of scores, with darker hues indicating a larger proportion of documents are assigned scores in that range.
+
+[p. 9 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: TableGroup]
+Table 3: Ablation study on the key components of our training strategy. Models Avg. Stack Excha nge Coc ling Tl neorem-ba ased Bio. Earth. Econ. Psy. Rob. Stack. Sus. Leet. Pony AoPS TheoQ. TheoT. Qwen2.5-7B-Instruct 39.9 41.2 21.0 31.4 17.0 16.9 22.7 12.1 15.7 3.9 14.2 38.7 + SFT + RL (Composite Reward) 53.7 55.9 35.6 47.9 34.0 35.6 39.3 17.6 29.8 9.6 35.4 45.0 + only-SFT 30.1 46.9 51.3 29.1 37.4 24.4 28.4 35.0 15.7 20.6 7.9 27.9 36.6 + only-RL (Composite Reward) 35.1 56.7 52.9 33.2 45.1 28.1 32.5 35.8 21.2 36.3 8.6 29.8 41.0 + SFT + RL (Intra-Reward) 33.2 49.4 51.8 29.9 44.2 27.6 33.4 36.4 20.1 23.3 8.6 32.0 41.3 + SFT + RL (Inter-Reward) 30.8 43.6 48.7 30.8 36.7 25.6 28.5 37.7 13.1 28.6 5.6 30.6 40.6
+
+[p. 9 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: FigureGroup]
+Figure 5: Training dynamics of Retro* (7B) during the RL stage. ( Left ): The training reward steadily increases over training steps. ( Right ): along with the improved reward, the retrieval accuracy (nDCG@10) improves consistently with the training steps.
+
+[p. 9 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: Text]
+for measuring relevance. As shown in Figure 4, this deficiency is evident. The score distributions of RankLLaMA for positive and negative documents are heavily mixed, making it impossible to establish a meaningful threshold to filter out the negative documents. Similarly, while Rank1's scores exhibit a binary tendency, a significant number of negative documents still receive high probability scores, undermining the reliability of its relevance scoring.
+
+[p. 9 | section: 4.5 SCORING OF RELEVANCE (FOR RQ5) | type: Text]
+In contrast, Retro* demonstrates a clean and consistent separation between positive and negative documents. Aligned with its explicit relevance rubric, positive documents consistently receive high scores (typically above 60), while negative documents are assigned low scores. This clear separation demonstrates that Retro* not only excels at relative ranking but also successfully provides the crucial functionality of relevance measurement, a key advantage for downstream applications.
+
+[p. 9 | section: 4.6 ABLATION STUDY (FOR RQ6) | type: Text]
+We conduct ablation studies on the 7B model to validate the contribution of each component in our training strategy. All variants follow the same training data and process as the main experiments, differing only in the component being ablated. Results are shown in the Table 3. As a baseline, the backbone Qwen2.5-7B-Instruct achieves an average nDCG@10 of 22.9 without any training. After our two-stage training with the composite reward, the performance significantly improves to 36.6.
+
+[p. 10 | section: 4.6 ABLATION STUDY (FOR RQ6) | type: Text]
+The following experiments analyze the contribution of each component to this overall improvement of 13.7 points.
+
+[p. 10 | section: 4.6 ABLATION STUDY (FOR RQ6) | type: Text]
+Effect of the Two-Stage Training. Training with SFT alone improves performance to 30.1 (+7.2), indicating that learning from the teacher model's reasoning trajectories provides the model with an initial ranking ability. In comparison, training with RL alone achieves a higher score of 35.1 (+12.2), also outperforming other baselines of similar model size, demonstrating the importance of rankingoriented rewards in enhancing the model's performance. Furthermore, training with both SFT and RL produces a better result of 36.6 (+13.7). This result indicates that combining the two stages helps the model perform more effective exploration and exploitation during the RL stage, while also demonstrating that the teacher-generated SFT trajectories are not strictly required, as smaller models trained with RL alone can already achieve competitive performance.
+
+[p. 10 | section: 4.6 ABLATION STUDY (FOR RQ6) | type: Text]
+Effect of the Composite Rewards. We analyze the contribution of both intra-reward and interreward under the full two-stage training setup. Training with intra-reward improves performance from 30.1 to 33.2, while using only the inter-reward has a limited improvement to 30.8. In contrast, combining both rewards results in a final score of 36.6. These results demonstrate that without intra-reward, the model cannot generate a reliable trajectory for a given query-document, which introduces noisy learning signals and hinders effective learning. Without inter-reward, the model struggles to distinguish between the positive and negative documents. With composite reward, the model learns more steadily, as illustrated in Figure 5, which shows that both the training reward and nDCG@10 on the BRIGHT benchmark steadily increase throughout the training process.
+
+[p. 10 | section: 5 CONCLUSION | type: Text]
+This paper proposes Retro*, a novel approach for reasoning-intensive document retrieval. Retro* introduces a rubric-based relevance scoring mechanism, which enables the LLMs to reason about the relationship between a task and a document based on well-defined criteria. Additionally, Retro* also supports test- time scaling by combining multiple reasoning trajectories via score integration, which produces more reliable relevance estimates. To optimize Retro*'s reasoning capabilities for document retrieval tasks, we propose a two-stage training strategy which includes SFT for warm up and RL with composite rewards for scoring and ranking functionalities. Empirical experiments on the BRIGHT benchmark demonstrate that Retro* outperforms existing methods and achieves state-of-the-art performance, with flexible test-time scalability and massive parallelism capability.

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+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0066", "section": "REFERENCES", "page_start": 12, "page_end": 12, "type": "ListGroup", "text": "Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Advances in neural information processing systems , 35: 27730–27744, 2022. Long Phan, Alice Gatti, Ziwen Han, Nathaniel Li, Josephina Hu, Hugh Zhang, Chen Bo Calvin Zhang, Mohamed Shaaban, John Ling, Sean Shi, et al. Humanity's last exam. arXiv preprint arXiv:2501.14249 , 2025. Ronak Pradeep, Sahel Sharifymoghaddam, and Jimmy Lin. Rankzephyr: Effective and robust zeroshot listwise reranking is a breeze! arXiv preprint arXiv:2312.02724 , 2023. Qwen, :, An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tianyi Tang, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 technical report, 2025. URL . Rulin Shao, Rui Qiao, Varsha Kishore, Niklas Muennighoff, Xi Victoria Lin, Daniela Rus, Bryan Kian Hsiang Low, Sewon Min, Wen-tau Yih, Pang Wei Koh, et al. Reasonir: Training retrievers for reasoning tasks. arXiv preprint arXiv:2504.20595 , 2025. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300 , 2024. Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. Hybridflow: A flexible and efficient rlhf framework. In Proceedings of the Twentieth European Conference on Computer Systems , pp. 1279–1297, 2025. Hongjin Su, Howard Yen, Mengzhou Xia, Weijia Shi, Niklas Muennighoff, Han-yu Wang, Haisu Liu, Quan Shi, Zachary S Siegel, Michael Tang, et al. Bright: A realistic and challenging benchmark for reasoning-intensive retrieval. arXiv preprint arXiv:2407.12883 , 2024. Weiwei Sun, Lingyong Yan, Xinyu Ma, Shuaiqiang Wang, Pengjie Ren, Zhumin Chen, Dawei Yin, and Zhaochun Ren. Is chatgpt good at search? investigating large language models as re-ranking agents. arXiv preprint arXiv:2304.09542 , 2023. Nandan Thakur, Nils Reimers, Andreas Rücklé, Abhishek Srivastava, and Iryna Gurevych. Beir: A heterogenous benchmark for zero-shot evaluation of information retrieval models. arXiv preprint arXiv:2104.08663 , 2021. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288 , 2023. Liang Wang, Nan Yang, Xiaolong Huang, Linjun Yang, Rangan Majumder, and Furu Wei. Improving text embeddings with large language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pp. 11897–11916, 2024. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171 , 2022. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems , 35:24824–24837, 2022. Jason Wei, Zhiqing Sun, Spencer Papay, Scott McKinney, Jeffrey Han, Isa Fulford, Hyung Won Chung, Alex Tachard Passos, William Fedus, and Amelia Glaese. Browsecomp: A simple yet challenging benchmark for browsing agents, 2025. URL 12516 .", "source": "marker_v2", "marker_block_id": "/page/11/ListGroup/207"}
+{"paper_id": "0WGl8PNMSA", "chunk_id": "0WGl8PNMSA:0067", "section": "REFERENCES", "page_start": 13, "page_end": 13, "type": "ListGroup", "text": "Orion Weller, Kathryn Ricci, Eugene Yang, Andrew Yates, Dawn Lawrie, and Benjamin Van Durme. Rank1: Test-time compute for reranking in information retrieval. arXiv preprint arXiv:2502.18418 , 2025. Shitao Xiao, Zheng Liu, Peitian Zhang, Niklas Muennighoff, Defu Lian, and Jian-Yun Nie. C-pack: Packed resources for general chinese embeddings. In Proceedings of the 47th international ACM SIGIR conference on research and development in information retrieval , pp. 641–649, 2024. Yuxi Xie, Anirudh Goyal, Wenyue Zheng, Min-Yen Kan, Timothy P Lillicrap, Kenji Kawaguchi, and Michael Shieh. Monte carlo tree search boosts reasoning via iterative preference learning. arXiv preprint arXiv:2405.00451 , 2024. An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388 , 2025a. Eugene Yang, Andrew Yates, Kathryn Ricci, Orion Weller, Vivek Chari, Benjamin Van Durme, and Dawn Lawrie. Rank-k: Test-time reasoning for listwise reranking. arXiv preprint arXiv:2505.14432 , 2025b. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad vances in neural information processing systems , 36:11809–11822, 2023. Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Livia Sun, Jeff Huang, Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E Gonzalez, et al. Sglang: Efficient execution of structured language model programs. Advances in neural information processing systems , 37: 62557–62583, 2024a. Yaowei Zheng, Richong Zhang, Junhao Zhang, Yanhan Ye, Zheyan Luo, Zhangchi Feng, and Yongqiang Ma. Llamafactory: Unified efficient fine-tuning of 100+ language models. arXiv preprint arXiv:2403.13372 , 2024b. Shengyao Zhuang, Honglei Zhuang, Bevan Koopman, and Guido Zuccon. A setwise approach for effective and highly efficient zero-shot ranking with large language models. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval , pp. 38–47, 2024. Shengyao Zhuang, Xueguang Ma, Bevan Koopman, Jimmy Lin, and Guido Zuccon. Rank-r1: Enhancing reasoning in llm-based document rerankers via reinforcement learning. arXiv preprint arXiv:2503.06034 , 2025.", "source": "marker_v2", "marker_block_id": "/page/12/ListGroup/139"}

iclr26/0WGl8PNMSA/reference_text_v3.txt

@@ -0,0 +1,17 @@
+[p. 10 | section: REFERENCES | type: Text]
+Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774 , 2023.
+
+[p. 10 | section: REFERENCES | type: Text]
+Payal Bajaj, Daniel Campos, Nick Craswell, Li Deng, Jianfeng Gao, Xiaodong Liu, Rangan Majumder, Andrew McNamara, Bhaskar Mitra, Tri Nguyen, et al. Ms marco: A human generated machine reading comprehension dataset. arXiv preprint arXiv:1611.09268 , 2016.
+
+[p. 10 | section: REFERENCES | type: Text]
+Jun Shern Chan, Neil Chowdhury, Oliver Jaffe, James Aung, Dane Sherburn, Evan Mays, Giulio Starace, Kevin Liu, Leon Maksin, Tejal Patwardhan, et al. Mle-bench: Evaluating machine learning agents on machine learning engineering. arXiv preprint arXiv:2410.07095 , 2024.
+
+[p. 11 | section: REFERENCES | type: ListGroup]
+Wenhu Chen, Ming Yin, Max Ku, Pan Lu, Yixin Wan, Xueguang Ma, Jianyu Xu, Xinyi Wang, and Tony Xia. Theoremqa: A theorem-driven question answering dataset. arXiv preprint arXiv:2305.12524 , 2023. Yunfan Gao, Yun Xiong, Xinyu Gao, Kangxiang Jia, Jinliu Pan, Yuxi Bi, Yixin Dai, Jiawei Sun, Haofen Wang, and Haofen Wang. Retrieval-augmented generation for large language models: A survey. arXiv preprint arXiv:2312.10997 , 2(1), 2023. Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948 , 2025. Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai o1 system card. arXiv preprint arXiv:2412.16720 , 2024. Albert Q. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, Lélio Renard Lavaud, Marie-Anne Lachaux, Pierre Stock, Teven Le Scao, Thibaut Lavril, Thomas Wang, Timothée Lacroix, and William El Sayed. Mistral 7b, 2023. URL https: //arxiv.org/abs/2310.06825 . Carlos E Jimenez, John Yang, Alexander Wettig, Shunyu Yao, Kexin Pei, Ofir Press, and Karthik Narasimhan. Swe-bench: Can language models resolve real-world github issues? arXiv preprint arXiv:2310.06770 , 2023. Bowen Jin, Hansi Zeng, Zhenrui Yue, Jinsung Yoon, Sercan Arik, Dong Wang, Hamed Zamani, and Jiawei Han. Search-r1: Training llms to reason and leverage search engines with reinforcement learning. arXiv preprint arXiv:2503.09516 , 2025. Vladimir Karpukhin, Barlas Oguz, Sewon Min, Patrick SH Lewis, Ledell Wu, Sergey Edunov, Danqi Chen, and Wen-tau Yih. Dense passage retrieval for open-domain question answering. In EMNLP (1) , pp. 6769–6781, 2020. Kenton Lee, Ming-Wei Chang, and Kristina Toutanova. Latent retrieval for weakly supervised open domain question answering. arXiv preprint arXiv:1906.00300 , 2019. Patrick Lewis, Ethan Perez, Aleksandra Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Küttler, Mike Lewis, Wen-tau Yih, Tim Rocktäschel, et al. Retrieval-augmented generation for knowledge-intensive nlp tasks. Advances in neural information processing systems , 33: 9459–9474, 2020. Lei Li, Xiao Zhou, and Zheng Liu. R2med: A benchmark for reasoning-driven medical retrieval. arXiv preprint arXiv:2505.14558 , 2025. Jimmy Lin, Xueguang Ma, Sheng-Chieh Lin, Jheng-Hong Yang, Ronak Pradeep, and Rodrigo Nogueira. Pyserini: A python toolkit for reproducible information retrieval research with sparse and dense representations. In Proceedings of the 44th international ACM SIGIR conference on research and development in information retrieval , pp. 2356–2362, 2021. Wenhan Liu, Xinyu Ma, Weiwei Sun, Yutao Zhu, Yuchen Li, Dawei Yin, and Zhicheng Dou. Reasonrank: Empowering passage ranking with strong reasoning ability. arXiv preprint arXiv:2508.07050 , 2025. Xueguang Ma, Liang Wang, Nan Yang, Furu Wei, and Jimmy Lin. Fine-tuning llama for multi-stage text retrieval. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval , pp. 2421–2425, 2024. Tong Niu, Shafiq Joty, Ye Liu, Caiming Xiong, Yingbo Zhou, and Semih Yavuz. Judgerank: Leveraging large language models for reasoning-intensive reranking. arXiv preprint arXiv:2411.00142 , 2024.
+
+[p. 12 | section: REFERENCES | type: ListGroup]
+Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Advances in neural information processing systems , 35: 27730–27744, 2022. Long Phan, Alice Gatti, Ziwen Han, Nathaniel Li, Josephina Hu, Hugh Zhang, Chen Bo Calvin Zhang, Mohamed Shaaban, John Ling, Sean Shi, et al. Humanity's last exam. arXiv preprint arXiv:2501.14249 , 2025. Ronak Pradeep, Sahel Sharifymoghaddam, and Jimmy Lin. Rankzephyr: Effective and robust zeroshot listwise reranking is a breeze! arXiv preprint arXiv:2312.02724 , 2023. Qwen, :, An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tianyi Tang, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 technical report, 2025. URL . Rulin Shao, Rui Qiao, Varsha Kishore, Niklas Muennighoff, Xi Victoria Lin, Daniela Rus, Bryan Kian Hsiang Low, Sewon Min, Wen-tau Yih, Pang Wei Koh, et al. Reasonir: Training retrievers for reasoning tasks. arXiv preprint arXiv:2504.20595 , 2025. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300 , 2024. Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. Hybridflow: A flexible and efficient rlhf framework. In Proceedings of the Twentieth European Conference on Computer Systems , pp. 1279–1297, 2025. Hongjin Su, Howard Yen, Mengzhou Xia, Weijia Shi, Niklas Muennighoff, Han-yu Wang, Haisu Liu, Quan Shi, Zachary S Siegel, Michael Tang, et al. Bright: A realistic and challenging benchmark for reasoning-intensive retrieval. arXiv preprint arXiv:2407.12883 , 2024. Weiwei Sun, Lingyong Yan, Xinyu Ma, Shuaiqiang Wang, Pengjie Ren, Zhumin Chen, Dawei Yin, and Zhaochun Ren. Is chatgpt good at search? investigating large language models as re-ranking agents. arXiv preprint arXiv:2304.09542 , 2023. Nandan Thakur, Nils Reimers, Andreas Rücklé, Abhishek Srivastava, and Iryna Gurevych. Beir: A heterogenous benchmark for zero-shot evaluation of information retrieval models. arXiv preprint arXiv:2104.08663 , 2021. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288 , 2023. Liang Wang, Nan Yang, Xiaolong Huang, Linjun Yang, Rangan Majumder, and Furu Wei. Improving text embeddings with large language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pp. 11897–11916, 2024. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171 , 2022. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems , 35:24824–24837, 2022. Jason Wei, Zhiqing Sun, Spencer Papay, Scott McKinney, Jeffrey Han, Isa Fulford, Hyung Won Chung, Alex Tachard Passos, William Fedus, and Amelia Glaese. Browsecomp: A simple yet challenging benchmark for browsing agents, 2025. URL 12516 .
+
+[p. 13 | section: REFERENCES | type: ListGroup]
+Orion Weller, Kathryn Ricci, Eugene Yang, Andrew Yates, Dawn Lawrie, and Benjamin Van Durme. Rank1: Test-time compute for reranking in information retrieval. arXiv preprint arXiv:2502.18418 , 2025. Shitao Xiao, Zheng Liu, Peitian Zhang, Niklas Muennighoff, Defu Lian, and Jian-Yun Nie. C-pack: Packed resources for general chinese embeddings. In Proceedings of the 47th international ACM SIGIR conference on research and development in information retrieval , pp. 641–649, 2024. Yuxi Xie, Anirudh Goyal, Wenyue Zheng, Min-Yen Kan, Timothy P Lillicrap, Kenji Kawaguchi, and Michael Shieh. Monte carlo tree search boosts reasoning via iterative preference learning. arXiv preprint arXiv:2405.00451 , 2024. An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388 , 2025a. Eugene Yang, Andrew Yates, Kathryn Ricci, Orion Weller, Vivek Chari, Benjamin Van Durme, and Dawn Lawrie. Rank-k: Test-time reasoning for listwise reranking. arXiv preprint arXiv:2505.14432 , 2025b. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad vances in neural information processing systems , 36:11809–11822, 2023. Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Livia Sun, Jeff Huang, Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E Gonzalez, et al. Sglang: Efficient execution of structured language model programs. Advances in neural information processing systems , 37: 62557–62583, 2024a. Yaowei Zheng, Richong Zhang, Junhao Zhang, Yanhan Ye, Zheyan Luo, Zhangchi Feng, and Yongqiang Ma. Llamafactory: Unified efficient fine-tuning of 100+ language models. arXiv preprint arXiv:2403.13372 , 2024b. Shengyao Zhuang, Honglei Zhuang, Bevan Koopman, and Guido Zuccon. A setwise approach for effective and highly efficient zero-shot ranking with large language models. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval , pp. 38–47, 2024. Shengyao Zhuang, Xueguang Ma, Bevan Koopman, Jimmy Lin, and Guido Zuccon. Rank-r1: Enhancing reasoning in llm-based document rerankers via reinforcement learning. arXiv preprint arXiv:2503.06034 , 2025.

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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0077", "section": "A.1 RESULTS", "page_start": 13, "page_end": 13, "type": "Text", "text": "The tables 6, 7, 8, and 9 show the extended results of table 1. The accuracy for each method is listed, as well as its accuracy correlation with the scores.", "source": "marker_v2", "marker_block_id": "/page/12/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0078", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 13, "page_end": 13, "type": "Text", "text": "We present some examples of when the PAS score fails to predict the target accuracy. The figure 6 shows examples of misclassified images from the P ( Pascal VOC 2012 ) domain of the ImageCLEF benchmark. Many images contain more than one object. The sample may be very similar to a class present in the image. However, the true class refers to another object also contained in the image. In such cases, the PAS value is high, but the accuracy is low.", "source": "marker_v2", "marker_block_id": "/page/12/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0079", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 14, "page_end": 14, "type": "TableGroup", "text": "Table 6: Target accuracy of domain adaptation methods and transferability scores for the Office-Home dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A С P | R Correlation on with PAS Source C P R A P R A C R A C P Pearson Spearman DAN 57.7 54.9 66.2 45.6 40.0 49.1 67.7 63.8 77.9 73.9 66.0 74.5 0.74 0.81 DANN 55.8 55.8 71.1 53.8 55.1 60.7 62.6 67.3 81.1 74.0 67.3 77.9 0.91 0.85 ADDA 59.7 61.4 71.1 52.6 52.5 58.6 62.9 68.0 80.2 74.0 68.8 77.6 0.84 0.80 JAN 60.6 60.5 71.0 50.8 49.6 55.9 71.9 68.3 80.5 76.5 68.7 76.9 0.78 0.81 CDAN 62.0 62.4 75.5 55.2 54.3 61.0 72.4 69.7 83.8 77.6 70.9 80.5 0.85 0.83 MCD 63.7 61.5 74.5 51.7 52.8 58.4 72.2 69.5 81.8 78.2 70.8 78.0 0.78 0.83 ResNet-50 BSP 61.0 60.9 73.4 54.7 55.2 60.3 67.7 69.4 81.2 76.2 70.9 80.2 0.85 0.80 AFN 65.0 65.0 72.3 53.2 51.4 57.8 72.7 71.3 82.4 76.8 72.3 77.9 0.73 0.78 MDD 63.5 62.5 73.5 56.2 54.8 60.9 75.4 72.1 84.5 79.6 73.8 79.9 0.80 0.78 MCC 67.5 66.6 74.4 58.4 54.8 61.4 79.6 77.0 85.6 83.0 78.5 81.8 0.70 0.76 FixMatch 65.3 67.2 74.9 56.4 56.4 63.5 76.4 73.8 84.3 79.9 71.2 80.6 0.81 0.87 Avg. 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 0.81 0.82 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 TRANS-DA 69.7 68.6 73.5 57.7 56.3 58.5 80.8 83 85 81.5 80.1 81.5 0.69 0.79 WinTR 76.8 73.4 77.2 65.3 60 63.1 84.1 84.5 86.8 85 84.4 85.7 0.64 0.78 DeiT-Small DOT 74.9 72.4 76.4 63.7 61 64.1 82.2 84.3 86.7 84.3 83 84.8 0.68 0.79 Del I-Siliali CDTrans 75.6 72.5 77 60.6 56.7 59.1 79.5 81 85.5 82.4 82.3 84.4 0.63 0.76 Avg. 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86 83.3 82.5 84.1 0.67 0.78 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 DOT 80 78.2 79.7 69 65.4 67.3 85.6 85.2 89.3 87 86.4 87.9 0.66 0.75 CDTrans 81.5 79.6 82 68.8 63.3 66 85 87.1 90.6 86.9 87.3 88.2 0.62 0.73 DeiT-Base PMTrans 83 78.5 81.7 71.8 67.4 70.7 87.3 87.7 92 88.3 87.8 89.3 0.67 0.73 Avg. 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 0.65 0.73 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 SSRT 79.9 80.7 82 67 66 69.4 84.2 84.3 89.9 88.3 87.6 88.3 0.69 0.84 ViT-Small SAMB 80.2 78.8 82.4 65.7 64.4 67 84 84.1 88 87.7 86.7 88.6 0.67 0.82 VII-SIIIaii Avg. 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 0.68 0.83 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 SAMB 80.8 81.6 84.1 68.7 68.7 70.9 85 86 91.1 88.9 88.3 90.2 0.77 0.88 DoT 81.8 81.2 82.9 72.9 70.6 72.2 89.8 89.6 90.8 90.3 90.1 92.4 0.75 0.84 TVT 77.4 75.6 79.1 67.1 64.9 67.2 83.5 85 88 87.3 85.6 86.6 0.78 0.85 ViT-Base SSRT 85.1 85 85.7 75.2 74.2 78.6 89 88.3 91.8 91.1 90 91.3 0.76 0.87 VII-Base BCAT 84.2 84.1 85.7 74.2 74.5 74.8 90.6 90.9 92.2 90.9 89.9 90.8 0.74 0.83 PMTrans 88.9 88.5 89.5 81.2 80 82.4 91.6 91.6 94.5 92.4 93 93.4 0.74 0.84 Avg. 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 0.76 0.85 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 PMTrans 88.4 87.9 89 81.3 80.4 80.9 92.9 93.4 94.8 92.8 93.2 93 0.75 0.72 Swin-Base BCAT 88.6 87.4 86.7 75.3 73.7 75.4 90 90.3 93.5 92.9 92.7 92.5 0.68 0.74 Swiii-Base Avg. 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 0.72 0.72 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384", "source": "marker_v2", "marker_block_id": "/page/13/TableGroup/14"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0080", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 7: Target accuracy of domain adaptation methods and transferability scores for the Office-31 dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A D W Correlation with PAS Source D W A W A D Pearson Spearman DANN 73.3 70.4 83.6 100.0 91.4 97.9 0.78 0.66 ADDA 69.6 72.5 90.0 99.7 94.6 97.5 0.67 0.60 BSP 74.1 73.8 88.2 100.0 92.7 97.9 0.75 0.66 DAN 66.9 65.2 87.3 100.0 84.2 98.4 0.83 0.83 JAN 69.2 71.0 89.4 100.0 93.7 98.4 0.70 0.60 CDAN 73.4 70.4 89.9 100.0 93.8 98.5 0.71 0.66 ResNet-50 MCD 68.3 67.6 87.3 100.0 90.4 98.5 0.76 0.66 AFN 72.9 71.1 94.4 100.0 94.0 98.9 0.67 0.83 MDD 76.6 72.2 94.4 100.0 95.6 98.6 0.65 0.66 MCC 75.5 74.2 95.6 99.8 94.1 98.4 0.66 0.83 FixMatch 70.0 68.1 95.4 100.0 86.4 98.2 0.75 0.83 Avg. 71.1 70.0 89.6 99.9 90.6 98.1 0.73 0.66 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 TRANS-DA 77 77.1 94.8 100 95.8 98.8 0.69 0.71 CDTrans 78.4 78 94.6 99.6 93.5 98.2 0.74 0.94 DeiT-Small Avg. 77.7 77.6 94.7 99.8 94.65 98.5 0.72 0.94 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 CDTrans 81.1 81.9 97 100 96.7 99 0.69 0.83 PMTrans 81.4 82.1 96.5 100 99 99.4 0.64 0.71 DeiT-Base Avg. 81.3 82.0 96.8 100.0 97.9 99.2 0.66 0.71 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 SSRT 83.5 82.2 98.6 100 97.7 99.2 0.61 0.94 ViT-Small PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 DoT 85.1 86.8 96.7 100 96.6 99.4 0.74 0.83 TVT 84.9 86.1 96.4 100 96.4 99.4 0.75 0.75 SSRT 79.2 79.9 95.8 100 95.7 99.2 0.72 0.83 ViT-Base BCAT 84.9 85.8 97.5 100 96.1 99.1 0.73 0.83 PMTrans 85.7 86.3 99.4 100 99.1 99.6 0.62 0.83 Avg. 84.0 85.0 97.2 100.0 96.8 99.3 0.71 0.83 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 PMTrans 86.7 86.5 99.8 100 99.5 99.4 0.61 0.83 BCAT 85.7 86.1 99.6 100 99.2 99.5 0.63 0.89 Swin-Base Avg. 86.2 86.3 99.7 100 99.4 99.5 0.62 0.89 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/500"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0081", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 8: Target accuracy of domain adaptation methods and transferability scores for the Image-CLEF dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target | ( C I ] P Correlation on with PAS Source I P С P C I Pearson Spearman RTN 95.3 92.2 86.9 86.8 72.7 75.6 0.29 0.49 MADA 96.0 92.2 88.8 87.9 75.2 75.0 0.20 0.26 iCAN 94.7 92 89.9 89.7 78.5 79.5 0.23 0.49 CDAN-E 97.7 94.3 91.3 90.7 74.2 77.7 0.27 0.49 SymNets 97.0 96.4 93.4 93.6 78.7 80.2 0.17 0.60 MEDA 95.7 95.5 92.2 92.5 78.5 79.7 0.16 0.60 ResNet-50 SPL 96.7 96.3 95.7 94.5 80.5 78.3 0.02 0.26 DS-c 92.8 91.3 87.3 86.7 70.4 78.7 0.39 0.49 CAN 95.5 95.2 91.6 91.8 76.4 78.5 0.19 0.60 JAN 94.7 91.7 89.5 88.0 74.2 76.8 0.24 0.49 CDAN 98.3 94 90.7 88.3 76.7 77.2 0.22 0.49 Avg. 95.9 93.7 90.7 90.0 76.0 77.9 0.22 0.49 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 DeiT-small TRANS-DA 97.5 97.5 93.7 95.2 78.3 80.8 0.41 0.52 Del I-siliali PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 VT-ADA 97.3 96.0 96.2 94.1 78.9 81.8 0.55 0.49 ViT-Base CSTrans 98.2 98.2 97.0 97.2 80.0 82.0 0.54 0.62 vii-Dase Avg. 97.8 97.1 96.6 95.7 79.5 81.9 0.55 0.54 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/22"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0082", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 9: Target accuracy of domain adaptation methods and transferability scores for the DomainNet dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target l С P 1 R 1 S Correlation on with PAS Source P R S C R S C P S C P R Pearson Spearman DAN 45.9 50.8 56.1 38.8 49.8 45.9 55.2 59.0 55.5 43.9 40.8 38.9 0.54 0.49 DANN 41.7 50.7 55.0 37.9 50.8 45.0 54.3 55.6 54.5 44.4 36.8 40.1 0.53 0.46 JAN 47.2 54.2 56.6 40.5 52.6 46.2 56.7 59.9 55.5 45.1 43.0 41.9 0.63 0.58 CDAN 45.1 55.6 57.2 40.4 53.6 46.4 56.8 58.4 55.7 46.1 40.5 43.0 0.60 0.50 ResNet-50 MCD 44.6 52.0 55.5 37.5 51.5 44.6 52.9 54.5 52.0 44.0 41.6 39.7 0.57 0.47 MDD 48.6 58.3 58.7 42.9 53.7 46.5 59.5 59.4 57.7 47.5 42.6 46.2 0.60 0.59 MCC 45.4 54.4 58.1 37.7 53.1 46.3 55.7 59.8 56.2 42.6 39.9 37.0 0.57 0.43 Avg. 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 0.58 0.53 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 WinTR 53.2 70.5 51.6 62.0 71.3 50.1 63.1 55.9 48.8 65.3 54.1 70.1 0.32 0.54 DOT 51.3 67.6 51.7 58.5 70.4 47.2 62.3 57 49.4 64.6 49.9 65.4 0.42 0.52 DeiT-Small CDTRANS 52.5 68.3 53.2 55.4 67.4 48 61.5 56.8 47.2 64.3 53.2 66.2 0.41 0.55 Avg. 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 0.39 0.57 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 DOT 53.6 71.2 55.2 61.8 72.2 50.5 62.9 56.9 49.3 67.3 52.9 69.8 0.27 0.45 CDTRANS 57.2 72.6 58.1 62.9 72.1 53.9 66.2 61.5 52.9 69.0 59.0 72.5 0.33 0.43 DeiT-Base WINTR 56.3 72.8 57.3 69.2 74.4 55.6 68.2 59.8 55.1 69.9 58.1 73.1 0.20 0.39 Avg 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 0.26 0.44 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 SAMB 60.5 77.8 61.8 63.8 77.1 56.8 68 64.7 58.4 71.1 64 77.5 0.38 0.43 DoT 61.3 79.6 60.4 73.2 79.2 59.7 71.1 63.2 56.4 72.6 61.9 78.3 0.24 0.31 ViT-Base SSRT 60.2 75.8 59.8 61.7 71.4 55.2 69.9 66.0 58.9 70.6 62.2 73.2 0.50 0.46 Avg. 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 0.37 0.35 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/23"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0083", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(a) Predicted: Car |True: Bottle (b) Predicted: Horse |True: Person", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/105"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0084", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(c) Predicted: Motorcycle |True: Car", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/106"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0085", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(d) Predicted: Plane |True: Bus (e) Predicted: Person |True: Bot-", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/107"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0086", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "tle", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/108"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0087", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(f) Predicted: Dog |True: Bird", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/109"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0088", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(g) Predicted: Bike |True: Bus (h) Predicted: Car |True: Person (i) Predicted: Motorcycle |True: Person", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/112"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0089", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "Caption", "text": "Figure 6: Examples of images misclassified by the domain adaptation method DANN in the dataset P ( Pascal VOC 2012 ) of the ImageCLEF benchmark", "source": "marker_v2", "marker_block_id": "/page/16/Caption/19"}

iclr26/0Z2l4XtTdz/appendix_text_v3.txt

@@ -0,0 +1,38 @@
+[p. 13 | section: A.1 RESULTS | type: Text]
+The tables 6, 7, 8, and 9 show the extended results of table 1. The accuracy for each method is listed, as well as its accuracy correlation with the scores.
+
+[p. 13 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: Text]
+We present some examples of when the PAS score fails to predict the target accuracy. The figure 6 shows examples of misclassified images from the P ( Pascal VOC 2012 ) domain of the ImageCLEF benchmark. Many images contain more than one object. The sample may be very similar to a class present in the image. However, the true class refers to another object also contained in the image. In such cases, the PAS value is high, but the accuracy is low.
