144 lines
5.2 KiB
Markdown
144 lines
5.2 KiB
Markdown
---
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language:
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- en
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license: apache-2.0
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base_model: HuggingFaceTB/SmolLM3-3B
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tags:
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- smollm
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- smolreasoner
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- reasoning
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- instruction-tuned
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- arcade
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- sc-orthogonal
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pipeline_tag: text-generation
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---
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# Arcade-3B — SmolReasoner
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[](https://doi.org/10.5281/zenodo.19029063)[](https://opensource.org/licenses/Apache-2.0)
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[](https://huggingface.co/HuggingFaceTB/SmolLM3-3B)
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[](https://huggingface.co/NoesisLab)
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[](https://huggingface.co/NoesisLab/Arcade-3B)
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[](https://huggingface.co/NoesisLab/Arcade-3B)
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**Arcade-3B** is a 3B instruction-following and reasoning model built on [SmolLM3-3B](https://huggingface.co/HuggingFaceTB/SmolLM3-3B).
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It is the first public release from the **ARCADE** project at [NoesisLab](https://huggingface.co/NoesisLab), which investigates the *State–Constraint Orthogonality Hypothesis*: standard Transformer hidden states conflate factual content and reasoning structure in the same subspace, and explicitly decoupling them improves generalization.
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---
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## Method: SC-Orthogonal Training
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Standard Transformer hidden states conflate two distinct functions:
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| Half | Symbol | Role |
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|------|--------|------|
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| `H[..., :D/2]` | **S** (State) | *What* the model knows — factual content |
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| `H[..., D/2:]` | **C** (Constraint) | *How* to retrieve it — reasoning structure |
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ARCADE's **SCOrthoTrainer** injects an orthogonality penalty on the final hidden layer, encouraging S and C to decouple in representation space without modifying any attention operators:
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$$\mathcal{L}_{\text{total}} = \mathcal{L}_{\text{CE}} + \frac{\lambda}{B \cdot L} \sum_{b,l} \left( \mathbf{S}_{b,l} \cdot \mathbf{C}_{b,l} \right)^2$$
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with **λ = 0.1**. This soft regularization reduces divergence errors at inference time at zero architectural cost.
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---
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## Training Details
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| Setting | Value |
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|---------|-------|
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| Base model | `HuggingFaceTB/SmolLM3-3B` |
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| λ (orth penalty) | 0.1 |
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| Max sequence length | 2048 |
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| Learning rate | 2e-4 (cosine) |
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| Steps | 10 000 |
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| Effective batch | 16 sequences/step |
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| Hardware | 1 × A100-80 GB |
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| Precision | bfloat16 |
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### Training Data
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| Dataset | Split | Sampling weight |
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|---------|-------|-----------------|
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| [nohurry/Opus-4.6-Reasoning-3000x-filtered](https://huggingface.co/datasets/nohurry/Opus-4.6-Reasoning-3000x-filtered) | train (2.3 K) | 10 % |
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| [HuggingFaceTB/smol-smoltalk](https://huggingface.co/datasets/HuggingFaceTB/smol-smoltalk) | train (460 K) | 45 % |
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| [OpenDataArena/ODA-Mixture-500k](https://huggingface.co/datasets/OpenDataArena/ODA-Mixture-500k) | train (500 K) | 45 % |
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Reasoning samples are wrapped with `<think>…</think>` tags and upsampled 10× to compensate for the small dataset size.
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---
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## Evaluation
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Results from [lm-evaluation-harness](https://github.com/EleutherAI/lm-evaluation-harness):
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### Comparison with Peer Models
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> `< 10%` entries are displayed as `<10%` in the chart.
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| Benchmark | Arcade-3B | Gemma-2-2B | Llama-2-7B | Qwen1.5-1.8B | OpenLLaMA-v2-3B |
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|-----------|-----------|------------|------------|--------------|-----------------|
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| MMLU | **52.9%** | 52.4% | 45.3% | 46.8% | 41.0% |
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| GSM8K | **62.9%** | 50.9% | 14.6% | 37.8% | < 10% |
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| HumanEval | **41.5%** | 32.3% | 12.8% | 27.4% | < 10% |
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| ARC-Challenge | 52.6% | **53.1%** | 46.2% | 41.2% | 34.2% |
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| ARC-Easy | 74.4% | **75.9%** | 75.3% | 66.8% | 68.1% |
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### Arcade-3B Detailed Scores
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| Benchmark | Few-shot | Metric | Score | ± |
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|-----------|----------|--------|-------|---|
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| GSM8K | 5 | flexible-extract / exact_match | **0.6293** | 0.0133 |
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| HumanEval | 0 | pass@1 | **0.4146** | 0.0386 |
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| ARC-Challenge | 25 | acc_norm | **0.5256** | 0.0146 |
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| ARC-Easy | 0 | acc | **0.7437** | 0.0090 |
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| MMLU | 0 | acc | **0.5293** | 0.0040 |
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---
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## Usage
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```python
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from transformers import AutoTokenizer, AutoModelForCausalLM
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import torch
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model_id = "NoesisLab/Arcade-3B"
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tok = AutoTokenizer.from_pretrained(model_id)
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model = AutoModelForCausalLM.from_pretrained(
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model_id,
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torch_dtype=torch.bfloat16,
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device_map="auto",
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)
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messages = [{"role": "user", "content": "Solve step by step: If a train travels 120 km in 1.5 hours, what is its average speed?"}]
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input_ids = tok.apply_chat_template(messages, add_generation_prompt=True, return_tensors="pt").to(model.device)
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output = model.generate(input_ids, max_new_tokens=512, temperature=0.7, do_sample=True)
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print(tok.decode(output[0][input_ids.shape[-1]:], skip_special_tokens=True))
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```
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For step-by-step reasoning, the model may emit a `<think>…</think>` block before the final answer.
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---
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## Citation
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```bibtex
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@misc{noesislab2025arcade,
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title = {ARCADE: State-Constraint Orthogonal Training},
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author = {NoesisLab},
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year = {2025},
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howpublished = {\url{https://huggingface.co/NoesisLab/Arcade-3B}},
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}
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```
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---
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## License
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Apache 2.0 — inherited from SmolLM3-3B.
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