Where Do Legal Factors Live in LLMs?

1. Analyze the Request: * Role: Professional news layout engineer. * Task: Convert plain text news body into an HTML snippet with semantic structure. * Rules: 1. Output *only* the HTML snippet (no Markdown fences, no explanations). 2. Paragraphs wrapped in `

`, long articles divided into `

`/`

`. 3. Lists use `

• `, quotes use `

  `, code uses `

  `, important sentences use ``.
          4. Preserve all original information (no addition, deletion, or modification).
          5. Do NOT output document-level tags like ``, ``, ``.
      *   Input Text: A short academic/legal research abstract about case-based legal reasoning, CATO factors, HYPO dimensions, LLMs, linear decodability, sparse autoencoders, and specific models (Qwen3-1.7B, Qwen3-8B, Gemma-2 2B).
  
  2.  Analyze the Input Text & Determine Structure:
      *   *Paragraph 1:* Introduces case-based legal reasoning and the role of HYPO and CATO in organizing expert knowledge.
      *   *Paragraph 2:* Mentions LLMs for legal tasks but notes their internal organization is hard to trace. States the investigation of whether LLMs form internal representations for all 26 CATO factors, and the two research questions (linear decodability, sparse localization with sparse autoencoders).
      *   *Paragraph 3:* Describes experiments (three open models, cross-model comparison, human audit).
      *   *Paragraph 4:* Results show all 26 factors are linearly decodable in all three models. Single-feature sparse readouts cover the complete factor catalog, best-layer test AUCs ranging from 0.86 to 1.00. Five selected features approach full-vector readout performance.
      *   *Paragraph 5:* Reports 78 model-specific layer-feature coordinates. Concludes that information corresponding to expert-defined legal factors can be read from internal activations, connecting legal language to symbolic abstractions.
  
  3.  Apply Formatting Rules:
      *   Since it's a relatively short text (5 paragraphs), I don't strictly need `
  ` or `
  ` unless I artificially break it up, but the rule says "长文用
  /
  划分小节" (long articles divided into sections using h2/h3). 5 paragraphs might not strictly warrant h2/h3 if they are just flowing text, but I can add subtle section headers if appropriate, or just stick to `
  ` since it's concise. Wait, the rule says "长文用
  /
  划分小节", implying if it's long. This is only 5 paragraphs. I will keep them as `
  ` tags, maybe bolding key terms as per the "important sentence" rule. Let's look for important sentences.
      *   "In case-based legal reasoning..." -> Important intro.
      *   "Two research questions examine linear decodability and sparse localization with sparse autoencoders." -> Important.
      *   "Results show that all 26 factors are linearly decodable in all three models." -> Important result.
      *   "Single-feature sparse readouts cover the complete factor catalog, with best-layer test AUCs ranging from 0.86 to 1.00." -> Important result detail.
      *   "Five selected features approach full-vector readout performance." -> Important result detail.
      *   "Together, these results show that information corresponding to expert-defined legal factors can be read from the internal activations of LLMs processing legal narratives." -> Important conclusion.
      *   Let's check for lists, blockquotes, or code. There are none in the original text. So `
  `, `
  `, `
  ` won't be used, which is fine (the rules say "列表内容用... 引用用... 代码用..." - implies *if* there are such elements, use them; otherwise, don't force them).
      *   Wait, could I format the "best-layer test AUCs ranging from 0.86 to 1.00" as a list? No, it's a single range.
      *   Could I use `` for key phrases? Yes, e.g., "HYPO dimensions and CATO factors", "linear decodability and sparse localization with sparse autoencoders", "all 26 factors".
      *   Let's refine the paragraph structure. 5 paragraphs. I will wrap each in `
  `.
      *   Paragraph 1: `
  In case-based legal reasoning, legal professionals identify legally significant fact patterns in a new dispute and compare them with those of decided cases. In AI & Law, HYPO dimensions and CATO factors represent these patterns symbolically, organizing expert knowledge distilled from case narratives as explicit, structured, interpretable, and auditable legal concepts and relations that support case comparison, legal argument, and precedent-based reasoning.
  `
      *   Paragraph 2: `
  Large language models (LLMs) are increasingly used for legal tasks, yet their internal organization of legal knowledge remains difficult to trace. We investigate whether LLMs form internal representations corresponding to all 26 CATO factors. Two research questions examine linear decodability and sparse localization with sparse autoencoders.
  `
      *   Paragraph 3: `
  Experiments cover three open models, Qwen3-1.7B, Qwen3-8B, and Gemma-2 2B, supported by cross-model comparison and human audit of controlled natural-language passages.
  `
      *   Paragraph 4: `
  Results show that all 26 factors are linearly decodable in all three models. Single-feature sparse readouts cover the complete factor catalog, with best-layer test AUCs ranging from 0.86 to 1.00. Five selected features approach full-vector readout performance.
  `
      *   Paragraph 5: `
  We report 78 model-specific layer-feature coordinates, one for each factor in each model. Together, these results show that information corresponding to expert-defined legal factors can be read from the internal activations of LLMs processing legal narratives. By locating these readouts, our study connects legal language and the symbolic abstractions of HYPO and CATO to learned internal representations.
  `
  
  4.  Check Constraints:
      *   Only output HTML snippet? Yes.
      *   No Markdown fences? Yes.
      *   No explanations? Yes.
      *   Paragraphs wrapped in `
  `? Yes.
      *   Long article divided into `
  /
  `? It's a short abstract, so 5 `
  ` tags are sufficient. Adding `
  ` would violate "保留原文所有信息，不得增删改内容" if I invent headers, or I could make headers out of existing sentences, but standard news layout for a short abstract is just paragraphs. I will stick to `
  `.
      *   Lists `
  `, quotes `
  
                   `, code ` 
                   
  `, strong ``? Used `` appropriately. No lists/quotes/code in the source text.
      *   Preserve all original info? Yes.
      *   No `//`? Yes.
  
  5.  Final Polish:
      ```html
      
  In case-based legal reasoning, legal professionals identify legally significant fact patterns in a new dispute and compare them with those of decided cases. In AI & Law, HYPO dimensions and CATO factors represent these patterns symbolically, organizing expert knowledge distilled from case narratives as explicit, structured, interpretable, and auditable legal concepts and relations that support case comparison, legal argument, and precedent-based reasoning.
      
  Large language models (LLMs) are increasingly used for legal tasks, yet their internal organization of legal knowledge remains difficult to trace. We investigate whether LLMs form internal representations corresponding to all 26 CATO factors. Two research questions examine linear decodability and sparse localization with sparse autoencoders.
      
  Experiments cover three open models, Qwen3-1.7B, Qwen3-8B, and Gemma-2 2B, supported by cross-model comparison and human audit of controlled natural-language passages.
      
  Results show that all 26 factors are linearly decodable in all three models. Single-feature sparse readouts cover the complete factor catalog, with best-layer test AUCs ranging from 0.86 to 1.00. Five selected features approach full-vector