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Model: Dat1710/nexus-1.5b Source: Original Platform
2026-05-22 07:36:18 +08:00
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--- a/README.md
+++ b/README.md
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+---
+library_name: transformers
+tags:
+  - math
+  - reasoning
+  - reinforcement-learning
+  - qwen2
+  - mathematics
+  - chain-of-thought
+license: apache-2.0
+language:
+  - en
+  - zh
+base_model: Qwen/Qwen2.5-Math-1.5B-Instruct
+pipeline_tag: text-generation
+---
+
+# Nexus-1.5B
+
+<p align="center">
+  <img src="https://img.shields.io/badge/Base%20Model-Qwen2.5--Math--1.5B--Instruct-orange" />
+  <img src="https://img.shields.io/badge/Parameters-1.54B-blue" />
+  <img src="https://img.shields.io/badge/Method-LPRO-green" />
+  <img src="https://img.shields.io/badge/MATH--500-80.2-red" />
+  <img src="https://img.shields.io/badge/GSM8K-85.2-red" />
+</p>
+
+**Nexus-1.5B** is a 1.54-billion-parameter mathematical reasoning model developed by [Neuriton](https://www.facebook.com/neuriton), trained via **Length-Penalized Reward Optimization (LPRO)** — a novel reinforcement learning alignment method that improves both accuracy and response conciseness simultaneously.
+
+Built on top of `Qwen2.5-Math-1.5B-Instruct`, Nexus-1.5B achieves **80.2 on MATH-500** and **85.2 on GSM8K** (CoT), surpassing its base model by **+4.4 points** on MATH-500 while reducing average response length by **14%**.
+
+---
+
+## What is LPRO?
+
+Standard GRPO (Group Relative Policy Optimization) suffers from two key problems:
+
+1. **Length bias** — short responses receive disproportionately large gradient signals, implicitly penalizing long correct derivations.
+2. **Entropy collapse** — symmetric probability-ratio clipping causes the policy to converge to a narrow set of solution patterns, limiting further improvement.
+
+**LPRO** fixes both with three targeted modifications:
+
+| Component | What it does |
+|---|---|
+| **Asymmetric clipping** | Decouples the lower and upper clip bounds (`ε_low=0.20`, `ε_high=0.28`) to preserve policy entropy |
+| **Token-level normalization** | Replaces per-response weight `1/G` with global weight `1/Σ|oᵢ|` to produce an unbiased gradient estimate |
+| **Length-penalized advantage** | Adds a group-standardized length penalty: `Aᵢ = (rᵢ - μᵣ)/(σᵣ + ε) - λ·(Lᵢ - μ_L)/(σ_L + ε)` |
+
+The final objective is:
+
+$$\mathcal{J}_{\text{LPRO}}(\theta) = \mathbb{E}\left[\frac{1}{\sum_{i=1}^{G}|o_i|} \sum_{i=1}^{G}\sum_{t=1}^{|o_i|} \min\!\left(r_{i,t}(\theta)\,\hat{A}_{i,t},\ \text{clip}_{\text{asym}}(r_{i,t}(\theta))\,\hat{A}_{i,t}\right)\right]$$
+
+---
+
+## Model Details
+
+| Property | Value |
+|---|---|
+| **Base model** | `Qwen/Qwen2.5-Math-1.5B-Instruct` |
+| **Parameters** | 1.54B |
+| **Architecture** | Transformer Decoder (28 layers, GQA, RoPE, SwiGLU, RMSNorm) |
+| **Context length** | 8,192 tokens |
+| **Vocabulary size** | 128,256 |
+| **Training method** | LPRO (RL fine-tuning, no distillation) |
+| **Training data** | 100 difficulty-filtered problems from MATH-500 |
+| **Group size G** | 4 |
+| **Length penalty λ** | 0.10 |
+| **Learning rate** | 1e-6 |
+| **PPO epochs/iter** | 4 |
+
+---
+
+## Benchmark Results
+
+### Chain-of-Thought (CoT)
+
+| Model | GSM8K | MATH-500 | MMLU-STEM | CMATH | GaoKao Cloze | GaoKao QA |
