---
language:
- en
license: apache-2.0
base_model: HuggingFaceTB/SmolLM3-3B
tags:
- smollm
- smolreasoner
- reasoning
- instruction-tuned
- arcade
- sc-orthogonal
pipeline_tag: text-generation
---
# Arcade-3B — SmolReasoner
[](https://doi.org/10.5281/zenodo.19029063)[](https://opensource.org/licenses/Apache-2.0)
[](https://huggingface.co/HuggingFaceTB/SmolLM3-3B)
[](https://huggingface.co/NoesisLab)
[](https://huggingface.co/NoesisLab/Arcade-3B)
[](https://huggingface.co/NoesisLab/Arcade-3B)
**Arcade-3B** is a 3B instruction-following and reasoning model built on [SmolLM3-3B](https://huggingface.co/HuggingFaceTB/SmolLM3-3B).
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.
---
## Method: SC-Orthogonal Training
Standard Transformer hidden states conflate two distinct functions:
| Half | Symbol | Role |
|------|--------|------|
| `H[..., :D/2]` | **S** (State) | *What* the model knows — factual content |
| `H[..., D/2:]` | **C** (Constraint) | *How* to retrieve it — reasoning structure |
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:
$$\mathcal{L}_{\text{total}} = \mathcal{L}_{\text{CE}} + \frac{\lambda}{B \cdot L} \sum_{b,l} \left( \mathbf{S}_{b,l} \cdot \mathbf{C}_{b,l} \right)^2$$
with **λ = 0.1**. This soft regularization reduces divergence errors at inference time at zero architectural cost.
---
## Training Details
| Setting | Value |
|---------|-------|
| Base model | `HuggingFaceTB/SmolLM3-3B` |
| λ (orth penalty) | 0.1 |
| Max sequence length | 2048 |
| Learning rate | 2e-4 (cosine) |
| Steps | 10 000 |
| Effective batch | 16 sequences/step |
| Hardware | 1 × A100-80 GB |
| Precision | bfloat16 |
### Training Data
| Dataset | Split | Sampling weight |
|---------|-------|-----------------|
| [nohurry/Opus-4.6-Reasoning-3000x-filtered](https://huggingface.co/datasets/nohurry/Opus-4.6-Reasoning-3000x-filtered) | train (2.3 K) | 10 % |
| [HuggingFaceTB/smol-smoltalk](https://huggingface.co/datasets/HuggingFaceTB/smol-smoltalk) | train (460 K) | 45 % |
| [OpenDataArena/ODA-Mixture-500k](https://huggingface.co/datasets/OpenDataArena/ODA-Mixture-500k) | train (500 K) | 45 % |
Reasoning samples are wrapped with `…` tags and upsampled 10× to compensate for the small dataset size.
---
## Evaluation
Results from [lm-evaluation-harness](https://github.com/EleutherAI/lm-evaluation-harness):
### Comparison with Peer Models
> `< 10%` entries are displayed as `<10%` in the chart.
| Benchmark | Arcade-3B | Gemma-2-2B | Llama-2-7B | Qwen1.5-1.8B | OpenLLaMA-v2-3B |
|-----------|-----------|------------|------------|--------------|-----------------|
| MMLU | **52.9%** | 52.4% | 45.3% | 46.8% | 41.0% |
| GSM8K | **62.9%** | 50.9% | 14.6% | 37.8% | < 10% |
| HumanEval | **41.5%** | 32.3% | 12.8% | 27.4% | < 10% |
| ARC-Challenge | 52.6% | **53.1%** | 46.2% | 41.2% | 34.2% |
| ARC-Easy | 74.4% | **75.9%** | 75.3% | 66.8% | 68.1% |
### Arcade-3B Detailed Scores
| Benchmark | Few-shot | Metric | Score | ± |
|-----------|----------|--------|-------|---|
| GSM8K | 5 | flexible-extract / exact_match | **0.6293** | 0.0133 |
| HumanEval | 0 | pass@1 | **0.4146** | 0.0386 |
| ARC-Challenge | 25 | acc_norm | **0.5256** | 0.0146 |
| ARC-Easy | 0 | acc | **0.7437** | 0.0090 |
| MMLU | 0 | acc | **0.5293** | 0.0040 |
---
## Usage
```python
from transformers import AutoTokenizer, AutoModelForCausalLM
import torch
model_id = "NoesisLab/Arcade-3B"
tok = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(
model_id,
torch_dtype=torch.bfloat16,
device_map="auto",
)
messages = [{"role": "user", "content": "Solve step by step: If a train travels 120 km in 1.5 hours, what is its average speed?"}]
input_ids = tok.apply_chat_template(messages, add_generation_prompt=True, return_tensors="pt").to(model.device)
output = model.generate(input_ids, max_new_tokens=512, temperature=0.7, do_sample=True)
print(tok.decode(output[0][input_ids.shape[-1]:], skip_special_tokens=True))
```
For step-by-step reasoning, the model may emit a `…` block before the final answer.
---
## Citation
```bibtex
@misc{noesislab2025arcade,
title = {ARCADE: State-Constraint Orthogonal Training},
author = {NoesisLab},
year = {2025},
howpublished = {\url{https://huggingface.co/NoesisLab/Arcade-3B}},
}
```
---
## License
Apache 2.0 — inherited from SmolLM3-3B.