Create README.md

README.md

@@ -0,0 +1,115 @@
+---
+tags:
+- bayesian-inference
+- liquid-networks
+- uncertainty-quantification
+- classics-revival
+- experimental
+license: apache-2.0
+library_name: pytorch
+---
+
+# Liquid Bayes Chain - The Classics Revival
+
+**Probabilistic Control of Continuous Dynamics with Bayesian Feedback**
+
+**Experimental Research Code** - Functional but unoptimized, expect rough edges
+
+## What Is This?
+
+Liquid Bayes Chain combines liquid neural networks with Bayesian inference to create a system where probabilistic confidence directly modulates continuous dynamics. The network's liquid state evolves based on Bayesian uncertainty, creating adaptive exploration-exploitation behavior.
+
+**Core Innovation**: Bayesian confidence estimates control liquid time constants and dynamics, creating a feedback loop between probabilistic reasoning and continuous neural evolution.
+
+## Architecture Highlights
+
+- **Confidence-Modulated Dynamics**: Bayesian uncertainty controls liquid evolution speed
+- **Adaptive Time Constants**: Neural dynamics adjust based on confidence levels
+- **Probabilistic Feedback Loop**: Continuous dynamics inform Bayesian updates
+- **Multi-Step Chain Processing**: Sequential confidence-guided evolution steps
+- **Uncertainty Quantification**: Full probabilistic output with confidence measures
+- **Exploration-Exploitation Balance**: High confidence → stability, low confidence → exploration
+
+## Quick Start
+```python
+from liquid_bayes import LiquidBayesChain
+
+# Create liquid-Bayesian system
+model = LiquidBayesChain(
+    input_dim=32,
+    state_dim=64,
+    output_dim=10,
+    num_chain_steps=4
+)
+
+# Process input with uncertainty quantification
+input_signal = torch.randn(batch_size, input_dim)
+output = model(input_signal, return_chain_states=True)
+
+# Get uncertainty information
+uncertainty_info = model.predict_with_uncertainty(input_signal)
+print(f"Confidence: {uncertainty_info['confidence'].mean():.3f}")
+```
+
+## Current Status
+- **Working**: Liquid dynamics, Bayesian networks, confidence modulation, chain evolution, uncertainty quantification
+- **Rough Edges**: No benchmarking on standard tasks, chain length optimization needed
+- **Still Missing**: Advanced Bayesian structures, variational inference, distributed chain processing
+- **Performance**: Good convergence on toy problems, needs validation on real tasks
+- **Memory Usage**: Moderate, scales with chain length and state dimension
+- **Speed**: Sequential chain processing, parallelization opportunities exist
+
+## Mathematical Foundation
+The liquid dynamics evolve according to:
+```
+dx/dt = -x/τ(confidence) + W_rec·σ(x) + W_in·u + noise(1-confidence)
+```
+
+Bayesian confidence estimation uses:
+```
+P(belief|evidence) ∝ P(evidence|belief) × P(belief)
+confidence = 1 - H(P(belief|evidence))
+```
+
+Where H is Shannon entropy. High confidence leads to stable dynamics (large τ), while low confidence increases exploration through noise injection and faster adaptation.
+
+The chain processes through multiple steps:
+```
+x_{t+1} = LiquidEvolution(x_t, u, confidence_t)
+confidence_{t+1} = BayesianUpdate(x_{t+1})
+```
+
+## Research Applications
+- **Adaptive control systems with uncertainty**
+- **Robotics with confidence-aware planning**
+- **Financial modeling with risk adaptation**
+- **Autonomous systems requiring exploration-exploitation**
+- **Scientific computing with adaptive dynamics**
+
+## Installation 
+```bash
+pip install torch numpy scipy
+# Download liquid_bayes.py from this repo
+```
+
+## The Classics Revival Collection
+
+Liquid Bayes Chain is part of a larger exploration of foundational algorithms enhanced with modern neural techniques:
+
+-  Evolutionary Turing Machine
+-  Hebbian Bloom Filter  
+-  Hopfield Decision Graph
+- **Liquid Bayes Chain** ← You are here
+-  Liquid State Space Model
+-  Möbius Markov Chain
+-  Memory Forest
+
+## Citation
+```bibtex
+@misc{liquidbayes2025,
+  title={Liquid Bayes Chain: Probabilistic Control of Continuous Dynamics},
+  author={Jae Parker 𓅸 1990two},
+  year={2025},
+  note={Part of The Classics Revival Collection}
+}
+```