+|---|---|---|---|---|---|---|
+| Qwen2-Math-1.5B-Instruct | 84.2 | 69.4 | 54.9 | 79.6 | 59.7 | 50.7 |
+| Qwen2.5-Math-1.5B-Instruct | 84.8 | 75.8 | 57.5 | 83.0 | 65.5 | 54.1 |
+| **Nexus-1.5B** | **85.2** | **80.2** | **60.3** | **83.5** | **67.2** | **56.9** |
+
+### Tool-Integrated Reasoning (TIR)
+
+| Model | MATH-500 | Minerva Math | GaoKao 2023 EN | Olympiad Bench | College Math |
+|---|---|---|---|---|---|
+| Qwen2.5-Math-1.5B-Instruct | 80.0 | 34.0 | 68.0 | 49.0 | 54.0 |
+| **Nexus-1.5B** | **84.0** | **40.0** | **74.0** | **56.0** | **57.0** |
+
+### Ablation: Effect of Length Penalty (λ)
+
+| λ | MATH-500 Acc. | Avg. Response Length |
+|---|---|---|
+| 0.0 (GRPO baseline) | 77.4 | 312 tokens |
+| **0.1 (Nexus-1.5B)** | **80.2** | **268 tokens** |
+| 0.3 (over-penalized) | 78.0 | 201 tokens |
+
+> **Key insight:** At λ=0.1, accuracy and conciseness improve simultaneously. The length penalty acts as a de-noising regularizer — discouraging redundant steps rather than suppressing genuinely long derivations.
+
+---
+
+## How to Use
+
+```python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+
+model_name = "Dat1710/nexus-1.5b"
+
+tokenizer = AutoTokenizer.from_pretrained(model_name)
+model = AutoModelForCausalLM.from_pretrained(
+    model_name,
+    torch_dtype="auto",
+    device_map="auto"
+)
+
+# Chain-of-Thought prompt
+system_prompt = "Please reason step by step, and put your final answer within \\boxed{}."
+
+messages = [
+    {"role": "system", "content": system_prompt},
+    {"role": "user", "content": "Find all functions f: ℝ⁺ → ℝ⁺ such that for each x ∈ ℝ⁺, there is exactly one y ∈ ℝ⁺ satisfying xf(y) + yf(x) ≤ 2."}
+]
+
+text = tokenizer.apply_chat_template(
+    messages,
+    tokenize=False,
+    add_generation_prompt=True
+)
+
+model_inputs = tokenizer([text], return_tensors="pt").to(model.device)
+
+generated_ids = model.generate(
+    **model_inputs,
+    max_new_tokens=2048,
+    temperature=0.7,
+    do_sample=True,
+)
+
+generated_ids = [
+    output_ids[len(input_ids):]
+    for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
+]
+
+response = tokenizer.batch_decode(generated_ids, skip_special_tokens=True)[0]
+print(response)
+```
+
+### Tool-Integrated Reasoning (TIR)
+
+```python
+system_prompt = (
+    "Please integrate natural language reasoning with programs to solve the problem above, "
+    "and put your final answer within \\boxed{}."
+)
+```
+
+---
+
+## Evaluation Prompt Format
+
+**CoT (8-shot for GSM8K, 4-shot for MATH-500):**
+```
+<|im_start|>system
+Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
+<|im_start|>user
+{problem}<|im_end|>
+<|im_start|>assistant
+```
+
+**TIR (zero-shot):**
+```
+<|im_start|>system
+Please integrate natural language reasoning with programs to solve the problem above,
+and put your final answer within \boxed{}.<|im_end|>
+<|im_start|>user
+{problem}<|im_end|>
+<|im_start|>assistant
+```
+
+---
+
+## Training Details
+
+### Data Curation
+
+Training problems are sourced from **MATH-500** and filtered by difficulty using a learnable-zone criterion: a problem is retained if, among 8 sampled solutions from the base model, **between 2 and 5 are correct**. This yields 100 training problems that provide meaningful gradient signal — neither trivially easy nor intractably hard.