+
+[p. 14 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: TableGroup]
+Table 6: Target accuracy of domain adaptation methods and transferability scores for the Office-Home dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A С P | R Correlation on with PAS Source C P R A P R A C R A C P Pearson Spearman DAN 57.7 54.9 66.2 45.6 40.0 49.1 67.7 63.8 77.9 73.9 66.0 74.5 0.74 0.81 DANN 55.8 55.8 71.1 53.8 55.1 60.7 62.6 67.3 81.1 74.0 67.3 77.9 0.91 0.85 ADDA 59.7 61.4 71.1 52.6 52.5 58.6 62.9 68.0 80.2 74.0 68.8 77.6 0.84 0.80 JAN 60.6 60.5 71.0 50.8 49.6 55.9 71.9 68.3 80.5 76.5 68.7 76.9 0.78 0.81 CDAN 62.0 62.4 75.5 55.2 54.3 61.0 72.4 69.7 83.8 77.6 70.9 80.5 0.85 0.83 MCD 63.7 61.5 74.5 51.7 52.8 58.4 72.2 69.5 81.8 78.2 70.8 78.0 0.78 0.83 ResNet-50 BSP 61.0 60.9 73.4 54.7 55.2 60.3 67.7 69.4 81.2 76.2 70.9 80.2 0.85 0.80 AFN 65.0 65.0 72.3 53.2 51.4 57.8 72.7 71.3 82.4 76.8 72.3 77.9 0.73 0.78 MDD 63.5 62.5 73.5 56.2 54.8 60.9 75.4 72.1 84.5 79.6 73.8 79.9 0.80 0.78 MCC 67.5 66.6 74.4 58.4 54.8 61.4 79.6 77.0 85.6 83.0 78.5 81.8 0.70 0.76 FixMatch 65.3 67.2 74.9 56.4 56.4 63.5 76.4 73.8 84.3 79.9 71.2 80.6 0.81 0.87 Avg. 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 0.81 0.82 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 TRANS-DA 69.7 68.6 73.5 57.7 56.3 58.5 80.8 83 85 81.5 80.1 81.5 0.69 0.79 WinTR 76.8 73.4 77.2 65.3 60 63.1 84.1 84.5 86.8 85 84.4 85.7 0.64 0.78 DeiT-Small DOT 74.9 72.4 76.4 63.7 61 64.1 82.2 84.3 86.7 84.3 83 84.8 0.68 0.79 Del I-Siliali CDTrans 75.6 72.5 77 60.6 56.7 59.1 79.5 81 85.5 82.4 82.3 84.4 0.63 0.76 Avg. 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86 83.3 82.5 84.1 0.67 0.78 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 DOT 80 78.2 79.7 69 65.4 67.3 85.6 85.2 89.3 87 86.4 87.9 0.66 0.75 CDTrans 81.5 79.6 82 68.8 63.3 66 85 87.1 90.6 86.9 87.3 88.2 0.62 0.73 DeiT-Base PMTrans 83 78.5 81.7 71.8 67.4 70.7 87.3 87.7 92 88.3 87.8 89.3 0.67 0.73 Avg. 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 0.65 0.73 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 SSRT 79.9 80.7 82 67 66 69.4 84.2 84.3 89.9 88.3 87.6 88.3 0.69 0.84 ViT-Small SAMB 80.2 78.8 82.4 65.7 64.4 67 84 84.1 88 87.7 86.7 88.6 0.67 0.82 VII-SIIIaii Avg. 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 0.68 0.83 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 SAMB 80.8 81.6 84.1 68.7 68.7 70.9 85 86 91.1 88.9 88.3 90.2 0.77 0.88 DoT 81.8 81.2 82.9 72.9 70.6 72.2 89.8 89.6 90.8 90.3 90.1 92.4 0.75 0.84 TVT 77.4 75.6 79.1 67.1 64.9 67.2 83.5 85 88 87.3 85.6 86.6 0.78 0.85 ViT-Base SSRT 85.1 85 85.7 75.2 74.2 78.6 89 88.3 91.8 91.1 90 91.3 0.76 0.87 VII-Base BCAT 84.2 84.1 85.7 74.2 74.5 74.8 90.6 90.9 92.2 90.9 89.9 90.8 0.74 0.83 PMTrans 88.9 88.5 89.5 81.2 80 82.4 91.6 91.6 94.5 92.4 93 93.4 0.74 0.84 Avg. 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 0.76 0.85 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 PMTrans 88.4 87.9 89 81.3 80.4 80.9 92.9 93.4 94.8 92.8 93.2 93 0.75 0.72 Swin-Base BCAT 88.6 87.4 86.7 75.3 73.7 75.4 90 90.3 93.5 92.9 92.7 92.5 0.68 0.74 Swiii-Base Avg. 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 0.72 0.72 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384
+
+[p. 15 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: TableGroup]
+Table 7: Target accuracy of domain adaptation methods and transferability scores for the Office-31 dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A D W Correlation with PAS Source D W A W A D Pearson Spearman DANN 73.3 70.4 83.6 100.0 91.4 97.9 0.78 0.66 ADDA 69.6 72.5 90.0 99.7 94.6 97.5 0.67 0.60 BSP 74.1 73.8 88.2 100.0 92.7 97.9 0.75 0.66 DAN 66.9 65.2 87.3 100.0 84.2 98.4 0.83 0.83 JAN 69.2 71.0 89.4 100.0 93.7 98.4 0.70 0.60 CDAN 73.4 70.4 89.9 100.0 93.8 98.5 0.71 0.66 ResNet-50 MCD 68.3 67.6 87.3 100.0 90.4 98.5 0.76 0.66 AFN 72.9 71.1 94.4 100.0 94.0 98.9 0.67 0.83 MDD 76.6 72.2 94.4 100.0 95.6 98.6 0.65 0.66 MCC 75.5 74.2 95.6 99.8 94.1 98.4 0.66 0.83 FixMatch 70.0 68.1 95.4 100.0 86.4 98.2 0.75 0.83 Avg. 71.1 70.0 89.6 99.9 90.6 98.1 0.73 0.66 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 TRANS-DA 77 77.1 94.8 100 95.8 98.8 0.69 0.71 CDTrans 78.4 78 94.6 99.6 93.5 98.2 0.74 0.94 DeiT-Small Avg. 77.7 77.6 94.7 99.8 94.65 98.5 0.72 0.94 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 CDTrans 81.1 81.9 97 100 96.7 99 0.69 0.83 PMTrans 81.4 82.1 96.5 100 99 99.4 0.64 0.71 DeiT-Base Avg. 81.3 82.0 96.8 100.0 97.9 99.2 0.66 0.71 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 SSRT 83.5 82.2 98.6 100 97.7 99.2 0.61 0.94 ViT-Small PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 DoT 85.1 86.8 96.7 100 96.6 99.4 0.74 0.83 TVT 84.9 86.1 96.4 100 96.4 99.4 0.75 0.75 SSRT 79.2 79.9 95.8 100 95.7 99.2 0.72 0.83 ViT-Base BCAT 84.9 85.8 97.5 100 96.1 99.1 0.73 0.83 PMTrans 85.7 86.3 99.4 100 99.1 99.6 0.62 0.83 Avg. 84.0 85.0 97.2 100.0 96.8 99.3 0.71 0.83 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 PMTrans 86.7 86.5 99.8 100 99.5 99.4 0.61 0.83 BCAT 85.7 86.1 99.6 100 99.2 99.5 0.63 0.89 Swin-Base Avg. 86.2 86.3 99.7 100 99.4 99.5 0.62 0.89 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56
+
+[p. 16 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: TableGroup]
+Table 8: Target accuracy of domain adaptation methods and transferability scores for the Image-CLEF dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target | ( C I ] P Correlation on with PAS Source I P С P C I Pearson Spearman RTN 95.3 92.2 86.9 86.8 72.7 75.6 0.29 0.49 MADA 96.0 92.2 88.8 87.9 75.2 75.0 0.20 0.26 iCAN 94.7 92 89.9 89.7 78.5 79.5 0.23 0.49 CDAN-E 97.7 94.3 91.3 90.7 74.2 77.7 0.27 0.49 SymNets 97.0 96.4 93.4 93.6 78.7 80.2 0.17 0.60 MEDA 95.7 95.5 92.2 92.5 78.5 79.7 0.16 0.60 ResNet-50 SPL 96.7 96.3 95.7 94.5 80.5 78.3 0.02 0.26 DS-c 92.8 91.3 87.3 86.7 70.4 78.7 0.39 0.49 CAN 95.5 95.2 91.6 91.8 76.4 78.5 0.19 0.60 JAN 94.7 91.7 89.5 88.0 74.2 76.8 0.24 0.49 CDAN 98.3 94 90.7 88.3 76.7 77.2 0.22 0.49 Avg. 95.9 93.7 90.7 90.0 76.0 77.9 0.22 0.49 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 DeiT-small TRANS-DA 97.5 97.5 93.7 95.2 78.3 80.8 0.41 0.52 Del I-siliali PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 VT-ADA 97.3 96.0 96.2 94.1 78.9 81.8 0.55 0.49 ViT-Base CSTrans 98.2 98.2 97.0 97.2 80.0 82.0 0.54 0.62 vii-Dase Avg. 97.8 97.1 96.6 95.7 79.5 81.9 0.55 0.54 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363
+
+[p. 16 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: TableGroup]
+Table 9: Target accuracy of domain adaptation methods and transferability scores for the DomainNet dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target l С P 1 R 1 S Correlation on with PAS Source P R S C R S C P S C P R Pearson Spearman DAN 45.9 50.8 56.1 38.8 49.8 45.9 55.2 59.0 55.5 43.9 40.8 38.9 0.54 0.49 DANN 41.7 50.7 55.0 37.9 50.8 45.0 54.3 55.6 54.5 44.4 36.8 40.1 0.53 0.46 JAN 47.2 54.2 56.6 40.5 52.6 46.2 56.7 59.9 55.5 45.1 43.0 41.9 0.63 0.58 CDAN 45.1 55.6 57.2 40.4 53.6 46.4 56.8 58.4 55.7 46.1 40.5 43.0 0.60 0.50 ResNet-50 MCD 44.6 52.0 55.5 37.5 51.5 44.6 52.9 54.5 52.0 44.0 41.6 39.7 0.57 0.47 MDD 48.6 58.3 58.7 42.9 53.7 46.5 59.5 59.4 57.7 47.5 42.6 46.2 0.60 0.59 MCC 45.4 54.4 58.1 37.7 53.1 46.3 55.7 59.8 56.2 42.6 39.9 37.0 0.57 0.43 Avg. 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 0.58 0.53 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 WinTR 53.2 70.5 51.6 62.0 71.3 50.1 63.1 55.9 48.8 65.3 54.1 70.1 0.32 0.54 DOT 51.3 67.6 51.7 58.5 70.4 47.2 62.3 57 49.4 64.6 49.9 65.4 0.42 0.52 DeiT-Small CDTRANS 52.5 68.3 53.2 55.4 67.4 48 61.5 56.8 47.2 64.3 53.2 66.2 0.41 0.55 Avg. 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 0.39 0.57 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 DOT 53.6 71.2 55.2 61.8 72.2 50.5 62.9 56.9 49.3 67.3 52.9 69.8 0.27 0.45 CDTRANS 57.2 72.6 58.1 62.9 72.1 53.9 66.2 61.5 52.9 69.0 59.0 72.5 0.33 0.43 DeiT-Base WINTR 56.3 72.8 57.3 69.2 74.4 55.6 68.2 59.8 55.1 69.9 58.1 73.1 0.20 0.39 Avg 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 0.26 0.44 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 SAMB 60.5 77.8 61.8 63.8 77.1 56.8 68 64.7 58.4 71.1 64 77.5 0.38 0.43 DoT 61.3 79.6 60.4 73.2 79.2 59.7 71.1 63.2 56.4 72.6 61.9 78.3 0.24 0.31 ViT-Base SSRT 60.2 75.8 59.8 61.7 71.4 55.2 69.9 66.0 58.9 70.6 62.2 73.2 0.50 0.46 Avg. 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 0.37 0.35 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+(a) Predicted: Car |True: Bottle (b) Predicted: Horse |True: Person
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+(c) Predicted: Motorcycle |True: Car
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+(d) Predicted: Plane |True: Bus (e) Predicted: Person |True: Bot-
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+tle
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+(f) Predicted: Dog |True: Bird
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: PictureGroup]
+(g) Predicted: Bike |True: Bus (h) Predicted: Car |True: Person (i) Predicted: Motorcycle |True: Person
+
+[p. 17 | section: A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK | type: Caption]
+Figure 6: Examples of images misclassified by the domain adaptation method DANN in the dataset P ( Pascal VOC 2012 ) of the ImageCLEF benchmark

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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0000", "section": "ABSTRACT", "page_start": 1, "page_end": 1, "type": "Text", "text": "The goal of domain adaptation is to make predictions for unlabeled samples from a target domain with the help of labeled samples from a different but related source domain. The performance of domain adaptation methods is highly influenced by the choice of source domain and pre-trained feature extractor. However, the selection of source data and pre-trained model is not trivial due to the absence of a labeled validation set for the target domain and the large number of available pre-trained models. In this work, we propose Potential Adaptability Score (PAS), a novel score designed to estimate the transferability of a source domain set and a pre-trained feature extractor to a target classification task before actually performing domain adaptation. PAS leverages the generalization power of pretrained models and assesses source-target compatibility based on the pre-trained feature embeddings. We integrate PAS into a framework that indicates the most relevant pre-trained model and source domain among multiple candidates, thus improving target accuracy while reducing the computational overhead. Extensive experiments on image classification benchmarks demonstrate that PAS correlates strongly with actual target accuracy and consistently guides the selection of the best-performing pre-trained model and source domain for adaptation.", "source": "marker_v2", "marker_block_id": "/page/0/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0001", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "Text", "text": "In many real applications, data is collected from diverse domains, e.g., data obtained from different equipment, collecting procedures, geographic locations, or periods in time. Such differences may lead to a distribution shift between the domains that must be assessed. Unsupervised domain adaptation is a paradigm where only unlabeled data is available for the domain of interest, the target domain. However, labeled data is obtained from a related source domain.", "source": "marker_v2", "marker_block_id": "/page/0/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0002", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "Text", "text": "One factor that affects the success of domain adaptation methods is the choice of the source domain data. Domain adaptation methods often rely on many assumptions about the relationship between source and target domains, like the existence of invariant discriminative features, the similarity of the label distribution, or the invariance of the task. Unfortunately, as the labels for the target samples are not available, such assumptions may not be verified in real applications for selecting the most appropriate source data. Violating the data assumptions and", "source": "marker_v2", "marker_block_id": "/page/0/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0003", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1: The Potential Adaptability Score (PAS) estimates the performance of adapting to an unlabeled target domain given a pre-trained feature extractor and a labeled source domain. It helps in the selection of the best pre-trained model and best source domain among many candidates and is highly correlated with the final target accuracy after domain adaptation.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/213"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0004", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "considering an irrelevant or distant source domain may introduce noise and conflicting patterns during the domain adaptation process. In the worst-case scenario, selecting an undesirable source domain may hurt the target domain performance, a scenario known as negative transfer Zhang et al. (2022) . If many source domains are available, it is reasonable to assume that not all of them may contribute equally to the target adaptation. Wisely selecting the source domain that may improve the performance on the target data while avoiding negative transfer is an essential requirement in many real-world applications.", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0005", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Another key factor that influences the domain adaptation performance is the choice of the pre-trained model. Pre-training on large-scale data allows the models to learn generic features and patterns that are often transferable across domains and tasks, making them valuable for domain adaptation. Recently, practitioners can choose from a vast number of publicly available pre-trained models, spanning diverse architectures and training paradigms. Each pre-trained model may have its own inductive bias and may capture distinct patterns in the data that may be more or less useful when transferring knowledge between domains.", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0006", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Caption", "text": "Figure 2: Source and target samples in the embedding space of a pre-trained model. (top left) Ideally, a target sample from a given class should be more similar, and hence closer in the embedding space of the pre-trained model, to a source sample from the same class. (top right) If new discriminative features need to be learned, the chances of overfitting on the source domain during adaptation increase. (bottom) Illustration of the distances from a target sample to all source class centroids. Our PAS score considers the relationship between distances d 1 and d2, which correspond to the shortest and second shortest distances, respectively.", "source": "marker_v2", "marker_block_id": "/page/1/Caption/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0007", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Despite the importance of selecting a suitable source data and a pre-trained model for the success of domain adaptation, it is still an underexplored topic. Current methods of transferability estimation aim to select the best pre-trained model for transfer learning. However, these methods are not applicable to the domain adaptation scenario since they require target labels Bao et al. (2019) ; Nguyen et al. (2020) ; You et al. (2021) . One could employ such methods for selecting the best pre-training model using only the labeled source data and ignoring the unlabeled target data. Nevertheless, considering the target data is essential, as transferring to an easy target domain should lead to different results than transferring to a harder one.", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0008", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Another approach for the problem would be performing domain adaptation for each combination of available source domains and pretrained models, and applying some model selection strategy Ericsson et al. (2023) ; You et al. (2019) ; Sun et al. (2021) . However, this approach is very time-consuming since it needs to run a domain adaptation algorithm for each combination.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0009", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "A third approach would be to measure the distance between source and target feature distributions in the embedding space of the pretrained model. This approach is also challenging as the popular metrics for the distance between two feature distributions are symmetric, e.g., Maximum Mean Discrepancy (MMD) Gretton et al. (2006) , Wasserstein distance Val lender (1974) , and CORAL Sun & Saenko (2016) . However, a metric suitable for our scenario should be asymmetric because transfer-", "source": "marker_v2", "marker_block_id": "/page/1/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0010", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "ring from an easy to a hard domain is more challenging than transferring from the harder domain to the easier one.", "source": "marker_v2", "marker_block_id": "/page/1/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0011", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "In this work, we examine the interplay between the three key components in the domain adaptation setting for classification: (1) target data, (2) source data, and (3) the pre-trained model. We propose the Potential Adaptability Score (PAS), a simple but effective novel measure to quantify the potential success of using a pre-trained model to transfer knowledge from a source domain to the target", "source": "marker_v2", "marker_block_id": "/page/1/Text/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0012", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "domain. Our experiments show how the PAS score is highly correlated to the final target accuracy after adaptation.", "source": "marker_v2", "marker_block_id": "/page/2/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0013", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "To the best of our knowledge, this is the first proposal for transferability estimation for the domain adaptation setting. We demonstrate how PAS can help to select the most relevant source domain and/or pre-trained model among a set of candidates, indicating the options that are most likely to lead to the best accuracy on the unlabeled target data (See an overview in figure 1. ). Our framework selects the most suitable options before actually performing domain adaptation, demanding fewer computational resources and reducing the training time.", "source": "marker_v2", "marker_block_id": "/page/2/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0014", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "PAS leverages the generalization power of models pre-trained on a large-scale dataset, such as the popular ImageNet-1k Deng et al. (2009) . Specifically for domain adaptation, initializing with a good pre-trained model appears to be a fundamental step in achieving a good transferability between domains Peng et al. (2018) ; Tang & Jia (2023) ; Kim et al. (2022) ; Li et al. (2023) ; Teterwak et al. (2023) . We assume that a good pre-trained model can extract general discriminative features that are robust across all domains. If this assumption is true, samples from the same class are expected to be closer together in the embedding space generated by the pre-trained model, compared to samples from different classes, even in the presence of feature distribution shift. This ideal scenario is illustrated in the top left of the figure 2. Otherwise, as shown in the example on the top right of the figure, the model should learn new discriminative features during the adaptation from the limited labeled source data to enable the classification task, increasing the chances of overfitting to the source domain. Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987) . We modify the original Silhouette score to measure the similarity of the unlabeled target samples to some of the known source class clusters defined in the pre-trained embedding space.", "source": "marker_v2", "marker_block_id": "/page/2/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0015", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "We summarize our contributions as follows:", "source": "marker_v2", "marker_block_id": "/page/2/Text/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0016", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "ListGroup", "text": "We propose PAS, a simple novel measure to quantify the potential contribution of a pretrained model and labeled source domain in the adaptation to an unlabeled target domain before performing domain adaptation. We propose a framework to select the most relevant pre-trained model or source domain from a collection of potential candidates for performing domain adaptation. We empirically validate our framework using different domain adaptation methods and image classification benchmarks, and show how our score has a high correlation with the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/2/ListGroup/294"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0017", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Unsupervised domain adaptation. The goal of unsupervised domain adaptation (UDA) is to transfer the knowledge learned from a labeled domain to a different unlabeled target domain. Usually, this goal is achieved by learning a latent representation that is invariant across domains. Several works minimize the distribution discrepancy on the representation using statically defined distance metrics such as Maximum Mean Discrepancy (MMD) (e.g., DAN Long et al. (2015) , DDC Tzeng et al. (2014) , JAN Long et al. (2017) ), covariance (e.g., DCORAL Sun & Saenko (2016) ), or Wasserstein distance (e.g., DeepJDOT Damodaran et al. (2018) ). The popularization of generative models inspired the proposal of methods that adopt adversarial learning to align data across different domains. DANN Ganin et al. (2016) , CDAN Long et al. (2018) , and ADDA Tzeng et al. (2017) are examples of widely adopted UDA methods that have shown promising results. Self-training is another promising paradigm that exploits the pseudo-labels predicted for the target domain to enhance the model. CST Liu et al. (2021) , CRST Zou et al. (2019) , FixMatch Sohn et al. (2020) and MCC Jin et al. (2020) are examples of methods that explore pseudo-labeling. Most recently, with the dissemination of transformers and foundation models, new works explore the cross-attention mechanism to propose transformer-based domain adaptation methods, such as PMTrans Zhu et al. (2023) and DoT Ren et al. (2024) . See Liu et al. (2022) ; Deng & Jia (2023) ; Alijani et al. (2024) for a comprehensive survey on domain adaptation methods.", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0018", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Pre-training and domain adaptation Recent works suggest that the choice of the pre-trained feature extractor can significantly improve the result of domain adaptation methods. Teterwak et al. (2023) show that simply adopting a model with better weight initialization can help the robustness", "source": "marker_v2", "marker_block_id": "/page/2/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0019", "section": "2 RELATED WORK", "page_start": 4, "page_end": 4, "type": "Text", "text": "of a model to out-of-distribution samples. Similarly, Kim et al. (2022) empirically show that SOTA pre-training outperforms SOTA domain adaptation methods even without access to a target domain. With a modern pre-trained backbone, older domain adaptation methods perform better than SOTA methods, but no method is consistently better in all benchmarks, and negative transfer can occur. Li et al. (2023) empirically show how, in some cases, the performance of the pre-trained model in an unseen target domain is already decent. However, no single pre-trained model performs well in all target datasets. Tang & Jia (2023) study the effects of pre-training on the domain adaptation between synthetic and real images. Without pre-training, none of the methods considered in the study outperformed the baseline trained only on the labeled source data. Other studies have also proposed new datasets and pre-training techniques that achieve competitive performance in the target domain Shen et al. (2022); Luo et al. (2024). We leverage the potential relationship between pre-training and domain adaptation success to estimate transferability between domains.", "source": "marker_v2", "marker_block_id": "/page/3/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0020", "section": "2 RELATED WORK", "page_start": 4, "page_end": 4, "type": "Text", "text": "Transferability estimation In the past years, many works have proposed scorees for quantitatively estimating the transferability of a pre-trained model to a target task. One of the primary practical applications of such estimation is selecting the best pre-trained model for fine-tuning on the target data. H-score Bao et al. (2019), NCE Tran et al. (2019), LEEP Nguyen et al. (2020) and LogME You et al. (2021) are widely adopted transferability estimation scores. More closely related to our proposal, some works propose scores for transferability estimation by examining the separability of classes in the embedding space encoded by the pre-trained model. Pándy et al. (2022) apply the Bhattacharyya coefficient to quantify the target class separability. Similarly, Meiseles & Rokach (2020) employ the Silhouette score to assess the transferability of time series data. The current methods on transferability estimation focus on the transfer learning problem, where a pre-trained model is adapted to a target task with a few labeled samples. Unfortunately, these methods can not be applied to the domain adaptation problem, where the target labels are not available.", "source": "marker_v2", "marker_block_id": "/page/3/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0021", "section": "3.1 Definitions", "page_start": 4, "page_end": 4, "type": "Text", "text": "Unsupervised domain adaptation aims to transfer knowledge from a labeled source domain to an unlabeled target domain in the presence of distribution shift. Let \\mathcal{X} \\subseteq \\mathbb{R}^d define the input space and \\mathcal{Y} = \\{1,\\ldots,C\\} the label space. The labeled source dataset is denoted by \\mathcal{D}^S = \\{(x_i^S,y_i^S)\\}_{i=1}^{|\\mathcal{D}^S|} and the unlabeled target dataset is denoted by \\mathcal{D}^T = \\{x_i^T\\}_{j=1}^{|\\mathcal{D}^T|} , with x_i^S, x_i^T \\in \\mathcal{X} and y_i^S \\in \\mathcal{Y} . S_c^S denotes the set of source samples from class c. The source and target feature distributions are sampled from different but related distributions, P_S(\\mathcal{X}) and P_T(\\mathcal{X}) , respectively, being P_S \\neq P_T . This scenario is also known as covariate shift . The goal is to learn a hypothesis h: \\mathcal{X} \\to \\mathcal{Y} that performs well on the target domain.", "source": "marker_v2", "marker_block_id": "/page/3/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0022", "section": "3.1 Definitions", "page_start": 4, "page_end": 4, "type": "Text", "text": "Let \\theta be the parameters of a feature extractor f_{\\theta}: \\mathcal{X} \\to \\mathcal{Z} pre-trained on a large-scale dataset. z_i^S = f_{\\theta}(x_i^S) and z_i^T = f_{\\theta}(x_i^T) denote, respectively, the embedding of a source and a target sample in the embedding space defined by f_{\\theta} .", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0023", "section": "3.2 ASSUMPTIONS", "page_start": 4, "page_end": 4, "type": "Text", "text": "We assume that a good pre-trained model f_{\\theta} is able to extract a wide range of patterns and high-level concepts from an input, including discriminative features that are invariant across different domains. We expect that samples from the same class are more similar, having many concepts in common. As a result, two samples from the same class should be closer together in the embedding space \\mathcal{Z} , no matter the domain. On the other hand, samples from different classes should have very few concepts in common, resulting in a dissimilar embedding representation. Due to the distribution shift between the source and target domains, samples from the same domain are expected to have more concepts in common and, therefore, have more similar representations than samples from different domains. Such assumptions lead to a scenario similar to the one represented in the top left of figure 2. The embeddings of samples from the same domain and class form a well-defined cluster in the space encoded by f_{\\theta} . Also, the clusters of samples from the same class, but different domains, are closer together and, ideally, both are distant from all the other clusters.", "source": "marker_v2", "marker_block_id": "/page/3/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0024", "section": "3.2 ASSUMPTIONS", "page_start": 5, "page_end": 5, "type": "Text", "text": "To summarize, we assume that 1) a good pre-trained model can extract invariant discriminative features, 2) samples from the same class are close in the embedding space, even if they are from different domains, and 3) samples from different classes are distant in the embedding space. Similar assumptions are proposed by Shen et al. (2022) when studying the generalization of embeddings to out-of-distribution samples.", "source": "marker_v2", "marker_block_id": "/page/4/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0025", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "We introduce the Potential Adaptability Score (PAS) as a measure of the distance from a labeled source dataset to an unlabeled target dataset in the embedding space encoded by a pre-trained feature extractor. The PAS score is based on the expectation that each target sample is as close as possible to source samples from a single class and significantly distant from source samples from all other classes in the embedding space defined by a pre-trained model f_{\\theta} . This means that a target sample is very similar to source samples from one class and has only a few concepts in common with source samples from all other classes, as illustrated in figure 2. The higher the PAS value, the stronger the evidence that the pre-trained model can identify invariant discriminative features between the domains and, consequently, the higher the chances that the pre-trained feature extractor f_{\\theta} has a good transferability from the source to the target samples.", "source": "marker_v2", "marker_block_id": "/page/4/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0026", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "The samples are normalized to unit length, and the distance between samples is calculated using the cosine distance. We assume that the samples from the class c \\in \\mathcal{Y} are clustered together. We follow Dhillon & Modha (2001) and compute the centroid of each source class cluster c so they represent the vector that, on average, has the highest cosine similarity to all the samples in the cluster.", "source": "marker_v2", "marker_block_id": "/page/4/Text/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0027", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mu_c = \\frac{\\sum_{x_i^S \\in S_c^S} f_{\\theta}(x_i^S)}{\\|\\sum_{x_i^S \\in S_c^S} f_{\\theta}(x_i^S)\\|}. (1)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0028", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "For each target sample x_i^T , we calculate its cosine distance to the centroid of each source cluster:", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0029", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_c) = 1 - (f_{\\theta}(x_i^T) \\cdot \\mu_c). \\tag{2}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0030", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Let D_i = \\{ \\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_1), ..., \\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_C) \\} be the set of distances of the j-th target sample to all the source clusters and sort(D_i) the sorted version of the set in ascending order. We define d_{1i} = sort(D_i)[1] and d_{2i} = sort(D_i)[2] as the shortest and the second shortest of the distances, respectively, as illustrated at the bottom of figure 2.", "source": "marker_v2", "marker_block_id": "/page/4/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0031", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Finally, the PAS score is defined by", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0032", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mathbf{PAS}(\\theta, \\mathcal{D}^{\\mathbf{S}}, \\mathcal{D}^{\\mathbf{T}}) = \\frac{1}{|\\mathcal{D}^{T}|} \\sum_{i}^{|\\mathcal{D}^{T}|} \\frac{d_{2i} - d_{1i}}{d_{2i}}. (3)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0033", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given one or more candidate source domains and a set of pre-trained models, the PAS score can help to select the options that are more likely to lead to the best accuracy on the target samples. The selection is done by computing the PAS score for each trio of target domain, source domain, and pre-trained model. The combination with the highest PAS value is chosen. The selection is done before any domain adaptation training. A single-source domain adaptation method can then be trained with the selected source domain and pre-trained feature extractor.", "source": "marker_v2", "marker_block_id": "/page/4/Text/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0034", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987). The Silhouette is a supervised score calculated by (b-a)/max\\{a,b\\} , where a is the mean intra-cluster distance and b is the mean nearest-cluster distance for each sample. It ranges from -1 to 1, with higher values indicating strong intra-class cohesion and clear inter-class separation. Note that the Silhouette score is fully supervised and designed for IID samples and its original form is not suitable for the domain adaptation problem. Our PAS score is an adaptation to accommodate unlabeled target samples and domain shift. We consider the closest source cluster as the true class for each target sample. This assumption makes a always smaller than b, and restricts our score to the interval [0,1]. The PAS score is close to one if the samples from the target domain", "source": "marker_v2", "marker_block_id": "/page/4/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0035", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 6, "page_end": 6, "type": "FigureGroup", "text": "Figure 3: The correlation between the PAS score value and the target accuracy after the domain adaptation. Each box summarizes the target accuracy of different domain adaptation methods for a given source-target pair and a pre-trained feature extractor. Higher values for the PAS score are strongly correlated with higher target accuracy.", "source": "marker_v2", "marker_block_id": "/page/5/FigureGroup/166"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0036", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 6, "page_end": 6, "type": "Text", "text": "are similar to the centroid of the source class cluster. However, due to the mismatch between the domains, the target samples exhibit a shift in the feature distribution, making a larger than in the IID scenario. As a result, the values for our score are typically smaller. Alternative design choices are discussed and evaluated in section 4.4.", "source": "marker_v2", "marker_block_id": "/page/5/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0037", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Datasets. We evaluate PAS on four of the most popular benchmarks for domain adaptation: Office-Home Venkateswara et al. (2017), Office-31 Saenko et al. (2010), ImageCLEF <sup>1</sup>, and DomainNet Peng et al. (2019). The benchmarks' statistics are listed in the table 2.", "source": "marker_v2", "marker_block_id": "/page/5/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0038", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "FigureGroup", "text": "Figure 4: The PAS value and target accuracy for the DANN and MCC methods using different pretrained feature extractors. The PAS score can help to select the feature extractor that leads to higher accuracy. ( left ) A \\rightarrow C adaptation in the Office-Home benchmark. ( right ) W \\rightarrow A adaptation in the Office-31 benchmark.", "source": "marker_v2", "marker_block_id": "/page/5/FigureGroup/167"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0039", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Junguang Jiang (2020), Wang et al. (2023), and from the original papers.", "source": "marker_v2", "marker_block_id": "/page/5/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0040", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Baselines To the best of our knowledge, PAS is the first asymmetric score proposed for transferability estimation for domain adaptation. We, therefore, compare PAS with the symetric metrics Maximum Mean Discrepancy (MMD) Gretton et al. (2012) and \\mathcal{A} -distance Peng et al. (2019). The MMD distance is computed using a Gaussian kernel. Due to the quadratic nature of MMD, we restrict its computation to a maximum of 10,000 randomly selected samples per domain for the DomainNet benchmark. The \\mathcal{A} -distance is computed using C-Support Vector Classification. We also report the results for an oracle baseline. The oracle is similar to PAS , defined as \\frac{1}{|\\mathcal{D}^T|} \\sum_{i}^{|\\mathcal{D}^T|} \\frac{d_{2i} - d_{1i}}{max\\{d_{1i}, d_{2i}\\}}. The d_{1i} distance is the cosine distance to the centroid of the true class of the target sample (not known in real scenarios), and d_{2i} is the distance to the closest cluster's", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0041", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Footnote", "text": "1", "source": "marker_v2", "marker_block_id": "/page/5/Footnote/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0042", "section": "4 EXPERIMENTS", "page_start": 7, "page_end": 7, "type": "Caption", "text": "Table 1: Average target accuracy of domain adaptation methods and transferability scores for different image classification benchmarks. The highest values are highlighted. Our PAS has a high correlation with the target accuracy and, for each target domain, attributes the highest value for the source domain that leads to the highest target accuracy in most scenarios. * Oracle baseline that considers the target labels.", "source": "marker_v2", "marker_block_id": "/page/6/Caption/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0043", "section": "(a) Office-Home", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target | A С P R Correlation on with acc. Source C P R A P R A C R A C P Pearson Spearman Acc. (avg.) 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 MMD (neg.) -0.135 -0.113 -0.052 -0.135 -0.097 -0.125 -0.113 -0.097 -0.033 -0.052 -0.125 -0.033 0.77 0.72 ResNet-50 A-distance (neg.) -1.876 -1.810 -1.333 -1.876 -1.827 -1.814 -1.810 -1.827 -1.424 -1.333 -1.814 -1.424 0.76 0.78 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 0.81 0.82 Oracle* 0.041 0.037 0.093 -0.022 -0.018 -0.022 0.103 0.100 0.218 0.165 0.096 0.195 0.98 0.93 Acc. (avg.) 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86.0 83.3 82.5 84.1 MMD (neg.) -0.106 -0.058 -0.024 -0.106 -0.077 -0.102 -0.058 -0.077 -0.026 -0.024 -0.102 -0.026 0.56 0.57 DeiT-Small A-distance (neg.) -1.865 -1.761 -1.26 -1.865 -1.843 -1.796 -1.761 -1.843 -1.37 -1.26 -1.796 -1.37 0.52 0.57 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 0.67 0.78 Oracle* 0.086 0.112 0.18 0.038 0.037 0.047 0.194 0.155 0.291 0.243 0.147 0.246 0.90 0.93 Acc. (avg.) 