BLiqNet: Bidirectional Liquid Neural Networks

The first continuous-time liquid neural network capable of bidirectional flow.

BLiqNet is a general-purpose inference engine designed to solve complex, many-to-one inverse problems without suffering from mode collapse. By integrating Liquid Time-Constant (LTC) dynamics with stochastic manifold sampling, BLiqNet learns the underlying topology of continuous data, allowing for high-precision forward mapping and probabilistic inverse reconstruction.

🚀 Quick Start (One-Line Install)

Complexity kills adoption. Install BLiqNet directly via pip:

pip install bliqnet

(For development, clone the repository and run pip install -e .)

General Purpose Initialization & Training

import torch
from bliq.model import BLiqNet

# 1. Initialize for a high-dimensional mapping problem (e.g., 10D -> 2D)
model = BLiqNet(input_dim=10, output_dim=2, hidden_dim=128)

# 2. Train using bidirectional dual-consistency flow
model.fit(train_x, train_y, epochs=1000, lambda_inv=2.0)

# 3. Probabilistic Inverse Sampling (Many-to-One Resolution)
with torch.no_grad():
    # Sample 50 distinct valid candidates for an observation 'y'
    samples = [model.inverse(y, noise_level=0.5) for _ in range(50)]

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🧠 Mathematical Core: The Liquid Mechanism

Unlike standard Neural ODEs, BLiqNet governs its latent state $h$ using the Liquid Time-Constant (LTC) formulation:

$$\frac{dh}{dt} = -\left[\frac{1}{\tau} + f(h, u)\right]h + f(h, u)A$$

This ensures the system is truly "Liquid"—its internal update speed effectively changes in response to the input $u$. By deploying this in a bidirectional flow paradigm, the model synchronizes forward ($x \to y$) and inverse ($y \to x$) pathways, allowing it to navigate singularities, self-intersections, and complex topologies (like 3D helices and Bernoulli Lemniscates) with extreme numerical stability.

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📊 Visual Proof: Manifold Learning

By injecting stochastic latent perturbations into its Liquid Time-Constant (LTC) ODE, it probabilistically explores the continuous time-space. It successfully learns and reconstructs every valid branch of the self-intersecting manifold. The baseline model's error permanently plateaus because it cannot resolve the intersections. BLiqNet's generative loss reliably converges toward zero. This heatmap displays the continuous-time synaptic conductances that allow BLiqNet to dynamically speed up, slow down, and switch directions at topological singularities.

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📝 Citation & Academic Use

To ensure the longevity of this framework, BLiqNet is officially indexed. If you use this software or architecture in your research, please cite the foundational publications and the software itself.

1. The Official Journal Application

For the application of BLiqNet to geodata and ground motion:

@article{neelamraju2026ground,
  title={Ground Motion Modelling with Bidirectional Liquid Neural Network (BLiqNet)},
  author={Neelamraju, Pavan Mohan and Raghukanth, STG},
  journal={Geodata and AI},
  pages={100080},
  year={2026},
  publisher={Elsevier},
  doi={10.1016/j.geoai.2026.100080}
}

2. General Architecture & Documentation (arXiv)

For general architecture details, math, and the underlying bidirectional framework:

@article{neelamraju2026bliqnet,
  title={BLiqNet: A General Framework for Bidirectional Liquid Neural Networks},
  author={Neelamraju, Pavan Mohan},
  journal={arXiv preprint arXiv:26XX.XXXXX},
  year={2026}
}

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🤝 Contributing & License

We welcome contributions from the community to expand the capabilities of continuous-time deep learning. This project is licensed under the MIT License - see the LICENSE file for details.