+
+### Training Procedure
+
+1. **Group sampling:** For each prompt, sample G=4 responses from the current policy.
+2. **Reward computation:** Rule-based binary reward (correctness via symbolic answer matching) + small format bonus (α=0.1) for well-formed `\boxed{}` output.
+3. **Advantage computation:** Compute length-penalized group z-score advantages.
+4. **Policy update:** Maximize LPRO objective for 4 epochs per iteration.
+5. **Iterate:** Set old policy ← new policy and repeat.
+
+### Reward Function
+
+$$r_i = \mathbf{1}[\hat{a}(o_i) = a^*] + 0.1 \cdot \mathbf{1}[\text{format}(o_i)]$$
+
+where $\hat{a}(o_i)$ is the extracted answer from the last `\boxed{}` expression, verified via symbolic equivalence.
+
+---
+
+## Limitations
+
+- **Scale:** Nexus-1.5B operates at 1.54B parameters. Hard olympiad problems (e.g., AIME) remain challenging for models at this scale.
+- **Language:** Primarily optimized for English and Chinese mathematical text. Performance on other languages is not evaluated.
+- **Domain:** Designed for mathematical reasoning. General language understanding or instruction-following tasks are outside the model's training distribution.
+- **TIR dependency:** Tool-integrated reasoning requires a sandboxed Python interpreter at inference time.
+
+---
+
+## Citation
+
+If you use Nexus-1.5B in your research, please cite:
+
+```bibtex
+@techreport{neuriton2026nexus,
+  title     = {Nexus-1.5B: Length-Penalized Reward Optimization for Robust Mathematical Reasoning},
+  author    = {Neuriton Team},
+  institution = {Neuriton},
+  year      = {2026},
+  month     = {Summer},
+  note      = {Technical Report}
+}
+```
+
+---
+
+## Acknowledgements
+
+We thank the Qwen Team at Alibaba Group for open-sourcing the Qwen2.5-Math model family, and the authors of DAPO for the asymmetric clipping insight that is central to LPRO.
+
+---
+
+*Developed by [Neuriton](https://neuriton.ai) · Summer 2026*
--- a/added_tokens.json
+++ b/added_tokens.json
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--- a/chat_template.jinja
+++ b/chat_template.jinja
@@ -0,0 +1,54 @@
+{%- if tools %}
+    {{- '<|im_start|>system\n' }}
+    {%- if messages[0]['role'] == 'system' %}
+        {{- messages[0]['content'] }}
+    {%- else %}
+        {{- 'Please reason step by step, and put your final answer within \\boxed{}.' }}
+    {%- endif %}
+    {{- "\n\n# Tools\n\nYou may call one or more functions to assist with the user query.\n\nYou are provided with function signatures within <tools></tools> XML tags:\n<tools>" }}
+    {%- for tool in tools %}
+        {{- "\n" }}
+        {{- tool | tojson }}
+    {%- endfor %}
+    {{- "\n</tools>\n\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\n<tool_call>\n{\"name\": <function-name>, \"arguments\": <args-json-object>}\n</tool_call><|im_end|>\n" }}
+{%- else %}
+    {%- if messages[0]['role'] == 'system' %}
+        {{- '<|im_start|>system\n' + messages[0]['content'] + '<|im_end|>\n' }}
+    {%- else %}
+        {{- '<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n' }}
+    {%- endif %}
+{%- endif %}
+{%- for message in messages %}
+    {%- if (message.role == "user") or (message.role == "system" and not loop.first) or (message.role == "assistant" and not message.tool_calls) %}
+        {{- '<|im_start|>' + message.role + '\n' + message.content + '<|im_end|>' + '\n' }}
+    {%- elif message.role == "assistant" %}
+        {{- '<|im_start|>' + message.role }}
+        {%- if message.content %}
+            {{- '\n' + message.content }}
+        {%- endif %}
+        {%- for tool_call in message.tool_calls %}
+            {%- if tool_call.function is defined %}
+                {%- set tool_call = tool_call.function %}
+            {%- endif %}
+            {{- '\n<tool_call>\n{"name": "' }}