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 MMD (neg.) -0.099 -0.056 -0.028 -0.099 -0.091 -0.11 -0.056 -0.091 -0.023 -0.028 -0.11 -0.023 0.56 0.57 DeiT-Base A-distance (neg.) -1.832 -1.81 -1.372 -1.832 -1.907 -1.823 -1.81 -1.907 -1.502 -1.372 -1.823 -1.502 0.48 0.51 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 0.65 0.73 Oracle* 0.09 0.112 0.184 0.048 0.049 0.062 0.191 0.158 0.293 0.245 0.154 0.248 0.88 0.88 Acc. (avg.) 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 MMD (neg.) -0.116 -0.082 -0.032 -0.116 -0.115 -0.122 -0.082 -0.115 -0.034 -0.032 -0.122 -0.034 0.61 0.49 ViT-Small A-distance (neg.) -1.885 -1.883 -1.348 -1.885 -1.927 -1.862 -1.883 -1.927 -1.515 -1.348 -1.862 -1.515 0.53 0.59 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 0.68 0.83 Oracle* 0.132 0.147 0.212 0.084 0.102 0.113 0.211 0.195 0.321 0.26 0.189 0.285 0.87 0.92 Acc. (avg.) 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 MMD (neg.) -0.101 -0.069 -0.031 -0.101 -0.106 -0.11 -0.069 -0.106 -0.025 -0.031 -0.11 -0.025 0.59 0.57 ViT-Base A-distance (neg.) -1.85 -1.845 -1.389 -1.85 -1.952 -1.885 -1.845 -1.952 -1.595 -1.389 -1.885 -1.595 0.47 0.51 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 0.76 0.85 Oracle* 0.215 0.233 0.311 0.173 0.188 0.207 0.317 0.295 0.425 0.37 0.286 0.382 0.88 0.92 Acc. (avg.) 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 MMD (neg.) -0.081 -0.085 -0.039 -0.081 -0.104 -0.097 -0.085 -0.104 -0.033 -0.039 -0.097 -0.033 0.48 0.45 Swin-Base A-distance (neg.) -1.853 -1.892 -1.401 -1.853 -1.95 -1.917 -1.892 -1.95 -1.57 -1.401 -1.917 -1.57 0.42 0.37 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384 0.72 0.72 Oracle* 0.198 0.214 0.287 0.162 0.177 0.195 0.295 0.282 0.403 0.343 0.27 0.356 0.83 0.81", "source": "marker_v2", "marker_block_id": "/page/6/Table/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0044", "section": "(b) Office-31", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target A 1 ) | V V Correlation on with acc. Source D W A W A D Pearson Spearman Acc. (avg.) 71.8 70.6 90.5 100.0 91.9 98.3 MMD (neg.) -0.145 -0.165 -0.145 -0.046 -0.165 -0.046 0.71 0.72 ResNet-50 A-distance (neg.) -2.00 -2.00 -2.00 -1.783 -2.00 -1.783 0.72 0.83 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 0.73 0.66 Oracle* 0.192 0.166 0.246 0.445 0.188 0.407 0.80 0.83 Acc. (avg.) 77.7 77.6 94.7 94.65 MMD (neg.) -0.123 -0.129 -0.123 -0.058 -0.129 -0.058 0.66 0.84 DeiT-Small A-distance (neg.) -2.00 -1.994 -2.00 -1.969 -1.994 -1.969 0.65 0.60 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 0.72 0.94 Oracle* 0.2 0.193 0.263 0.465 0.239 0.438 0.80 1.00 Acc. (avg.) 81.3 82.0 96.8 100.0 97.9 99.2 MMD (neg.) -0.113 -0.134 -0.113 -0.074 -0.134 -0.074 0.54 0.60 DeiT-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 0.66 0.71 Oracle* 0.212 0.192 0.273 0.44 0.224 0.414 0.73 0.89 Acc. (avg.) 83.5 82.2 98.6 100.0 97.7 99.2 MMD (neg.) -0.175 -0.197 -0.175 -0.098 -0.197 -0.098 0.56 0.84 ViT-Small A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 0.61 0.94 Oracle* 0.23 0.22 0.286 0.506 0.256 0.467 0.69 1.00 Acc. (avg.) 84.0 85.0 97.2 100.0 96.8 99.3 MMD (neg.) -0.098 -0.118 -0.098 -0.071 -0.118 -0.071 0.57 0.72 ViT-Base A-distance (neg.) -2.00 -2.00 -2.00 -1.953 -2.00 -1.953 0.64 0.72 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 0.71 0.83 Oracle* 0.373 0.347 0.434 0.589 0.393 0.554 0.79 0.94 Acc. (avg.) 86.2 86.3 99.7 100.0 99.4 99.5 MMD (neg.) -0.168 -0.169 -0.168 -0.086 -0.169 -0.086 0.51 0.60 Swin-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56 0.62 0.89 Oracle* 0.321 0.313 0.388 0.589 0.366 0.558 0.69 0.89", "source": "marker_v2", "marker_block_id": "/page/6/Table/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0045", "section": "(c) ImageCLEF", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target | ( 3 1 I 1 P Correlation on with acc. Source I P C P C I Pearson Spearman Acc. (avg.) 95.9 93.7 90.7 90.0 76.0 77.9 MMD (neg.) -0.074 -0.097 -0.074 -0.022 -0.097 -0.022 -0.17 -0.12 ResNet-50 A-distance (neg.) -1.583 -1.731 -1.583 -0.807 -1.731 -0.807 -0.24 -0.12 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 0.22 0.49 Oracle* 0.287 0.243 0.195 0.254 0.111 0.2 0.84 0.71 Acc. (avg.) 97.5 97.5 93.7 95.2 78.3 80.8 MMD (neg.) -0.072 -0.081 -0.072 -0.02 -0.081 -0.02 -0.17 -0.11 DeiT-Small A-distance (neg.) -1.417 -1.748 -1.417 -0.807 -1.748 -0.807 -0.07 -0.11 PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 0.41 0.52 Oracle* 0.333 0.293 0.239 0.31 0.169 0.25 0.83 0.83 Acc. (avg.) 97.8 97.1 96.6 95.7 79.5 81.9 MMD (neg.) -0.078 -0.095 -0.078 -0.022 -0.095 -0.022 -0.13 -0.12 ViT-Base A-distance (neg.) -1.483 -1.714 -1.483 -0.655 -1.714 -0.655 -0.14 -0.12 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363 0.55 0.54 Oracle* 0.391 0.352 0.295 0.37 0.205 0.286 0.84 0.83", "source": "marker_v2", "marker_block_id": "/page/6/Table/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0046", "section": "(d) DomainNet", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target C P R S Correlation on with acc. Source P R S C R S C P S C P R Pearson Spearman Acc. (avg.) 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 MMD (neg.) -0.113 -0.158 -0.079 -0.113 -0.075 -0.108 -0.158 -0.075 -0.173 -0.079 -0.108 -0.173 0.04 0.20 ResNet-101 A-distance (neg.) -1.789 -1.73 -1.638 -1.789 -1.656 -1.777 -1.73 -1.656 -1.821 -1.638 -1.777 -1.821 0.50 0.45 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 0.58 0.53 Oracle* -0.109 -0.124 -0.042 -0.06 -0.024 -0.04 0.037 0.092 0.031 -0.087 -0.11 -0.156 0.70 0.67 Acc. (avg.) 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 MMD (neg.) -0.128 -0.146 -0.088 -0.128 -0.052 -0.16 -0.146 -0.052 -0.186 -0.088 -0.16 -0.186 0.26 0.28 DeiT-Small A-distance (neg.) -1.784 -1.734 -1.655 -1.784 -1.639 -1.768 -1.734 -1.639 -1.823 -1.655 -1.768 -1.823 0.30 0.33 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 0.39 0.57 Oracle* -0.125 -0.118 -0.055 -0.066 -0.015 -0.051 0.031 0.093 0.015 -0.12 -0.163 -0.183 -0.19 -0.17 Acc. (avg.) 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 MMD (neg.) -0.123 -0.153 -0.095 -0.123 -0.06 -0.171 -0.153 -0.06 -0.227 -0.095 -0.171 -0.227 0.19 0.35 DeiT-Base A-distance (neg.) -1.796 -1.746 -1.655 -1.796 -1.682 -1.79 -1.746 -1.682 -1.838 -1.655 -1.79 -1.838 0.26 0.37 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 0.26 0.44 Oracle* -0.115 -0.097 -0.044 -0.047 0.004 -0.04 0.044 0.105 0.022 -0.109 -0.162 -0.154 -0.17 -0.08 Acc. (avg.) 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 MMD (neg.) -0.14 -0.157 -0.108 -0.14 -0.116 -0.175 -0.157 -0.116 -0.25 -0.108 -0.175 -0.25 0.07 0.15 ViT-Base A-distance (neg.) -1.814 -1.771 -1.686 -1.814 -1.734 -1.807 -1.771 -1.734 -1.859 -1.686 -1.807 -1.859 0.18 0.21 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17 0.37 0.35 Oracle* -0.003 0.018 0.042 0.012 0.066 0.007 0.135 0.184 0.103 -0.021 -0.075 -0.062 -0.13 -0.08", "source": "marker_v2", "marker_block_id": "/page/6/Table/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0047", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 2: Statistics of the benchmarks used in the experiments. Dataset #Samples #Classes Domains Office-Home 15,588 65 A (Art), C (Clipart), P (Product), R (Real-world) Office-31 4,110 31 A (Amazon), D (DSLR), W (Webcam) ImageCLEF 1,800 12 C (Caltech-256), I (ImageNet ILSVRC 2012), P (Pascal VOC 2012) DomainNet 569,010 345 C (Clipart), P (Painting), R (Real), S (Sketch) Table 3: Correlation with the average target accuracy after adaptation. Showing Pearson correlation / Spearman's rank correlation.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/82"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0048", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "Table", "text": "Office-Home Office-31 ImageCLEF DomainNet Total MMD 0.55 / 0.51 0.45 / 0.53 -0.14 / -0.08 -0.09 / -0.03 0.37 / 0.37 \\mathcal{A} -distance 0.32 / 0.17 0.26 / 0.35 -0.13 / -0.07 0.07 / 0.06 0.04 / -0.16 PAS (our) 0.76 / 0.81 0.63 / 0.78 0.44 / 0.60 0.53 / 0.56 0.83 / 0.88 Oracle* 0.89 / 0.90 0.71 / 0.86 0.78 / 0.85 0.21 / 0.21 0.88 / 0.91", "source": "marker_v2", "marker_block_id": "/page/7/Table/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0049", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "Text", "text": "centroid that is not the true class. In the ideal case where the closest class centroid is the actual class of the sample, the oracle is the same as PAS , otherwise, the oracle value is smaller. The oracle validates the existing relationship between the clusters distance and the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/7/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0050", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "The results for the four benchmark datasets are presented in Table 1 (a) - (d). For each source-target pair in the benchmarks, we group the domain adaptation methods using the same pre-trained feature extractor and report their average target accuracy, followed by the baselines and our PAS score. We highlight the highest values among the different choices of source domains. We also report the correlation (Pearson and Spearman's rank correlation) between the average target accuracy and the scores. The detailed results for each individual domain adaptation method are presented in the Supplementary Material A.1.", "source": "marker_v2", "marker_block_id": "/page/7/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0051", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "We report in Table 3 the overall correlation for all scenarios of each benchmark (all target domains, source domains and pre-trained models). The results show that the PAS score is strongly correlated with target accuracy. We observe an overall Spearman's rank correlation of 0.88 over all the results.", "source": "marker_v2", "marker_block_id": "/page/7/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0052", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "The most important results are reported in Table 4, where we present the correlation for each target domain. This correlation is the most useful for users in real-world scenarios. Given a target domain of interest and many options of source domains and pre-trained models, we show that our PAS score has a strong correlation with the final target accuracy. The empirical results indicate that our proposed PAS score is effective in selecting the best source domain among many candidates.", "source": "marker_v2", "marker_block_id": "/page/7/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0053", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "We summarize our results in Figure 3. Each box in the graph represents the target accuracy of different domain adaptation methods using the same pre-trained backbone for a source-target domains pair. We observe that higher PAS values are consistently related to high accuracy on the target domain. This indicates that PAS may be useful not only for selecting the most appropriate source domain, but also to estimate beforehand the success of the domain adaptation.", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0054", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 4: Correlation with the average target accuracy after adaptation for each target domain. Each cell considers the results for a target domain and all available source domains and pre-trained models. Showing Pearson correlation / Spearman's rank correlation. Office -Home 1 Office-31 1 ImageCLEF Doma ainNet A C P R A D W C I P С P R S MMD 0.41 / 0.26 0.28 / 0.21 0.41 / 0.29 0.25 / 0.21 -0.02 / -0.15 0.44 / 0.60 0.45 / 0.36 0.54 / 0.49 -0.03 / -0.22 0.61 / 0.60 -0.56 / -0.42 0.33 / 0.20 0.23 / 0.47 -0.38 / -0.42 A-distance 0.12 / -0.13 -0.46 / -0.43 0.15 / -0.09 -0.05 / -0.26 -0.19 / -0.31 0.27 / 0.28 0.14 / 0.07 0.43 / 0.38 0.10 / 0.05 0.64 / 0.60 0.09 / -0.04 0.35 / 0.17 0.27 / 0.30 -0.10 / -0.32 PAS (our) 0.70 / 0.70 0.81 / 0.78 0.79 / 0.74 0.75 / 0.75 0.65 / 0.81 0.70 / 0.81 0.70 / 0.75 0.82 / 0.76 0.73 / 0.66 0.87 / 0.83 0.71 0.67 0.75 / 0.76 0.59 / 0.71 0.48 / 0.35 Oracle* 0.82 / 0.85 0.91 / 0.90 0.84 / 0.81 0.80 / 0.87 0.74 / 0.88 0.73 / 0.90 0.74 / 0.78 0.81 / 0.76 0.74 / 0.66 0.97 / 0.94 0.36 / 0.50 0.71 / 0.62 0.61 / 0.72 0.28 / 0.33", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/83"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0055", "section": "4.1 Selection of the Source Domain", "page_start": 9, "page_end": 9, "type": "Text", "text": "The results on the ImageCLEF benchmark illustrate the scenarios where the PAS score is not effective. This benchmark (especially the P domain) contains images with multiple objects. In many cases, the sample is very close to the centroid of one class that is indeed present in the image, but the true label is related to another object in the scene. In these cases, the PAS for the sample is high, showing a high similarity with one source class, but the final accuracy is low, as the sample is classified as the wrong class. We show examples in the supplementary material A.2", "source": "marker_v2", "marker_block_id": "/page/8/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0056", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "FigureGroup", "text": "Figure 5: The PAS value varying with the number of samples for the Office-Home . The PAS values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.", "source": "marker_v2", "marker_block_id": "/page/8/FigureGroup/168"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0057", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "Text", "text": "may be applied for the selection of the pre-trained model.", "source": "marker_v2", "marker_block_id": "/page/8/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0058", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "Text", "text": "The results in the literature presented in table 1 compare methods with different backbones and demonstrate that PAS can be applied to select the most suitable pretrained feature extractor. However, they do not consider the impact of different pre-trained feature extractors over the same domain adaptation method. For analyzing the robustness of PAS over different choices of pre-trained methods, we keep the domain adaptation method fixed and vary the pre-trained backbone. We select two of the most challenging domain adaptation scenarios: the A \\rightarrow C adaptation in the Office-Home benchmark and W \\rightarrow A adaptation in the Office-31 benchmark. We show results for two popular domain adaptation methods: DANN Ganin et al. (2016) and MCC Jin et al. (2020). We train each method following the code provided by the Tllib library Jiang et al. (2022); Junguang Jiang (2020) with the default hyperparameters. The results are shown in figure 4. Higher PAS values are attributed to pretrained models that lead to higher target accuracy before performing domain adaptation, indicating that our score", "source": "marker_v2", "marker_block_id": "/page/8/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0059", "section": "4.3 THE IMPACT OF THE SAMPLE SIZE", "page_start": 9, "page_end": 9, "type": "Text", "text": "The time complexity of the PAS computation is linear in the number of samples. This can be limiting for a quick evaluation of larger datasets and scenarios with many candidate source domains.", "source": "marker_v2", "marker_block_id": "/page/8/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0060", "section": "4.3 THE IMPACT OF THE SAMPLE SIZE", "page_start": 9, "page_end": 9, "type": "Text", "text": "To optimize the computation time, we show that our score can be calculated using only a subset of the samples. We randomly select a subset of the samples of both source and target domains. The results are presented in the figure 5. The PAS values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.", "source": "marker_v2", "marker_block_id": "/page/8/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0061", "section": "4.4 DESIGN CHOICES", "page_start": 9, "page_end": 9, "type": "Text", "text": "The PAS score considers the cosine distance between each target sample and the source class centroids. We experimentally evaluated alternative design choices and compare the correlation between the score and the target accuracy. The results are shown in table 5 and demonstrate how the overall correlation between the target accuracy and PAS, as proposed, is higher.", "source": "marker_v2", "marker_block_id": "/page/8/Text/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0062", "section": "4.4 DESIGN CHOICES", "page_start": 9, "page_end": 9, "type": "Text", "text": "We change PAS to consider the Euclidean distance instead of the cosine distance. In the domain adaptation setting, the cosine distance has advantages over using the Euclidean distance in the original latent space, as it ignores the magnitude of", "source": "marker_v2", "marker_block_id": "/page/8/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0063", "section": "4.4 DESIGN CHOICES", "page_start": 9, "page_end": 9, "type": "TableGroup", "text": "Office-Home Office-31 ImageCLEF DomainNet Total PAS 0.76 0.63 0.44 0.58 0.79 Euclidean distance 0.70 0.69 0.27 0.54 0.68 Average cosine distance 0.66 0.52 0.12 0.48 0.66 Table 5: Pearson correlation between the target accuracy and the PAS score, which considers the cosine distance to the cluster centroid, and modifications using the Euclidean distance to the centroid and the average cosine distance to the source cluster samples. The maximum correlation value for each benchmark is highlighted. The design choices of PAS lead to the higher overall correlation between the score and the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/8/TableGroup/169"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0064", "section": "4.4 DESIGN CHOICES", "page_start": 10, "page_end": 10, "type": "Text", "text": "representations (e.g., a difference in the illumination in images that reflects on the intensity of the features detected by the model) and focuses only on the differences in the angles (the difference between classes). Also, the cosine distance is less affected by the high-dimensionality of the data (the phenomenon known as curse of dimensionality Bellman (1966) ).", "source": "marker_v2", "marker_block_id": "/page/9/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0065", "section": "4.4 DESIGN CHOICES", "page_start": 10, "page_end": 10, "type": "Text", "text": "We also modify PAS to use the average pairwise distance to the source samples instead of the distance to the source cluster centroid. The pairwise distance is a good summarization of the closeness of the target sample to the source samples of the class. On the other hand, the distance to the centroid measures how well the target sample is aligned to the dimensions of greatest alignment between the samples in the cluster, as the centroid formulation 1/|D S | P|D S | i =1 x S i makes samples pointing in similar directions add up in that direction.", "source": "marker_v2", "marker_block_id": "/page/9/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0066", "section": "5 CONCLUSION AND FUTURE WORK", "page_start": 10, "page_end": 10, "type": "Text", "text": "We present Potential Adaptability Score (PAS), a new score to select, among many candidates, the source domain or pre-trained model that are likely to lead to the best target accuracy when used for unsupervised domain adaptation. We evaluate our score on four of the most popular benchmarks for domain adaptation and show that it has a high correlation with the target accuracy and selects the best source domain in most cases. We also show that PAS can be computed more efficiently with fewer samples.", "source": "marker_v2", "marker_block_id": "/page/9/Text/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0067", "section": "5 CONCLUSION AND FUTURE WORK", "page_start": 10, "page_end": 10, "type": "Text", "text": "We suggest two improvements for future work. Although our score could be applied to any classification task, we focus on vision problems, specifically the image classification task, which is the most common task in the domain adaptation literature. Showing its efficacy on other modalities and tasks demands the availability of a diverse set of benchmarks and specialized domain adaptation methods. Also, we focus on the single-source domain adaptation problem, where only a single source domain is considered during the training. Future works may extend our work to select multiple source domains, in the setting known as multi-source domain adaptation.", "source": "marker_v2", "marker_block_id": "/page/9/Text/5"}
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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0077", "section": "A.1 RESULTS", "page_start": 13, "page_end": 13, "type": "Text", "text": "The tables 6, 7, 8, and 9 show the extended results of table 1. The accuracy for each method is listed, as well as its accuracy correlation with the scores.", "source": "marker_v2", "marker_block_id": "/page/12/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0078", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 13, "page_end": 13, "type": "Text", "text": "We present some examples of when the PAS score fails to predict the target accuracy. The figure 6 shows examples of misclassified images from the P ( Pascal VOC 2012 ) domain of the ImageCLEF benchmark. Many images contain more than one object. The sample may be very similar to a class present in the image. However, the true class refers to another object also contained in the image. In such cases, the PAS value is high, but the accuracy is low.", "source": "marker_v2", "marker_block_id": "/page/12/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0079", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 14, "page_end": 14, "type": "TableGroup", "text": "Table 6: Target accuracy of domain adaptation methods and transferability scores for the Office-Home dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A С P | R Correlation on with PAS Source C P R A P R A C R A C P Pearson Spearman DAN 57.7 54.9 66.2 45.6 40.0 49.1 67.7 63.8 77.9 73.9 66.0 74.5 0.74 0.81 DANN 55.8 55.8 71.1 53.8 55.1 60.7 62.6 67.3 81.1 74.0 67.3 77.9 0.91 0.85 ADDA 59.7 61.4 71.1 52.6 52.5 58.6 62.9 68.0 80.2 74.0 68.8 77.6 0.84 0.80 JAN 60.6 60.5 71.0 50.8 49.6 55.9 71.9 68.3 80.5 76.5 68.7 76.9 0.78 0.81 CDAN 62.0 62.4 75.5 55.2 54.3 61.0 72.4 69.7 83.8 77.6 70.9 80.5 0.85 0.83 MCD 63.7 61.5 74.5 51.7 52.8 58.4 72.2 69.5 81.8 78.2 70.8 78.0 0.78 0.83 ResNet-50 BSP 61.0 60.9 73.4 54.7 55.2 60.3 67.7 69.4 81.2 76.2 70.9 80.2 0.85 0.80 AFN 65.0 65.0 72.3 53.2 51.4 57.8 72.7 71.3 82.4 76.8 72.3 77.9 0.73 0.78 MDD 63.5 62.5 73.5 56.2 54.8 60.9 75.4 72.1 84.5 79.6 73.8 79.9 0.80 0.78 MCC 67.5 66.6 74.4 58.4 54.8 61.4 79.6 77.0 85.6 83.0 78.5 81.8 0.70 0.76 FixMatch 65.3 67.2 74.9 56.4 56.4 63.5 76.4 73.8 84.3 79.9 71.2 80.6 0.81 0.87 Avg. 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 0.81 0.82 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 TRANS-DA 69.7 68.6 73.5 57.7 56.3 58.5 80.8 83 85 81.5 80.1 81.5 0.69 0.79 WinTR 76.8 73.4 77.2 65.3 60 63.1 84.1 84.5 86.8 85 84.4 85.7 0.64 0.78 DeiT-Small DOT 74.9 72.4 76.4 63.7 61 64.1 82.2 84.3 86.7 84.3 83 84.8 0.68 0.79 Del I-Siliali CDTrans 75.6 72.5 77 60.6 56.7 59.1 79.5 81 85.5 82.4 82.3 84.4 0.63 0.76 Avg. 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86 83.3 82.5 84.1 0.67 0.78 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 DOT 80 78.2 79.7 69 65.4 67.3 85.6 85.2 89.3 87 86.4 87.9 0.66 0.75 CDTrans 81.5 79.6 82 68.8 63.3 66 85 87.1 90.6 86.9 87.3 88.2 0.62 0.73 DeiT-Base PMTrans 83 78.5 81.7 71.8 67.4 70.7 87.3 87.7 92 88.3 87.8 89.3 0.67 0.73 Avg. 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 0.65 0.73 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 SSRT 79.9 80.7 82 67 66 69.4 84.2 84.3 89.9 88.3 87.6 88.3 0.69 0.84 ViT-Small SAMB 80.2 78.8 82.4 65.7 64.4 67 84 84.1 88 87.7 86.7 88.6 0.67 0.82 VII-SIIIaii Avg. 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 0.68 0.83 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 SAMB 80.8 81.6 84.1 68.7 68.7 70.9 85 86 91.1 88.9 88.3 90.2 0.77 0.88 DoT 81.8 81.2 82.9 72.9 70.6 72.2 89.8 89.6 90.8 90.3 90.1 92.4 0.75 0.84 TVT 77.4 75.6 79.1 67.1 64.9 67.2 83.5 85 88 87.3 85.6 86.6 0.78 0.85 ViT-Base SSRT 85.1 85 85.7 75.2 74.2 78.6 89 88.3 91.8 91.1 90 91.3 0.76 0.87 VII-Base BCAT 84.2 84.1 85.7 74.2 74.5 74.8 90.6 90.9 92.2 90.9 89.9 90.8 0.74 0.83 PMTrans 88.9 88.5 89.5 81.2 80 82.4 91.6 91.6 94.5 92.4 93 93.4 0.74 0.84 Avg. 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 0.76 0.85 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 PMTrans 88.4 87.9 89 81.3 80.4 80.9 92.9 93.4 94.8 92.8 93.2 93 0.75 0.72 Swin-Base BCAT 88.6 87.4 86.7 75.3 73.7 75.4 90 90.3 93.5 92.9 92.7 92.5 0.68 0.74 Swiii-Base Avg. 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 0.72 0.72 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384", "source": "marker_v2", "marker_block_id": "/page/13/TableGroup/14"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0080", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 7: Target accuracy of domain adaptation methods and transferability scores for the Office-31 dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target A D W Correlation with PAS Source D W A W A D Pearson Spearman DANN 73.3 70.4 83.6 100.0 91.4 97.9 0.78 0.66 ADDA 69.6 72.5 90.0 99.7 94.6 97.5 0.67 0.60 BSP 74.1 73.8 88.2 100.0 92.7 97.9 0.75 0.66 DAN 66.9 65.2 87.3 100.0 84.2 98.4 0.83 0.83 JAN 69.2 71.0 89.4 100.0 93.7 98.4 0.70 0.60 CDAN 73.4 70.4 89.9 100.0 93.8 98.5 0.71 0.66 ResNet-50 MCD 68.3 67.6 87.3 100.0 90.4 98.5 0.76 0.66 AFN 72.9 71.1 94.4 100.0 94.0 98.9 0.67 0.83 MDD 76.6 72.2 94.4 100.0 95.6 98.6 0.65 0.66 MCC 75.5 74.2 95.6 99.8 94.1 98.4 0.66 0.83 FixMatch 70.0 68.1 95.4 100.0 86.4 98.2 0.75 0.83 Avg. 71.1 70.0 89.6 99.9 90.6 98.1 0.73 0.66 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 TRANS-DA 77 77.1 94.8 100 95.8 98.8 0.69 0.71 CDTrans 78.4 78 94.6 99.6 93.5 98.2 0.74 0.94 DeiT-Small Avg. 77.7 77.6 94.7 99.8 94.65 98.5 0.72 0.94 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 CDTrans 81.1 81.9 97 100 96.7 99 0.69 0.83 PMTrans 81.4 82.1 96.5 100 99 99.4 0.64 0.71 DeiT-Base Avg. 81.3 82.0 96.8 100.0 97.9 99.2 0.66 0.71 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 SSRT 83.5 82.2 98.6 100 97.7 99.2 0.61 0.94 ViT-Small PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 DoT 85.1 86.8 96.7 100 96.6 99.4 0.74 0.83 TVT 84.9 86.1 96.4 100 96.4 99.4 0.75 0.75 SSRT 79.2 79.9 95.8 100 95.7 99.2 0.72 0.83 ViT-Base BCAT 84.9 85.8 97.5 100 96.1 99.1 0.73 0.83 PMTrans 85.7 86.3 99.4 100 99.1 99.6 0.62 0.83 Avg. 84.0 85.0 97.2 100.0 96.8 99.3 0.71 0.83 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 PMTrans 86.7 86.5 99.8 100 99.5 99.4 0.61 0.83 BCAT 85.7 86.1 99.6 100 99.2 99.5 0.63 0.89 Swin-Base Avg. 86.2 86.3 99.7 100 99.4 99.5 0.62 0.89 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/500"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0081", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 8: Target accuracy of domain adaptation methods and transferability scores for the Image-CLEF dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target | ( C I ] P Correlation on with PAS Source I P С P C I Pearson Spearman RTN 95.3 92.2 86.9 86.8 72.7 75.6 0.29 0.49 MADA 96.0 92.2 88.8 87.9 75.2 75.0 0.20 0.26 iCAN 94.7 92 89.9 89.7 78.5 79.5 0.23 0.49 CDAN-E 97.7 94.3 91.3 90.7 74.2 77.7 0.27 0.49 SymNets 97.0 96.4 93.4 93.6 78.7 80.2 0.17 0.60 MEDA 95.7 95.5 92.2 92.5 78.5 79.7 0.16 0.60 ResNet-50 SPL 96.7 96.3 95.7 94.5 80.5 78.3 0.02 0.26 DS-c 92.8 91.3 87.3 86.7 70.4 78.7 0.39 0.49 CAN 95.5 95.2 91.6 91.8 76.4 78.5 0.19 0.60 JAN 94.7 91.7 89.5 88.0 74.2 76.8 0.24 0.49 CDAN 98.3 94 90.7 88.3 76.7 77.2 0.22 0.49 Avg. 95.9 93.7 90.7 90.0 76.0 77.9 0.22 0.49 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 DeiT-small TRANS-DA 97.5 97.5 93.7 95.2 78.3 80.8 0.41 0.52 Del I-siliali PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 VT-ADA 97.3 96.0 96.2 94.1 78.9 81.8 0.55 0.49 ViT-Base CSTrans 98.2 98.2 97.0 97.2 80.0 82.0 0.54 0.62 vii-Dase Avg. 97.8 97.1 96.6 95.7 79.5 81.9 0.55 0.54 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/22"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0082", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 9: Target accuracy of domain adaptation methods and transferability scores for the DomainNet dataset. The highest values are highlighted. * Oracle baseline that considers the target labels. Target l С P 1 R 1 S Correlation on with PAS Source P R S C R S C P S C P R Pearson Spearman DAN 45.9 50.8 56.1 38.8 49.8 45.9 55.2 59.0 55.5 43.9 40.8 38.9 0.54 0.49 DANN 41.7 50.7 55.0 37.9 50.8 45.0 54.3 55.6 54.5 44.4 36.8 40.1 0.53 0.46 JAN 47.2 54.2 56.6 40.5 52.6 46.2 56.7 59.9 55.5 45.1 43.0 41.9 0.63 0.58 CDAN 45.1 55.6 57.2 40.4 53.6 46.4 56.8 58.4 55.7 46.1 40.5 43.0 0.60 0.50 ResNet-50 MCD 44.6 52.0 55.5 37.5 51.5 44.6 52.9 54.5 52.0 44.0 41.6 39.7 0.57 0.47 MDD 48.6 58.3 58.7 42.9 53.7 46.5 59.5 59.4 57.7 47.5 42.6 46.2 0.60 0.59 MCC 45.4 54.4 58.1 37.7 53.1 46.3 55.7 59.8 56.2 42.6 39.9 37.0 0.57 0.43 Avg. 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 0.58 0.53 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 WinTR 53.2 70.5 51.6 62.0 71.3 50.1 63.1 55.9 48.8 65.3 54.1 70.1 0.32 0.54 DOT 51.3 67.6 51.7 58.5 70.4 47.2 62.3 57 49.4 64.6 49.9 65.4 0.42 0.52 DeiT-Small CDTRANS 52.5 68.3 53.2 55.4 67.4 48 61.5 56.8 47.2 64.3 53.2 66.2 0.41 0.55 Avg. 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 0.39 0.57 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 DOT 53.6 71.2 55.2 61.8 72.2 50.5 62.9 56.9 49.3 67.3 52.9 69.8 0.27 0.45 CDTRANS 57.2 72.6 58.1 62.9 72.1 53.9 66.2 61.5 52.9 69.0 59.0 72.5 0.33 0.43 DeiT-Base WINTR 56.3 72.8 57.3 69.2 74.4 55.6 68.2 59.8 55.1 69.9 58.1 73.1 0.20 0.39 Avg 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 0.26 0.44 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 SAMB 60.5 77.8 61.8 63.8 77.1 56.8 68 64.7 58.4 71.1 64 77.5 0.38 0.43 DoT 61.3 79.6 60.4 73.2 79.2 59.7 71.1 63.2 56.4 72.6 61.9 78.3 0.24 0.31 ViT-Base SSRT 60.2 75.8 59.8 61.7 71.4 55.2 69.9 66.0 58.9 70.6 62.2 73.2 0.50 0.46 Avg. 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 0.37 0.35 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/23"}
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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0088", "section": "A.2 EXAMPLES OF SAMPLES IN THE ImageCLEF BENCHMARK", "page_start": 17, "page_end": 17, "type": "PictureGroup", "text": "(g) Predicted: Bike |True: Bus (h) Predicted: Car |True: Person (i) Predicted: Motorcycle |True: Person", "source": "marker_v2", "marker_block_id": "/page/16/PictureGroup/112"}
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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0000", "section": "ABSTRACT", "page_start": 1, "page_end": 1, "type": "Text", "text": "The goal of domain adaptation is to make predictions for unlabeled samples from a target domain with the help of labeled samples from a different but related source domain. The performance of domain adaptation methods is highly influenced by the choice of source domain and pre-trained feature extractor. However, the selection of source data and pre-trained model is not trivial due to the absence of a labeled validation set for the target domain and the large number of available pre-trained models. In this work, we propose Potential Adaptability Score (PAS), a novel score designed to estimate the transferability of a source domain set and a pre-trained feature extractor to a target classification task before actually performing domain adaptation. PAS leverages the generalization power of pretrained models and assesses source-target compatibility based on the pre-trained feature embeddings. We integrate PAS into a framework that indicates the most relevant pre-trained model and source domain among multiple candidates, thus improving target accuracy while reducing the computational overhead. Extensive experiments on image classification benchmarks demonstrate that PAS correlates strongly with actual target accuracy and consistently guides the selection of the best-performing pre-trained model and source domain for adaptation.", "source": "marker_v2", "marker_block_id": "/page/0/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0001", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "Text", "text": "In many real applications, data is collected from diverse domains, e.g., data obtained from different equipment, collecting procedures, geographic locations, or periods in time. Such differences may lead to a distribution shift between the domains that must be assessed. Unsupervised domain adaptation is a paradigm where only unlabeled data is available for the domain of interest, the target domain. However, labeled data is obtained from a related source domain.", "source": "marker_v2", "marker_block_id": "/page/0/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0002", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "Text", "text": "One factor that affects the success of domain adaptation methods is the choice of the source domain data. Domain adaptation methods often rely on many assumptions about the relationship between source and target domains, like the existence of invariant discriminative features, the similarity of the label distribution, or the invariance of the task. Unfortunately, as the labels for the target samples are not available, such assumptions may not be verified in real applications for selecting the most appropriate source data. Violating the data assumptions and", "source": "marker_v2", "marker_block_id": "/page/0/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0003", "section": "1 INTRODUCTION", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1: The Potential Adaptability Score (PAS) estimates the performance of adapting to an unlabeled target domain given a pre-trained feature extractor and a labeled source domain. It helps in the selection of the best pre-trained model and best source domain among many candidates and is highly correlated with the final target accuracy after domain adaptation.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/213"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0004", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "considering an irrelevant or distant source domain may introduce noise and conflicting patterns during the domain adaptation process. In the worst-case scenario, selecting an undesirable source domain may hurt the target domain performance, a scenario known as negative transfer Zhang et al. (2022) . If many source domains are available, it is reasonable to assume that not all of them may contribute equally to the target adaptation. Wisely selecting the source domain that may improve the performance on the target data while avoiding negative transfer is an essential requirement in many real-world applications.", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0005", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Another key factor that influences the domain adaptation performance is the choice of the pre-trained model. Pre-training on large-scale data allows the models to learn generic features and patterns that are often transferable across domains and tasks, making them valuable for domain adaptation. Recently, practitioners can choose from a vast number of publicly available pre-trained models, spanning diverse architectures and training paradigms. Each pre-trained model may have its own inductive bias and may capture distinct patterns in the data that may be more or less useful when transferring knowledge between domains.", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0006", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Caption", "text": "Figure 2: Source and target samples in the embedding space of a pre-trained model. (top left) Ideally, a target sample from a given class should be more similar, and hence closer in the embedding space of the pre-trained model, to a source sample from the same class. (top right) If new discriminative features need to be learned, the chances of overfitting on the source domain during adaptation increase. (bottom) Illustration of the distances from a target sample to all source class centroids. Our PAS score considers the relationship between distances d 1 and d2, which correspond to the shortest and second shortest distances, respectively.", "source": "marker_v2", "marker_block_id": "/page/1/Caption/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0007", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Despite the importance of selecting a suitable source data and a pre-trained model for the success of domain adaptation, it is still an underexplored topic. Current methods of transferability estimation aim to select the best pre-trained model for transfer learning. However, these methods are not applicable to the domain adaptation scenario since they require target labels Bao et al. (2019) ; Nguyen et al. (2020) ; You et al. (2021) . One could employ such methods for selecting the best pre-training model using only the labeled source data and ignoring the unlabeled target data. Nevertheless, considering the target data is essential, as transferring to an easy target domain should lead to different results than transferring to a harder one.", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0008", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "Another approach for the problem would be performing domain adaptation for each combination of available source domains and pretrained models, and applying some model selection strategy Ericsson et al. (2023) ; You et al. (2019) ; Sun et al. (2021) . However, this approach is very time-consuming since it needs to run a domain adaptation algorithm for each combination.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0009", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "A third approach would be to measure the distance between source and target feature distributions in the embedding space of the pretrained model. This approach is also challenging as the popular metrics for the distance between two feature distributions are symmetric, e.g., Maximum Mean Discrepancy (MMD) Gretton et al. (2006) , Wasserstein distance Val lender (1974) , and CORAL Sun & Saenko (2016) . However, a metric suitable for our scenario should be asymmetric because transfer-", "source": "marker_v2", "marker_block_id": "/page/1/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0010", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "ring from an easy to a hard domain is more challenging than transferring from the harder domain to the easier one.", "source": "marker_v2", "marker_block_id": "/page/1/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0011", "section": "1 INTRODUCTION", "page_start": 2, "page_end": 2, "type": "Text", "text": "In this work, we examine the interplay between the three key components in the domain adaptation setting for classification: (1) target data, (2) source data, and (3) the pre-trained model. We propose the Potential Adaptability Score (PAS), a simple but effective novel measure to quantify the potential success of using a pre-trained model to transfer knowledge from a source domain to the target", "source": "marker_v2", "marker_block_id": "/page/1/Text/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0012", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "domain. Our experiments show how the PAS score is highly correlated to the final target accuracy after adaptation.", "source": "marker_v2", "marker_block_id": "/page/2/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0013", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "To the best of our knowledge, this is the first proposal for transferability estimation for the domain adaptation setting. We demonstrate how PAS can help to select the most relevant source domain and/or pre-trained model among a set of candidates, indicating the options that are most likely to lead to the best accuracy on the unlabeled target data (See an overview in figure 1. ). Our framework selects the most suitable options before actually performing domain adaptation, demanding fewer computational resources and reducing the training time.", "source": "marker_v2", "marker_block_id": "/page/2/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0014", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "PAS leverages the generalization power of models pre-trained on a large-scale dataset, such as the popular ImageNet-1k Deng et al. (2009) . Specifically for domain adaptation, initializing with a good pre-trained model appears to be a fundamental step in achieving a good transferability between domains Peng et al. (2018) ; Tang & Jia (2023) ; Kim et al. (2022) ; Li et al. (2023) ; Teterwak et al. (2023) . We assume that a good pre-trained model can extract general discriminative features that are robust across all domains. If this assumption is true, samples from the same class are expected to be closer together in the embedding space generated by the pre-trained model, compared to samples from different classes, even in the presence of feature distribution shift. This ideal scenario is illustrated in the top left of the figure 2. Otherwise, as shown in the example on the top right of the figure, the model should learn new discriminative features during the adaptation from the limited labeled source data to enable the classification task, increasing the chances of overfitting to the source domain. Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987) . We modify the original Silhouette score to measure the similarity of the unlabeled target samples to some of the known source class clusters defined in the pre-trained embedding space.", "source": "marker_v2", "marker_block_id": "/page/2/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0015", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "Text", "text": "We summarize our contributions as follows:", "source": "marker_v2", "marker_block_id": "/page/2/Text/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0016", "section": "1 INTRODUCTION", "page_start": 3, "page_end": 3, "type": "ListGroup", "text": "We propose PAS, a simple novel measure to quantify the potential contribution of a pretrained model and labeled source domain in the adaptation to an unlabeled target domain before performing domain adaptation. We propose a framework to select the most relevant pre-trained model or source domain from a collection of potential candidates for performing domain adaptation. We empirically validate our framework using different domain adaptation methods and image classification benchmarks, and show how our score has a high correlation with the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/2/ListGroup/294"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0017", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Unsupervised domain adaptation. The goal of unsupervised domain adaptation (UDA) is to transfer the knowledge learned from a labeled domain to a different unlabeled target domain. Usually, this goal is achieved by learning a latent representation that is invariant across domains. Several works minimize the distribution discrepancy on the representation using statically defined distance metrics such as Maximum Mean Discrepancy (MMD) (e.g., DAN Long et al. (2015) , DDC Tzeng et al. (2014) , JAN Long et al. (2017) ), covariance (e.g., DCORAL Sun & Saenko (2016) ), or Wasserstein distance (e.g., DeepJDOT Damodaran et al. (2018) ). The popularization of generative models inspired the proposal of methods that adopt adversarial learning to align data across different domains. DANN Ganin et al. (2016) , CDAN Long et al. (2018) , and ADDA Tzeng et al. (2017) are examples of widely adopted UDA methods that have shown promising results. Self-training is another promising paradigm that exploits the pseudo-labels predicted for the target domain to enhance the model. CST Liu et al. (2021) , CRST Zou et al. (2019) , FixMatch Sohn et al. (2020) and MCC Jin et al. (2020) are examples of methods that explore pseudo-labeling. Most recently, with the dissemination of transformers and foundation models, new works explore the cross-attention mechanism to propose transformer-based domain adaptation methods, such as PMTrans Zhu et al. (2023) and DoT Ren et al. (2024) . See Liu et al. (2022) ; Deng & Jia (2023) ; Alijani et al. (2024) for a comprehensive survey on domain adaptation methods.", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0018", "section": "2 RELATED WORK", "page_start": 3, "page_end": 3, "type": "Text", "text": "Pre-training and domain adaptation Recent works suggest that the choice of the pre-trained feature extractor can significantly improve the result of domain adaptation methods. Teterwak et al. (2023) show that simply adopting a model with better weight initialization can help the robustness", "source": "marker_v2", "marker_block_id": "/page/2/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0019", "section": "2 RELATED WORK", "page_start": 4, "page_end": 4, "type": "Text", "text": "of a model to out-of-distribution samples. Similarly, Kim et al. (2022) empirically show that SOTA pre-training outperforms SOTA domain adaptation methods even without access to a target domain. With a modern pre-trained backbone, older domain adaptation methods perform better than SOTA methods, but no method is consistently better in all benchmarks, and negative transfer can occur. Li et al. (2023) empirically show how, in some cases, the performance of the pre-trained model in an unseen target domain is already decent. However, no single pre-trained model performs well in all target datasets. Tang & Jia (2023) study the effects of pre-training on the domain adaptation between synthetic and real images. Without pre-training, none of the methods considered in the study outperformed the baseline trained only on the labeled source data. Other studies have also proposed new datasets and pre-training techniques that achieve competitive performance in the target domain Shen et al. (2022); Luo et al. (2024). We leverage the potential relationship between pre-training and domain adaptation success to estimate transferability between domains.", "source": "marker_v2", "marker_block_id": "/page/3/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0020", "section": "2 RELATED WORK", "page_start": 4, "page_end": 4, "type": "Text", "text": "Transferability estimation In the past years, many works have proposed scorees for quantitatively estimating the transferability of a pre-trained model to a target task. One of the primary practical applications of such estimation is selecting the best pre-trained model for fine-tuning on the target data. H-score Bao et al. (2019), NCE Tran et al. (2019), LEEP Nguyen et al. (2020) and LogME You et al. (2021) are widely adopted transferability estimation scores. More closely related to our proposal, some works propose scores for transferability estimation by examining the separability of classes in the embedding space encoded by the pre-trained model. Pándy et al. (2022) apply the Bhattacharyya coefficient to quantify the target class separability. Similarly, Meiseles & Rokach (2020) employ the Silhouette score to assess the transferability of time series data. The current methods on transferability estimation focus on the transfer learning problem, where a pre-trained model is adapted to a target task with a few labeled samples. Unfortunately, these methods can not be applied to the domain adaptation problem, where the target labels are not available.", "source": "marker_v2", "marker_block_id": "/page/3/Text/2"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0021", "section": "3.1 Definitions", "page_start": 4, "page_end": 4, "type": "Text", "text": "Unsupervised domain adaptation aims to transfer knowledge from a labeled source domain to an unlabeled target domain in the presence of distribution shift. Let \\mathcal{X} \\subseteq \\mathbb{R}^d define the input space and \\mathcal{Y} = \\{1,\\ldots,C\\} the label space. The labeled source dataset is denoted by \\mathcal{D}^S = \\{(x_i^S,y_i^S)\\}_{i=1}^{|\\mathcal{D}^S|} and the unlabeled target dataset is denoted by \\mathcal{D}^T = \\{x_i^T\\}_{j=1}^{|\\mathcal{D}^T|} , with x_i^S, x_i^T \\in \\mathcal{X} and y_i^S \\in \\mathcal{Y} . S_c^S denotes the set of source samples from class c. The source and target feature distributions are sampled from different but related distributions, P_S(\\mathcal{X}) and P_T(\\mathcal{X}) , respectively, being P_S \\neq P_T . This scenario is also known as covariate shift . The goal is to learn a hypothesis h: \\mathcal{X} \\to \\mathcal{Y} that performs well on the target domain.", "source": "marker_v2", "marker_block_id": "/page/3/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0022", "section": "3.1 Definitions", "page_start": 4, "page_end": 4, "type": "Text", "text": "Let \\theta be the parameters of a feature extractor f_{\\theta}: \\mathcal{X} \\to \\mathcal{Z} pre-trained on a large-scale dataset. z_i^S = f_{\\theta}(x_i^S) and z_i^T = f_{\\theta}(x_i^T) denote, respectively, the embedding of a source and a target sample in the embedding space defined by f_{\\theta} .", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0023", "section": "3.2 ASSUMPTIONS", "page_start": 4, "page_end": 4, "type": "Text", "text": "We assume that a good pre-trained model f_{\\theta} is able to extract a wide range of patterns and high-level concepts from an input, including discriminative features that are invariant across different domains. We expect that samples from the same class are more similar, having many concepts in common. As a result, two samples from the same class should be closer together in the embedding space \\mathcal{Z} , no matter the domain. On the other hand, samples from different classes should have very few concepts in common, resulting in a dissimilar embedding representation. Due to the distribution shift between the source and target domains, samples from the same domain are expected to have more concepts in common and, therefore, have more similar representations than samples from different domains. Such assumptions lead to a scenario similar to the one represented in the top left of figure 2. The embeddings of samples from the same domain and class form a well-defined cluster in the space encoded by f_{\\theta} . Also, the clusters of samples from the same class, but different domains, are closer together and, ideally, both are distant from all the other clusters.", "source": "marker_v2", "marker_block_id": "/page/3/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0024", "section": "3.2 ASSUMPTIONS", "page_start": 5, "page_end": 5, "type": "Text", "text": "To summarize, we assume that 1) a good pre-trained model can extract invariant discriminative features, 2) samples from the same class are close in the embedding space, even if they are from different domains, and 3) samples from different classes are distant in the embedding space. Similar assumptions are proposed by Shen et al. (2022) when studying the generalization of embeddings to out-of-distribution samples.", "source": "marker_v2", "marker_block_id": "/page/4/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0025", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "We introduce the Potential Adaptability Score (PAS) as a measure of the distance from a labeled source dataset to an unlabeled target dataset in the embedding space encoded by a pre-trained feature extractor. The PAS score is based on the expectation that each target sample is as close as possible to source samples from a single class and significantly distant from source samples from all other classes in the embedding space defined by a pre-trained model f_{\\theta} . This means that a target sample is very similar to source samples from one class and has only a few concepts in common with source samples from all other classes, as illustrated in figure 2. The higher the PAS value, the stronger the evidence that the pre-trained model can identify invariant discriminative features between the domains and, consequently, the higher the chances that the pre-trained feature extractor f_{\\theta} has a good transferability from the source to the target samples.", "source": "marker_v2", "marker_block_id": "/page/4/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0026", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "The samples are normalized to unit length, and the distance between samples is calculated using the cosine distance. We assume that the samples from the class c \\in \\mathcal{Y} are clustered together. We follow Dhillon & Modha (2001) and compute the centroid of each source class cluster c so they represent the vector that, on average, has the highest cosine similarity to all the samples in the cluster.", "source": "marker_v2", "marker_block_id": "/page/4/Text/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0027", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mu_c = \\frac{\\sum_{x_i^S \\in S_c^S} f_{\\theta}(x_i^S)}{\\|\\sum_{x_i^S \\in S_c^S} f_{\\theta}(x_i^S)\\|}. (1)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0028", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "For each target sample x_i^T , we calculate its cosine distance to the centroid of each source cluster:", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0029", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_c) = 1 - (f_{\\theta}(x_i^T) \\cdot \\mu_c). \\tag{2}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0030", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Let D_i = \\{ \\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_1), ..., \\operatorname{dist}(f_{\\theta}(x_i^T), \\mu_C) \\} be the set of distances of the j-th target sample to all the source clusters and sort(D_i) the sorted version of the set in ascending order. We define d_{1i} = sort(D_i)[1] and d_{2i} = sort(D_i)[2] as the shortest and the second shortest of the distances, respectively, as illustrated at the bottom of figure 2.", "source": "marker_v2", "marker_block_id": "/page/4/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0031", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Finally, the PAS score is defined by", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0032", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mathbf{PAS}(\\theta, \\mathcal{D}^{\\mathbf{S}}, \\mathcal{D}^{\\mathbf{T}}) = \\frac{1}{|\\mathcal{D}^{T}|} \\sum_{i}^{|\\mathcal{D}^{T}|} \\frac{d_{2i} - d_{1i}}{d_{2i}}. (3)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0033", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Given one or more candidate source domains and a set of pre-trained models, the PAS score can help to select the options that are more likely to lead to the best accuracy on the target samples. The selection is done by computing the PAS score for each trio of target domain, source domain, and pre-trained model. The combination with the highest PAS value is chosen. The selection is done before any domain adaptation training. A single-source domain adaptation method can then be trained with the selected source domain and pre-trained feature extractor.", "source": "marker_v2", "marker_block_id": "/page/4/Text/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0034", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 5, "page_end": 5, "type": "Text", "text": "Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987). The Silhouette is a supervised score calculated by (b-a)/max\\{a,b\\} , where a is the mean intra-cluster distance and b is the mean nearest-cluster distance for each sample. It ranges from -1 to 1, with higher values indicating strong intra-class cohesion and clear inter-class separation. Note that the Silhouette score is fully supervised and designed for IID samples and its original form is not suitable for the domain adaptation problem. Our PAS score is an adaptation to accommodate unlabeled target samples and domain shift. We consider the closest source cluster as the true class for each target sample. This assumption makes a always smaller than b, and restricts our score to the interval [0,1]. The PAS score is close to one if the samples from the target domain", "source": "marker_v2", "marker_block_id": "/page/4/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0035", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 6, "page_end": 6, "type": "FigureGroup", "text": "Figure 3: The correlation between the PAS score value and the target accuracy after the domain adaptation. Each box summarizes the target accuracy of different domain adaptation methods for a given source-target pair and a pre-trained feature extractor. Higher values for the PAS score are strongly correlated with higher target accuracy.", "source": "marker_v2", "marker_block_id": "/page/5/FigureGroup/166"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0036", "section": "3.3 THE POTENTIAL ADAPTABILITY SCORE", "page_start": 6, "page_end": 6, "type": "Text", "text": "are similar to the centroid of the source class cluster. However, due to the mismatch between the domains, the target samples exhibit a shift in the feature distribution, making a larger than in the IID scenario. As a result, the values for our score are typically smaller. Alternative design choices are discussed and evaluated in section 4.4.", "source": "marker_v2", "marker_block_id": "/page/5/Text/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0037", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Datasets. We evaluate PAS on four of the most popular benchmarks for domain adaptation: Office-Home Venkateswara et al. (2017), Office-31 Saenko et al. (2010), ImageCLEF <sup>1</sup>, and DomainNet Peng et al. (2019). The benchmarks' statistics are listed in the table 2.", "source": "marker_v2", "marker_block_id": "/page/5/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0038", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "FigureGroup", "text": "Figure 4: The PAS value and target accuracy for the DANN and MCC methods using different pretrained feature extractors. The PAS score can help to select the feature extractor that leads to higher accuracy. ( left ) A \\rightarrow C adaptation in the Office-Home benchmark. ( right ) W \\rightarrow A adaptation in the Office-31 benchmark.", "source": "marker_v2", "marker_block_id": "/page/5/FigureGroup/167"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0039", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Junguang Jiang (2020), Wang et al. (2023), and from the original papers.", "source": "marker_v2", "marker_block_id": "/page/5/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0040", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Text", "text": "Baselines To the best of our knowledge, PAS is the first asymmetric score proposed for transferability estimation for domain adaptation. We, therefore, compare PAS with the symetric metrics Maximum Mean Discrepancy (MMD) Gretton et al. (2012) and \\mathcal{A} -distance Peng et al. (2019). The MMD distance is computed using a Gaussian kernel. Due to the quadratic nature of MMD, we restrict its computation to a maximum of 10,000 randomly selected samples per domain for the DomainNet benchmark. The \\mathcal{A} -distance is computed using C-Support Vector Classification. We also report the results for an oracle baseline. The oracle is similar to PAS , defined as \\frac{1}{|\\mathcal{D}^T|} \\sum_{i}^{|\\mathcal{D}^T|} \\frac{d_{2i} - d_{1i}}{max\\{d_{1i}, d_{2i}\\}}. The d_{1i} distance is the cosine distance to the centroid of the true class of the target sample (not known in real scenarios), and d_{2i} is the distance to the closest cluster's", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0041", "section": "4 EXPERIMENTS", "page_start": 6, "page_end": 6, "type": "Footnote", "text": "1", "source": "marker_v2", "marker_block_id": "/page/5/Footnote/11"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0042", "section": "4 EXPERIMENTS", "page_start": 7, "page_end": 7, "type": "Caption", "text": "Table 1: Average target accuracy of domain adaptation methods and transferability scores for different image classification benchmarks. The highest values are highlighted. Our PAS has a high correlation with the target accuracy and, for each target domain, attributes the highest value for the source domain that leads to the highest target accuracy in most scenarios. * Oracle baseline that considers the target labels.", "source": "marker_v2", "marker_block_id": "/page/6/Caption/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0043", "section": "(a) Office-Home", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target | A С P R Correlation on with acc. Source C P R A P R A C R A C P Pearson Spearman Acc. (avg.) 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 MMD (neg.) -0.135 -0.113 -0.052 -0.135 -0.097 -0.125 -0.113 -0.097 -0.033 -0.052 -0.125 -0.033 0.77 0.72 ResNet-50 A-distance (neg.) -1.876 -1.810 -1.333 -1.876 -1.827 -1.814 -1.810 -1.827 -1.424 -1.333 -1.814 -1.424 0.76 0.78 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 0.81 0.82 Oracle* 0.041 0.037 0.093 -0.022 -0.018 -0.022 0.103 0.100 0.218 0.165 0.096 0.195 0.98 0.93 Acc. (avg.) 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86.0 83.3 82.5 84.1 MMD (neg.) -0.106 -0.058 -0.024 -0.106 -0.077 -0.102 -0.058 -0.077 -0.026 -0.024 -0.102 -0.026 0.56 0.57 DeiT-Small A-distance (neg.) -1.865 -1.761 -1.26 -1.865 -1.843 -1.796 -1.761 -1.843 -1.37 -1.26 -1.796 -1.37 0.52 0.57 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 0.67 0.78 Oracle* 0.086 0.112 0.18 0.038 0.037 0.047 0.194 0.155 0.291 0.243 0.147 0.246 0.90 0.93 Acc. (avg.) 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 MMD (neg.) -0.099 -0.056 -0.028 -0.099 -0.091 -0.11 -0.056 -0.091 -0.023 -0.028 -0.11 -0.023 0.56 0.57 DeiT-Base A-distance (neg.) -1.832 -1.81 -1.372 -1.832 -1.907 -1.823 -1.81 -1.907 -1.502 -1.372 -1.823 -1.502 0.48 0.51 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 0.65 0.73 Oracle* 0.09 0.112 0.184 0.048 0.049 0.062 0.191 0.158 0.293 0.245 0.154 0.248 0.88 0.88 Acc. (avg.) 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 MMD (neg.) -0.116 -0.082 -0.032 -0.116 -0.115 -0.122 -0.082 -0.115 -0.034 -0.032 -0.122 -0.034 0.61 0.49 ViT-Small A-distance (neg.) -1.885 -1.883 -1.348 -1.885 -1.927 -1.862 -1.883 -1.927 -1.515 -1.348 -1.862 -1.515 0.53 0.59 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 0.68 0.83 Oracle* 0.132 0.147 0.212 0.084 0.102 0.113 0.211 0.195 0.321 0.26 0.189 0.285 0.87 0.92 Acc. (avg.) 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 MMD (neg.) -0.101 -0.069 -0.031 -0.101 -0.106 -0.11 -0.069 -0.106 -0.025 -0.031 -0.11 -0.025 0.59 0.57 ViT-Base A-distance (neg.) -1.85 -1.845 -1.389 -1.85 -1.952 -1.885 -1.845 -1.952 -1.595 -1.389 -1.885 -1.595 0.47 0.51 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 0.76 0.85 Oracle* 0.215 0.233 0.311 0.173 0.188 0.207 0.317 0.295 0.425 0.37 0.286 0.382 0.88 0.92 Acc. (avg.) 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 MMD (neg.) -0.081 -0.085 -0.039 -0.081 -0.104 -0.097 -0.085 -0.104 -0.033 -0.039 -0.097 -0.033 0.48 0.45 Swin-Base A-distance (neg.) -1.853 -1.892 -1.401 -1.853 -1.95 -1.917 -1.892 -1.95 -1.57 -1.401 -1.917 -1.57 0.42 0.37 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384 0.72 0.72 Oracle* 0.198 0.214 0.287 0.162 0.177 0.195 0.295 0.282 0.403 0.343 0.27 0.356 0.83 0.81", "source": "marker_v2", "marker_block_id": "/page/6/Table/3"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0044", "section": "(b) Office-31", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target A 1 ) | V V Correlation on with acc. Source D W A W A D Pearson Spearman Acc. (avg.) 71.8 70.6 90.5 100.0 91.9 98.3 MMD (neg.) -0.145 -0.165 -0.145 -0.046 -0.165 -0.046 0.71 0.72 ResNet-50 A-distance (neg.) -2.00 -2.00 -2.00 -1.783 -2.00 -1.783 0.72 0.83 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 0.73 0.66 Oracle* 0.192 0.166 0.246 0.445 0.188 0.407 0.80 0.83 Acc. (avg.) 77.7 77.6 94.7 94.65 MMD (neg.) -0.123 -0.129 -0.123 -0.058 -0.129 -0.058 0.66 0.84 DeiT-Small A-distance (neg.) -2.00 -1.994 -2.00 -1.969 -1.994 -1.969 0.65 0.60 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 0.72 0.94 Oracle* 0.2 0.193 0.263 0.465 0.239 0.438 0.80 1.00 Acc. (avg.) 81.3 82.0 96.8 100.0 97.9 99.2 MMD (neg.) -0.113 -0.134 -0.113 -0.074 -0.134 -0.074 0.54 0.60 DeiT-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 0.66 0.71 Oracle* 0.212 0.192 0.273 0.44 0.224 0.414 0.73 0.89 Acc. (avg.) 83.5 82.2 98.6 100.0 97.7 99.2 MMD (neg.) -0.175 -0.197 -0.175 -0.098 -0.197 -0.098 0.56 0.84 ViT-Small A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 0.61 0.94 Oracle* 0.23 0.22 0.286 0.506 0.256 0.467 0.69 1.00 Acc. (avg.) 84.0 85.0 97.2 100.0 96.8 99.3 MMD (neg.) -0.098 -0.118 -0.098 -0.071 -0.118 -0.071 0.57 0.72 ViT-Base A-distance (neg.) -2.00 -2.00 -2.00 -1.953 -2.00 -1.953 0.64 0.72 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 0.71 0.83 Oracle* 0.373 0.347 0.434 0.589 0.393 0.554 0.79 0.94 Acc. (avg.) 86.2 86.3 99.7 100.0 99.4 99.5 MMD (neg.) -0.168 -0.169 -0.168 -0.086 -0.169 -0.086 0.51 0.60 Swin-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56 0.62 0.89 Oracle* 0.321 0.313 0.388 0.589 0.366 0.558 0.69 0.89", "source": "marker_v2", "marker_block_id": "/page/6/Table/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0045", "section": "(c) ImageCLEF", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target | ( 3 1 I 1 P Correlation on with acc. Source I P C P C I Pearson Spearman Acc. (avg.) 95.9 93.7 90.7 90.0 76.0 77.9 MMD (neg.) -0.074 -0.097 -0.074 -0.022 -0.097 -0.022 -0.17 -0.12 ResNet-50 A-distance (neg.) -1.583 -1.731 -1.583 -0.807 -1.731 -0.807 -0.24 -0.12 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 0.22 0.49 Oracle* 0.287 0.243 0.195 0.254 0.111 0.2 0.84 0.71 Acc. (avg.) 97.5 97.5 93.7 95.2 78.3 80.8 MMD (neg.) -0.072 -0.081 -0.072 -0.02 -0.081 -0.02 -0.17 -0.11 DeiT-Small A-distance (neg.) -1.417 -1.748 -1.417 -0.807 -1.748 -0.807 -0.07 -0.11 PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 0.41 0.52 Oracle* 0.333 0.293 0.239 0.31 0.169 0.25 0.83 0.83 Acc. (avg.) 97.8 97.1 96.6 95.7 79.5 81.9 MMD (neg.) -0.078 -0.095 -0.078 -0.022 -0.095 -0.022 -0.13 -0.12 ViT-Base A-distance (neg.) -1.483 -1.714 -1.483 -0.655 -1.714 -0.655 -0.14 -0.12 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363 0.55 0.54 Oracle* 0.391 0.352 0.295 0.37 0.205 0.286 0.84 0.83", "source": "marker_v2", "marker_block_id": "/page/6/Table/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0046", "section": "(d) DomainNet", "page_start": 7, "page_end": 7, "type": "Table", "text": "Target C P R S Correlation on with acc. Source P R S C R S C P S C P R Pearson Spearman Acc. (avg.) 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 MMD (neg.) -0.113 -0.158 -0.079 -0.113 -0.075 -0.108 -0.158 -0.075 -0.173 -0.079 -0.108 -0.173 0.04 0.20 ResNet-101 A-distance (neg.) -1.789 -1.73 -1.638 -1.789 -1.656 -1.777 -1.73 -1.656 -1.821 -1.638 -1.777 -1.821 0.50 0.45 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 0.58 0.53 Oracle* -0.109 -0.124 -0.042 -0.06 -0.024 -0.04 0.037 0.092 0.031 -0.087 -0.11 -0.156 0.70 0.67 Acc. (avg.) 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 MMD (neg.) -0.128 -0.146 -0.088 -0.128 -0.052 -0.16 -0.146 -0.052 -0.186 -0.088 -0.16 -0.186 0.26 0.28 DeiT-Small A-distance (neg.) -1.784 -1.734 -1.655 -1.784 -1.639 -1.768 -1.734 -1.639 -1.823 -1.655 -1.768 -1.823 0.30 0.33 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 0.39 0.57 Oracle* -0.125 -0.118 -0.055 -0.066 -0.015 -0.051 0.031 0.093 0.015 -0.12 -0.163 -0.183 -0.19 -0.17 Acc. (avg.) 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 MMD (neg.) -0.123 -0.153 -0.095 -0.123 -0.06 -0.171 -0.153 -0.06 -0.227 -0.095 -0.171 -0.227 0.19 0.35 DeiT-Base A-distance (neg.) -1.796 -1.746 -1.655 -1.796 -1.682 -1.79 -1.746 -1.682 -1.838 -1.655 -1.79 -1.838 0.26 0.37 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 0.26 0.44 Oracle* -0.115 -0.097 -0.044 -0.047 0.004 -0.04 0.044 0.105 0.022 -0.109 -0.162 -0.154 -0.17 -0.08 Acc. (avg.) 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 MMD (neg.) -0.14 -0.157 -0.108 -0.14 -0.116 -0.175 -0.157 -0.116 -0.25 -0.108 -0.175 -0.25 0.07 0.15 ViT-Base A-distance (neg.) -1.814 -1.771 -1.686 -1.814 -1.734 -1.807 -1.771 -1.734 -1.859 -1.686 -1.807 -1.859 0.18 0.21 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17 0.37 0.35 Oracle* -0.003 0.018 0.042 0.012 0.066 0.007 0.135 0.184 0.103 -0.021 -0.075 -0.062 -0.13 -0.08", "source": "marker_v2", "marker_block_id": "/page/6/Table/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0047", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 2: Statistics of the benchmarks used in the experiments. Dataset #Samples #Classes Domains Office-Home 15,588 65 A (Art), C (Clipart), P (Product), R (Real-world) Office-31 4,110 31 A (Amazon), D (DSLR), W (Webcam) ImageCLEF 1,800 12 C (Caltech-256), I (ImageNet ILSVRC 2012), P (Pascal VOC 2012) DomainNet 569,010 345 C (Clipart), P (Painting), R (Real), S (Sketch) Table 3: Correlation with the average target accuracy after adaptation. Showing Pearson correlation / Spearman's rank correlation.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/82"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0048", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "Table", "text": "Office-Home Office-31 ImageCLEF DomainNet Total MMD 0.55 / 0.51 0.45 / 0.53 -0.14 / -0.08 -0.09 / -0.03 0.37 / 0.37 \\mathcal{A} -distance 0.32 / 0.17 0.26 / 0.35 -0.13 / -0.07 0.07 / 0.06 0.04 / -0.16 PAS (our) 0.76 / 0.81 0.63 / 0.78 0.44 / 0.60 0.53 / 0.56 0.83 / 0.88 Oracle* 0.89 / 0.90 0.71 / 0.86 0.78 / 0.85 0.21 / 0.21 0.88 / 0.91", "source": "marker_v2", "marker_block_id": "/page/7/Table/4"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0049", "section": "(d) DomainNet", "page_start": 8, "page_end": 8, "type": "Text", "text": "centroid that is not the true class. In the ideal case where the closest class centroid is the actual class of the sample, the oracle is the same as PAS , otherwise, the oracle value is smaller. The oracle validates the existing relationship between the clusters distance and the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/7/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0050", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "The results for the four benchmark datasets are presented in Table 1 (a) - (d). For each source-target pair in the benchmarks, we group the domain adaptation methods using the same pre-trained feature extractor and report their average target accuracy, followed by the baselines and our PAS score. We highlight the highest values among the different choices of source domains. We also report the correlation (Pearson and Spearman's rank correlation) between the average target accuracy and the scores. The detailed results for each individual domain adaptation method are presented in the Supplementary Material A.1.", "source": "marker_v2", "marker_block_id": "/page/7/Text/7"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0051", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "We report in Table 3 the overall correlation for all scenarios of each benchmark (all target domains, source domains and pre-trained models). The results show that the PAS score is strongly correlated with target accuracy. We observe an overall Spearman's rank correlation of 0.88 over all the results.", "source": "marker_v2", "marker_block_id": "/page/7/Text/8"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0052", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "The most important results are reported in Table 4, where we present the correlation for each target domain. This correlation is the most useful for users in real-world scenarios. Given a target domain of interest and many options of source domains and pre-trained models, we show that our PAS score has a strong correlation with the final target accuracy. The empirical results indicate that our proposed PAS score is effective in selecting the best source domain among many candidates.", "source": "marker_v2", "marker_block_id": "/page/7/Text/9"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0053", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "Text", "text": "We summarize our results in Figure 3. Each box in the graph represents the target accuracy of different domain adaptation methods using the same pre-trained backbone for a source-target domains pair. We observe that higher PAS values are consistently related to high accuracy on the target domain. This indicates that PAS may be useful not only for selecting the most appropriate source domain, but also to estimate beforehand the success of the domain adaptation.", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0054", "section": "4.1 Selection of the Source Domain", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 4: Correlation with the average target accuracy after adaptation for each target domain. Each cell considers the results for a target domain and all available source domains and pre-trained models. Showing Pearson correlation / Spearman's rank correlation. Office -Home 1 Office-31 1 ImageCLEF Doma ainNet A C P R A D W C I P С P R S MMD 0.41 / 0.26 0.28 / 0.21 0.41 / 0.29 0.25 / 0.21 -0.02 / -0.15 0.44 / 0.60 0.45 / 0.36 0.54 / 0.49 -0.03 / -0.22 0.61 / 0.60 -0.56 / -0.42 0.33 / 0.20 0.23 / 0.47 -0.38 / -0.42 A-distance 0.12 / -0.13 -0.46 / -0.43 0.15 / -0.09 -0.05 / -0.26 -0.19 / -0.31 0.27 / 0.28 0.14 / 0.07 0.43 / 0.38 0.10 / 0.05 0.64 / 0.60 0.09 / -0.04 0.35 / 0.17 0.27 / 0.30 -0.10 / -0.32 PAS (our) 0.70 / 0.70 0.81 / 0.78 0.79 / 0.74 0.75 / 0.75 0.65 / 0.81 0.70 / 0.81 0.70 / 0.75 0.82 / 0.76 0.73 / 0.66 0.87 / 0.83 0.71 0.67 0.75 / 0.76 0.59 / 0.71 0.48 / 0.35 Oracle* 0.82 / 0.85 0.91 / 0.90 0.84 / 0.81 0.80 / 0.87 0.74 / 0.88 0.73 / 0.90 0.74 / 0.78 0.81 / 0.76 0.74 / 0.66 0.97 / 0.94 0.36 / 0.50 0.71 / 0.62 0.61 / 0.72 0.28 / 0.33", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/83"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0055", "section": "4.1 Selection of the Source Domain", "page_start": 9, "page_end": 9, "type": "Text", "text": "The results on the ImageCLEF benchmark illustrate the scenarios where the PAS score is not effective. This benchmark (especially the P domain) contains images with multiple objects. In many cases, the sample is very close to the centroid of one class that is indeed present in the image, but the true label is related to another object in the scene. In these cases, the PAS for the sample is high, showing a high similarity with one source class, but the final accuracy is low, as the sample is classified as the wrong class. We show examples in the supplementary material A.2", "source": "marker_v2", "marker_block_id": "/page/8/Text/1"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0056", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "FigureGroup", "text": "Figure 5: The PAS value varying with the number of samples for the Office-Home . The PAS values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.", "source": "marker_v2", "marker_block_id": "/page/8/FigureGroup/168"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0057", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "Text", "text": "may be applied for the selection of the pre-trained model.", "source": "marker_v2", "marker_block_id": "/page/8/Text/5"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0058", "section": "4.2 The selection of the pre-trained feature extractor", "page_start": 9, "page_end": 9, "type": "Text", "text": "The results in the literature presented in table 1 compare methods with different backbones and demonstrate that PAS can be applied to select the most suitable pretrained feature extractor. However, they do not consider the impact of different pre-trained feature extractors over the same domain adaptation method. For analyzing the robustness of PAS over different choices of pre-trained methods, we keep the domain adaptation method fixed and vary the pre-trained backbone. We select two of the most challenging domain adaptation scenarios: the A \\rightarrow C adaptation in the Office-Home benchmark and W \\rightarrow A adaptation in the Office-31 benchmark. We show results for two popular domain adaptation methods: DANN Ganin et al. (2016) and MCC Jin et al. (2020). We train each method following the code provided by the Tllib library Jiang et al. (2022); Junguang Jiang (2020) with the default hyperparameters. The results are shown in figure 4. Higher PAS values are attributed to pretrained models that lead to higher target accuracy before performing domain adaptation, indicating that our score", "source": "marker_v2", "marker_block_id": "/page/8/Text/6"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0059", "section": "4.3 THE IMPACT OF THE SAMPLE SIZE", "page_start": 9, "page_end": 9, "type": "Text", "text": "The time complexity of the PAS computation is linear in the number of samples. This can be limiting for a quick evaluation of larger datasets and scenarios with many candidate source domains.", "source": "marker_v2", "marker_block_id": "/page/8/Text/8"}
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+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0062", "section": "4.4 DESIGN CHOICES", "page_start": 9, "page_end": 9, "type": "Text", "text": "We change PAS to consider the Euclidean distance instead of the cosine distance. In the domain adaptation setting, the cosine distance has advantages over using the Euclidean distance in the original latent space, as it ignores the magnitude of", "source": "marker_v2", "marker_block_id": "/page/8/Text/12"}
+{"paper_id": "0Z2l4XtTdz", "chunk_id": "0Z2l4XtTdz:0063", "section": "4.4 DESIGN CHOICES", "page_start": 9, "page_end": 9, "type": "TableGroup", "text": "Office-Home Office-31 ImageCLEF DomainNet Total PAS 0.76 0.63 0.44 0.58 0.79 Euclidean distance 0.70 0.69 0.27 0.54 0.68 Average cosine distance 0.66 0.52 0.12 0.48 0.66 Table 5: Pearson correlation between the target accuracy and the PAS score, which considers the cosine distance to the cluster centroid, and modifications using the Euclidean distance to the centroid and the average cosine distance to the source cluster samples. The maximum correlation value for each benchmark is highlighted. The design choices of PAS lead to the higher overall correlation between the score and the target accuracy.", "source": "marker_v2", "marker_block_id": "/page/8/TableGroup/169"}
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@@ -0,0 +1,203 @@
+[p. 1 | section: ABSTRACT | type: Text]
+The goal of domain adaptation is to make predictions for unlabeled samples from a target domain with the help of labeled samples from a different but related source domain. The performance of domain adaptation methods is highly influenced by the choice of source domain and pre-trained feature extractor. However, the selection of source data and pre-trained model is not trivial due to the absence of a labeled validation set for the target domain and the large number of available pre-trained models. In this work, we propose Potential Adaptability Score (PAS), a novel score designed to estimate the transferability of a source domain set and a pre-trained feature extractor to a target classification task before actually performing domain adaptation. PAS leverages the generalization power of pretrained models and assesses source-target compatibility based on the pre-trained feature embeddings. We integrate PAS into a framework that indicates the most relevant pre-trained model and source domain among multiple candidates, thus improving target accuracy while reducing the computational overhead. Extensive experiments on image classification benchmarks demonstrate that PAS correlates strongly with actual target accuracy and consistently guides the selection of the best-performing pre-trained model and source domain for adaptation.
