s0-tuning 0.1.1

Tune the initial recurrent state of hybrid models. Zero inference overhead.

S₀ Tuning

S₀ Tuning: Zero-Overhead Adaptation of Hybrid Recurrent-Attention Models

Jack Young

Paper | Website

S₀ Tuning optimizes the initial hidden state (S₀) of recurrent layers in hybrid architectures (GatedDeltaNet, Mamba-2). The learned states are injected before each forward pass, adding zero latency at inference since recurrent models already maintain state. Trained states are 48 MB, training takes ~3 minutes on one GPU.

Results

All results on Qwen3.5-4B with 20 optimization steps per task. p-values from Welch's t-test (unequal variances) across independent seed runs.

Benchmark	Base	+ S₀ Tuning	Delta	Seeds	p-value
HumanEval	48.8%	72.2%	+23.6pp	10	< 10⁻¹¹
MATH-500	51.4%	56.2%	+4.8pp	8	0.00002
GSM8K	85.3%	88.1%	+2.8pp	10	0.0003
Spider (boundary test)	~72%	~72%	+0.0pp	5 alphas	n.s.

The Spider result (no improvement on out-of-distribution SQL) supports the trajectory-steering mechanism: S₀ Tuning biases the model toward solution trajectories already in its distribution, rather than injecting new knowledge.

Scaling. Gains increase with model size: +2.7pp at 0.8B, +23.6pp at 4B, +44.0pp at 9B (HumanEval).

Cross-architecture. On FalconH1-7B (Mamba-2): 71.8% vs 71.4% LoRA baseline (experimental).

Usage

from s0 import S0Trainer

trainer = S0Trainer.from_pretrained("Qwen/Qwen3.5-4B")

prompt = "Q: What is 2+2?\nA:"
answer = " 4"
full_text = prompt + answer

# prompt_length = number of prompt tokens (for completion-only loss masking)
tokens = trainer.tokenizer(prompt)
prompt_length = len(tokens["input_ids"])

data = [(full_text, prompt_length)]
trainer.train(data)
trainer.activate()

output = trainer.generate("Q: What is 2+2?\nA:")
print(output)

trainer.save("./my_s0_states")

Loading saved states on a new instance:

trainer = S0Trainer.from_pretrained("Qwen/Qwen3.5-4B")
trainer.load("./my_s0_states")
trainer.activate()
output = trainer.generate("Q: What is 2+2?\nA:")

Installation

pip install s0-tuning

Requires PyTorch 2.0+, transformers >= 4.51.0, and a GPU with >= 10 GB VRAM for training.

Supported Models

Model Family	Architecture	Recurrent Layers	Default Alpha	Status
Qwen3.5	GatedDeltaNet	linear_attention layers	0.07	Tested
FalconH1	Mamba-2	mamba layers	0.65	Experimental

To add a new hybrid architecture, the model needs (1) identifiable recurrent layers and (2) an initial_state argument in the recurrent kernel. See _detect_architecture and _patch_gdn / _patch_mamba2 in trainer.py.

How It Works

Recurrent models process sequences starting from S₀ = 0. S₀ Tuning creates learnable state tensors, patches them into the model as initial_state, and optimizes via next-token prediction loss on correct completions. At inference, learned states are scaled by alpha (e.g. 0.07 for GatedDeltaNet) to prevent distribution shift. The result: the model starts each sequence from a task-informed state rather than zeros, biasing generation toward correct solution trajectories without modifying any model weights.

Configuration

S0Config controls training:

Parameter	Default	Description
n_steps	20	Optimization steps
lr	1e-3	Learning rate
l2_lambda	5e-4	L2 regularization weight
alpha	None	Scaling factor (auto-detected per architecture if None)
normalize	False	Normalize states before scaling
grad_clip	1.0	Gradient clipping norm
max_length	2048	Maximum sequence length

Citation

If you use this codebase, or otherwise found our work valuable, please cite:

@article{young2026s0tuning,
  title={S$_0$ Tuning: Zero-Overhead Adaptation of Hybrid Recurrent-Attention Models},
  author={Young, Jack},
  year={2026}
}

License

MIT