初始化项目，由ModelHub XC社区提供模型

Model: rishiu/lucida-1.5b
Source: Original Platform

README.md

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+---
+base_model:
+- Qwen/Qwen2.5-Math-1.5B-Instruct
+pipeline_tag: text-generation
+---
+
+# Lucida 1.5B
+
+**Lucida** is a fine-tuned version of [Qwen2.5-Math-1.5B-Instruct](https://huggingface.co/Qwen/Qwen2.5-Math-1.5B-Instruct) trained to decompose mathematical equations into hierarchical explanation trees that build genuine intuition.
+
+Given any named equation, Lucida breaks it down into its meaningful sub-components — explaining not just *what* each part is, but *why* it exists and what changes when it grows or shrinks.
+
+## What it does
+
+Input: a LaTeX equation with an optional name and description.
+
+Output: a structured decomposition tree where each node contains:
+- The LaTeX fragment
+- A node type (`expression`, `variable`, `constant`, `operator`, `function`, `other`)
+- A short label (2–5 words)
+- An intuition — the "aha" a great teacher would say
+
+### Example
+
+**Input:** `K = \frac{1}{2}mv^2` — Kinetic Energy
+
+**Output:**
+```
+K = \frac{1}{2}mv^2 | expression | Kinetic Energy Equation | Moving objects store energy proportional to mass and the square of speed — doubling speed quadruples energy
+  K | variable | Kinetic Energy | Total mechanical energy of motion — zero when still, grows rapidly as speed increases
+  \frac{1}{2}mv^2 | expression | Energy of Motion | Mass times squared speed, halved — the ½ comes from integrating F=ma over distance from rest
+    \frac{1}{2} | other | Scaling Factor
+    m | variable | Mass | How much matter is moving — more mass means proportionally more energy at the same speed
+    v^2 | expression | Squared Speed | Speed multiplied by itself — squaring means fast objects carry disproportionately more energy than slow ones
+      v | variable | Speed | How fast the object is moving — the dominant factor since it appears squared
+  = | operator | —
+```
+
+## Training
+
+Lucida was trained in two stages:
+
+1. **SFT** on ~950 equations annotated in the 4-field compact format using frontier model annotations (Gemini 2.5 Flash) guided by 12 hand-written oracle examples spanning physics, chemistry, ML, calculus, linear algebra, economics, and probability.
+
+2. **GRPO** starting from the SFT checkpoint, with three reward signals:
+   - **Format reward** — output parses cleanly into the compact tree format
+   - **Reconstruction reward** — children tokens cover their parent's tokens at every level
+   - **Judge reward** — LLM judge scores label quality, intuition quality, and structure quality against oracle exemplars
+
+**Eval results (50 equations):**
+
+| Metric | SFT baseline | Lucida (GRPO) |
+|---|---|---|
+| Parseable | 88% | 94% |
+| Recon mean | 0.814 | 0.863 |
+| Depth mean | 0.790 | 0.902 |
+| Combined | 0.832 | 0.895 |
+
+## Usage
+
+```python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+
+model_id = "rishiu/lucida-1.5b"
+tokenizer = AutoTokenizer.from_pretrained(model_id)
+model = AutoModelForCausalLM.from_pretrained(model_id, torch_dtype="auto")
+
+SYSTEM_PROMPT = """You decompose mathematical equations into hierarchical explanation trees that teach intuition.
+
+Output format — one line per node, 2 spaces of indent per depth level:
+<latex_fragment> | <type> | <short_label> | <intuition>
+
+Types: expression, variable, constant, operator, function, other
+
+Rules:
+- The root node is the full equation
+- Recurse until every leaf is a single variable, named constant, or operator
+- Short label: 2–5 words
+- Intuition: the "aha" moment — for variables, what changes if this gets bigger?
+- Omit intuition for operators and bare numeric factors"""
+
+def decompose(latex, name=""):
+    user = f"Name: {name}\n" if name else ""
+    user += f"Equation: {latex}\n\nDecompose:"
+    messages = [
+        {"role": "system", "content": SYSTEM_PROMPT},
+        {"role": "user", "content": user},
+    ]
+    prompt = tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)
+    inputs = tokenizer(prompt, return_tensors="pt")
+    out = model.generate(**inputs, max_new_tokens=1024, do_sample=False)
+    generated = out[0][inputs["input_ids"].shape[1]:]
+    return tokenizer.decode(generated, skip_special_tokens=True).strip()
+
+print(decompose(r"\frac{1}{2}mv^2", name="Kinetic Energy"))
+```
+
+## Limitations
+
+- Best on standard named equations from physics, chemistry, ML, and mathematics
+- May produce factual errors on highly specialized or obscure equations
+- Partial derivative notation (e.g. ∂u/∂t) is occasionally split incorrectly into independent symbols
+- Output quality depends on equation complexity — very long equations may be truncated