+
+[p. 1 | section: 1 INTRODUCTION | type: Text]
+In many real applications, data is collected from diverse domains, e.g., data obtained from different equipment, collecting procedures, geographic locations, or periods in time. Such differences may lead to a distribution shift between the domains that must be assessed. Unsupervised domain adaptation is a paradigm where only unlabeled data is available for the domain of interest, the target domain. However, labeled data is obtained from a related source domain.
+
+[p. 1 | section: 1 INTRODUCTION | type: Text]
+One factor that affects the success of domain adaptation methods is the choice of the source domain data. Domain adaptation methods often rely on many assumptions about the relationship between source and target domains, like the existence of invariant discriminative features, the similarity of the label distribution, or the invariance of the task. Unfortunately, as the labels for the target samples are not available, such assumptions may not be verified in real applications for selecting the most appropriate source data. Violating the data assumptions and
+
+[p. 1 | section: 1 INTRODUCTION | type: FigureGroup]
+Figure 1: The Potential Adaptability Score (PAS) estimates the performance of adapting to an unlabeled target domain given a pre-trained feature extractor and a labeled source domain. It helps in the selection of the best pre-trained model and best source domain among many candidates and is highly correlated with the final target accuracy after domain adaptation.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+considering an irrelevant or distant source domain may introduce noise and conflicting patterns during the domain adaptation process. In the worst-case scenario, selecting an undesirable source domain may hurt the target domain performance, a scenario known as negative transfer Zhang et al. (2022) . If many source domains are available, it is reasonable to assume that not all of them may contribute equally to the target adaptation. Wisely selecting the source domain that may improve the performance on the target data while avoiding negative transfer is an essential requirement in many real-world applications.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+Another key factor that influences the domain adaptation performance is the choice of the pre-trained model. Pre-training on large-scale data allows the models to learn generic features and patterns that are often transferable across domains and tasks, making them valuable for domain adaptation. Recently, practitioners can choose from a vast number of publicly available pre-trained models, spanning diverse architectures and training paradigms. Each pre-trained model may have its own inductive bias and may capture distinct patterns in the data that may be more or less useful when transferring knowledge between domains.
+
+[p. 2 | section: 1 INTRODUCTION | type: Caption]
+Figure 2: Source and target samples in the embedding space of a pre-trained model. (top left) Ideally, a target sample from a given class should be more similar, and hence closer in the embedding space of the pre-trained model, to a source sample from the same class. (top right) If new discriminative features need to be learned, the chances of overfitting on the source domain during adaptation increase. (bottom) Illustration of the distances from a target sample to all source class centroids. Our PAS score considers the relationship between distances d 1 and d2, which correspond to the shortest and second shortest distances, respectively.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+Despite the importance of selecting a suitable source data and a pre-trained model for the success of domain adaptation, it is still an underexplored topic. Current methods of transferability estimation aim to select the best pre-trained model for transfer learning. However, these methods are not applicable to the domain adaptation scenario since they require target labels Bao et al. (2019) ; Nguyen et al. (2020) ; You et al. (2021) . One could employ such methods for selecting the best pre-training model using only the labeled source data and ignoring the unlabeled target data. Nevertheless, considering the target data is essential, as transferring to an easy target domain should lead to different results than transferring to a harder one.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+Another approach for the problem would be performing domain adaptation for each combination of available source domains and pretrained models, and applying some model selection strategy Ericsson et al. (2023) ; You et al. (2019) ; Sun et al. (2021) . However, this approach is very time-consuming since it needs to run a domain adaptation algorithm for each combination.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+A third approach would be to measure the distance between source and target feature distributions in the embedding space of the pretrained model. This approach is also challenging as the popular metrics for the distance between two feature distributions are symmetric, e.g., Maximum Mean Discrepancy (MMD) Gretton et al. (2006) , Wasserstein distance Val lender (1974) , and CORAL Sun & Saenko (2016) . However, a metric suitable for our scenario should be asymmetric because transfer-
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+ring from an easy to a hard domain is more challenging than transferring from the harder domain to the easier one.
+
+[p. 2 | section: 1 INTRODUCTION | type: Text]
+In this work, we examine the interplay between the three key components in the domain adaptation setting for classification: (1) target data, (2) source data, and (3) the pre-trained model. We propose the Potential Adaptability Score (PAS), a simple but effective novel measure to quantify the potential success of using a pre-trained model to transfer knowledge from a source domain to the target
+
+[p. 3 | section: 1 INTRODUCTION | type: Text]
+domain. Our experiments show how the PAS score is highly correlated to the final target accuracy after adaptation.
+
+[p. 3 | section: 1 INTRODUCTION | type: Text]
+To the best of our knowledge, this is the first proposal for transferability estimation for the domain adaptation setting. We demonstrate how PAS can help to select the most relevant source domain and/or pre-trained model among a set of candidates, indicating the options that are most likely to lead to the best accuracy on the unlabeled target data (See an overview in figure 1. ). Our framework selects the most suitable options before actually performing domain adaptation, demanding fewer computational resources and reducing the training time.
+
+[p. 3 | section: 1 INTRODUCTION | type: Text]
+PAS leverages the generalization power of models pre-trained on a large-scale dataset, such as the popular ImageNet-1k Deng et al. (2009) . Specifically for domain adaptation, initializing with a good pre-trained model appears to be a fundamental step in achieving a good transferability between domains Peng et al. (2018) ; Tang & Jia (2023) ; Kim et al. (2022) ; Li et al. (2023) ; Teterwak et al. (2023) . We assume that a good pre-trained model can extract general discriminative features that are robust across all domains. If this assumption is true, samples from the same class are expected to be closer together in the embedding space generated by the pre-trained model, compared to samples from different classes, even in the presence of feature distribution shift. This ideal scenario is illustrated in the top left of the figure 2. Otherwise, as shown in the example on the top right of the figure, the model should learn new discriminative features during the adaptation from the limited labeled source data to enable the classification task, increasing the chances of overfitting to the source domain. Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987) . We modify the original Silhouette score to measure the similarity of the unlabeled target samples to some of the known source class clusters defined in the pre-trained embedding space.
+
+[p. 3 | section: 1 INTRODUCTION | type: Text]
+We summarize our contributions as follows:
+
+[p. 3 | section: 1 INTRODUCTION | type: ListGroup]
+We propose PAS, a simple novel measure to quantify the potential contribution of a pretrained model and labeled source domain in the adaptation to an unlabeled target domain before performing domain adaptation. We propose a framework to select the most relevant pre-trained model or source domain from a collection of potential candidates for performing domain adaptation. We empirically validate our framework using different domain adaptation methods and image classification benchmarks, and show how our score has a high correlation with the target accuracy.
+
+[p. 3 | section: 2 RELATED WORK | type: Text]
+Unsupervised domain adaptation. The goal of unsupervised domain adaptation (UDA) is to transfer the knowledge learned from a labeled domain to a different unlabeled target domain. Usually, this goal is achieved by learning a latent representation that is invariant across domains. Several works minimize the distribution discrepancy on the representation using statically defined distance metrics such as Maximum Mean Discrepancy (MMD) (e.g., DAN Long et al. (2015) , DDC Tzeng et al. (2014) , JAN Long et al. (2017) ), covariance (e.g., DCORAL Sun & Saenko (2016) ), or Wasserstein distance (e.g., DeepJDOT Damodaran et al. (2018) ). The popularization of generative models inspired the proposal of methods that adopt adversarial learning to align data across different domains. DANN Ganin et al. (2016) , CDAN Long et al. (2018) , and ADDA Tzeng et al. (2017) are examples of widely adopted UDA methods that have shown promising results. Self-training is another promising paradigm that exploits the pseudo-labels predicted for the target domain to enhance the model. CST Liu et al. (2021) , CRST Zou et al. (2019) , FixMatch Sohn et al. (2020) and MCC Jin et al. (2020) are examples of methods that explore pseudo-labeling. Most recently, with the dissemination of transformers and foundation models, new works explore the cross-attention mechanism to propose transformer-based domain adaptation methods, such as PMTrans Zhu et al. (2023) and DoT Ren et al. (2024) . See Liu et al. (2022) ; Deng & Jia (2023) ; Alijani et al. (2024) for a comprehensive survey on domain adaptation methods.
+
+[p. 3 | section: 2 RELATED WORK | type: Text]
+Pre-training and domain adaptation Recent works suggest that the choice of the pre-trained feature extractor can significantly improve the result of domain adaptation methods. Teterwak et al. (2023) show that simply adopting a model with better weight initialization can help the robustness
+
+[p. 4 | section: 2 RELATED WORK | type: Text]
+of a model to out-of-distribution samples. Similarly, Kim et al. (2022) empirically show that SOTA pre-training outperforms SOTA domain adaptation methods even without access to a target domain. With a modern pre-trained backbone, older domain adaptation methods perform better than SOTA methods, but no method is consistently better in all benchmarks, and negative transfer can occur. Li et al. (2023) empirically show how, in some cases, the performance of the pre-trained model in an unseen target domain is already decent. However, no single pre-trained model performs well in all target datasets. Tang & Jia (2023) study the effects of pre-training on the domain adaptation between synthetic and real images. Without pre-training, none of the methods considered in the study outperformed the baseline trained only on the labeled source data. Other studies have also proposed new datasets and pre-training techniques that achieve competitive performance in the target domain Shen et al. (2022); Luo et al. (2024). We leverage the potential relationship between pre-training and domain adaptation success to estimate transferability between domains.
+
+[p. 4 | section: 2 RELATED WORK | type: Text]
+Transferability estimation In the past years, many works have proposed scorees for quantitatively estimating the transferability of a pre-trained model to a target task. One of the primary practical applications of such estimation is selecting the best pre-trained model for fine-tuning on the target data. H-score Bao et al. (2019), NCE Tran et al. (2019), LEEP Nguyen et al. (2020) and LogME You et al. (2021) are widely adopted transferability estimation scores. More closely related to our proposal, some works propose scores for transferability estimation by examining the separability of classes in the embedding space encoded by the pre-trained model. Pándy et al. (2022) apply the Bhattacharyya coefficient to quantify the target class separability. Similarly, Meiseles & Rokach (2020) employ the Silhouette score to assess the transferability of time series data. The current methods on transferability estimation focus on the transfer learning problem, where a pre-trained model is adapted to a target task with a few labeled samples. Unfortunately, these methods can not be applied to the domain adaptation problem, where the target labels are not available.
+
+[p. 4 | section: 3.1 Definitions | type: Text]
+Unsupervised domain adaptation aims to transfer knowledge from a labeled source domain to an unlabeled target domain in the presence of distribution shift. Let \mathcal{X} \subseteq \mathbb{R}^d define the input space and \mathcal{Y} = \{1,\ldots,C\} the label space. The labeled source dataset is denoted by \mathcal{D}^S = \{(x_i^S,y_i^S)\}_{i=1}^{|\mathcal{D}^S|} and the unlabeled target dataset is denoted by \mathcal{D}^T = \{x_i^T\}_{j=1}^{|\mathcal{D}^T|} , with x_i^S, x_i^T \in \mathcal{X} and y_i^S \in \mathcal{Y} . S_c^S denotes the set of source samples from class c. The source and target feature distributions are sampled from different but related distributions, P_S(\mathcal{X}) and P_T(\mathcal{X}) , respectively, being P_S \neq P_T . This scenario is also known as covariate shift . The goal is to learn a hypothesis h: \mathcal{X} \to \mathcal{Y} that performs well on the target domain.
+
+[p. 4 | section: 3.1 Definitions | type: Text]
+Let \theta be the parameters of a feature extractor f_{\theta}: \mathcal{X} \to \mathcal{Z} pre-trained on a large-scale dataset. z_i^S = f_{\theta}(x_i^S) and z_i^T = f_{\theta}(x_i^T) denote, respectively, the embedding of a source and a target sample in the embedding space defined by f_{\theta} .
+
+[p. 4 | section: 3.2 ASSUMPTIONS | type: Text]
+We assume that a good pre-trained model f_{\theta} is able to extract a wide range of patterns and high-level concepts from an input, including discriminative features that are invariant across different domains. We expect that samples from the same class are more similar, having many concepts in common. As a result, two samples from the same class should be closer together in the embedding space \mathcal{Z} , no matter the domain. On the other hand, samples from different classes should have very few concepts in common, resulting in a dissimilar embedding representation. Due to the distribution shift between the source and target domains, samples from the same domain are expected to have more concepts in common and, therefore, have more similar representations than samples from different domains. Such assumptions lead to a scenario similar to the one represented in the top left of figure 2. The embeddings of samples from the same domain and class form a well-defined cluster in the space encoded by f_{\theta} . Also, the clusters of samples from the same class, but different domains, are closer together and, ideally, both are distant from all the other clusters.
+
+[p. 5 | section: 3.2 ASSUMPTIONS | type: Text]
+To summarize, we assume that 1) a good pre-trained model can extract invariant discriminative features, 2) samples from the same class are close in the embedding space, even if they are from different domains, and 3) samples from different classes are distant in the embedding space. Similar assumptions are proposed by Shen et al. (2022) when studying the generalization of embeddings to out-of-distribution samples.
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+We introduce the Potential Adaptability Score (PAS) as a measure of the distance from a labeled source dataset to an unlabeled target dataset in the embedding space encoded by a pre-trained feature extractor. The PAS score is based on the expectation that each target sample is as close as possible to source samples from a single class and significantly distant from source samples from all other classes in the embedding space defined by a pre-trained model f_{\theta} . This means that a target sample is very similar to source samples from one class and has only a few concepts in common with source samples from all other classes, as illustrated in figure 2. The higher the PAS value, the stronger the evidence that the pre-trained model can identify invariant discriminative features between the domains and, consequently, the higher the chances that the pre-trained feature extractor f_{\theta} has a good transferability from the source to the target samples.
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+The samples are normalized to unit length, and the distance between samples is calculated using the cosine distance. We assume that the samples from the class c \in \mathcal{Y} are clustered together. We follow Dhillon & Modha (2001) and compute the centroid of each source class cluster c so they represent the vector that, on average, has the highest cosine similarity to all the samples in the cluster.
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Equation]
+\mu_c = \frac{\sum_{x_i^S \in S_c^S} f_{\theta}(x_i^S)}{\|\sum_{x_i^S \in S_c^S} f_{\theta}(x_i^S)\|}. (1)
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+For each target sample x_i^T , we calculate its cosine distance to the centroid of each source cluster:
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Equation]
+\operatorname{dist}(f_{\theta}(x_i^T), \mu_c) = 1 - (f_{\theta}(x_i^T) \cdot \mu_c). \tag{2}
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+Let D_i = \{ \operatorname{dist}(f_{\theta}(x_i^T), \mu_1), ..., \operatorname{dist}(f_{\theta}(x_i^T), \mu_C) \} be the set of distances of the j-th target sample to all the source clusters and sort(D_i) the sorted version of the set in ascending order. We define d_{1i} = sort(D_i)[1] and d_{2i} = sort(D_i)[2] as the shortest and the second shortest of the distances, respectively, as illustrated at the bottom of figure 2.
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+Finally, the PAS score is defined by
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Equation]
+\mathbf{PAS}(\theta, \mathcal{D}^{\mathbf{S}}, \mathcal{D}^{\mathbf{T}}) = \frac{1}{|\mathcal{D}^{T}|} \sum_{i}^{|\mathcal{D}^{T}|} \frac{d_{2i} - d_{1i}}{d_{2i}}. (3)
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+Given one or more candidate source domains and a set of pre-trained models, the PAS score can help to select the options that are more likely to lead to the best accuracy on the target samples. The selection is done by computing the PAS score for each trio of target domain, source domain, and pre-trained model. The combination with the highest PAS value is chosen. The selection is done before any domain adaptation training. A single-source domain adaptation method can then be trained with the selected source domain and pre-trained feature extractor.
+
+[p. 5 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987). The Silhouette is a supervised score calculated by (b-a)/max\{a,b\} , where a is the mean intra-cluster distance and b is the mean nearest-cluster distance for each sample. It ranges from -1 to 1, with higher values indicating strong intra-class cohesion and clear inter-class separation. Note that the Silhouette score is fully supervised and designed for IID samples and its original form is not suitable for the domain adaptation problem. Our PAS score is an adaptation to accommodate unlabeled target samples and domain shift. We consider the closest source cluster as the true class for each target sample. This assumption makes a always smaller than b, and restricts our score to the interval [0,1]. The PAS score is close to one if the samples from the target domain
+
+[p. 6 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: FigureGroup]
+Figure 3: The correlation between the PAS score value and the target accuracy after the domain adaptation. Each box summarizes the target accuracy of different domain adaptation methods for a given source-target pair and a pre-trained feature extractor. Higher values for the PAS score are strongly correlated with higher target accuracy.
+
+[p. 6 | section: 3.3 THE POTENTIAL ADAPTABILITY SCORE | type: Text]
+are similar to the centroid of the source class cluster. However, due to the mismatch between the domains, the target samples exhibit a shift in the feature distribution, making a larger than in the IID scenario. As a result, the values for our score are typically smaller. Alternative design choices are discussed and evaluated in section 4.4.
+
+[p. 6 | section: 4 EXPERIMENTS | type: Text]
+Datasets. We evaluate PAS on four of the most popular benchmarks for domain adaptation: Office-Home Venkateswara et al. (2017), Office-31 Saenko et al. (2010), ImageCLEF <sup>1</sup>, and DomainNet Peng et al. (2019). The benchmarks' statistics are listed in the table 2.
+
+[p. 6 | section: 4 EXPERIMENTS | type: FigureGroup]
+Figure 4: The PAS value and target accuracy for the DANN and MCC methods using different pretrained feature extractors. The PAS score can help to select the feature extractor that leads to higher accuracy. ( left ) A \rightarrow C adaptation in the Office-Home benchmark. ( right ) W \rightarrow A adaptation in the Office-31 benchmark.
+
+[p. 6 | section: 4 EXPERIMENTS | type: Text]
+Junguang Jiang (2020), Wang et al. (2023), and from the original papers.
+
+[p. 6 | section: 4 EXPERIMENTS | type: Text]
+Baselines To the best of our knowledge, PAS is the first asymmetric score proposed for transferability estimation for domain adaptation. We, therefore, compare PAS with the symetric metrics Maximum Mean Discrepancy (MMD) Gretton et al. (2012) and \mathcal{A} -distance Peng et al. (2019). The MMD distance is computed using a Gaussian kernel. Due to the quadratic nature of MMD, we restrict its computation to a maximum of 10,000 randomly selected samples per domain for the DomainNet benchmark. The \mathcal{A} -distance is computed using C-Support Vector Classification. We also report the results for an oracle baseline. The oracle is similar to PAS , defined as \frac{1}{|\mathcal{D}^T|} \sum_{i}^{|\mathcal{D}^T|} \frac{d_{2i} - d_{1i}}{max\{d_{1i}, d_{2i}\}}. The d_{1i} distance is the cosine distance to the centroid of the true class of the target sample (not known in real scenarios), and d_{2i} is the distance to the closest cluster's
+
+[p. 6 | section: 4 EXPERIMENTS | type: Footnote]
+1
+
+[p. 7 | section: 4 EXPERIMENTS | type: Caption]
+Table 1: Average target accuracy of domain adaptation methods and transferability scores for different image classification benchmarks. The highest values are highlighted. Our PAS has a high correlation with the target accuracy and, for each target domain, attributes the highest value for the source domain that leads to the highest target accuracy in most scenarios. * Oracle baseline that considers the target labels.
+
+[p. 7 | section: (a) Office-Home | type: Table]
+Target | A С P R Correlation on with acc. Source C P R A P R A C R A C P Pearson Spearman Acc. (avg.) 62.0 61.7 72.5 53.5 52.4 58.9 71.0 70.0 82.1 77.2 70.8 78.7 MMD (neg.) -0.135 -0.113 -0.052 -0.135 -0.097 -0.125 -0.113 -0.097 -0.033 -0.052 -0.125 -0.033 0.77 0.72 ResNet-50 A-distance (neg.) -1.876 -1.810 -1.333 -1.876 -1.827 -1.814 -1.810 -1.827 -1.424 -1.333 -1.814 -1.424 0.76 0.78 PAS (our) 0.107 0.143 0.201 0.128 0.156 0.166 0.182 0.168 0.288 0.217 0.147 0.254 0.81 0.82 Oracle* 0.041 0.037 0.093 -0.022 -0.018 -0.022 0.103 0.100 0.218 0.165 0.096 0.195 0.98 0.93 Acc. (avg.) 74.3 71.7 76.0 61.8 58.5 61.2 81.7 83.2 86.0 83.3 82.5 84.1 MMD (neg.) -0.106 -0.058 -0.024 -0.106 -0.077 -0.102 -0.058 -0.077 -0.026 -0.024 -0.102 -0.026 0.56 0.57 DeiT-Small A-distance (neg.) -1.865 -1.761 -1.26 -1.865 -1.843 -1.796 -1.761 -1.843 -1.37 -1.26 -1.796 -1.37 0.52 0.57 PAS (our) 0.143 0.183 0.25 0.175 0.186 0.204 0.261 0.221 0.348 0.295 0.2 0.301 0.67 0.78 Oracle* 0.086 0.112 0.18 0.038 0.037 0.047 0.194 0.155 0.291 0.243 0.147 0.246 0.90 0.93 Acc. (avg.) 81.5 78.8 81.1 69.9 65.4 68.0 86.0 86.7 90.6 87.4 87.2 88.5 MMD (neg.) -0.099 -0.056 -0.028 -0.099 -0.091 -0.11 -0.056 -0.091 -0.023 -0.028 -0.11 -0.023 0.56 0.57 DeiT-Base A-distance (neg.) -1.832 -1.81 -1.372 -1.832 -1.907 -1.823 -1.81 -1.907 -1.502 -1.372 -1.823 -1.502 0.48 0.51 PAS (our) 0.138 0.176 0.243 0.166 0.172 0.194 0.245 0.209 0.339 0.287 0.193 0.295 0.65 0.73 Oracle* 0.09 0.112 0.184 0.048 0.049 0.062 0.191 0.158 0.293 0.245 0.154 0.248 0.88 0.88 Acc. (avg.) 80.1 79.8 82.2 66.4 65.2 68.2 84.1 84.2 89.0 88.0 87.2 88.5 MMD (neg.) -0.116 -0.082 -0.032 -0.116 -0.115 -0.122 -0.082 -0.115 -0.034 -0.032 -0.122 -0.034 0.61 0.49 ViT-Small A-distance (neg.) -1.885 -1.883 -1.348 -1.885 -1.927 -1.862 -1.883 -1.927 -1.515 -1.348 -1.862 -1.515 0.53 0.59 PAS (our) 0.172 0.198 0.262 0.182 0.199 0.217 0.251 0.235 0.357 0.294 0.219 0.316 0.68 0.83 Oracle* 0.132 0.147 0.212 0.084 0.102 0.113 0.211 0.195 0.321 0.26 0.189 0.285 0.87 0.92 Acc. (avg.) 83.0 82.7 84.5 73.2 72.2 74.4 88.3 88.6 91.4 90.2 89.5 90.8 MMD (neg.) -0.101 -0.069 -0.031 -0.101 -0.106 -0.11 -0.069 -0.106 -0.025 -0.031 -0.11 -0.025 0.59 0.57 ViT-Base A-distance (neg.) -1.85 -1.845 -1.389 -1.85 -1.952 -1.885 -1.845 -1.952 -1.595 -1.389 -1.885 -1.595 0.47 0.51 PAS (our) 0.254 0.28 0.357 0.262 0.271 0.296 0.361 0.339 0.462 0.405 0.316 0.417 0.76 0.85 Oracle* 0.215 0.233 0.311 0.173 0.188 0.207 0.317 0.295 0.425 0.37 0.286 0.382 0.88 0.92 Acc. (avg.) 88.5 87.7 87.9 78.3 77.1 78.2 91.5 91.9 94.2 92.9 93.0 92.8 MMD (neg.) -0.081 -0.085 -0.039 -0.081 -0.104 -0.097 -0.085 -0.104 -0.033 -0.039 -0.097 -0.033 0.48 0.45 Swin-Base A-distance (neg.) -1.853 -1.892 -1.401 -1.853 -1.95 -1.917 -1.892 -1.95 -1.57 -1.401 -1.917 -1.57 0.42 0.37 PAS (our) 0.232 0.251 0.327 0.231 0.244 0.269 0.323 0.318 0.43 0.37 0.294 0.384 0.72 0.72 Oracle* 0.198 0.214 0.287 0.162 0.177 0.195 0.295 0.282 0.403 0.343 0.27 0.356 0.83 0.81
+
+[p. 7 | section: (b) Office-31 | type: Table]
+Target A 1 ) | V V Correlation on with acc. Source D W A W A D Pearson Spearman Acc. (avg.) 71.8 70.6 90.5 100.0 91.9 98.3 MMD (neg.) -0.145 -0.165 -0.145 -0.046 -0.165 -0.046 0.71 0.72 ResNet-50 A-distance (neg.) -2.00 -2.00 -2.00 -1.783 -2.00 -1.783 0.72 0.83 PAS (our) 0.265 0.239 0.286 0.454 0.236 0.423 0.73 0.66 Oracle* 0.192 0.166 0.246 0.445 0.188 0.407 0.80 0.83 Acc. (avg.) 77.7 77.6 94.7 94.65 MMD (neg.) -0.123 -0.129 -0.123 -0.058 -0.129 -0.058 0.66 0.84 DeiT-Small A-distance (neg.) -2.00 -1.994 -2.00 -1.969 -1.994 -1.969 0.65 0.60 PAS (our) 0.283 0.266 0.304 0.472 0.278 0.447 0.72 0.94 Oracle* 0.2 0.193 0.263 0.465 0.239 0.438 0.80 1.00 Acc. (avg.) 81.3 82.0 96.8 100.0 97.9 99.2 MMD (neg.) -0.113 -0.134 -0.113 -0.074 -0.134 -0.074 0.54 0.60 DeiT-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.268 0.241 0.304 0.443 0.251 0.418 0.66 0.71 Oracle* 0.212 0.192 0.273 0.44 0.224 0.414 0.73 0.89 Acc. (avg.) 83.5 82.2 98.6 100.0 97.7 99.2 MMD (neg.) -0.175 -0.197 -0.175 -0.098 -0.197 -0.098 0.56 0.84 ViT-Small A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.283 0.27 0.302 0.509 0.276 0.473 0.61 0.94 Oracle* 0.23 0.22 0.286 0.506 0.256 0.467 0.69 1.00 Acc. (avg.) 84.0 85.0 97.2 100.0 96.8 99.3 MMD (neg.) -0.098 -0.118 -0.098 -0.071 -0.118 -0.071 0.57 0.72 ViT-Base A-distance (neg.) -2.00 -2.00 -2.00 -1.953 -2.00 -1.953 0.64 0.72 PAS (our) 0.423 0.395 0.453 0.59 0.412 0.558 0.71 0.83 Oracle* 0.373 0.347 0.434 0.589 0.393 0.554 0.79 0.94 Acc. (avg.) 86.2 86.3 99.7 100.0 99.4 99.5 MMD (neg.) -0.168 -0.169 -0.168 -0.086 -0.169 -0.086 0.51 0.60 Swin-Base A-distance (neg.) -2.00 -2.00 -2.00 -2.00 -2.00 -2.00 0.0 0.0 PAS (our) 0.361 0.349 0.399 0.589 0.374 0.56 0.62 0.89 Oracle* 0.321 0.313 0.388 0.589 0.366 0.558 0.69 0.89
+
+[p. 7 | section: (c) ImageCLEF | type: Table]
+Target | ( 3 1 I 1 P Correlation on with acc. Source I P C P C I Pearson Spearman Acc. (avg.) 95.9 93.7 90.7 90.0 76.0 77.9 MMD (neg.) -0.074 -0.097 -0.074 -0.022 -0.097 -0.022 -0.17 -0.12 ResNet-50 A-distance (neg.) -1.583 -1.731 -1.583 -0.807 -1.731 -0.807 -0.24 -0.12 PAS (our) 0.299 0.251 0.235 0.27 0.223 0.297 0.22 0.49 Oracle* 0.287 0.243 0.195 0.254 0.111 0.2 0.84 0.71 Acc. (avg.) 97.5 97.5 93.7 95.2 78.3 80.8 MMD (neg.) -0.072 -0.081 -0.072 -0.02 -0.081 -0.02 -0.17 -0.11 DeiT-Small A-distance (neg.) -1.417 -1.748 -1.417 -0.807 -1.748 -0.807 -0.07 -0.11 PAS (our) 0.344 0.303 0.263 0.322 0.24 0.332 0.41 0.52 Oracle* 0.333 0.293 0.239 0.31 0.169 0.25 0.83 0.83 Acc. (avg.) 97.8 97.1 96.6 95.7 79.5 81.9 MMD (neg.) -0.078 -0.095 -0.078 -0.022 -0.095 -0.022 -0.13 -0.12 ViT-Base A-distance (neg.) -1.483 -1.714 -1.483 -0.655 -1.714 -0.655 -0.14 -0.12 PAS (our) 0.399 0.359 0.304 0.377 0.262 0.363 0.55 0.54 Oracle* 0.391 0.352 0.295 0.37 0.205 0.286 0.84 0.83
+
+[p. 7 | section: (d) DomainNet | type: Table]
+Target C P R S Correlation on with acc. Source P R S C R S C P S C P R Pearson Spearman Acc. (avg.) 45.5 53.7 56.7 39.4 52.2 45.8 55.9 58.1 55.3 44.8 40.7 41.0 MMD (neg.) -0.113 -0.158 -0.079 -0.113 -0.075 -0.108 -0.158 -0.075 -0.173 -0.079 -0.108 -0.173 0.04 0.20 ResNet-101 A-distance (neg.) -1.789 -1.73 -1.638 -1.789 -1.656 -1.777 -1.73 -1.656 -1.821 -1.638 -1.777 -1.821 0.50 0.45 PAS (our) 0.108 0.145 0.088 0.08 0.159 0.083 0.128 0.184 0.107 0.088 0.098 0.114 0.58 0.53 Oracle* -0.109 -0.124 -0.042 -0.06 -0.024 -0.04 0.037 0.092 0.031 -0.087 -0.11 -0.156 0.70 0.67 Acc. (avg.) 52.3 68.8 52.2 58.6 69.7 48.4 62.3 56.6 48.5 64.7 52.4 67.2 MMD (neg.) -0.128 -0.146 -0.088 -0.128 -0.052 -0.16 -0.146 -0.052 -0.186 -0.088 -0.16 -0.186 0.26 0.28 DeiT-Small A-distance (neg.) -1.784 -1.734 -1.655 -1.784 -1.639 -1.768 -1.734 -1.639 -1.823 -1.655 -1.768 -1.823 0.30 0.33 PAS (our) 0.13 0.152 0.093 0.091 0.175 0.086 0.139 0.218 0.11 0.096 0.117 0.127 0.39 0.57 Oracle* -0.125 -0.118 -0.055 -0.066 -0.015 -0.051 0.031 0.093 0.015 -0.12 -0.163 -0.183 -0.19 -0.17 Acc. (avg.) 55.7 72.2 56.9 64.6 72.9 53.3 65.8 59.4 52.4 68.7 56.7 71.8 MMD (neg.) -0.123 -0.153 -0.095 -0.123 -0.06 -0.171 -0.153 -0.06 -0.227 -0.095 -0.171 -0.227 0.19 0.35 DeiT-Base A-distance (neg.) -1.796 -1.746 -1.655 -1.796 -1.682 -1.79 -1.746 -1.682 -1.838 -1.655 -1.79 -1.838 0.26 0.37 PAS (our) 0.126 0.147 0.086 0.085 0.165 0.079 0.137 0.211 0.102 0.089 0.119 0.112 0.26 0.44 Oracle* -0.115 -0.097 -0.044 -0.047 0.004 -0.04 0.044 0.105 0.022 -0.109 -0.162 -0.154 -0.17 -0.08 Acc. (avg.) 60.7 77.7 60.7 66.2 75.9 57.2 69.7 64.6 57.9 71.4 62.7 76.3 MMD (neg.) -0.14 -0.157 -0.108 -0.14 -0.116 -0.175 -0.157 -0.116 -0.25 -0.108 -0.175 -0.25 0.07 0.15 ViT-Base A-distance (neg.) -1.814 -1.771 -1.686 -1.814 -1.734 -1.807 -1.771 -1.734 -1.859 -1.686 -1.807 -1.859 0.18 0.21 PAS (our) 0.185 0.226 0.162 0.145 0.233 0.128 0.223 0.282 0.176 0.151 0.171 0.17 0.37 0.35 Oracle* -0.003 0.018 0.042 0.012 0.066 0.007 0.135 0.184 0.103 -0.021 -0.075 -0.062 -0.13 -0.08
+
+[p. 8 | section: (d) DomainNet | type: TableGroup]
+Table 2: Statistics of the benchmarks used in the experiments. Dataset #Samples #Classes Domains Office-Home 15,588 65 A (Art), C (Clipart), P (Product), R (Real-world) Office-31 4,110 31 A (Amazon), D (DSLR), W (Webcam) ImageCLEF 1,800 12 C (Caltech-256), I (ImageNet ILSVRC 2012), P (Pascal VOC 2012) DomainNet 569,010 345 C (Clipart), P (Painting), R (Real), S (Sketch) Table 3: Correlation with the average target accuracy after adaptation. Showing Pearson correlation / Spearman's rank correlation.
