Tnlearn is an open source python library. It is based on the symbolic regression algorithm to generate task-based neurons, and then utilizes diverse neurons to build neural networks.

• Quick links
• Motivation
• Framework
• Features
• Dependencies
• Install
• Quick start
  • GPSymRegressor
  • PolyTensorRegressor
  • RLSymRegressor
  • LLMSymRegressor
  • Supported LLM Providers
• API documentation
• Benchmarks
• Resource
• Citation
• The Team
• License

• NuronAI inspired In the past decade, successful networks have primarily used a single type of neurons within novel architectures, yet recent deep learning studies have been inspired by the diversity of human brain neurons, leading to the proposal of new artificial neuron designs.

• Task-Based Neuron Design Given the human brain's reliance on task-based neurons, can artificial network design shift from focusing on task-based architecture to task-based neuron design?

• Enhanced Representation Since there are no universally applicable neurons, task-based neurons could enhance feature representation ability within the same structure, due to the intrinsic inductive bias for the task.

• Vectorized symbolic regression is employed to find optimal formulas that fit input data.

• We parameterize the obtained elementary formula to create learnable parameters, serving as the neuron's aggregation function.

Tnlearn declares torch>=1.12.0 and installs required Python dependencies automatically. For GPU usage, install a PyTorch build that matches your hardware from the official PyTorch selector before installing tnlearn.

From PyPI:

pip install tnlearn

From source:

git clone https://github.com/NewT123-WM/tnlearn.git
cd tnlearn
pip install -e .

If PyTorch is already installed with the correct CPU/GPU build, pip install -e . will use it as long as it satisfies torch>=1.12.0.

Choose one symbolic regressor, search a task-based neuron expression, then pass that expression to MLPRegressor. For local experiments, start with GPSymRegressor or PolyTensorRegressor; use LLMSymRegressor when an LLM API key is available.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from tnlearn import GPSymRegressor, MLPRegressor

X, y = make_regression(n_samples=80, n_features=4, random_state=1)
X_train, X_test, y_train, _ = train_test_split(X, y, random_state=1)

search = GPSymRegressor(
    mode='legacy',
    pop_size=40,
    max_generations=2,
    tournament_size=3,
)
search.fit(X_train, y_train)

model = MLPRegressor(search.neuron, layers_list=[8], max_iter=20, mode='legacy')
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

GPSymRegressor(mode='legacy') exports the legacy @ expression format, so the MLP also uses mode='legacy'.

VecSymRegressor is the historical class name for this legacy GP path. In other symbolic regressors, mode='legacy' has the same compatibility meaning: it selects the older simplified vectorized expression format without inner-product interaction terms. The default/base modes below export inner-product expressions for the current MLP API.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from tnlearn import MLPRegressor, PolyTensorRegressor

X, y = make_regression(n_samples=80, n_features=6, random_state=1)
X_train, X_test, y_train, _ = train_test_split(X, y, random_state=1)

search = PolyTensorRegressor(rank=2, poly_order=2, num_epochs=10, random_state=1)
search.fit(X_train, y_train)

model = MLPRegressor(search.neuron, layers_list=[8], max_iter=20)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from tnlearn import MLPRegressor, RLSymRegressor

X, y = make_regression(n_samples=80, n_features=4, random_state=1)
X_train, X_test, y_train, _ = train_test_split(X, y, random_state=1)

search = RLSymRegressor(
    max_episodes=10,
    max_terms_total=3,
    random_state=1,
    verbose=False,
)
search.fit(X_train, y_train)

model = MLPRegressor(search.neuron, layers_list=[8], max_iter=20)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

Set DEEPSEEK_API_KEY before running this example.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from tnlearn import LLMSymRegressor, MLPRegressor

X, y = make_regression(n_samples=80, n_features=4, random_state=1)
X_train, X_test, y_train, _ = train_test_split(X, y, random_state=1)

search = LLMSymRegressor(
    llm_config={'model': 'deepseek/deepseek-chat'},
    max_iterations=1,
    samples_per_iteration=1,
    verbose=0,
    mode='base',
)
search.fit(X_train, y_train)

model = MLPRegressor(search.neuron, layers_list=[8], max_iter=20)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

PolyTensorRegressor, RLSymRegressor, and LLMSymRegressor export inner-product expressions such as <w1, x**2> + <w2, x>*<w3, x>, which the default MLP mode understands directly.

For complete module references, class parameters, and advanced usage:

We select several advanced machine learning methods for comparison.

We test multiple advanced machine learning methods on two sets of real-world data. The test results (MSE) are shown in the following table:

Here is a resource summary for neuronal diversity in artificial networks.

If you find Tnlearn useful, please cite it in your publications.

@article{wang2026tnlearn,
  title={TNLearn: An Open Source Python Package for Task-based Neurons},
  author={Wang, Meng and Li, Tieyun and Fan, Juntong and Pei, Hanyu and Liao, Jing-Xiao and Yang, Yaodong and Ma, Jianwei and Fan, Fenglei},
  journal={arXiv preprint arXiv:2609.27564},
  year={2026}
}

@article{fan2026no,
  title={No one-size-fits-all neurons: Task-based neurons for artificial neural networks},
  author={Fan, Feng-Lei and Wang, Meng and Dong, Hang-Cheng and Ma, Jianwei and Zeng, Tieyong},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2026},
  publisher={IEEE}
}

Tnlearn is a work by Meng Wang, Juntong Fan, Hanyu Pei, Tieyun LI, Jingxiao Liao, Shuren Qi, Lizhao Xu, Zeyu LI, Renfeng Peng, Yudong Wang, Can Dong, Tansheng Zhu, Liangchen Tan, Feifei Zhang, Yihan Jin, Yiqing Zhang, Kairan Zhang and Fenglei Fan.

Tnlearn is released under Apache License 2.0.