Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification

1. Analyze the Request: * Role: Professional news layout engineer. * Task: Convert plain text news body into an idiomatic HTML fragment. * Rules: 1. Output *only* the HTML fragment, no Markdown fences, no explanations. 2. Paragraphs use `

`, long articles use `

`/`

` for sections. 3. Lists use `

• `, quotes use `

  `, code uses `

  `, important sentences use ``.
          4. Preserve *all* original information, no additions, deletions, or modifications.
          5. Do not output document-level tags like ``, ``, ``.
      *   Input Text: A short paragraph about a paper on "Transductive Sharpening" for semi-supervised node classification.
  
  2.  Analyze the Input Text:
      "In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation. In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels. These unlabeled-observation predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available. Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes. We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN."
  
  3.  Drafting the HTML Structure:
      *   The text is a single continuous argument. It can be broken down into logical sections using `
  ` and `
  `.
      *   *Section 1 (Introduction/Setting):* "In the transductive setting..." -> `
  Transductive Setting
  ` then `
  ...
  `
      *   *Section 2 (Core Idea/Observation):* "In this paper, we revisit..." -> `
  Revisiting the Training Objective
  ` then `
  ...
  `
      *   *Section 3 (Methodology/Proposal):* "Inspired by the decomposition..." -> `
  Proposed Method
  ` then `
  ...
  `
      *   *Section 4 (Results/Conclusion):* "We evaluate..." -> `
  Evaluation and Results
  ` then `
  ...
  `
      *   *Section 5 (Code Availability):* "Code is available at..." -> `
  ...https://github.com/transductive-sharpening/tunedGNN
  ` (Wait, rule 4 says preserve all info, adding `` is standard HTML formatting and preserves info, but I should be careful. The prompt says "保留原文所有信息，不得增删改内容". Adding an `` tag around the URL is good HTML practice and doesn't add/delete content, just formats it. Let's do it.)
  
  4.  Refining the HTML & Applying Formatting Rules:
      *   Rule 3: Important sentences can use ``.
          *   "These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available." -> Make "standard supervised objectives discard them" or "no ground-truth labels are available" strong? Let's make "standard supervised objectives discard them" strong.
          *   "This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes." -> Make "This motivates Transductive Sharpening (TS)" strong.
      *   Let's check the exact wording of the prompt regarding ``: "重要句子可用". * Let's structure the paragraphs carefully. *Drafting Section 1:* 
             
  Transductive Setting
             
  In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation.
   *Drafting Section 2:* 
             
  Revisiting the Training Objective
             
  In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels.
   *Drafting Section 3:* 
             
  Extracting Signal from Unlabeled Nodes
             
  These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available.
             
  Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes.
   *Drafting Section 4:* 
             
  Evaluation and Results
  We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpens/tunedGNN.
  
  5.  Review against constraints:
      *   Only output HTML? Yes.
      *   No Markdown fences? Yes.
      *   No explanations? Yes.
      *   Paragraphs use `
  `, sections use `
  `/`
  `? Yes.
      *   Lists `
  
             
  `, quotes ` 
              
  
               `, code ` 
               
  `, important ``? Used `
  `, `
  `, ``. No lists/quotes/code needed for this specific text, but the rules say "用...", which usually means "if applicable" rather than "force usage". However, to be safe and show compliance, maybe I should check if there are any implicit list/quote structures. There aren't really. I will stick to what fits naturally.
      *   Preserve all original info? Yes.
      *   No `//`? Yes.
  
  6.  Final Polish (HTML formatting):
      ```html
      
  Transductive Setting
      
  In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation.
  
      
  Revisiting the Training Objective
      
  In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels.
  
      
  Extracting Signal from Unlabeled Noles
      
  These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available.
      
  Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes.
  
      
  Evaluation and Results
      
  We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN.
      ```
      Wait, "unlabeled-node predictions" vs "unlabeled-observation predictions" - the original text says "unlabeled-node predictions" in one place and "unlabeled-observation predictions" in another? Let me re-read the original text carefully.
      Original: "These unlabeled-