+
+[p. 8 | section: (d) DomainNet | type: Table]
+Office-Home Office-31 ImageCLEF DomainNet Total MMD 0.55 / 0.51 0.45 / 0.53 -0.14 / -0.08 -0.09 / -0.03 0.37 / 0.37 \mathcal{A} -distance 0.32 / 0.17 0.26 / 0.35 -0.13 / -0.07 0.07 / 0.06 0.04 / -0.16 PAS (our) 0.76 / 0.81 0.63 / 0.78 0.44 / 0.60 0.53 / 0.56 0.83 / 0.88 Oracle* 0.89 / 0.90 0.71 / 0.86 0.78 / 0.85 0.21 / 0.21 0.88 / 0.91
+
+[p. 8 | section: (d) DomainNet | type: Text]
+centroid that is not the true class. In the ideal case where the closest class centroid is the actual class of the sample, the oracle is the same as PAS , otherwise, the oracle value is smaller. The oracle validates the existing relationship between the clusters distance and the target accuracy.
+
+[p. 8 | section: 4.1 Selection of the Source Domain | type: Text]
+The results for the four benchmark datasets are presented in Table 1 (a) - (d). For each source-target pair in the benchmarks, we group the domain adaptation methods using the same pre-trained feature extractor and report their average target accuracy, followed by the baselines and our PAS score. We highlight the highest values among the different choices of source domains. We also report the correlation (Pearson and Spearman's rank correlation) between the average target accuracy and the scores. The detailed results for each individual domain adaptation method are presented in the Supplementary Material A.1.
+
+[p. 8 | section: 4.1 Selection of the Source Domain | type: Text]
+We report in Table 3 the overall correlation for all scenarios of each benchmark (all target domains, source domains and pre-trained models). The results show that the PAS score is strongly correlated with target accuracy. We observe an overall Spearman's rank correlation of 0.88 over all the results.
+
+[p. 8 | section: 4.1 Selection of the Source Domain | type: Text]
+The most important results are reported in Table 4, where we present the correlation for each target domain. This correlation is the most useful for users in real-world scenarios. Given a target domain of interest and many options of source domains and pre-trained models, we show that our PAS score has a strong correlation with the final target accuracy. The empirical results indicate that our proposed PAS score is effective in selecting the best source domain among many candidates.
+
+[p. 8 | section: 4.1 Selection of the Source Domain | type: Text]
+We summarize our results in Figure 3. Each box in the graph represents the target accuracy of different domain adaptation methods using the same pre-trained backbone for a source-target domains pair. We observe that higher PAS values are consistently related to high accuracy on the target domain. This indicates that PAS may be useful not only for selecting the most appropriate source domain, but also to estimate beforehand the success of the domain adaptation.
+
+[p. 8 | section: 4.1 Selection of the Source Domain | type: TableGroup]
+Table 4: Correlation with the average target accuracy after adaptation for each target domain. Each cell considers the results for a target domain and all available source domains and pre-trained models. Showing Pearson correlation / Spearman's rank correlation. Office -Home 1 Office-31 1 ImageCLEF Doma ainNet A C P R A D W C I P С P R S MMD 0.41 / 0.26 0.28 / 0.21 0.41 / 0.29 0.25 / 0.21 -0.02 / -0.15 0.44 / 0.60 0.45 / 0.36 0.54 / 0.49 -0.03 / -0.22 0.61 / 0.60 -0.56 / -0.42 0.33 / 0.20 0.23 / 0.47 -0.38 / -0.42 A-distance 0.12 / -0.13 -0.46 / -0.43 0.15 / -0.09 -0.05 / -0.26 -0.19 / -0.31 0.27 / 0.28 0.14 / 0.07 0.43 / 0.38 0.10 / 0.05 0.64 / 0.60 0.09 / -0.04 0.35 / 0.17 0.27 / 0.30 -0.10 / -0.32 PAS (our) 0.70 / 0.70 0.81 / 0.78 0.79 / 0.74 0.75 / 0.75 0.65 / 0.81 0.70 / 0.81 0.70 / 0.75 0.82 / 0.76 0.73 / 0.66 0.87 / 0.83 0.71 0.67 0.75 / 0.76 0.59 / 0.71 0.48 / 0.35 Oracle* 0.82 / 0.85 0.91 / 0.90 0.84 / 0.81 0.80 / 0.87 0.74 / 0.88 0.73 / 0.90 0.74 / 0.78 0.81 / 0.76 0.74 / 0.66 0.97 / 0.94 0.36 / 0.50 0.71 / 0.62 0.61 / 0.72 0.28 / 0.33
+
+[p. 9 | section: 4.1 Selection of the Source Domain | type: Text]
+The results on the ImageCLEF benchmark illustrate the scenarios where the PAS score is not effective. This benchmark (especially the P domain) contains images with multiple objects. In many cases, the sample is very close to the centroid of one class that is indeed present in the image, but the true label is related to another object in the scene. In these cases, the PAS for the sample is high, showing a high similarity with one source class, but the final accuracy is low, as the sample is classified as the wrong class. We show examples in the supplementary material A.2
+
+[p. 9 | section: 4.2 The selection of the pre-trained feature extractor | type: FigureGroup]
+Figure 5: The PAS value varying with the number of samples for the Office-Home . The PAS values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.
+
+[p. 9 | section: 4.2 The selection of the pre-trained feature extractor | type: Text]
+may be applied for the selection of the pre-trained model.
+
+[p. 9 | section: 4.2 The selection of the pre-trained feature extractor | type: Text]
+The results in the literature presented in table 1 compare methods with different backbones and demonstrate that PAS can be applied to select the most suitable pretrained feature extractor. However, they do not consider the impact of different pre-trained feature extractors over the same domain adaptation method. For analyzing the robustness of PAS over different choices of pre-trained methods, we keep the domain adaptation method fixed and vary the pre-trained backbone. We select two of the most challenging domain adaptation scenarios: the A \rightarrow C adaptation in the Office-Home benchmark and W \rightarrow A adaptation in the Office-31 benchmark. We show results for two popular domain adaptation methods: DANN Ganin et al. (2016) and MCC Jin et al. (2020). We train each method following the code provided by the Tllib library Jiang et al. (2022); Junguang Jiang (2020) with the default hyperparameters. The results are shown in figure 4. Higher PAS values are attributed to pretrained models that lead to higher target accuracy before performing domain adaptation, indicating that our score
+
+[p. 9 | section: 4.3 THE IMPACT OF THE SAMPLE SIZE | type: Text]
+The time complexity of the PAS computation is linear in the number of samples. This can be limiting for a quick evaluation of larger datasets and scenarios with many candidate source domains.
+
+[p. 9 | section: 4.3 THE IMPACT OF THE SAMPLE SIZE | type: Text]
+To optimize the computation time, we show that our score can be calculated using only a subset of the samples. We randomly select a subset of the samples of both source and target domains. The results are presented in the figure 5. The PAS values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.
+
+[p. 9 | section: 4.4 DESIGN CHOICES | type: Text]
+The PAS score considers the cosine distance between each target sample and the source class centroids. We experimentally evaluated alternative design choices and compare the correlation between the score and the target accuracy. The results are shown in table 5 and demonstrate how the overall correlation between the target accuracy and PAS, as proposed, is higher.
+
+[p. 9 | section: 4.4 DESIGN CHOICES | type: Text]
+We change PAS to consider the Euclidean distance instead of the cosine distance. In the domain adaptation setting, the cosine distance has advantages over using the Euclidean distance in the original latent space, as it ignores the magnitude of
+
+[p. 9 | section: 4.4 DESIGN CHOICES | type: TableGroup]
+Office-Home Office-31 ImageCLEF DomainNet Total PAS 0.76 0.63 0.44 0.58 0.79 Euclidean distance 0.70 0.69 0.27 0.54 0.68 Average cosine distance 0.66 0.52 0.12 0.48 0.66 Table 5: Pearson correlation between the target accuracy and the PAS score, which considers the cosine distance to the cluster centroid, and modifications using the Euclidean distance to the centroid and the average cosine distance to the source cluster samples. The maximum correlation value for each benchmark is highlighted. The design choices of PAS lead to the higher overall correlation between the score and the target accuracy.
+
+[p. 10 | section: 4.4 DESIGN CHOICES | type: Text]
+representations (e.g., a difference in the illumination in images that reflects on the intensity of the features detected by the model) and focuses only on the differences in the angles (the difference between classes). Also, the cosine distance is less affected by the high-dimensionality of the data (the phenomenon known as curse of dimensionality Bellman (1966) ).
+
+[p. 10 | section: 4.4 DESIGN CHOICES | type: Text]
+We also modify PAS to use the average pairwise distance to the source samples instead of the distance to the source cluster centroid. The pairwise distance is a good summarization of the closeness of the target sample to the source samples of the class. On the other hand, the distance to the centroid measures how well the target sample is aligned to the dimensions of greatest alignment between the samples in the cluster, as the centroid formulation 1/|D S | P|D S | i =1 x S i makes samples pointing in similar directions add up in that direction.
+
+[p. 10 | section: 5 CONCLUSION AND FUTURE WORK | type: Text]
+We present Potential Adaptability Score (PAS), a new score to select, among many candidates, the source domain or pre-trained model that are likely to lead to the best target accuracy when used for unsupervised domain adaptation. We evaluate our score on four of the most popular benchmarks for domain adaptation and show that it has a high correlation with the target accuracy and selects the best source domain in most cases. We also show that PAS can be computed more efficiently with fewer samples.
+
+[p. 10 | section: 5 CONCLUSION AND FUTURE WORK | type: Text]
+We suggest two improvements for future work. Although our score could be applied to any classification task, we focus on vision problems, specifically the image classification task, which is the most common task in the domain adaptation literature. Showing its efficacy on other modalities and tasks demands the availability of a diverse set of benchmarks and specialized domain adaptation methods. Also, we focus on the single-source domain adaptation problem, where only a single source domain is considered during the training. Future works may extend our work to select multiple source domains, in the setting known as multi-source domain adaptation.

iclr26/0Z2l4XtTdz/paper.md

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+
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+{0}------------------------------------------------
+
+# PAS: ESTIMATING THE TARGET ACCURACY BEFORE DOMAIN ADAPTATION
+
+Raphaella Diniz, Jackson de Faria Junior & Martin Ester ´
+
+School of Computing Science Simon Fraser University Canada {raphaella diniz, jackson de faria junior, ester}@sfu.ca
+
+# ABSTRACT
+
+The goal of domain adaptation is to make predictions for unlabeled samples from a target domain with the help of labeled samples from a different but related source domain. The performance of domain adaptation methods is highly influenced by the choice of source domain and pre-trained feature extractor. However, the selection of source data and pre-trained model is not trivial due to the absence of a labeled validation set for the target domain and the large number of available pre-trained models. In this work, we propose Potential Adaptability Score (PAS), a novel score designed to estimate the transferability of a source domain set and a pre-trained feature extractor to a target classification task before actually performing domain adaptation. PAS leverages the generalization power of pretrained models and assesses source-target compatibility based on the pre-trained feature embeddings. We integrate PAS into a framework that indicates the most relevant pre-trained model and source domain among multiple candidates, thus improving target accuracy while reducing the computational overhead. Extensive experiments on image classification benchmarks demonstrate that PAS correlates strongly with actual target accuracy and consistently guides the selection of the best-performing pre-trained model and source domain for adaptation.
+
+# 1 INTRODUCTION
+
+In many real applications, data is collected from diverse domains, e.g., data obtained from different equipment, collecting procedures, geographic locations, or periods in time. Such differences may lead to a distribution shift between the domains that must be assessed. Unsupervised domain adaptation is a paradigm where only unlabeled data is available for the domain of interest, the target domain. However, labeled data is obtained from a related source domain.
+
+One factor that affects the success of domain adaptation methods is the choice of the source domain data. Domain adaptation methods often rely on many assumptions about the relationship between source and target domains, like the existence of invariant discriminative features, the similarity of the label distribution, or the invariance of the task. Unfortunately, as the labels for the target samples are not available, such assumptions may not be verified in real applications for selecting the most appropriate source data. Violating the data assumptions and
+
+<span id="page-0-0"></span>![](_page_0_Figure_9.jpeg)
+
+Figure 1: The Potential Adaptability Score (PAS) estimates the performance of adapting to an unlabeled target domain given a pre-trained feature extractor and a labeled source domain. It helps in the selection of the best pre-trained model and best source domain among many candidates and is highly correlated with the final target accuracy after domain adaptation.
+
+{1}------------------------------------------------
+
+considering an irrelevant or distant source domain may introduce noise and conflicting patterns during the domain adaptation process. In the worst-case scenario, selecting an undesirable source domain may hurt the target domain performance, a scenario known as negative transfer [Zhang et al.](#page-12-0) [\(2022\)](#page-12-0). If many source domains are available, it is reasonable to assume that not all of them may contribute equally to the target adaptation. Wisely selecting the source domain that may improve the performance on the target data while avoiding negative transfer is an essential requirement in many real-world applications.
+
+Another key factor that influences the domain adaptation performance is the choice of the pre-trained model. Pre-training on large-scale data allows the models to learn generic features and patterns that are often transferable across domains and tasks, making them valuable for domain adaptation. Recently, practitioners can choose from a vast number of publicly available pre-trained models, spanning diverse architectures and training paradigms. Each pre-trained model may have its own inductive bias and may capture distinct patterns in the data that may be more or less useful when transferring knowledge between domains.
+
+<span id="page-1-0"></span>![](_page_1_Figure_3.jpeg)
+
+Figure 2: Source and target samples in the embedding space of a pre-trained model. *(top left)* Ideally, a target sample from a given class should be more similar, and hence closer in the embedding space of the pre-trained model, to a source sample from the same class. *(top right)* If new discriminative features need to be learned, the chances of overfitting on the source domain during adaptation increase. *(bottom)* Illustration of the distances from a target sample to all source class centroids. Our PAS score considers the relationship between distances d<sup>1</sup> and d2, which correspond to the shortest and second shortest distances, respectively.
+
+Despite the importance of selecting a suitable source data and a pre-trained model for the success of domain adaptation, it is still an underexplored topic. Current methods of transferability estimation aim to select the best pre-trained model for transfer learning. However, these methods are not applicable to the domain adaptation scenario since they require target labels [Bao et al.](#page-9-0) [\(2019\)](#page-9-0); [Nguyen et al.](#page-10-0) [\(2020\)](#page-10-0); [You](#page-12-1) [et al.](#page-12-1) [\(2021\)](#page-12-1). One could employ such methods for selecting the best pre-training model using only the labeled source data and ignoring the unlabeled target data. Nevertheless, considering the target data is essential, as transferring to an easy target domain should lead to different results than transferring to a harder one.
+
+Another approach for the problem would be performing domain adaptation for each combination of available source domains and pretrained models, and applying some model selection strategy [Ericsson et al.](#page-10-1) [\(2023\)](#page-10-1); [You et al.](#page-12-2) [\(2019\)](#page-12-2); [Sun et al.](#page-11-0) [\(2021\)](#page-11-0). However, this approach is very time-consuming since it needs to run a domain adaptation algorithm for each combination.
+
+A third approach would be to measure the distance between source and target feature distributions in the embedding space of the pretrained model. This approach is also challenging as the popular metrics for the distance between two feature distributions are symmetric, e.g., Maximum Mean Discrepancy (MMD) [Gretton et al.](#page-10-2) [\(2006\)](#page-10-2), Wasserstein distance [Val](#page-11-1)[lender](#page-11-1) [\(1974\)](#page-11-1), and CORAL [Sun & Saenko](#page-11-2) [\(2016\)](#page-11-2). However, a metric suitable for our scenario should be asymmetric because transfer-
+
+ring from an easy to a hard domain is more challenging than transferring from the harder domain to the easier one.
+
+In this work, we examine the interplay between the three key components in the domain adaptation setting for classification: (1) target data, (2) source data, and (3) the pre-trained model. We propose the Potential Adaptability Score (PAS), a simple but effective novel measure to quantify the potential success of using a pre-trained model to transfer knowledge from a source domain to the target 
+
+{2}------------------------------------------------
+
+domain. Our experiments show how the PAS score is highly correlated to the final target accuracy after adaptation.
+
+To the best of our knowledge, this is the first proposal for transferability estimation for the domain adaptation setting. We demonstrate how PAS can help to select the most relevant source domain and/or pre-trained model among a set of candidates, indicating the options that are most likely to lead to the best accuracy on the unlabeled target data (See an overview in figure [1.](#page-0-0)). Our framework selects the most suitable options before actually performing domain adaptation, demanding fewer computational resources and reducing the training time.
+
+PAS leverages the generalization power of models pre-trained on a large-scale dataset, such as the popular ImageNet-1k [Deng et al.](#page-9-1) [\(2009\)](#page-9-1). Specifically for domain adaptation, initializing with a good pre-trained model appears to be a fundamental step in achieving a good transferability between domains [Peng et al.](#page-11-3) [\(2018\)](#page-11-3); [Tang & Jia](#page-11-4) [\(2023\)](#page-11-4); [Kim et al.](#page-10-3) [\(2022\)](#page-10-3); [Li et al.](#page-10-4) [\(2023\)](#page-10-4); [Teterwak et al.](#page-11-5) [\(2023\)](#page-11-5). We assume that a good pre-trained model can extract general discriminative features that are robust across all domains. If this assumption is true, samples from the same class are expected to be closer together in the embedding space generated by the pre-trained model, compared to samples from different classes, even in the presence of feature distribution shift. This ideal scenario is illustrated in the top left of the figure [2.](#page-1-0) Otherwise, as shown in the example on the top right of the figure, the model should learn new discriminative features during the adaptation from the limited labeled source data to enable the classification task, increasing the chances of overfitting to the source domain. Our PAS score is inspired by the Silhouette score, used for assessing the consistency of data clusters [Rousseeuw](#page-11-6) [\(1987\)](#page-11-6). We modify the original Silhouette score to measure the similarity of the unlabeled target samples to some of the known source class clusters defined in the pre-trained embedding space.
+
+We summarize our contributions as follows:
+
+- We propose PAS, a simple novel measure to quantify the potential contribution of a pretrained model and labeled source domain in the adaptation to an unlabeled target domain before performing domain adaptation.
+- We propose a framework to select the most relevant pre-trained model or source domain from a collection of potential candidates for performing domain adaptation.
+- We empirically validate our framework using different domain adaptation methods and image classification benchmarks, and show how our score has a high correlation with the target accuracy.
+
+# 2 RELATED WORK
+
+Unsupervised domain adaptation. The goal of unsupervised domain adaptation (UDA) is to transfer the knowledge learned from a labeled domain to a different unlabeled target domain. Usually, this goal is achieved by learning a latent representation that is invariant across domains. Several works minimize the distribution discrepancy on the representation using statically defined distance metrics such as Maximum Mean Discrepancy (MMD) (e.g., DAN [Long et al.](#page-10-5) [\(2015\)](#page-10-5), DDC [Tzeng](#page-11-7) [et al.](#page-11-7) [\(2014\)](#page-11-7), JAN [Long et al.](#page-10-6) [\(2017\)](#page-10-6)), covariance (e.g., DCORAL [Sun & Saenko](#page-11-2) [\(2016\)](#page-11-2)), or Wasserstein distance (e.g., DeepJDOT [Damodaran et al.](#page-9-2) [\(2018\)](#page-9-2)). The popularization of generative models inspired the proposal of methods that adopt adversarial learning to align data across different domains. DANN [Ganin et al.](#page-10-7) [\(2016\)](#page-10-7), CDAN [Long et al.](#page-10-8) [\(2018\)](#page-10-8), and ADDA [Tzeng et al.](#page-11-8) [\(2017\)](#page-11-8) are examples of widely adopted UDA methods that have shown promising results. Self-training is another promising paradigm that exploits the pseudo-labels predicted for the target domain to enhance the model. CST [Liu et al.](#page-10-9) [\(2021\)](#page-10-9), CRST [Zou et al.](#page-12-3) [\(2019\)](#page-12-3), FixMatch [Sohn et al.](#page-11-9) [\(2020\)](#page-11-9) and MCC [Jin](#page-10-10) [et al.](#page-10-10) [\(2020\)](#page-10-10) are examples of methods that explore pseudo-labeling. Most recently, with the dissemination of transformers and foundation models, new works explore the cross-attention mechanism to propose transformer-based domain adaptation methods, such as PMTrans [Zhu et al.](#page-12-4) [\(2023\)](#page-12-4) and DoT [Ren et al.](#page-11-10) [\(2024\)](#page-11-10). See [Liu et al.](#page-10-11) [\(2022\)](#page-10-11); [Deng & Jia](#page-9-3) [\(2023\)](#page-9-3); [Alijani et al.](#page-9-4) [\(2024\)](#page-9-4) for a comprehensive survey on domain adaptation methods.
+
+Pre-training and domain adaptation Recent works suggest that the choice of the pre-trained feature extractor can significantly improve the result of domain adaptation methods. [Teterwak et al.](#page-11-5) [\(2023\)](#page-11-5) show that simply adopting a model with better weight initialization can help the robustness 
+
+{3}------------------------------------------------
+
+of a model to out-of-distribution samples. Similarly, Kim et al. (2022) empirically show that SOTA pre-training outperforms SOTA domain adaptation methods even without access to a target domain. With a modern pre-trained backbone, older domain adaptation methods perform better than SOTA methods, but no method is consistently better in all benchmarks, and negative transfer can occur. Li et al. (2023) empirically show how, in some cases, the performance of the pre-trained model in an unseen target domain is already decent. However, no single pre-trained model performs well in all target datasets. Tang & Jia (2023) study the effects of pre-training on the domain adaptation between synthetic and real images. Without pre-training, none of the methods considered in the study outperformed the baseline trained only on the labeled source data. Other studies have also proposed new datasets and pre-training techniques that achieve competitive performance in the target domain Shen et al. (2022); Luo et al. (2024). We leverage the potential relationship between pre-training and domain adaptation success to estimate transferability between domains.
+
+**Transferability estimation** In the past years, many works have proposed scorees for quantitatively estimating the transferability of a pre-trained model to a target task. One of the primary practical applications of such estimation is selecting the best pre-trained model for fine-tuning on the target data. H-score Bao et al. (2019), NCE Tran et al. (2019), LEEP Nguyen et al. (2020) and LogME You et al. (2021) are widely adopted transferability estimation scores. More closely related to our proposal, some works propose scores for transferability estimation by examining the separability of classes in the embedding space encoded by the pre-trained model. Pándy et al. (2022) apply the Bhattacharyya coefficient to quantify the target class separability. Similarly, Meiseles & Rokach (2020) employ the Silhouette score to assess the transferability of time series data. The current methods on transferability estimation focus on the transfer learning problem, where a pre-trained model is adapted to a target task with a few labeled samples. Unfortunately, these methods can not be applied to the domain adaptation problem, where the target labels are not available.
+
+#### 3 Method
+
+#### 3.1 Definitions
+
+Unsupervised domain adaptation aims to transfer knowledge from a labeled source domain to an unlabeled target domain in the presence of distribution shift. Let  $\mathcal{X} \subseteq \mathbb{R}^d$  define the input space and  $\mathcal{Y} = \{1,\ldots,C\}$  the label space. The labeled source dataset is denoted by  $\mathcal{D}^S = \{(x_i^S,y_i^S)\}_{i=1}^{|\mathcal{D}^S|}$  and the unlabeled target dataset is denoted by  $\mathcal{D}^T = \{x_i^T\}_{j=1}^{|\mathcal{D}^T|}$ , with  $x_i^S, x_i^T \in \mathcal{X}$  and  $y_i^S \in \mathcal{Y}$ .  $S_c^S$  denotes the set of source samples from class c. The source and target feature distributions are sampled from different but related distributions,  $P_S(\mathcal{X})$  and  $P_T(\mathcal{X})$ , respectively, being  $P_S \neq P_T$ . This scenario is also known as *covariate shift*. The goal is to learn a hypothesis  $h: \mathcal{X} \to \mathcal{Y}$  that performs well on the target domain.
+
+Let  $\theta$  be the parameters of a feature extractor  $f_{\theta}: \mathcal{X} \to \mathcal{Z}$  pre-trained on a large-scale dataset.  $z_i^S = f_{\theta}(x_i^S)$  and  $z_i^T = f_{\theta}(x_i^T)$  denote, respectively, the embedding of a source and a target sample in the embedding space defined by  $f_{\theta}$ .
+
+### 3.2 ASSUMPTIONS
+
+We assume that a good pre-trained model  $f_{\theta}$  is able to extract a wide range of patterns and high-level concepts from an input, including discriminative features that are invariant across different domains. We expect that samples from the same class are more similar, having many concepts in common. As a result, two samples from the same class should be closer together in the embedding space  $\mathcal{Z}$ , no matter the domain. On the other hand, samples from different classes should have very few concepts in common, resulting in a dissimilar embedding representation. Due to the distribution shift between the source and target domains, samples from the same domain are expected to have more concepts in common and, therefore, have more similar representations than samples from different domains. Such assumptions lead to a scenario similar to the one represented in the top left of figure 2. The embeddings of samples from the same domain and class form a well-defined cluster in the space encoded by  $f_{\theta}$ . Also, the clusters of samples from the same class, but different domains, are closer together and, ideally, both are distant from all the other clusters.
+
+{4}------------------------------------------------
+
+To summarize, we assume that 1) a good pre-trained model can extract invariant discriminative features, 2) samples from the same class are close in the embedding space, even if they are from different domains, and 3) samples from different classes are distant in the embedding space. Similar assumptions are proposed by Shen et al. (2022) when studying the generalization of embeddings to out-of-distribution samples.
+
+#### 3.3 THE POTENTIAL ADAPTABILITY SCORE
+
+We introduce the Potential Adaptability Score (PAS) as a measure of the distance from a labeled source dataset to an unlabeled target dataset in the embedding space encoded by a pre-trained feature extractor. The PAS score is based on the expectation that each target sample is as close as possible to source samples from a single class and significantly distant from source samples from all other classes in the embedding space defined by a pre-trained model  $f_{\theta}$ . This means that a target sample is very similar to source samples from one class and has only a few concepts in common with source samples from all other classes, as illustrated in figure 2. The higher the PAS value, the stronger the evidence that the pre-trained model can identify invariant discriminative features between the domains and, consequently, the higher the chances that the pre-trained feature extractor  $f_{\theta}$  has a good transferability from the source to the target samples.
+
+The samples are normalized to unit length, and the distance between samples is calculated using the cosine distance. We assume that the samples from the class  $c \in \mathcal{Y}$  are clustered together. We follow Dhillon & Modha (2001) and compute the centroid of each source class cluster c so they represent the vector that, on average, has the highest cosine similarity to all the samples in the cluster.
+
+$$\mu_c = \frac{\sum_{x_i^S \in S_c^S} f_{\theta}(x_i^S)}{\|\sum_{x_i^S \in S_c^S} f_{\theta}(x_i^S)\|}.$$
+ (1)
+
+For each target sample  $x_i^T$ , we calculate its cosine distance to the centroid of each source cluster:
+
+$$\operatorname{dist}(f_{\theta}(x_i^T), \mu_c) = 1 - (f_{\theta}(x_i^T) \cdot \mu_c). \tag{2}$$
+
+Let  $D_i = \{ \operatorname{dist}(f_{\theta}(x_i^T), \mu_1), ..., \operatorname{dist}(f_{\theta}(x_i^T), \mu_C) \}$  be the set of distances of the j-th target sample to all the source clusters and  $sort(D_i)$  the sorted version of the set in ascending order. We define  $d_{1i} = sort(D_i)[1]$  and  $d_{2i} = sort(D_i)[2]$  as the shortest and the second shortest of the distances, respectively, as illustrated at the bottom of figure 2.
+
+Finally, the **PAS** score is defined by
+
+$$\mathbf{PAS}(\theta, \mathcal{D}^{\mathbf{S}}, \mathcal{D}^{\mathbf{T}}) = \frac{1}{|\mathcal{D}^{T}|} \sum_{i}^{|\mathcal{D}^{T}|} \frac{d_{2i} - d_{1i}}{d_{2i}}.$$
+(3)
+
+Given one or more candidate source domains and a set of pre-trained models, the **PAS** score can help to select the options that are more likely to lead to the best accuracy on the target samples. The selection is done by computing the **PAS** score for each trio of target domain, source domain, and pre-trained model. The combination with the highest **PAS** value is chosen. The selection is done before any domain adaptation training. A single-source domain adaptation method can then be trained with the selected source domain and pre-trained feature extractor.
+
+Our **PAS** score is inspired by the Silhouette score, used for assessing the consistency of data clusters Rousseeuw (1987). The Silhouette is a supervised score calculated by  $(b-a)/max\{a,b\}$ , where a is the mean intra-cluster distance and b is the mean nearest-cluster distance for each sample. It ranges from -1 to 1, with higher values indicating strong intra-class cohesion and clear inter-class separation. Note that the Silhouette score is fully supervised and designed for IID samples and its original form is not suitable for the domain adaptation problem. Our **PAS** score is an adaptation to accommodate unlabeled target samples and domain shift. We consider the closest source cluster as the true class for each target sample. This assumption makes a always smaller than b, and restricts our score to the interval [0,1]. The **PAS** score is close to one if the samples from the target domain
+
+{5}------------------------------------------------
+
+<span id="page-5-1"></span>![](_page_5_Figure_1.jpeg)
+
+Figure 3: The correlation between the **PAS** score value and the target accuracy after the domain adaptation. Each box summarizes the target accuracy of different domain adaptation methods for a given source-target pair and a pre-trained feature extractor. Higher values for the **PAS** score are strongly correlated with higher target accuracy.