+            {{- tool_call.name }}
+            {{- '", "arguments": ' }}
+            {{- tool_call.arguments | tojson }}
+            {{- '}\n</tool_call>' }}
+        {%- endfor %}
+        {{- '<|im_end|>\n' }}
+    {%- elif message.role == "tool" %}
+        {%- if (loop.index0 == 0) or (messages[loop.index0 - 1].role != "tool") %}
+            {{- '<|im_start|>user' }}
+        {%- endif %}
+        {{- '\n<tool_response>\n' }}
+        {{- message.content }}
+        {{- '\n</tool_response>' }}
+        {%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
+            {{- '<|im_end|>\n' }}
+        {%- endif %}
+    {%- endif %}
+{%- endfor %}
+{%- if add_generation_prompt %}
+    {{- '<|im_start|>assistant\n' }}
+{%- endif %}
--- a/config.json
+++ b/config.json
@@ -0,0 +1,58 @@
+{
+  "architectures": [
+    "Qwen2ForCausalLM"
+  ],
+  "attention_dropout": 0.0,
+  "bos_token_id": 151643,
+  "dtype": "float16",
+  "eos_token_id": 151645,
+  "hidden_act": "silu",
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+  "initializer_range": 0.02,
+  "intermediate_size": 8960,
+  "layer_types": [
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+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention"
+  ],
+  "max_position_embeddings": 4096,
+  "max_window_layers": 21,
+  "model_type": "qwen2",
+  "num_attention_heads": 12,
+  "num_hidden_layers": 28,
+  "num_key_value_heads": 2,
+  "rms_norm_eps": 1e-06,
+  "rope_scaling": null,
+  "rope_theta": 10000.0,
+  "sliding_window": null,
+  "tie_word_embeddings": true,
+  "transformers_version": "4.57.6",
+  "use_cache": true,
+  "use_sliding_window": false,
+  "vocab_size": 151936
+}
--- a/generation_config.json
+++ b/generation_config.json
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+{
+  "bos_token_id": 151643,
+  "eos_token_id": [
+    151645,
+    151643
+  ],
+  "pad_token_id": 151643,
+  "transformers_version": "4.57.6"
+}
--- a/merges.txt
+++ b/merges.txt
--- a/model.safetensors
+++ b/model.safetensors
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+oid sha256:bf4ce404d9c3633c485f27dbbbe4ee351f72091eb2586d77da1349f3b886b601
+size 3087466808
--- a/special_tokens_map.json
+++ b/special_tokens_map.json
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+{
+  "additional_special_tokens": [
+    "<|im_start|>",
+    "<|im_end|>",
+    "<|object_ref_start|>",
+    "<|object_ref_end|>",
+    "<|box_start|>",
+    "<|box_end|>",
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+    "<|video_pad|>"
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+}
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+    "151660": {
+      "content": "<|fim_middle|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151661": {
+      "content": "<|fim_suffix|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151662": {
+      "content": "<|fim_pad|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151663": {
+      "content": "<|repo_name|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151664": {
+      "content": "<|file_sep|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    }
+  },
+  "additional_special_tokens": [
+    "<|im_start|>",
+    "<|im_end|>",
+    "<|object_ref_start|>",
+    "<|object_ref_end|>",
+    "<|box_start|>",
+    "<|box_end|>",
+    "<|quad_start|>",
+    "<|quad_end|>",
+    "<|vision_start|>",
+    "<|vision_end|>",
+    "<|vision_pad|>",
+    "<|image_pad|>",
+    "<|video_pad|>"
+  ],
+  "bos_token": null,
+  "clean_up_tokenization_spaces": false,
+  "eos_token": "<|im_end|>",
+  "errors": "replace",
+  "extra_special_tokens": {},
+  "model_max_length": 131072,
+  "pad_token": "<|endoftext|>",
+  "split_special_tokens": false,
+  "tokenizer_class": "Qwen2Tokenizer",
+  "unk_token": null
+}
--- a/vocab.json
+++ b/vocab.json