| name | lattice-field-theory-neurons |
| description | Lattice Field Theory (LFT) framework for interpreting BCI recordings from real neural networks. Applies physics-based formalism to neural data analysis, connecting Maximum Entropy models with Free Energy Principle. |
| version | 1.0.0 |
| author | Simone Franchini, Giampiero Bardella |
| arxiv_id | 2604.05251 |
| created | 2026-05-30T00:00:00.000Z |
| category | neuroscience |
| tags | ["lattice field theory","neural network","BCI","maximum entropy","free energy principle","spike raster","computational neuroscience"] |
| activation_keywords | ["lattice field theory","LFT","neural field","maximum entropy","BCI interpretation","spike raster","free energy"] |
Lattice Field Theory for Neural Networks
Overview
A simplified Lattice Field Theory (LFT) framework that enables physics-grounded interpretation of experimental recordings from Brain-Computer Interfaces (BCIs), particularly spike rasters from single neuron activity measurements.
Source: arXiv:2604.05251 (Submitted 6 April 2026)
Authors: Simone Franchini, Giampiero Bardella
Category: Condensed Matter - Statistical Mechanics (cond-mat.stat-mech)
Conference: LATTICE2025 (42nd International Symposium on Lattice Field Theory)
Key Concepts
1. Lattice Field Theory Basics
- Physics formalism traditionally used for:
- Quantum field theory on discrete spacetime
- Statistical mechanics models
- Critical phenomena analysis
- New application: Neural network dynamics
2. Connection to Maximum Entropy Model
LFT → Modified Maximum Entropy Model → Time Evolution Included
→ Free Energy Principle Interpretation
- Extends Maximum Entropy approach
- Incorporates time evolution of neural systems
- Interpretable as Free Energy Principle (FEP) variant
3. BCI Data Interpretation
- Naturally tailored for:
- Chronic multi-site BCIs
- Spike rasters from single neuron recordings
- Long-term neural activity monitoring
4. Physical Grounding
- Neural activity → Field variables on lattice
- Network connections → Lattice coupling terms
- Neural dynamics → Field evolution equations
- Provides physics-based interpretation of neural data
Formalism
Lattice Structure
Neurons → Lattice sites (field variables φ_i)
Connections → Lattice couplings (interaction terms)
Activity → Field values (spike counts/rates)
Key Equations
Field Definition
- φ_i(t): Activity of neuron i at time t
- Discretized on neural lattice
Free Energy Functional
F[φ] = Σ_i local_terms(φ_i) + Σ_<i,j> coupling(φ_i, φ_j)
Maximum Entropy Extension
- Original: Static distribution P(φ)
- Extended: Time-dependent P(φ, t)