+
+are similar to the centroid of the source class cluster. However, due to the mismatch between the domains, the target samples exhibit a shift in the feature distribution, making a larger than in the IID scenario. As a result, the values for our score are typically smaller. Alternative design choices are discussed and evaluated in section 4.4.
+
+#### 4 EXPERIMENTS
+
+**Datasets.** We evaluate **PAS** on four of the most popular benchmarks for domain adaptation: **Office-Home** Venkateswara et al. (2017), **Office-31** Saenko et al. (2010), **ImageCLEF** <sup>1</sup>, and **DomainNet** Peng et al. (2019). The benchmarks' statistics are listed in the table 2.
+
+**Domain adaptation methods** Many domain adaptation methods have been proposed in the literature, but none have consistently outperformed the others in all benchmarks. For this reason, we obtained the published target accuracies of a large variety of state-of-the-art methods. We consider methods based on different paradigms and trained using diverse pre-trained feature extractors. The accuracy values are obtained from the popular open-source *Tllib* library for transfer learning Jiang et al. (2022); Junguang Jiang (2020) Wang et al. (2023), and
+
+<span id="page-5-2"></span>![](_page_5_Figure_7.jpeg)
+
+Figure 4: The **PAS** value and target accuracy for the *DANN* and *MCC* methods using different pretrained feature extractors. The **PAS** score can help to select the feature extractor that leads to higher accuracy. (*left*)  $A \rightarrow C$  adaptation in the *Office-Home* benchmark. (*right*)  $W \rightarrow A$  adaptation in the *Office-31* benchmark.
+
+Junguang Jiang (2020), Wang et al. (2023), and from the original papers.
+
+**Baselines** To the best of our knowledge, **PAS** is the first *asymmetric* score proposed for transferability estimation for domain adaptation. We, therefore, compare **PAS** with the symetric metrics **Maximum Mean Discrepancy (MMD)** Gretton et al. (2012) and  $\mathcal{A}$ -distance Peng et al. (2019). The MMD distance is computed using a Gaussian kernel. Due to the quadratic nature of MMD, we restrict its computation to a maximum of 10,000 randomly selected samples per domain for the DomainNet benchmark. The  $\mathcal{A}$ -distance is computed using C-Support Vector Classification. We also report the results for an oracle baseline. The oracle is similar to **PAS**, defined as  $\frac{1}{|\mathcal{D}^T|} \sum_{i}^{|\mathcal{D}^T|} \frac{d_{2i} - d_{1i}}{max\{d_{1i}, d_{2i}\}}.$  The  $d_{1i}$  distance is the cosine distance to the centroid of the true class of the target sample (not known in real scenarios), and  $d_{2i}$  is the distance to the closest cluster's
+
+<span id="page-5-0"></span><sup>1</sup>http://imageclef.org/2014/adaptation
+
+{6}------------------------------------------------
+
+<span id="page-6-0"></span>Table 1: Average target accuracy of domain adaptation methods and transferability scores for different image classification benchmarks. The highest values are highlighted. Our **PAS** has a high correlation with the target accuracy and, for each target domain, attributes the highest value for the source domain that leads to the highest target accuracy in most scenarios. \* Oracle baseline that considers the target labels.
+
+#### (a) Office-Home
+
+|            | Target            |        | A      |        |        | С      |        |        | P      |        |        | R      |        | Correlation | on with acc. |
+|------------|-------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|-------------|--------------|
+|            | Source            | C      | P      | R      | A      | P      | R      | A      | C      | R      | A      | C      | P      | Pearson     | Spearman     |
+|            | Acc. (avg.)       | 62.0   | 61.7   | 72.5   | 53.5   | 52.4   | 58.9   | 71.0   | 70.0   | 82.1   | 77.2   | 70.8   | 78.7   |             |              |
+|            | MMD (neg.)        | -0.135 | -0.113 | -0.052 | -0.135 | -0.097 | -0.125 | -0.113 | -0.097 | -0.033 | -0.052 | -0.125 | -0.033 | 0.77        | 0.72         |
+| ResNet-50  | A-distance (neg.) | -1.876 | -1.810 | -1.333 | -1.876 | -1.827 | -1.814 | -1.810 | -1.827 | -1.424 | -1.333 | -1.814 | -1.424 | 0.76        | 0.78         |
+|            | PAS (our)         | 0.107  | 0.143  | 0.201  | 0.128  | 0.156  | 0.166  | 0.182  | 0.168  | 0.288  | 0.217  | 0.147  | 0.254  | 0.81        | 0.82         |
+|            | Oracle*           | 0.041  | 0.037  | 0.093  | -0.022 | -0.018 | -0.022 | 0.103  | 0.100  | 0.218  | 0.165  | 0.096  | 0.195  | 0.98        | 0.93         |
+|            | Acc. (avg.)       | 74.3   | 71.7   | 76.0   | 61.8   | 58.5   | 61.2   | 81.7   | 83.2   | 86.0   | 83.3   | 82.5   | 84.1   |             |              |
+|            | MMD (neg.)        | -0.106 | -0.058 | -0.024 | -0.106 | -0.077 | -0.102 | -0.058 | -0.077 | -0.026 | -0.024 | -0.102 | -0.026 | 0.56        | 0.57         |
+| DeiT-Small | A-distance (neg.) | -1.865 | -1.761 | -1.26  | -1.865 | -1.843 | -1.796 | -1.761 | -1.843 | -1.37  | -1.26  | -1.796 | -1.37  | 0.52        | 0.57         |
+|            | PAS (our)         | 0.143  | 0.183  | 0.25   | 0.175  | 0.186  | 0.204  | 0.261  | 0.221  | 0.348  | 0.295  | 0.2    | 0.301  | 0.67        | 0.78         |
+|            | Oracle*           | 0.086  | 0.112  | 0.18   | 0.038  | 0.037  | 0.047  | 0.194  | 0.155  | 0.291  | 0.243  | 0.147  | 0.246  | 0.90        | 0.93         |
+|            | Acc. (avg.)       | 81.5   | 78.8   | 81.1   | 69.9   | 65.4   | 68.0   | 86.0   | 86.7   | 90.6   | 87.4   | 87.2   | 88.5   |             |              |
+|            | MMD (neg.)        | -0.099 | -0.056 | -0.028 | -0.099 | -0.091 | -0.11  | -0.056 | -0.091 | -0.023 | -0.028 | -0.11  | -0.023 | 0.56        | 0.57         |
+| DeiT-Base  | A-distance (neg.) | -1.832 | -1.81  | -1.372 | -1.832 | -1.907 | -1.823 | -1.81  | -1.907 | -1.502 | -1.372 | -1.823 | -1.502 | 0.48        | 0.51         |
+|            | PAS (our)         | 0.138  | 0.176  | 0.243  | 0.166  | 0.172  | 0.194  | 0.245  | 0.209  | 0.339  | 0.287  | 0.193  | 0.295  | 0.65        | 0.73         |
+|            | Oracle*           | 0.09   | 0.112  | 0.184  | 0.048  | 0.049  | 0.062  | 0.191  | 0.158  | 0.293  | 0.245  | 0.154  | 0.248  | 0.88        | 0.88         |
+|            | Acc. (avg.)       | 80.1   | 79.8   | 82.2   | 66.4   | 65.2   | 68.2   | 84.1   | 84.2   | 89.0   | 88.0   | 87.2   | 88.5   |             |              |
+|            | MMD (neg.)        | -0.116 | -0.082 | -0.032 | -0.116 | -0.115 | -0.122 | -0.082 | -0.115 | -0.034 | -0.032 | -0.122 | -0.034 | 0.61        | 0.49         |
+| ViT-Small  | A-distance (neg.) | -1.885 | -1.883 | -1.348 | -1.885 | -1.927 | -1.862 | -1.883 | -1.927 | -1.515 | -1.348 | -1.862 | -1.515 | 0.53        | 0.59         |
+|            | PAS (our)         | 0.172  | 0.198  | 0.262  | 0.182  | 0.199  | 0.217  | 0.251  | 0.235  | 0.357  | 0.294  | 0.219  | 0.316  | 0.68        | 0.83         |
+|            | Oracle*           | 0.132  | 0.147  | 0.212  | 0.084  | 0.102  | 0.113  | 0.211  | 0.195  | 0.321  | 0.26   | 0.189  | 0.285  | 0.87        | 0.92         |
+|            | Acc. (avg.)       | 83.0   | 82.7   | 84.5   | 73.2   | 72.2   | 74.4   | 88.3   | 88.6   | 91.4   | 90.2   | 89.5   | 90.8   |             |              |
+|            | MMD (neg.)        | -0.101 | -0.069 | -0.031 | -0.101 | -0.106 | -0.11  | -0.069 | -0.106 | -0.025 | -0.031 | -0.11  | -0.025 | 0.59        | 0.57         |
+| ViT-Base   | A-distance (neg.) | -1.85  | -1.845 | -1.389 | -1.85  | -1.952 | -1.885 | -1.845 | -1.952 | -1.595 | -1.389 | -1.885 | -1.595 | 0.47        | 0.51         |
+|            | PAS (our)         | 0.254  | 0.28   | 0.357  | 0.262  | 0.271  | 0.296  | 0.361  | 0.339  | 0.462  | 0.405  | 0.316  | 0.417  | 0.76        | 0.85         |
+|            | Oracle*           | 0.215  | 0.233  | 0.311  | 0.173  | 0.188  | 0.207  | 0.317  | 0.295  | 0.425  | 0.37   | 0.286  | 0.382  | 0.88        | 0.92         |
+|            | Acc. (avg.)       | 88.5   | 87.7   | 87.9   | 78.3   | 77.1   | 78.2   | 91.5   | 91.9   | 94.2   | 92.9   | 93.0   | 92.8   |             |              |
+|            | MMD (neg.)        | -0.081 | -0.085 | -0.039 | -0.081 | -0.104 | -0.097 | -0.085 | -0.104 | -0.033 | -0.039 | -0.097 | -0.033 | 0.48        | 0.45         |
+| Swin-Base  | A-distance (neg.) | -1.853 | -1.892 | -1.401 | -1.853 | -1.95  | -1.917 | -1.892 | -1.95  | -1.57  | -1.401 | -1.917 | -1.57  | 0.42        | 0.37         |
+|            | PAS (our)         | 0.232  | 0.251  | 0.327  | 0.231  | 0.244  | 0.269  | 0.323  | 0.318  | 0.43   | 0.37   | 0.294  | 0.384  | 0.72        | 0.72         |
+|            | Oracle*           | 0.198  | 0.214  | 0.287  | 0.162  | 0.177  | 0.195  | 0.295  | 0.282  | 0.403  | 0.343  | 0.27   | 0.356  | 0.83        | 0.81         |
+
+### (b) Office-31
+
+|            | Target            |        | A      | 1      | )      | V      | V      | Correlation | on with acc. |
+|------------|-------------------|--------|--------|--------|--------|--------|--------|-------------|--------------|
+|            | Source            | D      | W      | A      | W      | A      | D      | Pearson     | Spearman     |
+|            | Acc. (avg.)       | 71.8   | 70.6   | 90.5   | 100.0  | 91.9   | 98.3   |             |              |
+|            | MMD (neg.)        | -0.145 | -0.165 | -0.145 | -0.046 | -0.165 | -0.046 | 0.71        | 0.72         |
+| ResNet-50  | A-distance (neg.) | -2.00  | -2.00  | -2.00  | -1.783 | -2.00  | -1.783 | 0.72        | 0.83         |
+|            | PAS (our)         | 0.265  | 0.239  | 0.286  | 0.454  | 0.236  | 0.423  | 0.73        | 0.66         |
+|            | Oracle*           | 0.192  | 0.166  | 0.246  | 0.445  | 0.188  | 0.407  | 0.80        | 0.83         |
+|            | Acc. (avg.)       | 77.7   | 77.6   | 94.7   |        | 94.65  |        |             |              |
+|            | MMD (neg.)        | -0.123 | -0.129 | -0.123 | -0.058 | -0.129 | -0.058 | 0.66        | 0.84         |
+| DeiT-Small | A-distance (neg.) | -2.00  | -1.994 | -2.00  | -1.969 | -1.994 | -1.969 | 0.65        | 0.60         |
+|            | PAS (our)         | 0.283  | 0.266  | 0.304  | 0.472  | 0.278  | 0.447  | 0.72        | 0.94         |
+|            | Oracle*           | 0.2    | 0.193  | 0.263  | 0.465  | 0.239  | 0.438  | 0.80        | 1.00         |
+|            | Acc. (avg.)       | 81.3   | 82.0   | 96.8   | 100.0  | 97.9   | 99.2   |             |              |
+|            | MMD (neg.)        | -0.113 | -0.134 | -0.113 | -0.074 | -0.134 | -0.074 | 0.54        | 0.60         |
+| DeiT-Base  | A-distance (neg.) | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | 0.0         | 0.0          |
+|            | PAS (our)         | 0.268  | 0.241  | 0.304  | 0.443  | 0.251  | 0.418  | 0.66        | 0.71         |
+|            | Oracle*           | 0.212  | 0.192  | 0.273  | 0.44   | 0.224  | 0.414  | 0.73        | 0.89         |
+|            | Acc. (avg.)       | 83.5   | 82.2   | 98.6   | 100.0  | 97.7   | 99.2   |             |              |
+|            | MMD (neg.)        | -0.175 | -0.197 | -0.175 | -0.098 | -0.197 | -0.098 | 0.56        | 0.84         |
+| ViT-Small  | A-distance (neg.) | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | 0.0         | 0.0          |
+|            | PAS (our)         | 0.283  | 0.27   | 0.302  | 0.509  | 0.276  | 0.473  | 0.61        | 0.94         |
+|            | Oracle*           | 0.23   | 0.22   | 0.286  | 0.506  | 0.256  | 0.467  | 0.69        | 1.00         |
+|            | Acc. (avg.)       | 84.0   | 85.0   | 97.2   | 100.0  | 96.8   | 99.3   |             |              |
+|            | MMD (neg.)        | -0.098 | -0.118 | -0.098 | -0.071 | -0.118 | -0.071 | 0.57        | 0.72         |
+| ViT-Base   | A-distance (neg.) | -2.00  | -2.00  | -2.00  | -1.953 | -2.00  | -1.953 | 0.64        | 0.72         |
+|            | PAS (our)         | 0.423  | 0.395  | 0.453  | 0.59   | 0.412  | 0.558  | 0.71        | 0.83         |
+|            | Oracle*           | 0.373  | 0.347  | 0.434  | 0.589  | 0.393  | 0.554  | 0.79        | 0.94         |
+|            | Acc. (avg.)       | 86.2   | 86.3   | 99.7   | 100.0  | 99.4   | 99.5   |             |              |
+|            | MMD (neg.)        | -0.168 | -0.169 | -0.168 | -0.086 | -0.169 | -0.086 | 0.51        | 0.60         |
+| Swin-Base  | A-distance (neg.) | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | -2.00  | 0.0         | 0.0          |
+|            | PAS (our)         | 0.361  | 0.349  | 0.399  | 0.589  | 0.374  | 0.56   | 0.62        | 0.89         |
+|            | Oracle*           | 0.321  | 0.313  | 0.388  | 0.589  | 0.366  | 0.558  | 0.69        | 0.89         |
+
+# (c) ImageCLEF
+
+|            | Target            | (      | 3      | 1      | I      | 1      | P      | Correlation | on with acc. |
+|------------|-------------------|--------|--------|--------|--------|--------|--------|-------------|--------------|
+|            | Source            | I      | P      | C      | P      | C      | I      | Pearson     | Spearman     |
+|            | Acc. (avg.)       | 95.9   | 93.7   | 90.7   | 90.0   | 76.0   | 77.9   |             |              |
+|            | MMD (neg.)        | -0.074 | -0.097 | -0.074 | -0.022 | -0.097 | -0.022 | -0.17       | -0.12        |
+| ResNet-50  | A-distance (neg.) | -1.583 | -1.731 | -1.583 | -0.807 | -1.731 | -0.807 | -0.24       | -0.12        |
+|            | PAS (our)         | 0.299  | 0.251  | 0.235  | 0.27   | 0.223  | 0.297  | 0.22        | 0.49         |
+|            | Oracle*           | 0.287  | 0.243  | 0.195  | 0.254  | 0.111  | 0.2    | 0.84        | 0.71         |
+|            | Acc. (avg.)       | 97.5   | 97.5   | 93.7   | 95.2   | 78.3   | 80.8   |             |              |
+|            | MMD (neg.)        | -0.072 | -0.081 | -0.072 | -0.02  | -0.081 | -0.02  | -0.17       | -0.11        |
+| DeiT-Small | A-distance (neg.) | -1.417 | -1.748 | -1.417 | -0.807 | -1.748 | -0.807 | -0.07       | -0.11        |
+|            | PAS (our)         | 0.344  | 0.303  | 0.263  | 0.322  | 0.24   | 0.332  | 0.41        | 0.52         |
+|            | Oracle*           | 0.333  | 0.293  | 0.239  | 0.31   | 0.169  | 0.25   | 0.83        | 0.83         |
+|            | Acc. (avg.)       | 97.8   | 97.1   | 96.6   | 95.7   | 79.5   | 81.9   |             |              |
+|            | MMD (neg.)        | -0.078 | -0.095 | -0.078 | -0.022 | -0.095 | -0.022 | -0.13       | -0.12        |
+| ViT-Base   | A-distance (neg.) | -1.483 | -1.714 | -1.483 | -0.655 | -1.714 | -0.655 | -0.14       | -0.12        |
+|            | PAS (our)         | 0.399  | 0.359  | 0.304  | 0.377  | 0.262  | 0.363  | 0.55        | 0.54         |
+|            | Oracle*           | 0.391  | 0.352  | 0.295  | 0.37   | 0.205  | 0.286  | 0.84        | 0.83         |
+
+### (d) DomainNet
+
+|            | Target            |        | C      |        |        | P      |        |        | R      |        |        | S      |        | Correlation | on with acc. |
+|------------|-------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|-------------|--------------|
+|            | Source            | P      | R      | S      | C      | R      | S      | C      | P      | S      | C      | P      | R      | Pearson     | Spearman     |
+|            | Acc. (avg.)       | 45.5   | 53.7   | 56.7   | 39.4   | 52.2   | 45.8   | 55.9   | 58.1   | 55.3   | 44.8   | 40.7   | 41.0   |             |              |
+|            | MMD (neg.)        | -0.113 | -0.158 | -0.079 | -0.113 | -0.075 | -0.108 | -0.158 | -0.075 | -0.173 | -0.079 | -0.108 | -0.173 | 0.04        | 0.20         |
+| ResNet-101 | A-distance (neg.) | -1.789 | -1.73  | -1.638 | -1.789 | -1.656 | -1.777 | -1.73  | -1.656 | -1.821 | -1.638 | -1.777 | -1.821 | 0.50        | 0.45         |
+|            | PAS (our)         | 0.108  | 0.145  | 0.088  | 0.08   | 0.159  | 0.083  | 0.128  | 0.184  | 0.107  | 0.088  | 0.098  | 0.114  | 0.58        | 0.53         |
+|            | Oracle*           | -0.109 | -0.124 | -0.042 | -0.06  | -0.024 | -0.04  | 0.037  | 0.092  | 0.031  | -0.087 | -0.11  | -0.156 | 0.70        | 0.67         |
+|            | Acc. (avg.)       | 52.3   | 68.8   | 52.2   | 58.6   | 69.7   | 48.4   | 62.3   | 56.6   | 48.5   | 64.7   | 52.4   | 67.2   |             |              |
+|            | MMD (neg.)        | -0.128 | -0.146 | -0.088 | -0.128 | -0.052 | -0.16  | -0.146 | -0.052 | -0.186 | -0.088 | -0.16  | -0.186 | 0.26        | 0.28         |
+| DeiT-Small | A-distance (neg.) | -1.784 | -1.734 | -1.655 | -1.784 | -1.639 | -1.768 | -1.734 | -1.639 | -1.823 | -1.655 | -1.768 | -1.823 | 0.30        | 0.33         |
+|            | PAS (our)         | 0.13   | 0.152  | 0.093  | 0.091  | 0.175  | 0.086  | 0.139  | 0.218  | 0.11   | 0.096  | 0.117  | 0.127  | 0.39        | 0.57         |
+|            | Oracle*           | -0.125 | -0.118 | -0.055 | -0.066 | -0.015 | -0.051 | 0.031  | 0.093  | 0.015  | -0.12  | -0.163 | -0.183 | -0.19       | -0.17        |
+|            | Acc. (avg.)       | 55.7   | 72.2   | 56.9   | 64.6   | 72.9   | 53.3   | 65.8   | 59.4   | 52.4   | 68.7   | 56.7   | 71.8   |             |              |
+|            | MMD (neg.)        | -0.123 | -0.153 | -0.095 | -0.123 | -0.06  | -0.171 | -0.153 | -0.06  | -0.227 | -0.095 | -0.171 | -0.227 | 0.19        | 0.35         |
+| DeiT-Base  | A-distance (neg.) | -1.796 | -1.746 | -1.655 | -1.796 | -1.682 | -1.79  | -1.746 | -1.682 | -1.838 | -1.655 | -1.79  | -1.838 | 0.26        | 0.37         |
+|            | PAS (our)         | 0.126  | 0.147  | 0.086  | 0.085  | 0.165  | 0.079  | 0.137  | 0.211  | 0.102  | 0.089  | 0.119  | 0.112  | 0.26        | 0.44         |
+|            | Oracle*           | -0.115 | -0.097 | -0.044 | -0.047 | 0.004  | -0.04  | 0.044  | 0.105  | 0.022  | -0.109 | -0.162 | -0.154 | -0.17       | -0.08        |
+|            | Acc. (avg.)       | 60.7   | 77.7   | 60.7   | 66.2   | 75.9   | 57.2   | 69.7   | 64.6   | 57.9   | 71.4   | 62.7   | 76.3   |             |              |
+|            | MMD (neg.)        | -0.14  | -0.157 | -0.108 | -0.14  | -0.116 | -0.175 | -0.157 | -0.116 | -0.25  | -0.108 | -0.175 | -0.25  | 0.07        | 0.15         |
+| ViT-Base   | A-distance (neg.) | -1.814 | -1.771 | -1.686 | -1.814 | -1.734 | -1.807 | -1.771 | -1.734 | -1.859 | -1.686 | -1.807 | -1.859 | 0.18        | 0.21         |
+|            | PAS (our)         | 0.185  | 0.226  | 0.162  | 0.145  | 0.233  | 0.128  | 0.223  | 0.282  | 0.176  | 0.151  | 0.171  | 0.17   | 0.37        | 0.35         |
+|            | Oracle*           | -0.003 | 0.018  | 0.042  | 0.012  | 0.066  | 0.007  | 0.135  | 0.184  | 0.103  | -0.021 | -0.075 | -0.062 | -0.13       | -0.08        |
+
+{7}------------------------------------------------
+
+Table 2: Statistics of the benchmarks used in the experiments.
+
+<span id="page-7-0"></span>
+
+| Dataset     | #Samples | #Classes | Domains                                                        |
+|-------------|----------|----------|----------------------------------------------------------------|
+| Office-Home | 15,588   | 65       | A (Art), C (Clipart), P (Product), R (Real-world)              |
+| Office-31   | 4,110    | 31       | A (Amazon), D (DSLR), W (Webcam)                               |
+| ImageCLEF   | 1,800    | 12       | C (Caltech-256), I (ImageNet ILSVRC 2012), P (Pascal VOC 2012) |
+| DomainNet   | 569,010  | 345      | C (Clipart), P (Painting), R (Real), S (Sketch)                |
+
+<span id="page-7-1"></span>Table 3: Correlation with the average target accuracy after adaptation. Showing Pearson correlation / Spearman's rank correlation.
+
+|                         | Office-Home | Office-31   | ImageCLEF     | DomainNet     | Total        |
+|-------------------------|-------------|-------------|---------------|---------------|--------------|
+| MMD                     | 0.55 / 0.51 | 0.45 / 0.53 | -0.14 / -0.08 | -0.09 / -0.03 | 0.37 / 0.37  |
+| $\mathcal{A}$ -distance | 0.32 / 0.17 | 0.26 / 0.35 | -0.13 / -0.07 | 0.07 / 0.06   | 0.04 / -0.16 |
+| PAS (our)               | 0.76 / 0.81 | 0.63 / 0.78 | 0.44 / 0.60   | 0.53 / 0.56   | 0.83 / 0.88  |
+| Oracle*                 | 0.89 / 0.90 | 0.71 / 0.86 | 0.78 / 0.85   | 0.21 / 0.21   | 0.88 / 0.91  |
+
+centroid that is not the true class. In the ideal case where the closest class centroid is the actual class of the sample, the oracle is the same as **PAS**, otherwise, the oracle value is smaller. The oracle validates the existing relationship between the clusters distance and the target accuracy.
+
+#### 4.1 Selection of the Source Domain
+
+The results for the four benchmark datasets are presented in Table 1 (a) - (d). For each source-target pair in the benchmarks, we group the domain adaptation methods using the same pre-trained feature extractor and report their average target accuracy, followed by the baselines and our **PAS** score. We highlight the highest values among the different choices of source domains. We also report the correlation (Pearson and Spearman's rank correlation) between the average target accuracy and the scores. The detailed results for each individual domain adaptation method are presented in the Supplementary Material A.1.
+
+We report in Table 3 the overall correlation for all scenarios of each benchmark (all target domains, source domains and pre-trained models). The results show that the **PAS** score is strongly correlated with target accuracy. We observe an overall Spearman's rank correlation of **0.88** over all the results.
+
+The most important results are reported in Table 4, where we present the correlation for each target domain. This correlation is the most useful for users in real-world scenarios. Given a target domain of interest and many options of source domains and pre-trained models, we show that our **PAS** score has a strong correlation with the final target accuracy. The empirical results indicate that our proposed **PAS** score is effective in selecting the best source domain among many candidates.
+
+We summarize our results in Figure 3. Each box in the graph represents the target accuracy of different domain adaptation methods using the same pre-trained backbone for a source-target domains pair. We observe that higher **PAS** values are consistently related to high accuracy on the target domain. This indicates that **PAS** may be useful not only for selecting the most appropriate source domain, but also to estimate beforehand the success of the domain adaptation.
+
+<span id="page-7-2"></span>Table 4: Correlation with the average target accuracy after adaptation for each target domain. Each cell considers the results for a target domain and all available source domains and pre-trained models. Showing Pearson correlation / Spearman's rank correlation.
+
+|            |              | Office        | -Home        |               | 1             | Office-31   |             | 1           | ImageCLEF     |             |               | Doma        | ainNet      |               |
+|------------|--------------|---------------|--------------|---------------|---------------|-------------|-------------|-------------|---------------|-------------|---------------|-------------|-------------|---------------|
+|            | A            | C             | P            | R             | A             | D           | W           | C           | I             | P           | С             | P           | R           | S             |
+| MMD        | 0.41 / 0.26  | 0.28 / 0.21   | 0.41 / 0.29  | 0.25 / 0.21   | -0.02 / -0.15 | 0.44 / 0.60 | 0.45 / 0.36 | 0.54 / 0.49 | -0.03 / -0.22 | 0.61 / 0.60 | -0.56 / -0.42 | 0.33 / 0.20 | 0.23 / 0.47 | -0.38 / -0.42 |
+| A-distance | 0.12 / -0.13 | -0.46 / -0.43 | 0.15 / -0.09 | -0.05 / -0.26 | -0.19 / -0.31 | 0.27 / 0.28 | 0.14 / 0.07 | 0.43 / 0.38 | 0.10 / 0.05   | 0.64 / 0.60 | 0.09 / -0.04  | 0.35 / 0.17 | 0.27 / 0.30 | -0.10 / -0.32 |
+| PAS (our)  | 0.70 / 0.70  | 0.81 / 0.78   | 0.79 / 0.74  | 0.75 / 0.75   | 0.65 / 0.81   | 0.70 / 0.81 | 0.70 / 0.75 | 0.82 / 0.76 | 0.73 / 0.66   | 0.87 / 0.83 | 0.71 0.67     | 0.75 / 0.76 | 0.59 / 0.71 | 0.48 / 0.35   |
+| Oracle*    | 0.82 / 0.85  | 0.91 / 0.90   | 0.84 / 0.81  | 0.80 / 0.87   | 0.74 / 0.88   | 0.73 / 0.90 | 0.74 / 0.78 | 0.81 / 0.76 | 0.74 / 0.66   | 0.97 / 0.94 | 0.36 / 0.50   | 0.71 / 0.62 | 0.61 / 0.72 | 0.28 / 0.33   |
+
+{8}------------------------------------------------
+
+The results on the *ImageCLEF* benchmark illustrate the scenarios where the **PAS** score is not effective. This benchmark (especially the *P* domain) contains images with multiple objects. In many cases, the sample is very close to the centroid of one class that is indeed present in the image, but the true label is related to another object in the scene. In these cases, the **PAS** for the sample is high, showing a high similarity with one source class, but the final accuracy is low, as the sample is classified as the wrong class. We show examples in the supplementary material A.2
+
+#### 4.2 The selection of the pre-trained feature extractor
+
+<span id="page-8-1"></span>![](_page_8_Figure_3.jpeg)
+
+Figure 5: The **PAS** value varying with the number of samples for the *Office-Home*. The **PAS** values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.
+
+may be applied for the selection of the pre-trained model.
+
+The results in the literature presented in table 1 compare methods with different backbones and demonstrate that **PAS** can be applied to select the most suitable pretrained feature extractor. However, they do not consider the impact of different pre-trained feature extractors over the same domain adaptation method. For analyzing the robustness of PAS over different choices of pre-trained methods, we keep the domain adaptation method fixed and vary the pre-trained backbone. We select two of the most challenging domain adaptation scenarios: the  $A \rightarrow C$  adaptation in the Office-Home benchmark and  $W \rightarrow A$  adaptation in the *Office-31* benchmark. We show results for two popular domain adaptation methods: *DANN* Ganin et al. (2016) and *MCC* Jin et al. (2020). We train each method following the code provided by the Tllib library Jiang et al. (2022); Junguang Jiang (2020) with the default hyperparameters. The results are shown in figure 4. Higher PAS values are attributed to pretrained models that lead to higher target accuracy before performing domain adaptation, indicating that our score
+
+#### 4.3 THE IMPACT OF THE SAMPLE SIZE
+
+The time complexity of the PAS computation is linear in the number of samples. This can be limiting for a quick evaluation of larger datasets and scenarios with many candidate source domains.
+
+To optimize the computation time, we show that our score can be calculated using only a subset of the samples. We randomly select a subset of the samples of both source and target domains. The results are presented in the figure 5. The **PAS** values are quite robust to varying numbers of samples. Most importantly, the relative order of PAS values for different source domains remains unchanged.
+
+#### <span id="page-8-0"></span>4.4 DESIGN CHOICES
+
+The PAS score considers the cosine distance between each target sample and the source class centroids. We experimentally evaluated alternative design choices and compare the correlation between the score and the target accuracy. The results are shown in table 5 and demonstrate how the overall correlation between the target accuracy and PAS, as proposed, is higher.
+
+We change **PAS** to consider the Euclidean distance instead of the cosine distance. In the domain adaptation setting, the cosine distance has advantages over using the Euclidean distance in the original latent space, as it ignores the magnitude of
+
+<span id="page-8-2"></span>
+
+|                         | Office-Home | Office-31 | ImageCLEF | DomainNet | Total |      |
+|-------------------------|-------------|-----------|-----------|-----------|-------|------|
+| PAS                     | 0.76        | 0.63      | 0.44      |           | 0.58  | 0.79 |
+| Euclidean distance      | 0.70        | 0.69      | 0.27      | 0.54      | 0.68  |      |
+| Average cosine distance | 0.66        | 0.52      | 0.12      | 0.48      | 0.66  |      |
+
+Table 5: Pearson correlation between the target accuracy and the **PAS** score, which considers the cosine distance to the cluster centroid, and modifications using the Euclidean distance to the centroid and the average cosine distance to the source cluster samples. The maximum correlation value for each benchmark is highlighted. The design choices of **PAS** lead to the higher overall correlation between the score and the target accuracy.
+
+{9}------------------------------------------------
+
+representations (e.g., a difference in the illumination in images that reflects on the intensity of the features detected by the model) and focuses only on the differences in the angles (the difference between classes). Also, the cosine distance is less affected by the high-dimensionality of the data (the phenomenon known as *curse of dimensionality* [Bellman](#page-9-5) [\(1966\)](#page-9-5)).
+
+We also modify PAS to use the average pairwise distance to the source samples instead of the distance to the source cluster centroid. The pairwise distance is a good summarization of the closeness of the target sample to the source samples of the class. On the other hand, the distance to the centroid measures how well the target sample is aligned to the dimensions of greatest alignment between the samples in the cluster, as the centroid formulation 1/|D<sup>S</sup> | P|D<sup>S</sup> <sup>|</sup> <sup>i</sup>=1 x S <sup>i</sup> makes samples pointing in similar directions add up in that direction.
+
+# 5 CONCLUSION AND FUTURE WORK
+
+We present Potential Adaptability Score (PAS), a new score to select, among many candidates, the source domain or pre-trained model that are likely to lead to the best target accuracy when used for unsupervised domain adaptation. We evaluate our score on four of the most popular benchmarks for domain adaptation and show that it has a high correlation with the target accuracy and selects the best source domain in most cases. We also show that PAS can be computed more efficiently with fewer samples.
+
+We suggest two improvements for future work. Although our score could be applied to any classification task, we focus on vision problems, specifically the image classification task, which is the most common task in the domain adaptation literature. Showing its efficacy on other modalities and tasks demands the availability of a diverse set of benchmarks and specialized domain adaptation methods. Also, we focus on the single-source domain adaptation problem, where only a single source domain is considered during the training. Future works may extend our work to select multiple source domains, in the setting known as multi-source domain adaptation.
+
+# ETHICS STATEMENT
+
+Although our work does not directly address issues of social harm, we acknowledge that our PAS score is not immune to bias and fairness concerns. If a biased model achieves higher accuracy on the target data, our framework is likely to select it as the best pre-trained model for domain adaptation. In our experiments, we mitigate such risks by focusing on pre-trained models and benchmarks that are widely adopted within the research community.
+
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+
+# A SUPPLEMENTARY MATERIAL
+
+### <span id="page-12-7"></span>A.1 RESULTS
+
+The tables [6,](#page-13-0) [7,](#page-14-0) [8,](#page-15-0) and [9](#page-15-1) show the extended results of table [1.](#page-6-0) The accuracy for each method is listed, as well as its accuracy correlation with the scores.
