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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.
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| 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"] |
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)
LFT → Modified Maximum Entropy Model → Time Evolution Included
→ Free Energy Principle Interpretation
Neurons → Lattice sites (field variables φ_i)
Connections → Lattice couplings (interaction terms)
Activity → Field values (spike counts/rates)
F[φ] = Σ_i local_terms(φ_i) + Σ_<i,j> coupling(φ_i, φ_j)
BCI Data Analysis
Neural Network Characterization
Clinical Monitoring
class LatticeFieldNeuralAnalysis:
def __init__(self, spike_raster):
# Convert spike raster to lattice field
self.field = self._raster_to_field(spike_raster)
self.lattice_structure = self._identify_connections()
def compute_free_energy(self):
# Evaluate F[φ] for current state
local = self._local_terms()
coupling = self._coupling_terms()
return local + coupling
def extract_parameters(self):
# Infer effective couplings from data
return self._maximum_entropy_inference()
F = F_local + F_coupling + F_external
| Framework | Physics | Time | BCI | Biological |
|---|---|---|---|---|
| Maximum Entropy | Limited | No | Yes | Moderate |
| Ising Models | Yes | Static | No | Moderate |
| FEP | No | Yes | Yes | High |
| LFT (this) | Yes | Yes | Yes | High |
H[φ] = -Σ_i h_i φ_i - Σ_<i,j> J_ij φ_i φ_j
∂φ_i/∂t = -∂F/∂φ_i + noise
F = -kT ln Z
Z = Σ_φ exp(-H[φ]/kT)
P(φ, t) = exp(-F[φ(t)]/kT) / Z(t)
⟨φ_i φ_j⟩ - ⟨φ_i⟩⟨φ_j⟩ = correlation(i,j)
Activation Keywords: lattice field theory, LFT, neural field, maximum entropy, BCI interpretation, spike raster, free energy
Use When:
Core Insight: Physics-inspired Lattice Field Theory provides rigorous framework for interpreting neural recordings, extending Maximum Entropy models to include time evolution and connecting to the Free Energy Principle.