+
+### <span id="page-12-8"></span>A.2 EXAMPLES OF SAMPLES IN THE *ImageCLEF* BENCHMARK
+
+We present some examples of when the PAS score fails to predict the target accuracy. The figure [6](#page-16-0) shows examples of misclassified images from the P (*Pascal VOC 2012*) domain of the *ImageCLEF* benchmark. Many images contain more than one object. The sample may be very similar to a class present in the image. However, the true class refers to another object also contained in the image. In such cases, the PAS value is high, but the accuracy is low.
+
+{13}------------------------------------------------
+
+<span id="page-13-0"></span>Table 6: Target accuracy of domain adaptation methods and transferability scores for the *Office-Home* dataset. The highest values are highlighted. \* Oracle baseline that considers the target labels.
+
+|               | Target    |       | A     |       |       | С     |       |       | P     |       |       | R     |       | Correlation | on with PAS |
+|---------------|-----------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------------|-------------|
+|               | Source    | C     | P     | R     | A     | P     | R     | A     | C     | R     | A     | C     | P     | Pearson     | Spearman    |
+|               | DAN       | 57.7  | 54.9  | 66.2  | 45.6  | 40.0  | 49.1  | 67.7  | 63.8  | 77.9  | 73.9  | 66.0  | 74.5  | 0.74        | 0.81        |
+|               | DANN      | 55.8  | 55.8  | 71.1  | 53.8  | 55.1  | 60.7  | 62.6  | 67.3  | 81.1  | 74.0  | 67.3  | 77.9  | 0.91        | 0.85        |
+|               | ADDA      | 59.7  | 61.4  | 71.1  | 52.6  | 52.5  | 58.6  | 62.9  | 68.0  | 80.2  | 74.0  | 68.8  | 77.6  | 0.84        | 0.80        |
+|               | JAN       | 60.6  | 60.5  | 71.0  | 50.8  | 49.6  | 55.9  | 71.9  | 68.3  | 80.5  | 76.5  | 68.7  | 76.9  | 0.78        | 0.81        |
+|               | CDAN      | 62.0  | 62.4  | 75.5  | 55.2  | 54.3  | 61.0  | 72.4  | 69.7  | 83.8  | 77.6  | 70.9  | 80.5  | 0.85        | 0.83        |
+|               | MCD       | 63.7  | 61.5  | 74.5  | 51.7  | 52.8  | 58.4  | 72.2  | 69.5  | 81.8  | 78.2  | 70.8  | 78.0  | 0.78        | 0.83        |
+| ResNet-50     | BSP       | 61.0  | 60.9  | 73.4  | 54.7  | 55.2  | 60.3  | 67.7  | 69.4  | 81.2  | 76.2  | 70.9  | 80.2  | 0.85        | 0.80        |
+|               | AFN       | 65.0  | 65.0  | 72.3  | 53.2  | 51.4  | 57.8  | 72.7  | 71.3  | 82.4  | 76.8  | 72.3  | 77.9  | 0.73        | 0.78        |
+|               | MDD       | 63.5  | 62.5  | 73.5  | 56.2  | 54.8  | 60.9  | 75.4  | 72.1  | 84.5  | 79.6  | 73.8  | 79.9  | 0.80        | 0.78        |
+|               | MCC       | 67.5  | 66.6  | 74.4  | 58.4  | 54.8  | 61.4  | 79.6  | 77.0  | 85.6  | 83.0  | 78.5  | 81.8  | 0.70        | 0.76        |
+|               | FixMatch  | 65.3  | 67.2  | 74.9  | 56.4  | 56.4  | 63.5  | 76.4  | 73.8  | 84.3  | 79.9  | 71.2  | 80.6  | 0.81        | 0.87        |
+|               | Avg.      | 62.0  | 61.7  | 72.5  | 53.5  | 52.4  | 58.9  | 71.0  | 70.0  | 82.1  | 77.2  | 70.8  | 78.7  | 0.81        | 0.82        |
+|               | PAS (our) | 0.107 | 0.143 | 0.201 | 0.128 | 0.156 | 0.166 | 0.182 | 0.168 | 0.288 | 0.217 | 0.147 | 0.254 |             |             |
+|               | TRANS-DA  | 69.7  | 68.6  | 73.5  | 57.7  | 56.3  | 58.5  | 80.8  | 83    | 85    | 81.5  | 80.1  | 81.5  | 0.69        | 0.79        |
+|               | WinTR     | 76.8  | 73.4  | 77.2  | 65.3  | 60    | 63.1  | 84.1  | 84.5  | 86.8  | 85    | 84.4  | 85.7  | 0.64        | 0.78        |
+| DeiT-Small    | DOT       | 74.9  | 72.4  | 76.4  | 63.7  | 61    | 64.1  | 82.2  | 84.3  | 86.7  | 84.3  | 83    | 84.8  | 0.68        | 0.79        |
+| Del I-Siliali | CDTrans   | 75.6  | 72.5  | 77    | 60.6  | 56.7  | 59.1  | 79.5  | 81    | 85.5  | 82.4  | 82.3  | 84.4  | 0.63        | 0.76        |
+|               | Avg.      | 74.3  | 71.7  | 76.0  | 61.8  | 58.5  | 61.2  | 81.7  | 83.2  | 86    | 83.3  | 82.5  | 84.1  | 0.67        | 0.78        |
+|               | PAS (our) | 0.143 | 0.183 | 0.25  | 0.175 | 0.186 | 0.204 | 0.261 | 0.221 | 0.348 | 0.295 | 0.2   | 0.301 |             |             |
+|               | DOT       | 80    | 78.2  | 79.7  | 69    | 65.4  | 67.3  | 85.6  | 85.2  | 89.3  | 87    | 86.4  | 87.9  | 0.66        | 0.75        |
+|               | CDTrans   | 81.5  | 79.6  | 82    | 68.8  | 63.3  | 66    | 85    | 87.1  | 90.6  | 86.9  | 87.3  | 88.2  | 0.62        | 0.73        |
+| DeiT-Base     | PMTrans   | 83    | 78.5  | 81.7  | 71.8  | 67.4  | 70.7  | 87.3  | 87.7  | 92    | 88.3  | 87.8  | 89.3  | 0.67        | 0.73        |
+|               | Avg.      | 81.5  | 78.8  | 81.1  | 69.9  | 65.4  | 68.0  | 86.0  | 86.7  | 90.6  | 87.4  | 87.2  | 88.5  | 0.65        | 0.73        |
+|               | PAS (our) | 0.138 | 0.176 | 0.243 | 0.166 | 0.172 | 0.194 | 0.245 | 0.209 | 0.339 | 0.287 | 0.193 | 0.295 |             |             |
+|               | SSRT      | 79.9  | 80.7  | 82    | 67    | 66    | 69.4  | 84.2  | 84.3  | 89.9  | 88.3  | 87.6  | 88.3  | 0.69        | 0.84        |
+| ViT-Small     | SAMB      | 80.2  | 78.8  | 82.4  | 65.7  | 64.4  | 67    | 84    | 84.1  | 88    | 87.7  | 86.7  | 88.6  | 0.67        | 0.82        |
+| VII-SIIIaii   | Avg.      | 80.1  | 79.8  | 82.2  | 66.4  | 65.2  | 68.2  | 84.1  | 84.2  | 89.0  | 88.0  | 87.2  | 88.5  | 0.68        | 0.83        |
+|               | PAS (our) | 0.172 | 0.198 | 0.262 | 0.182 | 0.199 | 0.217 | 0.251 | 0.235 | 0.357 | 0.294 | 0.219 | 0.316 |             |             |
+|               | SAMB      | 80.8  | 81.6  | 84.1  | 68.7  | 68.7  | 70.9  | 85    | 86    | 91.1  | 88.9  | 88.3  | 90.2  | 0.77        | 0.88        |
+|               | DoT       | 81.8  | 81.2  | 82.9  | 72.9  | 70.6  | 72.2  | 89.8  | 89.6  | 90.8  | 90.3  | 90.1  | 92.4  | 0.75        | 0.84        |
+|               | TVT       | 77.4  | 75.6  | 79.1  | 67.1  | 64.9  | 67.2  | 83.5  | 85    | 88    | 87.3  | 85.6  | 86.6  | 0.78        | 0.85        |
+| ViT-Base      | SSRT      | 85.1  | 85    | 85.7  | 75.2  | 74.2  | 78.6  | 89    | 88.3  | 91.8  | 91.1  | 90    | 91.3  | 0.76        | 0.87        |
+| VII-Base      | BCAT      | 84.2  | 84.1  | 85.7  | 74.2  | 74.5  | 74.8  | 90.6  | 90.9  | 92.2  | 90.9  | 89.9  | 90.8  | 0.74        | 0.83        |
+|               | PMTrans   | 88.9  | 88.5  | 89.5  | 81.2  | 80    | 82.4  | 91.6  | 91.6  | 94.5  | 92.4  | 93    | 93.4  | 0.74        | 0.84        |
+|               | Avg.      | 83.0  | 82.7  | 84.5  | 73.2  | 72.2  | 74.4  | 88.3  | 88.6  | 91.4  | 90.2  | 89.5  | 90.8  | 0.76        | 0.85        |
+|               | PAS (our) | 0.254 | 0.28  | 0.357 | 0.262 | 0.271 | 0.296 | 0.361 | 0.339 | 0.462 | 0.405 | 0.316 | 0.417 |             |             |
+|               | PMTrans   | 88.4  | 87.9  | 89    | 81.3  | 80.4  | 80.9  | 92.9  | 93.4  | 94.8  | 92.8  | 93.2  | 93    | 0.75        | 0.72        |
+| Swin-Base     | BCAT      | 88.6  | 87.4  | 86.7  | 75.3  | 73.7  | 75.4  | 90    | 90.3  | 93.5  | 92.9  | 92.7  | 92.5  | 0.68        | 0.74        |
+| Swiii-Base    | Avg.      | 88.5  | 87.7  | 87.9  | 78.3  | 77.1  | 78.2  | 91.5  | 91.9  | 94.2  | 92.9  | 93.0  | 92.8  | 0.72        | 0.72        |
+|               | PAS (our) | 0.232 | 0.251 | 0.327 | 0.231 | 0.244 | 0.269 | 0.323 | 0.318 | 0.43  | 0.37  | 0.294 | 0.384 |             |             |
+
+{14}------------------------------------------------
+
+<span id="page-14-0"></span>Table 7: Target accuracy of domain adaptation methods and transferability scores for the *Office-31* dataset. The highest values are highlighted. \* Oracle baseline that considers the target labels.
+
+|            | Target    |       | A     |       | D     |       | W     |         | Correlation with PAS |
+|------------|-----------|-------|-------|-------|-------|-------|-------|---------|----------------------|
+|            | Source    | D     | W     | A     | W     | A     | D     | Pearson | Spearman             |
+|            | DANN      | 73.3  | 70.4  | 83.6  | 100.0 | 91.4  | 97.9  | 0.78    | 0.66                 |
+|            | ADDA      | 69.6  | 72.5  | 90.0  | 99.7  | 94.6  | 97.5  | 0.67    | 0.60                 |
+|            | BSP       | 74.1  | 73.8  | 88.2  | 100.0 | 92.7  | 97.9  | 0.75    | 0.66                 |
+|            | DAN       | 66.9  | 65.2  | 87.3  | 100.0 | 84.2  | 98.4  | 0.83    | 0.83                 |
+|            | JAN       | 69.2  | 71.0  | 89.4  | 100.0 | 93.7  | 98.4  | 0.70    | 0.60                 |
+|            | CDAN      | 73.4  | 70.4  | 89.9  | 100.0 | 93.8  | 98.5  | 0.71    | 0.66                 |
+| ResNet-50  | MCD       | 68.3  | 67.6  | 87.3  | 100.0 | 90.4  | 98.5  | 0.76    | 0.66                 |
+|            | AFN       | 72.9  | 71.1  | 94.4  | 100.0 | 94.0  | 98.9  | 0.67    | 0.83                 |
+|            | MDD       | 76.6  | 72.2  | 94.4  | 100.0 | 95.6  | 98.6  | 0.65    | 0.66                 |
+|            | MCC       | 75.5  | 74.2  | 95.6  | 99.8  | 94.1  | 98.4  | 0.66    | 0.83                 |
+|            | FixMatch  | 70.0  | 68.1  | 95.4  | 100.0 | 86.4  | 98.2  | 0.75    | 0.83                 |
+|            | Avg.      | 71.1  | 70.0  | 89.6  | 99.9  | 90.6  | 98.1  | 0.73    | 0.66                 |
+|            | PAS (our) | 0.265 | 0.239 | 0.286 | 0.454 | 0.236 | 0.423 |         |                      |
+|            | TRANS-DA  | 77    | 77.1  | 94.8  | 100   | 95.8  | 98.8  | 0.69    | 0.71                 |
+|            | CDTrans   | 78.4  | 78    | 94.6  | 99.6  | 93.5  | 98.2  | 0.74    | 0.94                 |
+| DeiT-Small | Avg.      | 77.7  | 77.6  | 94.7  | 99.8  | 94.65 | 98.5  | 0.72    | 0.94                 |
+|            | PAS (our) | 0.283 | 0.266 | 0.304 | 0.472 | 0.278 | 0.447 |         |                      |
+|            | CDTrans   | 81.1  | 81.9  | 97    | 100   | 96.7  | 99    | 0.69    | 0.83                 |
+|            | PMTrans   | 81.4  | 82.1  | 96.5  | 100   | 99    | 99.4  | 0.64    | 0.71                 |
+| DeiT-Base  | Avg.      | 81.3  | 82.0  | 96.8  | 100.0 | 97.9  | 99.2  | 0.66    | 0.71                 |
+|            | PAS (our) | 0.268 | 0.241 | 0.304 | 0.443 | 0.251 | 0.418 |         |                      |
+|            | SSRT      | 83.5  | 82.2  | 98.6  | 100   | 97.7  | 99.2  | 0.61    | 0.94                 |
+| ViT-Small  | PAS (our) | 0.283 | 0.27  | 0.302 | 0.509 | 0.276 | 0.473 |         |                      |
+|            | DoT       | 85.1  | 86.8  | 96.7  | 100   | 96.6  | 99.4  | 0.74    | 0.83                 |
+|            | TVT       | 84.9  | 86.1  | 96.4  | 100   | 96.4  | 99.4  | 0.75    | 0.75                 |
+|            | SSRT      | 79.2  | 79.9  | 95.8  | 100   | 95.7  | 99.2  | 0.72    | 0.83                 |
+| ViT-Base   | BCAT      | 84.9  | 85.8  | 97.5  | 100   | 96.1  | 99.1  | 0.73    | 0.83                 |
+|            | PMTrans   | 85.7  | 86.3  | 99.4  | 100   | 99.1  | 99.6  | 0.62    | 0.83                 |
+|            | Avg.      | 84.0  | 85.0  | 97.2  | 100.0 | 96.8  | 99.3  | 0.71    | 0.83                 |
+|            | PAS (our) | 0.423 | 0.395 | 0.453 | 0.59  | 0.412 | 0.558 |         |                      |
+|            | PMTrans   | 86.7  | 86.5  | 99.8  | 100   | 99.5  | 99.4  | 0.61    | 0.83                 |
+|            | BCAT      | 85.7  | 86.1  | 99.6  | 100   | 99.2  | 99.5  | 0.63    | 0.89                 |
+| Swin-Base  | Avg.      | 86.2  | 86.3  | 99.7  | 100   | 99.4  | 99.5  | 0.62    | 0.89                 |
+|            | PAS (our) | 0.361 | 0.349 | 0.399 | 0.589 | 0.374 | 0.56  |         |                      |
+
+{15}------------------------------------------------
+
+<span id="page-15-0"></span>Table 8: Target accuracy of domain adaptation methods and transferability scores for the *Image-CLEF* dataset. The highest values are highlighted. \* Oracle baseline that considers the target labels.
+
+|               | Target    | (     | C     |       | I     | ]     | P     | Correlation | on with PAS |
+|---------------|-----------|-------|-------|-------|-------|-------|-------|-------------|-------------|
+|               | Source    | I     | P     | С     | P     | C     | I     | Pearson     | Spearman    |
+|               | RTN       | 95.3  | 92.2  | 86.9  | 86.8  | 72.7  | 75.6  | 0.29        | 0.49        |
+|               | MADA      | 96.0  | 92.2  | 88.8  | 87.9  | 75.2  | 75.0  | 0.20        | 0.26        |
+|               | iCAN      | 94.7  | 92    | 89.9  | 89.7  | 78.5  | 79.5  | 0.23        | 0.49        |
+|               | CDAN-E    | 97.7  | 94.3  | 91.3  | 90.7  | 74.2  | 77.7  | 0.27        | 0.49        |
+|               | SymNets   | 97.0  | 96.4  | 93.4  | 93.6  | 78.7  | 80.2  | 0.17        | 0.60        |
+|               | MEDA      | 95.7  | 95.5  | 92.2  | 92.5  | 78.5  | 79.7  | 0.16        | 0.60        |
+| ResNet-50     | SPL       | 96.7  | 96.3  | 95.7  | 94.5  | 80.5  | 78.3  | 0.02        | 0.26        |
+|               | DS-c      | 92.8  | 91.3  | 87.3  | 86.7  | 70.4  | 78.7  | 0.39        | 0.49        |
+|               | CAN       | 95.5  | 95.2  | 91.6  | 91.8  | 76.4  | 78.5  | 0.19        | 0.60        |
+|               | JAN       | 94.7  | 91.7  | 89.5  | 88.0  | 74.2  | 76.8  | 0.24        | 0.49        |
+|               | CDAN      | 98.3  | 94    | 90.7  | 88.3  | 76.7  | 77.2  | 0.22        | 0.49        |
+|               | Avg.      | 95.9  | 93.7  | 90.7  | 90.0  | 76.0  | 77.9  | 0.22        | 0.49        |
+|               | PAS (our) | 0.299 | 0.251 | 0.235 | 0.27  | 0.223 | 0.297 |             |             |
+| DeiT-small    | TRANS-DA  | 97.5  | 97.5  | 93.7  | 95.2  | 78.3  | 80.8  | 0.41        | 0.52        |
+| Del I-siliali | PAS (our) | 0.344 | 0.303 | 0.263 | 0.322 | 0.24  | 0.332 |             |             |
+|               | VT-ADA    | 97.3  | 96.0  | 96.2  | 94.1  | 78.9  | 81.8  | 0.55        | 0.49        |
+| ViT-Base      | CSTrans   | 98.2  | 98.2  | 97.0  | 97.2  | 80.0  | 82.0  | 0.54        | 0.62        |
+| vii-Dase      | Avg.      | 97.8  | 97.1  | 96.6  | 95.7  | 79.5  | 81.9  | 0.55        | 0.54        |
+|               | PAS (our) | 0.399 | 0.359 | 0.304 | 0.377 | 0.262 | 0.363 |             |             |
+
+<span id="page-15-1"></span>Table 9: Target accuracy of domain adaptation methods and transferability scores for the *DomainNet* dataset. The highest values are highlighted. \* Oracle baseline that considers the target labels.
+
+|            | Target    | l     | С     |       |       | P     |       | 1     | R     |       | 1     | S     |       | Correlation | on with PAS |
+|------------|-----------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------------|-------------|
+|            | Source    | P     | R     | S     | C     | R     | S     | C     | P     | S     | C     | P     | R     | Pearson     | Spearman    |
+|            | DAN       | 45.9  | 50.8  | 56.1  | 38.8  | 49.8  | 45.9  | 55.2  | 59.0  | 55.5  | 43.9  | 40.8  | 38.9  | 0.54        | 0.49        |
+|            | DANN      | 41.7  | 50.7  | 55.0  | 37.9  | 50.8  | 45.0  | 54.3  | 55.6  | 54.5  | 44.4  | 36.8  | 40.1  | 0.53        | 0.46        |
+|            | JAN       | 47.2  | 54.2  | 56.6  | 40.5  | 52.6  | 46.2  | 56.7  | 59.9  | 55.5  | 45.1  | 43.0  | 41.9  | 0.63        | 0.58        |
+|            | CDAN      | 45.1  | 55.6  | 57.2  | 40.4  | 53.6  | 46.4  | 56.8  | 58.4  | 55.7  | 46.1  | 40.5  | 43.0  | 0.60        | 0.50        |
+| ResNet-50  | MCD       | 44.6  | 52.0  | 55.5  | 37.5  | 51.5  | 44.6  | 52.9  | 54.5  | 52.0  | 44.0  | 41.6  | 39.7  | 0.57        | 0.47        |
+|            | MDD       | 48.6  | 58.3  | 58.7  | 42.9  | 53.7  | 46.5  | 59.5  | 59.4  | 57.7  | 47.5  | 42.6  | 46.2  | 0.60        | 0.59        |
+|            | MCC       | 45.4  | 54.4  | 58.1  | 37.7  | 53.1  | 46.3  | 55.7  | 59.8  | 56.2  | 42.6  | 39.9  | 37.0  | 0.57        | 0.43        |
+|            | Avg.      | 45.5  | 53.7  | 56.7  | 39.4  | 52.2  | 45.8  | 55.9  | 58.1  | 55.3  | 44.8  | 40.7  | 41.0  | 0.58        | 0.53        |
+|            | PAS (our) | 0.108 | 0.145 | 0.088 | 0.08  | 0.159 | 0.083 | 0.128 | 0.184 | 0.107 | 0.088 | 0.098 | 0.114 |             |             |
+|            | WinTR     | 53.2  | 70.5  | 51.6  | 62.0  | 71.3  | 50.1  | 63.1  | 55.9  | 48.8  | 65.3  | 54.1  | 70.1  | 0.32        | 0.54        |
+|            | DOT       | 51.3  | 67.6  | 51.7  | 58.5  | 70.4  | 47.2  | 62.3  | 57    | 49.4  | 64.6  | 49.9  | 65.4  | 0.42        | 0.52        |
+| DeiT-Small | CDTRANS   | 52.5  | 68.3  | 53.2  | 55.4  | 67.4  | 48    | 61.5  | 56.8  | 47.2  | 64.3  | 53.2  | 66.2  | 0.41        | 0.55        |
+|            | Avg.      | 52.3  | 68.8  | 52.2  | 58.6  | 69.7  | 48.4  | 62.3  | 56.6  | 48.5  | 64.7  | 52.4  | 67.2  | 0.39        | 0.57        |
+|            | PAS (our) | 0.13  | 0.152 | 0.093 | 0.091 | 0.175 | 0.086 | 0.139 | 0.218 | 0.11  | 0.096 | 0.117 | 0.127 |             |             |
+|            | DOT       | 53.6  | 71.2  | 55.2  | 61.8  | 72.2  | 50.5  | 62.9  | 56.9  | 49.3  | 67.3  | 52.9  | 69.8  | 0.27        | 0.45        |
+|            | CDTRANS   | 57.2  | 72.6  | 58.1  | 62.9  | 72.1  | 53.9  | 66.2  | 61.5  | 52.9  | 69.0  | 59.0  | 72.5  | 0.33        | 0.43        |
+| DeiT-Base  | WINTR     | 56.3  | 72.8  | 57.3  | 69.2  | 74.4  | 55.6  | 68.2  | 59.8  | 55.1  | 69.9  | 58.1  | 73.1  | 0.20        | 0.39        |
+|            | Avg       | 55.7  | 72.2  | 56.9  | 64.6  | 72.9  | 53.3  | 65.8  | 59.4  | 52.4  | 68.7  | 56.7  | 71.8  | 0.26        | 0.44        |
+|            | PAS (our) | 0.126 | 0.147 | 0.086 | 0.085 | 0.165 | 0.079 | 0.137 | 0.211 | 0.102 | 0.089 | 0.119 | 0.112 |             |             |
+|            | SAMB      | 60.5  | 77.8  | 61.8  | 63.8  | 77.1  | 56.8  | 68    | 64.7  | 58.4  | 71.1  | 64    | 77.5  | 0.38        | 0.43        |
+|            | DoT       | 61.3  | 79.6  | 60.4  | 73.2  | 79.2  | 59.7  | 71.1  | 63.2  | 56.4  | 72.6  | 61.9  | 78.3  | 0.24        | 0.31        |
+| ViT-Base   | SSRT      | 60.2  | 75.8  | 59.8  | 61.7  | 71.4  | 55.2  | 69.9  | 66.0  | 58.9  | 70.6  | 62.2  | 73.2  | 0.50        | 0.46        |
+|            | Avg.      | 60.7  | 77.7  | 60.7  | 66.2  | 75.9  | 57.2  | 69.7  | 64.6  | 57.9  | 71.4  | 62.7  | 76.3  | 0.37        | 0.35        |
+|            | PAS (our) | 0.185 | 0.226 | 0.162 | 0.145 | 0.233 | 0.128 | 0.223 | 0.282 | 0.176 | 0.151 | 0.171 | 0.17  |             |             |
+
+{16}------------------------------------------------
+
+<span id="page-16-0"></span>![](_page_16_Picture_1.jpeg)
+
+![](_page_16_Picture_3.jpeg)
+
+(a) Predicted: Car |True: Bottle (b) Predicted: Horse |True: Person
+
+![](_page_16_Picture_5.jpeg)
+
+(c) Predicted: Motorcycle |True: Car
+
+![](_page_16_Picture_7.jpeg)
+
+(d) Predicted: Plane |True: Bus (e) Predicted: Person |True: Bot-
+
+![](_page_16_Picture_9.jpeg)
+
+tle
+
+![](_page_16_Picture_11.jpeg)
+
+(f) Predicted: Dog |True: Bird
+
+![](_page_16_Picture_13.jpeg)
+
+![](_page_16_Picture_15.jpeg)
+
+![](_page_16_Picture_17.jpeg)
+
+(g) Predicted: Bike |True: Bus (h) Predicted: Car |True: Person (i) Predicted: Motorcycle |True: Person
+
+Figure 6: Examples of images misclassified by the domain adaptation method *DANN* in the dataset *P* (*Pascal VOC 2012*) of the *ImageCLEF* benchmark

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+[p. 10 | section: REFERENCES | type: Text]
+Shadi Alijani, Jamil Fayyad, and Homayoun Najjaran. Vision transformers in domain adaptation and domain generalization: a study of robustness. Neural Computing and Applications , 36(29): 17979–18007, 2024.
+
+[p. 10 | section: REFERENCES | type: Text]
+Yajie Bao, Yang Li, Shao-Lun Huang, Lin Zhang, Lizhong Zheng, Amir Zamir, and Leonidas Guibas. An information-theoretic approach to transferability in task transfer learning. In 2019 IEEE international conference on image processing (ICIP) , pp. 2309–2313. IEEE, 2019.
+
+[p. 10 | section: REFERENCES | type: Text]
+Richard Bellman. Dynamic programming. science , 153(3731):34–37, 1966.
+
+[p. 10 | section: REFERENCES | type: Text]
+Bharath Bhushan Damodaran, Benjamin Kellenberger, Remi Flamary, Devis Tuia, and Nicolas ´ Courty. Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation. In Proceedings of the European conference on computer vision (ECCV) , pp. 447–463, 2018.
+
+[p. 10 | section: REFERENCES | type: Text]
+Bin Deng and Kui Jia. Universal domain adaptation from foundation models: A baseline study. arXiv preprint arXiv:2305.11092 , 2023.
+
+[p. 10 | section: REFERENCES | type: Text]
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition , pp. 248–255. Ieee, 2009.
+
+[p. 11 | section: REFERENCES | type: ListGroup]
+Inderjit S Dhillon and Dharmendra S Modha. Concept decompositions for large sparse text data using clustering. Machine learning , 42(1):143–175, 2001. Linus Ericsson, Da Li, and Timothy Hospedales. Better practices for domain adaptation. In Inter national Conference on Automated Machine Learning , pp. 4–1. PMLR, 2023. Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Franc¸ois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks. The journal of machine learning research , 17(1):2096–2030, 2016. Arthur Gretton, Karsten Borgwardt, Malte Rasch, Bernhard Scholkopf, and Alex Smola. A kernel ¨ method for the two-sample-problem. Advances in neural information processing systems , 19, 2006. Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Scholkopf, and Alexander Smola. ¨ A kernel two-sample test. The journal of machine learning research , 13(1):723–773, 2012. Junguang Jiang, Yang Shu, Jianmin Wang, and Mingsheng Long. Transferability in deep learning: A survey, 2022. Ying Jin, Ximei Wang, Mingsheng Long, and Jianmin Wang. Minimum class confusion for versatile domain adaptation. In Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXI 16 , pp. 464–480. Springer, 2020. Bo Fu Mingsheng Long Junguang Jiang, Baixu Chen. Transfer-learning-library. https:// github.com/thuml/Transfer-Learning-Library , 2020. Donghyun Kim, Kaihong Wang, Stan Sclaroff, and Kate Saenko. A broad study of pre-training for domain generalization and adaptation. In European Conference on Computer Vision , pp. 621– 638. Springer, 2022. Ziyue Li, Kan Ren, Xinyang Jiang, Yifei Shen, Haipeng Zhang, and Dongsheng Li. Simple: Specialized model-sample matching for domain generalization. In The Eleventh International Conference on Learning Representations , 2023. Hong Liu, Jianmin Wang, and Mingsheng Long. Cycle self-training for domain adaptation. Ad vances in Neural Information Processing Systems , 34:22968–22981, 2021. Xiaofeng Liu, Chaehwa Yoo, Fangxu Xing, Hyejin Oh, Georges El Fakhri, Je-Won Kang, Jonghye Woo, et al. Deep unsupervised domain adaptation: A review of recent advances and perspectives. APSIPA Transactions on Signal and Information Processing , 11(1), 2022. Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jordan. Learning transferable features with deep adaptation networks. In International conference on machine learning , pp. 97–105. PMLR, 2015. Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I Jordan. Deep transfer learning with joint adaptation networks. In International conference on machine learning , pp. 2208–2217. PMLR, 2017. Mingsheng Long, Zhangjie Cao, Jianmin Wang, and Michael I Jordan. Conditional adversarial domain adaptation. Advances in neural information processing systems , 31, 2018. Yiran Luo, Joshua Feinglass, Tejas Gokhale, Kuan-Cheng Lee, Chitta Baral, and Yezhou Yang. Grounding stylistic domain generalization with quantitative domain shift measures and synthetic scene images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 7303–7313, 2024. Amiel Meiseles and Lior Rokach. Source model selection for deep learning in the time series domain. IEEE Access , 8:6190–6200, 2020. Cuong Nguyen, Tal Hassner, Matthias Seeger, and Cedric Archambeau. Leep: A new measure to evaluate transferability of learned representations. In International Conference on Machine Learning , pp. 7294–7305. PMLR, 2020.
+
+[p. 12 | section: REFERENCES | type: ListGroup]
+Michal Pandy, Andrea Agostinelli, Jasper Uijlings, Vittorio Ferrari, and Thomas Mensink. Trans- ´ ferability estimation using bhattacharyya class separability. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 9172–9182, 2022. Xingchao Peng, Ben Usman, Kuniaki Saito, Neela Kaushik, Judy Hoffman, and Kate Saenko. Syn2real: A new benchmark forsynthetic-to-real visual domain adaptation. arXiv preprint arXiv:1806.09755 , 2018. Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. In Proceedings of the IEEE/CVF international conference on computer vision , pp. 1406–1415, 2019. Chuan-Xian Ren, Yiming Zhai, You-Wei Luo, and Hong Yan. Towards unsupervised domain adaptation via domain-transformer. International Journal of Computer Vision , 132(12):6163–6183, 2024. Peter J Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics , 20:53–65, 1987. Kate Saenko, Brian Kulis, Mario Fritz, and Trevor Darrell. Adapting visual category models to new domains. In Computer vision–ECCV 2010: 11th European conference on computer vision, Heraklion, Crete, Greece, September 5-11, 2010, proceedings, part iV 11 , pp. 213–226. Springer, 2010. Kendrick Shen, Robbie M Jones, Ananya Kumar, Sang Michael Xie, Jeff Z HaoChen, Tengyu Ma, and Percy Liang. Connect, not collapse: Explaining contrastive learning for unsupervised domain adaptation. In International conference on machine learning , pp. 19847–19878. PMLR, 2022. Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raffel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying semi-supervised learning with consistency and confidence. Advances in neural information processing systems , 33:596–608, 2020. Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In Computer vision–ECCV 2016 workshops: Amsterdam, the Netherlands, October 8-10 and 15-16, 2016, proceedings, part III 14 , pp. 443–450. Springer, 2016. Xiaoxiao Sun, Yunzhong Hou, Weijian Deng, Hongdong Li, and Liang Zheng. Ranking models in unlabeled new environments. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 11761–11771, 2021. Hui Tang and Kui Jia. A new benchmark: On the utility of synthetic data with blender for bare supervised learning and downstream domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 15954–15964, 2023. Piotr Teterwak, Kuniaki Saito, Theodoros Tsiligkaridis, Kate Saenko, and Bryan A Plummer. Erm++: An improved baseline for domain generalization. arXiv preprint arXiv:2304.01973 , 2023. Anh T Tran, Cuong V Nguyen, and Tal Hassner. Transferability and hardness of supervised classification tasks. In Proceedings of the IEEE/CVF international conference on computer vision , pp. 1395–1405, 2019. Eric Tzeng, Judy Hoffman, Ning Zhang, Kate Saenko, and Trevor Darrell. Deep domain confusion: Maximizing for domain invariance. arXiv preprint arXiv:1412.3474 , 2014. Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition , pp. 7167–7176, 2017. SS Vallender. Calculation of the wasserstein distance between probability distributions on the line. Theory of Probability & Its Applications , 18(4):784–786, 1974.
+
+[p. 13 | section: REFERENCES | type: ListGroup]
+Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pp. 5018–5027, 2017. Qian Wang, Fanlin Meng, and Toby P Breckon. Data augmentation with norm-ae and selective pseudo-labelling for unsupervised domain adaptation. Neural Networks , 161:614–625, 2023. Kaichao You, Ximei Wang, Mingsheng Long, and Michael Jordan. Towards accurate model selection in deep unsupervised domain adaptation. In International Conference on Machine Learning , pp. 7124–7133. PMLR, 2019. Kaichao You, Yong Liu, Jianmin Wang, and Mingsheng Long. Logme: Practical assessment of pre-trained models for transfer learning. In International Conference on Machine Learning , pp. 12133–12143. PMLR, 2021. Wen Zhang, Lingfei Deng, Lei Zhang, and Dongrui Wu. A survey on negative transfer. IEEE/CAA Journal of Automatica Sinica , 10(2):305–329, 2022. Jinjing Zhu, Haotian Bai, and Lin Wang. Patch-mix transformer for unsupervised domain adaptation: A game perspective. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pp. 3561–3571, 2023. Yang Zou, Zhiding Yu, Xiaofeng Liu, BVK Kumar, and Jinsong Wang. Confidence regularized self-training. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 5982–5991, 2019.

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